Bio-tribology of Plant Cell Walls: Measuring the

Bio-tribology of Plant Cell Walls: Measuring the

interactive forces between cell wall components

Grace Dolan

A thesis submitted for the degree of Doctor of Philosophy at

The University of Queensland in 2017

School of Chemical Engineering

i

Abstract

Plants have naturally evolved complex cell wall structures to give mechanical and friction

properties that facilitate plant growth and development. A biomimetic approach is employed to

gain insight into how plants are able to lubricate moving surfaces at multiple length scales. The

outcomes of this study advance the fundamental scientific understanding of plant cell wall biology.

New insights provided here may have significant implications for optimising the value of plant

material as a food source, biofuel precursor, and as a model for functional biomaterial design,

particularly for medical applications. A review of the plant cell wall structure, mechanics, and

extension processes is used to identify the forces and tribological contacts that are relevant for plant

growth. Plant cell walls are essentially hydrogel composites of cellulose fibres within a matrix of

biopolymers (e.g. hemicelluloses, pectin) and water. Plant tissue is comprised of a cluster of plant

cells where adjacent cell walls are mediated by a pectin rich middle lamella layer. Plant growth is

initiated by expansins which are proteins that disrupt cellulose fibre contact points, leading to the

extension of the cell wall matrix. As cells expand within the tissue structure, a sliding contact forms

between adjacent walls that are extending at different rates. The two critical length scales that are

considered here to influence plant growth are the contact between cellulose nano-fibres in the cell

wall matrix, and the sliding interface between adjacent cell walls.

A large component of this thesis is the development of techniques to mimic the two tribological

contacts; that is, fibre-fibre and cell-cell interactions. The sliding interface between two surfaces is

achieved using a rotational rheometer, which also allows in situ material characterisation of the

surfaces with pre-compression, relaxation, and oscillatory shear mechanical testing steps. The

interactive forces between nano-fibres are measured directly using an Atomic Force Microscope

(AFM) tip to laterally pull fibres out of a network. Bacterial cellulose networks are used as a model

system that is compatible with the developed techniques. Bacterial cellulose is a good model

because of the structural similarity to plant cellulose, and its ability to grow as a self-assembled

random fibre network with the shape and dimensions controlled by the vessel within which it is

grown. The lubricating role of individual cell wall components at the two tribological contacts is

examined; including arabinoxylan (AX), xyloglucan (XG), pectin, and expansins. This is achieved

ii

by growing composite bacterial cellulose networks with AX and XG, and by adding pectin or

expansin solutions to the liquid medium surrounding the pre-formed cellulose networks during

testing.

The unique aspect of this mechanical study is that the experimental results are analysed using

computation modelling. Appropriate models are used to simulate the behaviour of fibrous

assemblies at multiple length scales, and under conditions akin to the experimental set up. The

modelling component advances the interpretation of experimental results, down to the exact

contribution of individual cell wall components. One major discovery is that XG reduces the

adhesion between cellulose fibres at the nano-scale. The result is consistent with the macro-scale

measurement of static friction between two cellulose hydrogels, which is shown to be driven by

cellulose fibres interacting at the interface, and is reduced in the presence of XG. Expansins are

found to act in a similar way to XG in that they reduce the static friction between cellulose hydrogel

surfaces. Finally, pectin in solution acts as a viscous film that increases the separation between

hydrogel surfaces, and the reduced surface contact directly reduces the measured static friction.

In this thesis, I develop a suite of techniques (experimental and computational) that enable multi-

scale characterisation of soft matter systems comprising fibrous assemblies. The key outcome of

this work is the direct measurement of input parameters for the development of a multi-scale 3D

mechanical model of fibre networks. Such a model provides a predictive tool for enhancing our

understanding of the underlying principles that explain plant growth; which is hypothesised to be

driven by fibre-fibre interactions within the cell wall, and cell-cell friction.

iii

Declaration by author

This thesis is composed of my original work, and contains no material previously published or

written by another person except where due reference has been made in the text. I have clearly

stated the contribution by others to jointly-authored works that I have included in my thesis.

I have clearly stated the contribution of others to my thesis as a whole, including statistical

assistance, survey design, data analysis, significant technical procedures, professional editorial

advice, and any other original research work used or reported in my thesis. The content of my thesis

is the result of work I have carried out since the commencement of my research higher degree

candidature and does not include a substantial part of work that has been submitted to qualify for

the award of any other degree or diploma in any university or other tertiary institution. I have

clearly stated which parts of my thesis, if any, have been submitted to qualify for another award.

I acknowledge that an electronic copy of my thesis must be lodged with the University Library and,

subject to the policy and procedures of The University of Queensland, the thesis be made available

for research and study in accordance with the Copyright Act 1968 unless a period of embargo has

been approved by the Dean of the Graduate School.

I acknowledge that copyright of all material contained in my thesis resides with the copyright

holder(s) of that material. Where appropriate I have obtained copyright permission from the

copyright holder to reproduce material in this thesis.

iv

Publications during candidature

Peer-reviewed papers:

• G. K. Dolan, G. E. Yakubov, G. W. Greene, N. Amiralian, P. K. Annamalai, D. J. Martin

and J. R. Stokes, Langmuir, 2016, DOI: 10.1021/acs.langmuir.6b03467.

Publications included in this thesis

No publications included.

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Contributions by others to the thesis

This thesis was completed after review and editing suggestions from my RHD supervisors;

Professor Jason Stokes and Dr Gleb Yakubov.

Some of the analysis in Chapter 4: Section 4.3.1 is completed using a published poroelastic

mechanical model, for which the corresponding MATLAB files in Appendix E are provided by Dr

Mauricio Bonilla.

The ComsolTM Multiphysics model described in Chapter 4: Section 4.2.3 is constructed by Dr

Mauricio Bonilla.

SEM and TEM images in Chapter 5 are provided by Dr Nasim Amiralian (Australian Institute of

Biotechnology and Nanotechnology (AIBN), The University of Queensland), Dr George Greene

(Deakin University), and the Centre for Microscopy and Microanalysis (CMM) and the University

of Queensland.

For Chapter 5 Dr George Greene (Deakin University) supplied SPEEK fibre samples and

suggestions for how to analysis their interactions, Professor Darren Martin’s research group (AIBN)

supplied PVA, CNC and CNF fibre samples.

Dr Gleb Yakubov assisted in the analysis of the two different pulling scenarios in Chapter 5:

Section 5.3.1 and the calculation of the Hamaker constants in Chapter 5: Section 5.3.3.

Dr Mauricio Bonilla prepared the ComsolTM Multiphysics model and helped with its

implementation in Chapter 6: Section 6.3.2.

The AFM images in Chapter 6: Section 6.3.1 were performed by Dr Gleb Yakubov.

The expansins and the cellulose hydrogels used in Chapter 7 are provided by Professor Daniel

Cosgrove’s research group at Pennsylvania State University (PSU), PA, USA. The results in

Section 7.3.1 and most of Section 7.3.2 are from experiments performed at PSU.

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Statement of parts of the thesis submitted to

qualify for the award of another degree

None.

vii

Acknowledgements

My most sincere thanks go to my RHD advisors, Professor Jason Stokes and Dr Gleb Yakubov,

who provided constant support, guidance, and mentorship throughout my PhD. They have been

very generous with their time and resources and I am forever grateful. I have learnt an immense

amount from their wealth of knowledge in terms of scientific insights and research skills.

I thank a number of people for their technical support with training on instruments and procedures.

Particularly Dr Dongjie Wang and Deirdre Mikkelsen for their help with preparing bacterial

cellulose materials, Dr Lien Chau who provided assistance with all of my fabrication needs, Dr

Elena Taran who trained me on the AFM and confocal microscope, Dr Michael Boehm who trained

me on the Rheometer.

I would like to thank Professor Jason Stokes Lab, The Microbiology Lab at the Centre for Nutrition

and Food Science (CNAFS), and the Australian National Fabrication Facility Queensland at the

University of Queensland for letting me use their equipment.

Thank you to Professor Daniel Cosgrove’s and Federico Harte’s research groups who supported by

lab visit at PSU.

Thank you to the members of Professor Jason Stokes’ research group, and the Australian Research

Council (ARC) Centre of Excellence (CoE) in Plant Cell Walls for their support and constructive

feedback throughout my PhD. In particular I would mention the consistent and helpful feedback

given by Professor Mike Gidley.

I acknowledge funding from the Australian Postgraduate Award, UQ Advantage Top-up

Scholarship, ARC CoE in Plant Cell Walls (managed by Professor Jason Stokes), and the Graduate

School International Travel Award (GSITA).

viii

Keywords

Cellulose, plant cell walls, tribology, hydrogels, nano-fibres, adhesion, mechanics, poroelastic,

modelling, multi-scale.

Australian and New Zealand Standard

Research Classifications (ANZSRC)

ANZSRC code: 091209, Polymers and Plastics, 40%

ANZSRC code: 090408, Rheology, 30%

ANZSRC code: 029901, Biological Physics, 30%

Fields of Research (FoR) Classification

FoR code: 0912, Material Engineering, 40%

FoR code: 0904, Chemical Engineering, 30%

FoR code: 0299, Other Physical Sciences, 30%

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Table of Contents

Abstract ................................................................................................................................................ i

List of Figures and Tables .............................................................................................................. xiii

List of Abbreviations .................................................................................................................... xviii

Introduction ........................................................................................................................................ 1

1.1 Motivation .................................................................................................................................. 1

1.2 Aims and Objectives .................................................................................................................. 2

1.1 Thesis Outline ............................................................................................................................. 4

Literature Review .............................................................................................................................. 6

2.1 Bio-tribology and Bio-lubrication .............................................................................................. 6

2.2 Plant Cell Wall Structure, Mechanics and Growth .................................................................... 9

2.2.1 Plant Cell Wall Architecture.............................................................................................. 10

2.2.2 Cell Wall Mechanics ......................................................................................................... 17

2.2.3 Plant Growth and Cell Wall Extension .............................................................................. 20

2.2.4 Tribological Contacts in Plant Cell Walls ......................................................................... 26

2.2.5 Bacterial Cellulose as a Model System for Plant Cell Walls ............................................ 27

2.3 Mechanical and Friction Properties of Hydrogels .................................................................... 30

2.3.1 Hydrogel Material Characterisation .................................................................................. 31

2.3.2 Relating Hydrogel Mechanics to Friction Response ......................................................... 33

2.3.3 Cellulose Hydrogel Mechanics and the Relevance to Plant Cell Walls ............................ 37

2.4 Measurement of Fibre-Fibre Interactions ................................................................................. 38

2.4.1 Fibre Network Models ....................................................................................................... 39

x

2.4.2 Fibre Mechanics ................................................................................................................ 40

2.4.3 Experimental Approaches for Fibre-Fibre Measurement .................................................. 44

2.5 Future Perspective: Scope and Goal of Thesis ......................................................................... 46

References for Chapter 2 ................................................................................................................ 49

Research Methodology .................................................................................................................... 55

3.1 Materials ................................................................................................................................... 56

3.1.1 Electrospun Fibres ............................................................................................................. 56

3.1.2 Cellulose Nano-fibres Extracted from a Plant Source ....................................................... 57

3.1.3 Bacterial Cellulose ............................................................................................................. 58

3.1.4 Pectin Solutions ................................................................................................................. 60

3.1.5 Bacterial Expansins ........................................................................................................... 61

3.2 Measurements ........................................................................................................................... 61

3.2.1 Tribo-rheological Technique in a Rotational Rheometer .................................................. 61

3.2.2 Dip-and-drag Technique in an AFM ................................................................................. 63

References for Chapter 3 ................................................................................................................ 67

Friction, lubrication, and in situ mechanics of poroelastic cellulose hydrogels ......................... 68

4.1 Introduction and Background ................................................................................................... 68

4.2 Experimental Section ............................................................................................................... 71

4.2.1 Physical characterisation of hydrogel mechanics and friction .......................................... 71

4.2.2 Modelling the hydrogel mechanics during compression-relaxation .................................. 74

4.2.3 Simulating the interface between hydrogels during compression-relaxation .................... 75

4.2.4 Pectin solution and viscosity measurements ..................................................................... 77

4.3 Results and Discussion ............................................................................................................. 78

4.3.1 Mechanical properties of poroelastic hydrogels ................................................................ 78

4.3.2 Contact area between poroelastic hydrogels ..................................................................... 85

4.3.3 Tribo-rheological response between hydrogels ................................................................. 88

xi

4.3.4 Influence of substrate mechanics on interfacial friction .................................................... 91

4.3.5 Influence of solvent viscosity on interfacial friction ......................................................... 94

4.3.6 Interfacial friction at the true contact area ......................................................................... 96

4.3.7 Stick-slip and stiction behaviour ....................................................................................... 99

4.4 Concluding Remarks .............................................................................................................. 105

References for Chapter 4 .............................................................................................................. 107

Method development for measuring the adhesive forces between individual nano-fibres ..... 109

5.1 Introduction and Background ................................................................................................. 109

5.2 Experimental Section ............................................................................................................. 111

5.2.1 Model fibre systems......................................................................................................... 111

5.2.2 Dip-and-drag technique ................................................................................................... 111

5.3 Results and Discussion ........................................................................................................... 113

5.3.1 Dip-and-drag Lateral Force Spectroscopy of SPEEK electrospun mats of varying network

density .................................................................................................................................. 113

5.3.2 Dip-and-drag Lateral Force Spectroscopy of PVA network ........................................... 122

5.3.3 Analysis of adhesive forces between fibres ..................................................................... 122

5.3.4 Dip-and-drag Lateral Force Spectroscopy of CNC and CNF networks in air and water 124



Measuring the effect of hemicelluloses on the adhesive forces between cellulose fibres ......... 130

6.1 Introduction and Background ................................................................................................. 130


6.3 Results and Discussion ........................................................................................................... 132

6.3.1 Probing contacts between individual cellulose fibres ...................................................... 132

6.3.2 Simulating fibre-fibre detachment events ........................................................................ 136

6.3.3 The role of hemicellulose at contacts between cellulose fibres ....................................... 142


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The effect of bacterial expansins on cellulose fibre interactions ............................................... 149

7.1 Introduction ............................................................................................................................ 149

7.2 Background on the ‘wall-loosening’ activity of expansins .................................................... 150


7.3.1 Pre-treatment of bacterial cellulose hydrogels ................................................................ 154

7.3.2 Mechanical assay of expansin activity using the tribo-rheological technique ................ 155

7.3.1 Mechanical assay of expansin activity using the Dip-and-drag technique ...................... 155

7.4 Results .................................................................................................................................... 155

7.4.1 The effect of bacterial expansins on the mechanics of bacterial cellulose hydrogels ..... 155

7.4.2 The effect of bacterial expansins on the friction response between pairs of bacterial

cellulose hydrogels ................................................................................................................... 158

7.4.1 The effect of bacterial expansins on adhesion between cellulose fibres ......................... 161

7.5 Discussion .............................................................................................................................. 163



Concluding Remarks and Future Work ...................................................................................... 167


8.2 Recommendations for Future Work ....................................................................................... 169

Appendices ...................................................................................................................................... 172

Appendix A: Producing bacterial cellulose from Gluconacetobacter xylinus ............................. 172

Appendix B: Chromium Mask Fabrication .................................................................................. 178

Appendix C: SU-8 Master Fabrication ......................................................................................... 193

Appendix D: PDMS Microarray Fabrication ............................................................................... 196

Appendix E: MATLAB code for poroelastic mechanical model ................................................. 197

Appendix F: Text file of raw data for input into MATLAB code for the poroelastic mechanical

model ............................................................................................................................................ 204

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Appendix G: Raw data from the compression-relaxation steps for hydrogels (cellulose, CAX,

CXG) at all CRs ........................................................................................................................... 206

Appendix H: Raw data from the tribo-rheological test for all hydrogels and solvents ................ 212

Appendix I: Cellulose concentration based on the G’ of the hydrogels for cellulose, CAX, and

CXG .............................................................................................................................................. 216

Appendix J: Friction curves with angular velocity for hydrogel pairs (cellulose, CAX, CXG) at all

CRs ............................................................................................................................................... 217

Appendix K: Force-distance data for SPEEK fibres mats............................................................ 223

Appendix L: MATLAB code for finding the peaks in lateral force-distance curves from the dip-

and-drag technique ....................................................................................................................... 226

Appendix M: MATLAB code for measure the slope before the peaks in the lateral force-distance

curves from the dip-and-drag technique ....................................................................................... 231

Appendix N: Solving 3 non-linear simultaneous equations in MATLAB ................................... 232

Appendix O: Interfacial yield stress and G’ for triplicate hydrogel pairs for each treatment

(control, YOAJ, WWY, RKKQ, D82) ......................................................................................... 233

Appendix P: Raw data from dip-and-drag experiments on Cellulose, CAX, and CXG networks

with and without expansins .......................................................................................................... 236

Appendix Q: Histogram of peak heights for Cellulose, CAX, and CXG networks with and

without expansins ........................................................................................................................ 239

xiv

List of Figures and Tables

Figure 2.1. Tribology at multiple length scales from full-film lubrication ...................................................... 7

Figure 2.2. Pictorial representation of the viscous flow equation in 2.1 ....................................................... 8

Figure 2.3. Schematic of compression between two opposing cartilage ...................................................... 9

Figure 2.4. Structure of the primary cell wall ............................................................................................... 10

Figure 2.5. Predicted 36-chain CEF model with hexagonal cross-section .................................................... 11

Figure 2.6. Common artefacts with AFM topography .................................................................................. 12

Figure 2.7. Cellulose fibril orientation relative to axis of elongation ........................................................... 13

Figure 2.8. Transmission electron micrographs of tungsten/tantalum/carbon........................................... 14

Figure 2.9. The original tethered network model ........................................................................................ 14

Figure 2.10. Distribution of pectin epitopes in the outer epidermal wall .................................................... 16

Figure 2.11. Mechanical measurement of isolated cell walls using ............................................................. 19

Figure 2.12. Time lapsed images of growing root ........................................................................................ 27

Figure 2.13. Schematic of cellulose biosynthesis by Gluconacetobacter xylinus ......................................... 28

Figure 2.14. Model of bacterial cellulose fibre based on SANS and SAXS data ........................................... 29

Figure 2.15. Bacterial Cellulose Hydrogel ..................................................................................................... 30

Figure 2.16. Typical stress-time curve for compression-relaxation ............................................................. 32

Figure 2.17. Gel-Gel friction experiment in a rotational rheometer ............................................................ 35

Figure 2.18. An aerial image and corresponding side-view ......................................................................... 36

Figure 2.19. Cellulose fibres suspended over grating .................................................................................. 41

Figure 2.20. Force-distance curve obtained near the middle ...................................................................... 42

Figure 2.21. Fibre suspended across a trench of distance L......................................................................... 42

Figure 2.22. Schematic diagram of an AFM cantilever dragging ................................................................. 43

Figure 2.23. Force-cantilever and stress-strain curves in the elastic ........................................................... 44

Figure 2.24. Experimental configurations for fibre-fibre measurements .................................................... 45

Figure 2.25. Two fibre free ends arranged in parallel and cross-cylinder .................................................... 46

Figure 3.1. Bacterial cellulose hydrogels adhered to emery paper ............................................................. 63

Figure 3.2. Test procedure for mechanical and friction characterisation .................................................... 63

Figure 3.3. Cellulose micro-hydrogels grown in PDMS micro-array ............................................................ 64

Figure 3.4. An image taken after adhering micro-gels to the glass .............................................................. 65

Figure 3.5. AFM image of glued micro-gel showing the edge ...................................................................... 65

Figure 4.1. Schematic showing the steps for characterising the mechanics................................................ 72

xv

Figure 4.2. Sensitivity analysis of the compression speed on the friction ................................................... 73

Figure 4.3. Sensitivity analysis of the rotation rate on the friction response .............................................. 73

Figure 4.4. Representation of a cellulose hydrogel disk showing that the .................................................. 74

Figure 4.5. (a) Equivalent simulation system to the double hydrogel contact ............................................ 76

Figure 4.6. Viscosity of pectin solutions (0.5, 1, 2, and 4 wt%) across the .................................................. 78

Figure 4.7. Compression-relaxation profiles of pairs of (a) cellulose ........................................................... 80

Figure 4.8. Compression profiles of cellulose, CAX, and CXG hydrogel ....................................................... 81

Figure 4.9. Two consecutive compressions of a single (a) Cellulose ............................................................ 83

Figure 4.10. Recovery of the weight of a single bacterial cellulose hydrogel .............................................. 84

Figure 4.11. Simulated film thickness at the centre, i.e. r = 0 (filled symbols) ............................................ 86

Figure 4.12. The variation in film thickness with radial position in the ....................................................... 87

Figure 4.13. Logarithmic plot of the fraction of the interface that is in contact ......................................... 87

Figure 4.14. Simulated film thickness at the centre of the interface, i.e. r = 0 ............................................ 88

Figure 4.15. Logarithmic plot of the fraction of the interface that is in contact ......................................... 89

Figure 4.16. Characteristic tribological responses for hydrogels tested in water........................................ 89

Figure 4.17. Stress-strain curve of single Cellulose hydrogel glued to both ................................................ 90

Figure 4.18. (a) Axial and (b) Radial modulus from biphasic modelling ....................................................... 93

Figure 4.19. Logarithmic plot of the interfacial yield stress against G’ ........................................................ 94

Figure 4.20. Linear relationships between G’ and axial modulus ................................................................ 94

Figure 4.21. Tribological response of pairs of cellulose hydrogels .............................................................. 95

Figure 4.22. Logarithmic plot of the interfacial yield stress against ............................................................ 96

Figure 4.23. The corrected interfacial shear stress (τc) plotted against ....................................................... 98

Figure 4.24. Interfacial yield stress versus the cellulose concentration ...................................................... 99

Figure 4.25. Characteristic friction behaviours during the constant rotation ........................................... 100

Figure 4.26. Characterisation of stick-slip behaviour showing the elastic ................................................. 101

Figure 4.27. (a) Shear stress over time for constant rotation (CAX ........................................................... 101

Figure 4.28. Shear stress () and angular velocity () measured over time .............................................. 102

Figure 4.29. The peak in angular velocity (m during the slip cycle ......................................................... 103

Figure 4.30. The slope of the slip cycle, ksl, plotted against the peak in .................................................... 104

Figure 4.31. Scatterplot of the G’ against viscosity for the different sliding .............................................. 104

Figure 4.32. Shear stress and angular velocity measured over time for .................................................... 105

Figure 5.1. Microscopy images of nano-fibrous networks. (a) SEM .......................................................... 112

Figure 5.2. The AFM tip is engaged with the substrate at a constant ....................................................... 113

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Figure 5.3. Typical lateral force-distance curves for SPEEK samples ......................................................... 115

Figure 5.4. (a) and (b) show SEM images superimposed with proposed ................................................... 116

Figure 5.5. Analysis of example force distance curve for SPEEK sample ................................................... 117

Figure 5.6. SEM micrographs at 10 000 x magnification of electrospun ................................................... 118

Figure 5.7. (a) Illustrations of two possible scenarios for pulling a fibre ................................................... 121

Figure 5.8. (a) Representative force-distance curve for PVA and .............................................................. 122

Figure 5.9. Representative force-distance curves for (a) CNC in air .......................................................... 126

Figure 6.1. (a) and (b) AFM images of an air-dried cellulose network ....................................................... 133

Figure 6.2. Lateral force-distance curve showing a typical peak that ........................................................ 135

Figure 6.3. (a) Example force-distance curve for cellulose fibre network ................................................. 135

Figure 6.4. Force balance across a section of the fibre network ............................................................... 137

Figure 6.5. Simplified setup of the system depicted in Figure 6.3 ............................................................. 138

Figure 6.6. Predicted force curves for combinations of 2 different ........................................................... 139

Figure 6.7. Best surface fit describing the functional relationship ............................................................ 140

Figure 6.8. The slope, s, of the experimental force-distance curve ........................................................... 141

Figure 6.9. (a) Example force-distance curve for CAX network ................................................................. 143

Figure 6.10. SEM images of (a) cellulose, (b) CAX, and (c) CXG ................................................................. 143

Figure 6.11. Distribution of experimental values of the slope, s, for ......................................................... 144

Figure 6.12. Depiction of the contact between two cellulose fibres ......................................................... 145

Figure 7.1. (1) Expansin (red pacman) binds to cellulose fibres (brown lines) .......................................... 150

Figure 7.2. Protein structure of expansin, showing two distinct domains................................................. 151

Figure 7.3. Activities of selected variants of bacterial expansin protein ................................................... 151

Figure 7.4. Activities of variants of bacterial expansin protein on ............................................................. 152

Figure 7.5. Compression curves of (a) cellulose hydrogel pair treated ...................................................... 157

Figure 7.6. Shear stress over time for a constant rotation rate for the ..................................................... 159

Figure 7.7. Interfacial yield stress against G’ for pairs of bacterial ............................................................ 160

Figure 7.8. IYSR is the interfacial yield stress measured in the presence ................................................... 161

Figure 7.9. The pull-off force is calculated from the Jarzynski’s average .................................................. 163

Figure 8.1. Design for shape of cellulose networks grown in PDMS mould .............................................. 170

Figure G.1. Normal stress during compression-relaxation steps for .......................................................... 206




xvii






Figure G.10. Normal stress during compression-relaxation steps for ....................................................... 210



Figure H.1. Friction curves for Cellulose hydrogel pairs in water .............................................................. 212

Figure H.2. Friction curves for CAX hydrogel pairs in water ...................................................................... 212

Figure H.3. Friction curves for CXG hydrogel pairs in water ...................................................................... 213

Figure H.4. Friction curves for a pair of cellulose hydrogels in 0.5 wt% .................................................... 213

Figure H.5. Friction curves for a pair of cellulose hydrogels in 1 wt% ....................................................... 214



Figure J.1. Shear stress and angular velocity measured over time ............................................................ 217









Figure J.10. Shear stress and angular velocity measured over time .......................................................... 221



Figure K.1. Lateral force-distance curve of SPEEK sample A ...................................................................... 223

Figure K.2. Lateral force-distance curve of SPEEK sample B ...................................................................... 223

Figure K.3. Lateral force-distance curve of SPEEK sample C ...................................................................... 224

Figure K.4. Lateral force-distance curve of SPEEK sample D ...................................................................... 224

Figure K.5. Lateral force-distance curve of SPEEK sample E ...................................................................... 225

Figure O.1. Interfacial yield stress against G’ for 2 different ..................................................................... 233

Figure O.2. Interfacial yield stress against G’ for triplicate ........................................................................ 233

xviii





Figure P.1. Lateral deflection-distance curve for Cellulose network ......................................................... 236

Figure P.2. Lateral deflection-distance curve for Cellulose network ......................................................... 236

Figure P.3. Lateral deflection-distance curve for CAX network ................................................................. 237

Figure P.4. Lateral deflection-distance curve for CAX network ................................................................. 237

Figure P.5. Lateral deflection-distance curve for CXG network ................................................................. 238

Figure P.6. Lateral deflection-distance curve for CXG network ................................................................. 238

Figure Q.1. Histogram of peaks heights (n = 166) from lateral .................................................................. 239




Figure Q.5. Histogram of peaks heights (n = 64) from lateral .................................................................... 241


Table 2.1. A summary of key structural differences in cellulose fibres ....................................................... 30

Table 2.2. Summary of key findings from relevant studies on hydrogel ..................................................... 34

Table 3.1. Composition of 300 mL of Liquid HS medium ............................................................................. 59

Table 4.1. Material functions in the mechanical model ............................................................................... 74

Table 4.2. Mechanical parameters of pairs of cellulose and ........................................................................ 81

Table 4.3. Hysteresis areas for consecutive compressions of Cellulose ...................................................... 84

Table 4.4. The apparent linear viscoelastic moduli (G’, G’’ in kPa) of the ................................................... 85

Table 5.1. The exponentially averaged peak height values from a set ...................................................... 120

Table 5.2. The experimental and theoretical values of the Hamaker ........................................................ 125

Table 5.3. The Jarzynski’s average peak height value for CNC and CNF .................................................... 126

Table 6.1. Model parameters extracted from equations 6.5 - 6.7 using ................................................... 144

Table 7.1. The storage (G’) and loss (G”) moduli of hydrogel pairs that .................................................... 158

Table 7.2. The storage (G’) and loss (G”) moduli of hydrogel pairs that .................................................... 158

xix

List of Abbreviations

AX – Arabinoxylan

XG – Xyloglucan

DLVO – Derjaguin, Landau, Vervey, and Overbeek

AFM – Atomic Force Microscope

CEF – Cellulose Elementary Fibril

SANS – Small Angle Neutron Scattering

WAXS – Wide Angle X-ray Scattering

SAXS – Small Angle X-ray Scattering

NMR – Nuclear Magnetic Resonance

MD – Molecular Dynamics

HG – Homogalacturonan

RG – Rhamnogalacturonan

DE – Degree of Esterification

FEM – Finite Element Modelling

PME – Pectin Methyl Esterases

SEM – Scanning Electron Microscopy

XRD – X-ray Diffraction

SFA – Surface Force Apparatus

FT-IR – Fourier transform infrared

SPEEK – Sulfonated polyether ether ketone

PVA – Polyvinyl Alcohol

xx

CNF – Cellulose nanofibrils

CNC – Cellulose nanocrystals

TEM – Transmission Electron Microscopy

HS – Hestrin and Schramm

PDMS – Polydimethylsiloxane

RO – Reverse Osmosis

SAOS – Small Amplitude Oscillatory Shear

CR – Compression ratio

CZM – Cohesive Zone Model

PPBS – Putative Polysaccharide Binding Site

1

Chapter 1

Introduction

1.1 Motivation

Natural systems have evolved ways of controlling friction in water-based environments far

superior to engineered solutions which rely on the utility of oil-based lubricants. Animals

implement many self-lubricating systems such as observed in the gait of a snail, the passage

of food in the human digestive tract, and in synovial joints. These phenomena have been the

subject of biomimetic studies which aim to gain insight into the mechanistic details and

recreate these lubricating functions in man-made systems. Plants have received significantly

less attention among researchers for their equally remarkable tribological feats. Plant

tribology is readily observed in the self-cleaning ability of the lotus leaf which has surface

microstructures that control the spreadability of water droplets, and in the way plant roots

penetrate soil by shedding an external layer of cells which releases a water-based mucilage

material that lines the root channel. Plant materials have a desirable combination of high

strength and light weight material properties. Furthermore, plants are able to grow on long

time scales and respond to environmental changes (e.g. water pressure and wind) on short

time scales.

The major difference between plant and animal systems is that plant cells are surrounded by a

cell wall. Plant cell walls are remarkably complex composite materials that have a highly

controlled composition and architecture to facilitate a combination of high tensile strength for

resisting mechanical forces and extensibility for plant growth. During plant growth, turgor

pressure within cells is converted into mechanical energy that drives the cell wall matrix to

yield and extend as cellulose fibrils and surrounding polymers move relative to each other.

CHAPTER 1. INTRODUCTION Grace Dolan, PhD Thesis

2

Irreversible cell wall extension is typically initiated by the action of a wall protein called

expansin. A pectin-rich layer is sandwiched between neighbouring cell walls, facilitating the

coordinated expansion of adjoining cells by controlling friction and adhesion between the

surfaces. It is reasonable to consider that at multiple length scales within plant systems,

lubrication mechanisms are utilised for overcoming friction forces arising within and between

wall structures that would otherwise limit their growth and development. Evidence for these

critical tribological contacts and further details of cell wall architecture and plant growth

processes are reviewed extensively in Chapter 2.

Plant biotribology is a new, challenging and exciting area with a lot of potential for gaining

insight into natural lubrication and the fundamental science underpinning these mechanisms.

A major challenge in studying plant systems is experimentally achieving the length and time

scales relevant for plant growth processes. Based on advances in biotribology and

measurement capabilities, researchers are now in a position to tackle complex plant systems.

This will include developing techniques to mimic conditions akin to the growing plant cell

wall using model systems and controlled experimental parameters for a systematic approach.

The primary approach taken in this thesis is to investigate model fibrous systems with

material properties analogous to plant cell walls. I seek to apply novel approaches for

investigating gel-gel and fibre-fibre friction, as these are key tribological elements in the

context of plant growth. The unique aspect of this thesis is the use of computational

modelling to analyse the experimental results. In this way, key findings from the systematic

testing of model systems are used to generate universal relationships that apply to more

complex systems such as plant cell walls.

1.2 Aims and Objectives

A combined experimental and computational approach is used to gain insight into the

potential tribological interactions occurring within and between plant cells during growth and

mechanical deformation. This is divided in three more focussed research targets:

1. To consider the shear forces between plant cells by investigating the friction between

composite cellulose hydrogels as cell wall mimics.

➢ Develop a technique using model surfaces that represents the sliding contact

between adjacent cell walls and allows in situ mechanical characterisation.


3

➢ Use a poroelastic mechanical model to analyse experimental results and determine

the material functions that directly influence the mechanical and friction

responses.

2. To consider critical forces between cellulose fibres and their contribution to network

mechanics under elastic and plastic deformations.

➢ Develop a technique to probe the interactive forces (elastic, adhesive, and friction)

between nanofibers in model fibre networks.

➢ Use complementary simulations to determine the material parameters that directly

influence the measured adhesion between fibres.

3. To probe the influence of non-cellulosic plant polysaccharides (arabinoxylan,

xyloglucan and pectin) and growth proteins (expansins) on fibre-fibre and gel-gel

level interactions and infer potential lubricating mechanisms of individual cell wall

components.

➢ Apply the developed technique for measuring gel-gel friction to pairs of

composite cellulose hydrogels incorporating arabinoxylan (AX) and xyloglucan

(XG). Use poroelastic mechanical modelling to precisely determine the effect of

AX and XG on the interaction between cellulose fibres at the interface.

➢ Apply the developed technique for measuring gel-gel friction to pairs of cellulose

hydrogels separated by a film of pectin solution with varying concentration. Using

the poroelastic mechanical model and squeeze film lubrication theory, the

influence of solvent viscosity on the interaction between cellulose fibres at the

interface is determined.

➢ Apply the developed technique for measuring gel-gel friction to pairs of cellulose

hydrogels in the presence of expansins to assess whether they affect the formation

of cellulose fibre contacts at the interface.

➢ Apply the developed technique for measuring fibre-fibre interactive forces to

composite cellulose fibre networks incorporating AX and XG to investigate the

effect of these polymers on the adhesion force at fibre contacts.

➢ Apply the developed technique for measuring fibre-fibre interactive forces to

cellulose fibre and composite networks in the presence of expansins to investigate

their effect on preformed fibre contacts.


4

1.3 Thesis Outline

To address the aims and objectives listed above the thesis is broken down into the chapters

briefly described below.

Chapter 2 (Literature review): The structure and mechanics of the primary plant cell wall,

and the process of cell wall extension during plant growth are reviewed in detail. From the

combined evaluation of the cell wall structure and plant growth processes, the interface

between adjoining cell walls and the contact between individual cellulose fibres are identified

as important tribological contacts. In order to mimic these tribological contacts, experimental

techniques for measuring the friction between soft surfaces and measuring interactive forces

between nanofibers are reviewed. Due to the complexity of plant cell walls and the difficulty

performing controlled physical measurement on plant materials, the appropriateness of

bacterial cellulose as a model system is evaluated. Plant cellulose has a crystalline core

surrounded by a paracrystalline shell. The chemical and mechanical methods of extracting

plant cellulose disrupt the paracrystalline layer, which is the region that facilitates cellulose

interactions with the hemicellulose amorphous phase in plant cell walls. Bacterial cellulose

has a similar structure to plant cellulose in terms of the crystalline and paracrystalline phases

which makes it a good model for studying the interactions between cellulose and

hemicelluloses. In order to interpret the multi-scale mechanics of plant cell walls and

corresponding model systems, existing computational models that describe poroelastic

materials and fibre network assemblies are reviewed. Finally, a future perspective on this

field of research is presented.

Chapter 3 (Research Methodologies): In this section the methods for preparing bacterial

cellulose and composite hydrogels are outlined. The techniques that are developed for

measuring cell-cell and fibre-fibre interactions are summarised, with more specific protocol

included in the relevant results chapters.

Chapter 4 (Friction, lubrication and in situ mechanics of poroelastic cellulose hydrogels): A

rheo-tribological technique is developed using a rotational rheometer to measure the in situ

mechanics and friction response between pairs of poroelastic cellulose hydrogels. For the first

time, a poroelastic mechanical model is used to predict the area of contact at the interface as

pairs of hydrogels are compressed together prior to shearing. By accounting for the contact

area, the direct effect of cell wall components (AX, XG, and pectin) on the interactions


5

between cellulose fibres at the interface is determined. The key finding from this chapter

leads to the hypothesis that XG reduces the adhesion between cellulose fibres, which is tested

in Chapter 6. This chapter gives insight into how the composition and assembly of plant cell

walls influence the shear forces experienced at the interface between adjacent cell walls.

Chapter 5 (Method development for measuring the adhesive forces between individual nano-

fibres): This chapter details the development of a novel ‘Dip-and-drag’ technique in the

Atomic Force Microscope (AFM) for measuring the adhesive force between individual nano-

fibres. Model electrospun fibres are used to validate the technique due to their cylindrical

shape with relatively consistent dimensions, the ability to control network density, and the

fact that adhesive forces between the fibres are dominated by DLVO interactions. The

experimentally determined adhesive force is compared to the theoretically predicted value to

validate the technique.

Chapter 6 (Measuring the effect of hemicelluloses on the adhesive forces between cellulose

fibres): The Dip-and-drag technique developed in Chapter 5 is applied the bacterial cellulose

networks to measure the adhesive force between individual fibres. Composite networks with

AX and XG are also tested to measure the adhesive force at cellulose fibre contacts that are

mediated by these molecules. Simulations of fibre detachment events in silico are included in

this study to determine the specific effect of AX and XG on the physical properties of fibre

contacts. The key finding from this chapter is that XG reduces the adhesion between cellulose

fibres which is consistent with the results from the rheo-tribological technique in Chapter 4.

Chapter 7 (The effect of bacterial expansins on cellulose fibre contacts): the rheo-tribological

(Chapter 4) and Dip-and-drag (Chapter 5) techniques developed in this thesis provide two

mechanical assays for measuring the interaction between cellulose fibres. Thus the techniques

are applied to investigate the action of expansins on cellulose fibre contacts. In this chapter

the activity of native and mutant bacterial expansins at contacts between bacterial cellulose

fibres is evaluated to gain insight into the potential mechanism of action of plant expansins

on cell walls during growth.

Chapter 8 (Concluding remarks and future work): Major findings from this thesis are

presented with their key implications in the context of plant cell wall mechanics and growth

processes. Suggestions for future work in this research area are listed.

6

Chapter 2

Literature Review

2.1 Bio-tribology and Bio-lubrication

Tribology concerns the friction, wear and lubrication of interacting surfaces in relative

motion, whether it is rolling, sliding, normal approach or separation of surfaces1. A rubbing

contact formed by two solids and separated by a fluid is a dynamic system. The gap between

surfaces depends on rubbing speed, surface adhesion and mechanics, rheological properties

of the fluid, and presence of surface bound/adsorbed molecular layers. The forces that

dominate friction depend on the length scales of the gap relative to surface roughness, and the

range of surface forces.

Figure 2.1 highlights the system parameters that are critical for describing the tribological

response across a generic fluid film thickness range. The right-hand limit represents the

presence of a very thin or discontinuous fluid film between moving surfaces, where the

contact is mediated by surface bound or adsorbed molecular layers. This is referred to as the

boundary lubrication regime which is characteristic for system conditions of low fluid

viscosity, small relative velocity, and/or high normal load2. In this regime the surfaces are

engaged into direct contact and friction depends on the effective area of interacting asperities

and the energy of adhesion between them. Surface-bound molecules may enhance lubrication

by generating a repulsive force through some physical means, or conversely may increase

friction and adhesive forces through attractive interactions2-4.

CHAPTER 2. LITERATURE REVIEW Grace Dolan, PhD Thesis

7

Figure 2.1. Tribology at multiple length scales from full-film lubrication (left hand side) to

surface contact (right hand side). Full film lubrication is dominated by the properties of the

lubricant, specifically its viscosity. In the absence of a fluid film the friction is dominated by

the adhesive interaction between surfaces that are in contact.

If the rubbing speed is high enough, a viscous liquid produces a hydrodynamic lift force

sufficient to fully separate the surfaces. This regime, called hydrodynamic lubrication, is

represented on the left-hand side of the scale in Figure 2.1. In the presence of a full liquid

film with thickness much larger than the size of asperities, the surfaces are completely

separated and do not interact. The lubrication behaviour in this regime is dominated by

rheological properties of the pressurised fluid film separating the moving surfaces2. In the

case of Newtonian liquids, the full film lubrication is predictable and can be fully described

by the lubricant bulk viscosity and geometry of the rubbing surfaces. Viscous forces for

Newtonian films are calculated according to equation 2.1, which is represented pictorially in

Figure 2.2. In between full film lubrication and boundary friction, a mixed lubrication regime

exists where the interfaces between opposing surfaces in relative motion are partially

lubricated by solvent whilst some asperity contacts occur2. Friction is minimised at fluid film

thicknesses corresponding to the transition between the mixed and hydrodynamic regime, and

is influenced by a combination of the surface and fluid film properties of the given system.

𝜏 = 𝜇𝑑𝑉

𝑑𝑧

2.1

Water is the natural medium for biological systems and their lubrication processes. Water is

an excellent lubricant because it has a low viscosity and stays fluid even down to molecularly

thin films5. However, water as a lubricant has poor load-bearing capacity due to its low

viscosity at high pressures. Hence it is squeezed out from the gap at high loads leading to

asperity contact and increased friction. Water-based lubrication is achieved in many


8

Figure 2.2. Pictorial representation of the viscous flow equation in 2.1; the stress, τ, required

to shear a Newtonian fluid between two surfaces depends on the viscosity of the fluid, µ, and

the fluid film thickness, dz.

biological systems through biological lubricant components, such as heavily glycosylated

proteins (e.g. mucins and aggrecans), and polysaccharides that maximise the load-bearing

capacity of water through steric and electrostatic repulsion between surface bound aqueous

films6. The locomotion of land-based limbless animals, such as snails, provides an interesting

example of the use of water together with sugar molecules to control friction and lubrication

at the continuous interaction between the animal and substrate7. Snails secrete a water based

mucus layer with yield stress fluid behaviour. Periodic pulses of muscular (elastic)

deformation generated by the foot lead to transitions between solid behaviour and fluid flow

of the mucus layer, thereby driving motion. The mucus contains dissolved polysaccharides

which increase the viscosity of water. A lubricant with higher viscosity generates a larger

fluid film thickness, which reduces surface asperity interaction.

Biological lubricant additives not only enhance lubrication behaviour when dissolved in

solution, but also when the molecules are adsorbed to surfaces6. For example, mucins protect

and lubricate the surfaces of epithelial tissues lining ducts and lumens within the human

body8, 9. This lubrication mechanism relies on the bottle brush structure of the molecule. The

protein backbone attaches to surfaces and the hydrophilic sugar chains immobilise large

amounts of water in the contact zone protecting the lining of ducts from abrasion6.

Sugar-based bottle-brush molecules forming hierarchical structures have also been implicated

in the complex biological lubrication mechanism exhibited in human joints6, 10. Articular

cartilage effectively demonstrated the ability of lubricating molecules to achieve low friction

and significant load-bearing capacity in aqueous media10-12. The high density of sugar chains

in adsorbed polymer brush layers on opposing surfaces generate long-ranged repulsive forces


9

of both steric and osmotic origin4, 6, 13. Mutual interpenetration of opposing polymer chains is

restricted to a narrow interfacial region in Figure 2.3, thus the interface is maintained as a

highly fluid layer and the system has a high load-bearing capacity13-16.

Figure 2.3. Schematic of compression between two opposing cartilage surfaces with

aggrecan layers (reproduced from Han et al.17).

The architecture of molecules that are implicated in the lubrication mechanisms of biological

systems, such as aggrecan, is studied to determine the features that are essential for the

observed low friction. Good lubricity is achieved when molecules are extensively hydrated

and the hydration layer has high fluidity during shearing to minimise energy dissipation10, 18.

Boundary lubrication between opposing surfaces with pre-adsorbed polymeric layers is

enhanced by solvent properties that promote a more extended and hydrated film, which

consequently has a higher thickness19. We can extend this knowledge to predict candidate

lubricating molecules in plant systems, based on the physical and chemical structure.

2.2 Plant Cell Wall Structure, Mechanics and Growth

Plant systems are rarely the subject of tribological studies despite the relative movement of

multi-scale structures associated with growth processes that would require sophisticated

lubricating mechanisms. Here I will connect the bodies of knowledge surrounding the cell

wall composition and the assembly into individual cells and tissue (cell aggregates), multi-

scale mechanics, and growth processes to identify tribological contacts that are an essential

part of the strategy by which plants grow and maintain mechanical strength.


10

2.2.1 Plant Cell Wall Architecture

The plant cell wall has crucial roles in providing structural strength, a barrier to pathogens,

plant growth, cell differentiation, signalling, and water transport20. Cell walls are highly

heterogeneous and complex structures that possess a remarkable combination of tensile

strength and extensibility important for plant growth21. The primary cell wall consists of a

cellulose-hemicellulose framework embedded in an inter-fibrillar matrix of pectic

polysaccharides in Figure 2.4, all interacting with an independent domain of structural

proteins22.

Figure 2.4. Structure of the primary cell wall (reproduced from Smith23).

Cellulose

The cellulose fibres are the main load-bearing elements of the plant cell wall structure due to

their high tensile strength21, 24. Cellulose has a hierarchical structure made up of parallel

linear β-1,4-linked glucan chain aggregates25. Cellulose Elementary Fibrils (CEFs) are the

units synthesised by cellulose synthase rosettes at the plasma membrane. CEFs associate

through their hydrophilic faces to form microfibrils, which may contain a single or multiple

CEFs, and microfibrils bundle together to form macrofibrils or cellulose ribbons26. The

Atomic Force Microscope (AFM) has been used to measure the height and consequently infer

the diameter of single cellulose microfibrils from partially hydrated primary cell wall samples

isolated from onion (Allium cepa L.) and Arabidopsis thaliana (L.) Heynh27. The microfibrils

were found to be 4-6 nm in diameter in the cell walls and ca. 3 nm in walls that have been


11

treated to remove pectic polysaccharides. These results indicate that microfibrils largely

contain a single cellulose crystallite surrounded by non-cellulosic polysaccharides and no, or

only a few, cellulose aggregates (macrofibrils) exist. Ding et al.26 probe the morphology of

CEFs in maize cell walls using the AFM and reveal a hexagonal shape (3.2 x 5.3 nm) in

cross-section. Based on this measurement the authors propose a 36-chain CEF model, that is,

36 β-1,4-linked glucan chains aggregate to form a crystalline hexagonal shape CEF as

pictured in Figure 2.5. The size estimate of CEFs from plant sources has been measured using

SANS28, WAXS28, 29, SAXS, and NMR29 gives a diameter of ca. 3 nm. Fernandes et al.28

propose a 24-chain rectangular model based on this diameter. The structural characterisation

of CEFs using AFM estimates a size slightly larger than that measured using a suite of

scattering techniques. This discrepancy could be due to certain limitations associated with

AFM topography measurements. The first common artefact in topography measurements is

profile broadening due to tip-sample convolution. The thickness of the AFM tip leads to an

overestimation of the sample width, as depicted in Figure 2.6a. Secondly, the sample height

can be underestimated due to elastic deformation of non-rigid samples. Whilst cellulose

microfibres have a high modulus, the rigidity of the substrate underneath and the potential

deformation along the length of the fibre may affect sample height measurements.

Additionally, the samples for the reported AFM measurements are dried, which may lead to

aggregation of microfibrils and non-cellulosic polymers and overestimation of the CEF size.

The non-cellulosic polymers coating the microfibrils were shown by Davies and Harris27 to

significantly increase the measured CEF size. Whereas, for scattering techniques, the non-

cellulosic polymers do not have a significant effect due to the different crystallinity compared

to the CEF. Considering this, I conclude the CEF model that is most supported by experiment

data is the 24-chain model.

Figure 2.5. Predicted 36-chain CEF model with hexagonal cross-section and dimensions of

5.3 x 3.2 nm (reproduced from Ding et al.26).


12

a b

Figure 2.6. Common artefacts with AFM topography. a) shows the effect of the tip width on

profile broadening which leads to an overestimate of the sample width. b) elastic deformation

of the sample leads to an underestimate of the sample height.

The validity of 18-, 24-, and 36-chain CEF models has been investigated through molecular

dynamics (MD) simulations, and it is argued that the 18- and 24-chain structure are more

viable models30. The spacing of the cellulose chains in the CEF structure that are predicted

from the simulations correlate with previously published WAXS31 and x-ray diffraction

data32. Furthermore, the crystalline conformation of the 18- and 24-chain models are in better

agreement with high temperature molecular dynamic simulations produced by Matthews et

al.33.

The cellulose microfibrils in the plant cell wall are deposited in a controlled orientation,

typically perpendicular to the axis of cell elongation (Figure 2.7), thereby resisting lateral

swelling and permitting longitudinal expansion25, 34. The orientation of cellulose microfibrils

varies between the inner and outer scales, from a transverse through random to longitudinal

orientation respectively35-40.

AFM imaging of onion epidermis shows that the cellulose microfibrils come into close

proximity with one another in short segments, obscured by matrix material, rather that direct

cross-linking between cellulose36. The surface of cellulose is described as amorphous with a

crystalline domain in the core28, 41. A paracrystalline state of cellulose exists with

intermediate mechanical properties between crystalline (high modulus) and amorphous (low

modulus) phases. The paracrystalline phase has a partially ordered structure that might be


13

relevant for explaining the surface chains on cellulose microfibrils that are the interfaces

between crystalline cellulose and semicrystalline hemicellulose phases in the cell wall41.

Plant cell wall models consistently show that non-cellulosic polysaccharides in the inter-

fibrillar matrix are associated with the surfaces of cellulose microfibrils, however there is no

clear consensus on the nature of these associations. The current models for the roles of non-

cellulosic components within the plant cell wall are discussed below.

Figure 2.7. Cellulose fibril orientation relative to axis of elongation

Hemicelluloses

Hemicelluloses are major matrix polysaccharides that interact with the cellulose network in

the plant cell wall. The most abundant hemicelluloses across plant species are xyloglucan

(XG) and arabinoxylan (AX). Early models of primary cell walls based on selective

enzymatic degradation of suspension-cultured sycamore cell walls show hydrogen bonds

interconnecting XG and cellulose42. The nature of this interaction with cellulose could be via

entanglement with the amorphous glucans on the fibril surface43, tightly bound layers around

the fibril surface 44, physical entrapment inside the microfibril during synthesis45, or covalent

via a transglycosylation reaction46. It has been suggested that XG chains of the appropriate

length may crosslink microfibrils creating load-bearing tethers that reinforce the cell wall and

prevent self-association and lateral separation of adjacent microfibrils21, 47. This original

tethered-network model is supported by transmission electron micrographs of cellulose/XG

composites as seen in Figure 2.8.

The validity of the widely accepted ‘tethered network’ model was recently revisited by

investigating biomechanical changes induced by substrate-specific endoglucanases48. It was

found that endoglucanases that hydrolyse both XG and cellulose are required to induce creep,

suggesting that there is a minor, relatively inaccessible XG compartment that may be


14

Figure 2.8. Transmission electron micrographs of tungsten/tantalum/carbon replicas of

cellulose (left) and cellulose/xyloglucan composite (right) (reproduced from Chanliaud et

al.49).

intertwined or otherwise complexed with cellulose as shown in Figure 2.9. It is proposed that

structurally important XG is located in limited regions of tight contact between cellulose

microfibrils and these structures determine cell wall mechanics and enzyme-induced creep.

One possible interaction scheme could involve lateral non-covalent bonding by a single XG

layer mediating adhesion between adjacent microfibrils. The XG at these junctions may be

entangled with disordered surface glucans on adjacent microfibrils. Another possible

interpretation of the interaction at the junction points is that XG penetrates deeply into

cellulose microfibrils, resulting in disordered regions which are similarly attracted to other

disordered regions on adjacent microfibrils.

Figure 2.9. The original tethered network model (Left) and the revised plant cell wall

architecture (Right); red rods = cellulose fibrils, black lines = xyloglucan molecules

(reproduced from Park and Cosgrove48).

Unlike the interaction between XG and cellulose, AX is suggested to form strong non-

covalent bonds with itself and cellulose fibres based on in vitro cellulose binding experiments

on the walls of barley aleurone cells (containing 85% arabinoxylan)50. However, it has also

been proposed that for monocot cell walls, arabinoxylan could be linked to cellulose through

a paracrystalline interaction which is comparable to XG interacting with disordered surface


15

glucans or penetrating cellulose fibrils creating disordered regions51. The network of AX

chains and cellulose fibres adds strength to the cell walls50.

Pectic Polysaccharides

Pectic polysaccharides typically consist of a complex family of acidic polysaccharides built

from several structural domains. Homogalacturonan (HG) is the most abundant pectic

polysaccharide, followed by rhamnogalacturonan I (RG I), and smaller amounts of

Rhamnogalacturonan II, Xylogalacturonan, Arabinan, and Arabinogalactan I. All essentially

consist of galacturonan backbones with or without various side chain additions. Cross-linking

between pectic polysaccharides and other cell wall components is implicated in three-

dimensional network formation in the primary cell wall and middle lamella layer separating

adjacent cells, and is essential for intercellular adhesion. Adhesion between adjacent cells in

plant tissue facilitates plant growth and development, and is important for maintaining

mechanical strength.

There are three proposed cross-links connecting pectic molecules: (i) The negatively charged

carboxyl groups on blocks of galacturonic acid residues of two unesterified HG chains can

form cross-links with Ca2+ ions52, 53. (ii) Dimers of RG II are formed through borate-diol ester

cross-links54. (iii) Pectic polysaccharides may also be linked to relatively hydrophobic cell

wall components via galacturonoyl ester bonds55. The presence of different kinds of cross-

links is supported by a study of cell-cell adhesion in sugar-beet root parenchyma which was

found to depend on both ester and Ca2+ cross-linked polymers56.

In addition to self-association, early models of the primary cell wall suggest that a single

pectic polysaccharide is indirectly associated with multiple microfibrils through covalent

interaction with xyloglucan such that the interfibrillar matrix of directly linked pectin and

xyloglucan mechanically behave as a single entity42. Several pectic polysaccharides have also

been shown to exhibit direct cellulose binding capacities, most likely through hydrogen

bonding with their neutral side chains57. It is proposed that the arabinan and galactan chains

coat the microfibrils to create a continuous cellulose-pectin network. This leads to

competitive binding between XG and pectin with cellulose57-59, and both interactions may

have a load-bearing role60.

Pectic polymers are synthesized and deposited in cell walls in a highly esterified form61.

Subsequently, wall-based pectin methyl esterases (PMEs) hydrolyse (or remove) methyl-ester

groups from the HG backbone, which changes the molecular structure and the way it interacts


16

in the cell wall. Wall-based PMEs spatially regulate matrix properties by producing HG with

blockwise and non-blockwise distributions of methyl esters at discrete micro-domains within

the cell wall62. The blockwise de-esterified HG epitope contains long stretches of unesterified

HG, and is present at the cell wall lining intercellular spaces and the region of the wall closest

to the plasma membrane. A large increase in electrostatic interaction between calcium ions

and free carboxylic acids occurs with the level of de-esterification63, and nine consecutive

galacturonic residues are necessary for association with calcium ions53. This suggests that the

pectin epitope with long stretches of unesterified HG will be calcium cross-linked. The

activity of PMEs is balanced by pectin methyl-esterase inhibitors (PMEIs) to affect the

mechanical properties of the middle lamella in a controlled way64.

During plant growth, separation of adjacent cells tends to occur at cell corner junctions,

pictured in Figure 2.10, generating high separation stresses that are dissipated to the corners

of the intercellular space that is formed65. Thus the distribution of the calcium cross-linked

epitope at the intercellular space is particularly important for resisting the separation stresses

that are concentrated at this location.

Figure 2.10. Distribution of pectin epitopes in the outer epidermal wall and inner tissue walls

of maize coleoptiles (reproduced from Schindler et al.66).

Both the non-blockwise de-esterified and partially methyl-esterified HG epitopes were

identified in the cell wall lining the intercellular spaces62. The non-blockwise de-esterified

HG epitope occurs in large amounts at the corners of the intercellular space, whereas partially

methyl-esterified domains have an increased abundance in the region of the wall closest to


17

the plasma membrane62. This is in agreement with other models of the distribution of pectin

epitopes, one of which is presented in Figure 2.10. In these models, unesterified pectins are

restricted to the corner junctions and esterified pectins are present in the middle lamella far

away from the corner junction and in the primary walls61, 66. In the growing regions of

hypocotyl mung bean seedlings, a high content of methylesterified pectins are observed,

whereas non-growing regions are characterised by unesterified pectins63. The composition of

pectin in different areas of the plant tissue and at different areas of growth and non-growth is

complex. A possible interpretation of the controlled distribution of pectin is that

methylesterified pectins that do not form calcium cross-links facilitate cell separation and

movement within the walls and are thus located in the growing regions. Whereas the cross-

linked pectin concentrated at the corner junctions and non-growing regions contributes to

adhesion. Cell separation during development occurs through polygalacutonase-mediated

cleavage of the HG backbone of DE pectin64.

2.2.2 Cell Wall Mechanics

If we reflect on our everyday experience with plant material and compare the texture of say a

lettuce and a carrot, we get some appreciation for the vastly different mechanical properties

between different plant tissues from different species. In fact, the range of mechanical

properties has been captured by measuring the Young’s modulus and compressive strength of

plant material. If a given stress is applied to a material and the resultant deformation is

recorded as a strain, the Young’s modulus is taken as the slope of the linear region of the

stress-strain curve. The compressive strength is a measure of the stress required to ‘break’ a

material under compression. Gibson67 reports that the Young’s modulus spans 5 orders of

magnitude and the compressive strength spans 3 orders of magnitude for plant materials from

parenchyma to the densest palm. This range of mechanical properties is attributed to the

composition and microstructure of the cell walls, tissue level structure, and turgor pressure

for plant material with intact membranes. Thus it is very informative to measure the

composition and mechanics of the plant cell wall, the mechanics of an isolated plant cell, and

the mechanics of clusters of cells (plant tissue) for a single plant species. This type of holistic

investigation gives significant insights into how individual components and hierarchical

structures contribute to material properties. These insights can be extended to understand

biological phenomena such as plant growth, and could assist in the design of advanced

functional materials.


18

Zamil et al.68 cut wall fragments from the middle region of a single cell of onion epidermal

peel and performs uniaxial tensile tests in vacuo on the dried sample to characterise the

behaviour in the major and minor growth directions. The modulus was of the order of 4 GPa

for both directions. In a subsequent publication, Zamil et al.69 present stress-strain curves for

never-dried cell wall fragments without maintaining continuous hydration. The average

modulus value was 1.5 GPa. Interestingly, when the samples are tested under continuous

hydration, the shape of the stress-strain curves changes showing a first linear region, plateau

zone, and second linear zone. The author attributes this behaviour to the biphasic nature of

the material. A similar non-linear shape in the stress-strain curve is observed for an onion

epidermis tissue sample subjected to uniaxial tension, although the plateau region in between

the two linear regions is less pronounced than for hydrated samples70, 71. The Young’s

modulus from the slope of the first linear region is of the order of 5 MPa for transverse

orientation and 20 MPa for longitudinal orientation71. Comparing the results for cell wall

fragments and tissue samples shows that mechanical properties can vary by two orders of

magnitude depending on the length scale, and further highlights the complexity of

characterising the hierarchical structure of plant material.

The final piece of the puzzle to achieve a complete picture or mechanical model of plant

material is the mechanics of a whole cell. This differs from cell wall fragments because it

considers the cell geometry, which is particularly important for understanding the relationship

between turgor pressure and wall stress (this is critical for cell wall extension and will be

discussed in a separate section below). Mechanical measurement of isolated single cells have

been achieved using compression testing by micromanipulation with a cylindrical probe72 or

pyramidal tip73, 74, as shown in Figure 2.11. Digiuni et al.73 and Bonilla et al.74 show that

individual plant cells behave in a viscoelastic manner that is driven by their internal

hydrostatic turgor pressure. Wang et al.72 also show a time-dependent mechanical response

where water plays a significant role that is dependent on the deformation rate.

A mesh-free particle method is used to simulate the mechanics of an individual plant cell

which is modelled as an interior liquid phase surrounded by a viscoelastic solid material75.

Van Liedekerke et al.75 investigate the relaxation mechanics of a cell by running a simulation

starting from the cell in a stretched state, removing the stretching force, and letting it relax as

the strain is monitored. The relaxation behaviour of an isolated cell shows a viscoelastic

response where the relaxation time depends on the viscosity of the interior fluid. Thus it is not

only the cell wall mechanics measured from tensile testing of wall mechanics that determine


19

the mechanics of plant cells. Van Liedekerke et al.75 also perform simulations on cell

aggregates,

a b

Figure 2.11. Mechanical measurement of isolated cell walls using a) compression testing by

micromanipulation with a cylindrical probe (reproduced from Wang et al.72) and b)

indentation experiments using a pyramidal AFM tip (reproduced from Bonilla et al.74).

looking at the influence of cell geometry and intercellular voids. The most important

observation from this simulation is that stresses are not uniformly distributed in the

aggregates. All previous attempts to directly measure the mechanics of plant materials

reinforce their time- and length-scale dependent and heterogeneous nature.

What I see as a gap in the literature is a multi-scale approach using model systems to build up

relationships between important material parameters. With the current method of measuring

the mechanics of cellular and sub-cellular structures from the same plant material, there is a

limitation in relating the results to a generalised multi-scale model due to confounding factors

such as heterogeneity in composition and cell geometry, the interfacial middle lamella layer

between neighbouring cells, and the distribution of wall stress from turgor pressure and other

external forces. The key advantages of a model system are that they are largely homogenous

and enable the influence of individual components to be investigated through controlling the

composition. For example, I can alter one material property in a systematic way and

investigate the effect on the mechanics at one specific length scale. Furthermore,

measurements from these well-characterised model systems can be interpreted using

complementary finite element modelling (FEM) to produce generalised relationships that can

predict the behaviour of any system that is described by the same constitutive equations (e.g.

anisotropic, poroelastic etc.). This approach enables the development of a multi-scale model


20

of plant material that will give insight into the specific contributions of cell wall components

on cell wall and tissue level mechanics.

2.2.3 Plant Growth and Cell Wall Extension

The slow, time-dependent, irreversible extension of the cell wall during plant growth occurs

due to cellulose microfibrils and associated matrix polysaccharides in relative sliding

motion20. The irreversible yielding of growing cells is suggested to be due to biochemical

loosening of the wall and not the viscoelastic property of the wall itself76. The stress

relaxation of the wall, that is, the structural rearrangement of the wall leading to a decay in

the wall stress, is the driving force for water uptake and expansion of the cell76 77. The time

when stress relaxation begins and the rate of stress relaxation are found to correlate well with

the amount of hemicellulose in the cell wall based on a stress-relaxation assay on lettuce

hypocotyl treated with gibberellic acid78. Based on a physical model representing the stress-

relaxation phenomenon in the cell wall simulated with Maxwell viscoelastic elements,

increasing the molecular weight of hemicelluloses shifts the stress relaxation time spectrum

of the cell wall to higher relaxation times77. A mathematical model of hemicellulose cross-

link dynamics in an expanding cell wall also shows that increasing the crosslink rest length

increases stress relaxation79. The relaxation of cell walls may also be affected by pectic

polysaccharides where pectate cross-links affect the wall porosity and possibly the

accessibility of primary wall relaxation proteins to their substrate80. The change in porosity is

also likely to affect the resistance to water movement into the cell after stress relaxation.

Additionally, the high mobility of pectin influenced by hydration81 could directly affect the

relaxation behaviour of the biphasic cell wall.

Cell expansion is anisotropic for the majority of plant systems, which means that it

preferentially expands along one axis. The origin of the anisotropy is due to a mismatch in

either wall mechanics or applied stress in the lateral and transverse directions82, 83. Cell wall

extensibility is higher (lower apparent Young’s modulus) transverse compared with parallel

to the net cellulose alignment, thus the direction of growth anisotropy and maximal expansion

rate are qualitatively specified by the mean fibre orientation37, 38, 68, 69, 71, 79, 82, 84-89. However,

the degree of orientation among cellulose fibres does not quantitatively correlate with the

degree of growth anisotropy37, 38, 82. Thus orientation of cellulose fibres is not solely

responsible for growth anisotropy.


21

Mathematical modelling of hemicellulose cross-link dynamics, incorporating enzyme

mediated cross-link dynamics, demonstrates that enzymes targeting cross-links are effective

in softening the wall in its pre-yield state and the pectin matrix determines the post-yield

extensibility79. This is supported by the use of heat inactivation to show protein dependence

of extension transverse to the net cellulose orientation, consistent with an important role of

xyloglucan endotransglucosylase activity on cross-links for extension90. An alternative

explanation of growth anisotropy is the distribution of PME activity such that the wall along

the growth direction is more elastic due to its richness in low degree of methyl esterification

pectin91. Selective weakening of the longitudinal walls as the origin of anisotropic growth

only works in the context of a tissue. For an isolated cell the longitudinal wall would bulge in

the absence of transversely orientated fibres. The critical role of pectin is also shown by

Braybrook and Peaucelle92 where de-methyl esterification of pectin alone is sufficient to

induce local tissue growth in the meristem of Arabidopsis thaliana. In summary, the initial

controlled deposition of cellulose combined with biochemical loosening of one or both of XG

and pectin initiates anisotropic extension. This is followed by passive reorientation of

cellulose microfibrils parallel to the axis of elongation which slows growth.

Expansins

The biochemical loosening of the cell wall is consistently linked to the wall protein expansin;

however, the mechanism of action is unclear. Expansins are proteins secreted in plant cell

walls during growth to unlock the network of wall polysaccharides and permit turgor-driven

cell enlargement93. An ‘acid growth’ phenomenon is observed where expansins induce stress

relaxation and extension of isolated cell walls in a pH-dependent manner such that plant cell

walls typically extend faster at lower pH25, 93, 94. When expansins are applied to living cells

they stimulate cell enlargement which indicates that the proteins function under normal

physiological conditions in the walls of living cells, and that expansins can be naturally

present in plant tissue in sub-saturating amounts95. The action of expansins is immediate and

only small relative amounts of the protein are required to induce wall extension, suggesting

that the mechanism relies on a few ‘sticky’ spots or entanglements at a given time where

expansins act to promote polysaccharide slippage93. NMR studies support this claim, showing

that expansins do not increase the general mobility of wall polysaccharides96. The action of

expansins leads to longer and thinner walls after extension, but the cell wall is not weakened

or structurally changed in the long term.


22

The cell wall strength is determined by the sum of the strength provided by each load-bearing

bond. Wall relaxation occurs through these bonds being broken and new bonds formed so

that the load is transferred and the strength of the wall remains the same, thus the action of

expansins must be reversible97. Consistently, expansins are reported to reversibly disrupt non-

covalent binding between wall polymers that facilitates polymer slippage under stress97-102.

The mechanistic detail for expansin action is yet incomplete; some of the key hypotheses

from literature are listed below. It is noted that over the time of these references the cell wall

model has changed, in particular the role of XG as tethers, and the structure of the expansin

protein has become better characterised.

‘…we suggest that expansins act as a sort of biochemical grease…expansins might facilitate

polymer slippage under stress by disrupting noncovalent binding between wall polymers…’99

‘By ‘unzipping’ the glucans that tether cellulose microfibrils together, expansins may induce

wall stress relaxation…’100

‘…expansins lubricate glucan-glucan interactions allowing (in some instances) entangled

polymers (or fibrils) to slide relative to one another…’102.

‘…expansins have separate hydrophobic and hydrophilic regions, and thus, they may act in

part as surfactants…’103

‘…BsEXLX1 [bacterial expansin] could move on the surface of cellulose and disrupt

hydrogen bonds by twisting glucan chains.’104

McQueenmason and Cosgrove98 compare the activity of expansins extracted from plant

material to that of urea, which weakens all the hydrogen bonds between fibres in paper

causing stress relaxation. Results show that expansin activity causes slower stress relaxation

compared to the native cell wall substrate treated with urea, and may involve progressive

disruption of bonds and translocation of the protein as the fibres slide apart. However the

small concentrations of expansins relative to the number of fibre contact points required for

extension and the apparently immediate response to the presence of expansin argue against

this interpretation.

Cosgrove93 previously explained the relatively minor amounts of expansin needed for wall

extension as relating to a similarly small amount of critical junction zones or ‘sticky’ spots

existing in the wall. At these ‘sticky’ spots, glucans that are attached to microfibril surfaces


23

interact with each other or adjacent microfibrils forming tethers that need to be disentangled

to promote polysaccharide slippage. Expansin movement may be confined to lateral diffusion

along the surface of the cellulose microfibrils93. This would enable the bound protein to scan

the microfibril surface, locally loosening its attachment to the matrix, and allowing chain

movement and stress relaxation. Yet a number of theoretical difficulties with this ‘sticky’

network model are raised by Thompson105. These discrepancies include: the cell wall is

physically measured to be stronger than what would be predicted by the model, the work

done in wall expansion is greater than the energy stored in hydrogen bonding between tethers

and microfibrils, hemicellulose tethers are unlikely to limit wall extension because bacterial

cellulose networks with hemicellulose are weaker than pure cellulose networks, calcium

chelators promote creep, and contraction and extension of cell wall material is inhibited under

conditions of reduced relative permittivity.

Attempts to determine the mechanistic details of the action of expansins include the use of

techniques assessing hydrolytic and enzymatic activity, binding specificity, mechanical

properties and substrate microstructure. Expansin proteins extracted from plant cell walls do

not cause a time-dependent weakening of the cell wall and the effect on mechanical

properties is reversible, indicating that action is not through a hydrolase-type mechanism98,

106. Bacterial expansins possess no hydrolytic activity against cellulosic and hemicellulosic

substrates99 107-110 but have a synergistic effect with cellulase107-110. Wall hydrolases may

work synergistically with expansins by reducing the matrix viscosity thereby sensitising the

wall to expansin’s action111.

Binding specificity has been studied using endogenous alpha-expansins in Arabidopsis

thaliana hypocotyls wild type and XG deficient mutants48. Expansins cause increased

extension under constant stress, as well as increased stress relaxation for both the native and

XG deficient samples, with the highest activity observed for the native hypocotyl. These

results suggest that the target of alpha-expansin is most likely the cellulose-XG matrix, but

hydrogen bonded contacts between other (1-4) beta-glucan can also serve as substrates.

Furthermore, McQueenmason and Cosgrove99 show that expansins extracted from wall

fragments bind weakly to crystalline cellulose, and binding increases for cellulose coated

with hemicellulose. They conclude that expansins bind to insoluble matrix polymers that are

tightly associated with cellulose.


24

Wang et al.112 show that bacterial expansin binding is highly specific to cellulose domains

enriched with XG which could be a consequence of XG changing the crystallinity at the

cellulose fibre surface. McQueenmason and Cosgrove 99 also report the increased binding of

plant expansins to amorphous regions formed after native cellulose was treated with 4M

NaOH to form the less crystalline cellulose II, which contains more extensive amorphous

regions. However there is evidence to suggest that binding capacities of BsEXLX1 are not

specifically related to the crystallinity of the cellulosic substrate where binding order did not

match crystallinity order for a series of substrates113. Contradicting this, Bunterngsook et

al.114 report that binding capacity of expansins from a different bacterial strain is affected by

the degree of crystallinity of the cellulosic substrate. Binding efficiency to amorphous

cellulose (PASC) was higher than Avicel. However the binding efficiency of arabinoxylan,

which is the most amorphous substrate, falls in the middle and suggests that binding

preference is based on both the types of polysaccharides and the crystallinity state of the

substrates. This could explain why Kim et al.113 show microcrystalline cellulose from a

bacterial source has higher binding efficiency compared to the less crystalline Avicel because

the different sources of cellulose may have different compositions of the crystalline

allomorphs.

The structure of the BsEXLX1 protein suggests that it binds to a single glucan chain rather

than a highly crystalline surface110. Therefore, the expansin may directly reconfigure

polysaccharides at the cellulose-matrix interface, leading to cell wall creep. By binding a

glucan that is part of the load-bearing network, the resulting distortion in its shape could drive

slippage at the junction if the wall is in tension110. Seki et al.109 find no evidence for expansin

activity transforming the crystal structure of cellulose macroscopically from X-ray diffraction

results; however this does not discount the possibility of very minor (i.e. single glucan chain)

structural changes. This shape distortion mechanism may support some of the ideas presented

in the conformational defect model by Lipchinsky115. Lipchinsky115 proposes that a region of

a cellulose chain on the surface of a microfibril is released due to the action of expansin. This

causes a conformation defect that can move toward microfibril-matrix interfaces driven by

stress gradients on the microfibril surface. The defect then causes the interface to deflect and

leads to the dissociation of matrix polysaccharides from celluloses microfibrils. This mode of

action was proposed because it is better able to reconcile the large effect of a small amount of

expansin on initiating wall extension, which involves polysaccharide slippage at multiple

entanglements. The continued motion of the conformational defect means that expansins are


25

indirectly participating in dissociating multiple entanglements in the microfibril-matrix

complex. The Lipchinsky model is further supported by MD simulations of the binding of

BsEXLX1 to a single glucan chain, which shows that the chain can assume a stable twisted

conformation.

The activity of expansins is typically assessed using the following mechanical assays:

• Creep test: monitoring the extension under a constant applied stress.

• Stress relaxation test: Applying a constant extension and monitoring how the wall

stress decays over time.

• Tensile test: Apply an increasing stress and observed at the relationship between the

stress and extension, as well as the stress at which there is a critical failure in the

sample (referred to as the ‘tensile’ strength.

The substrates used in the assays above include plant tissue, cellulose paper (Whatmann filter

paper), and bacterial cellulose hydrogels. There are challenges to using plant tissue as a

means of elucidating the mechanism of action due to the inability to separate the contributing

factors. Park and Cosgrove48 compare a native and XG-deficient plant tissue to investigate

the contribution of XG, but comment on the potential compensation of other cell wall

components such as AX. Kim et al.107 report that BsEXLX1 reduces the tensile strength of

filter paper, and SEM images show some microstructural changes where fibrils were less

interconnected or overlapped compared to the absence of BsEXLX1. An important question

is whether filter paper is a good model of the cellulose interactions in plant cell walls because

the cellulose has been mechanically and chemically treated and dried to make the paper

product. Finally, Whitney et al.102 show that extracted alpha-expansin increased creep on a

hydrated bacterial cellulose composite material containing XG, compared to no effect on

cellulose-only materials. However, for the same samples, uniaxial extension tests shown that

expansins have an effect on both cellulose and cellulose-XG samples. For me, this is a strong

indication that the mechanism of expansin action is strongly dependent on the distribution of

stress in the system. Furthermore, model systems such as bacterial cellulose hydrogels are

appropriate for controlling the direction and extent of deformation.

What is lacking from this work is an understanding of how to precisely interpret the changes

in macroscale mechanical behaviour (e.g. creep, stress relaxation, tensile strength) in terms of

the microstructural features of the system. For example, does an increase in extensibility of a


26

cellulose network relate to a decrease in the number of fibre-fibre contact points in the

system, or a decrease in the yield stress or adhesion at the contact points? I will build on the

use of bacterial cellulose as a model system to answer questions such as these by looking at

fibre-fibre and network-network level interactions in the presence of expansins, with

accompanying FEM simulations to uncover the specific physical changes that explain

observed mechanical changes.

2.2.4 Tribological Contacts in Plant Cell Walls

Based on this review of plant mechanics and growth, I identify two critical tribological

contacts. The first is the interface between adjacent cell walls in a plant tissue. In the review

of pectic polysaccharides above, the pectin rich middle lamella layer is postulated to allow

cell separation during plant growth and development. However, to my knowledge, the

presence of shear forces and the role of friction at this interface have not been explicitly

referenced. From a modelling perspective, the boundary conditions at the interface between

two cells include an assumption of no-slip. The simplest model implementation of this is a

shared wall, i.e. wall-wall interactions are infinitely stiff75, 116. Results from such models

describe plant cell tissue where the pectins in the lamellae are anchored to the rest of well to

some degree. However, there is some experimental evidence that the no-slip boundary

condition does not always hold. Kwiatkowska and Dumais117 and Uyttewaal et al.118 find that

neighbouring cells can exhibit different growth rates. This growth rate heterogeneity is

observed in a Figure 2.12, which shows images from a time-course study of elongating root

cells119. A comparison of the images taken 4 hours apart reveals an apparent relative motion

between the columns of elongating cells. The relative extension rates of adjacent cell walls

will generate a sliding interface. For this case, the interactions at the middle lamella layer,

and the tensile and adhesive forces that arise between the cell walls during growth have not

been modelled.

The second tribological contact that is critical for plant growth is the interface between

individual cellulose fibres, often mediated by other cell wall polymers. The process of wall

extension during plant growth is detailed in the previous section of this literature review

chapter. It is understood that the loosening of fibre contacts drives wall stress relaxation, and

consequently cell expansion. Thus, during growth there is a large potential for sliding

contacts between cellulose fibres and other matrix polymers.


27

For both inter-cellular and inter-fibrillar sliding contacts, the shear forces will depend on the

(cell wall or fibre) mechanics, the adhesive interaction, and the tribo-rheological behaviour of

polymers located at the interface. Bringing all of these physical processes together is critical

to the development of a multiscale model that is capable of describing the mechanics during

plant growth.

Figure 2.12. Time lapsed images of growing root (reproduced from Anderson et al.119).

Tracking the ‘end-to-end’ interfaces between cell walls, (marked with a dotted and solid line)

shows that there is relative motion between adjacent cells.

2.2.5 Bacterial Cellulose as a Model System for Plant Cell Walls

A significant number of studies looking at the mechanics of the plant cell wall have utilised

living plant tissue and isolated cells or cell wall fragments. Plant cell walls are complex

systems to work with for the number of reasons expressed in this section of the literature

review. I have so far indicated where a model system, specifically bacterial cellulose

hydrogels, can provide a means to systematically interrogate the role of microstructural

features on the overall mechanical properties. These findings will be used to gain insight into

the influence of individual cell wall components, and their assembly, on the mechanics of

plant cell walls.

Gluconacetobacter xylinus is a species of bacteria that produces cellulose in an analogous

fashion to plants, offering an alternative and more systematic approach to look at the

mechanics of the primary cell wall using bacterial cellulose composites as a model system49,

120, 121. Cellulose molecules synthesised in the bacterial cell are extruded out of pores in the

outer and cytoplasmic membrane (elementary fibril). Subsequently, elementary fibrils


28

aggregate to form microfibrils which form ribbon-shaped macrofibrils120-122. This process is

illustrated in Figure 2.13.

The average cross-section of hydrated bacterial cellulose ribbons is ca. 36nm123. The

hierarchical structure of bacterial cellulose has been investigated using small angle scattering

techniques with XRD and SEM123. The scattering results for BC ribbons are consistent with a

core-shell model. In this model the core is composed of cellulose crystallites and the outer

region (shell) consists of solvent accessible paracrystalline cellulose, as shown in Figure 2.14.

XRD results reveal that the number of cellulose chains contained in the elementary fibrils of

BC is significantly greater than that previously reported for plant cellulose where the

dimension for BC are 5nm x 8nm (126-144 cellulose chains) versus 3nm x 3nm (24 cellulose

chains) for plants123. Furthermore, bacterial cellulose aggregates to form a flat ribbon shaped

microfiber with a cross section of the order of 35nm123.

Figure 2.13. Schematic of cellulose biosynthesis by Gluconacetobacter xylinus (reproduced

from Mikkelsen and Gidley121).

Results from morphological characterisation of composite bacterial cellulose hydrogels with

arabinoxylan and xyloglucan show that both hemicelluloses interact with the surface of

cellulose ribbons123. XG incorporation reduces the cellulose crystallinity, CEF size but not

overall microfibril dimensions, and XG cross bridges between CEFs are also seen123, 124. This

is not observed for arabinoxylan which interacts with the surface of the ribbons through non-

specific adsorption123.


29

The method for producing pure bacterial cellulose networks or pellicles, an example of which

is shown in Figure 2.15, involves the fermentation of Gluconacetobacter xylinus in Hestrin

and Schramm liquid medium121. In the bacterial cellulose model system the composition of

Figure 2.14. Model of bacterial cellulose fibre based on SANS and SAXS data (reproduced

from Martinez-Sanz et al.123).

the extracellular environment into which the secreted cellulose is deposited can be controlled

to investigate the role of cell wall polymers on the molecular, microscopic and macroscopic

properties of the material121. Cellulose-based composites can be produced by reviving,

culturing and fermenting Gluconacetobacter xylinus in the presence of hemicelluloses and/or

pectins. For all compositions the population of the aerobic bacteria initially increases, whilst

producing a limited amount of cellulose within the entire liquid phase, until the dissolved

oxygen supply is exhausted120. Following this, bacteria populating the liquid-air interface

maintain their activity and a cellulose gel grows on top of the liquid phase. The hydrogels are

then washed with copious amounts of water to remove bacteria and polymers that are held

non-specifically, and stored in 0.02 wt% sodium azide solution which acts as a biocide121.

The hydrogels are used as a general model for studying the assembly, structure, and

properties of the plant cell wall. The bacterial cellulose model has a number of advantages

over isolated plant cell wall material including elimination of microheterogeneity and harsh

extraction conditions, as well as the ability to produce multi-centimeter samples for

mechanical measurements. The use of bacterial cellulose as a model for plant cell walls has

been validated through microscopic observation of similar architectures, similarity in


30

Figure 2.15.1 Bacterial Cellulose Hydrogel

expansin activity between hemicellulose/cellulose composites and plant tissue, and reduced

cellulose crystallinity in the presence of hemicelluloses, suggesting that they can access

microfibrils prior to aggregation into the final ribbon assembly121. The structural differences

between plant and bacterial cellulose fibres and networks that should be considered are

summarised in Table 2.1 below.

Table 2.1. A summary of key structural differences in cellulose fibres and cellulose networks

from bacterial and plant sources.

Bacterial Plant

CEF 5x8 nm (~135 cellulose

chains)

3x3 nm (24 cellulose chains)

Cross-section size of macro-

fibre (shape)

35 nm (flat ribbon) 3 nm (cylindrical)

Orientation of cellulose

fibres in a network

Random Highly oriented (parallel).

2.3 Mechanical and Friction Properties of Hydrogels

One of the primary motivations of this thesis is to elucidate potential interactions occurring

between plant cell walls that undergo wall stress relaxation during plant growth and other

deformations experienced at the cellular level. I consider that studying the physics of

hydrogel tribology is relevant because plant cell walls are essentially hydrogel composites of

cellulose fibrils within a matrix of biopolymers (e.g. hemicelluloses, pectin) and water.

During dynamic growth processes, the load-bearing cross-links in the wall structure are

biochemically loosened, which leads to wall stress relaxation that drives cell expansion76, 77.

As cells expand within the tissue structure, I consider there to be a sliding contact between

adjacent extending walls. Thus plant cell walls require modes of lubrication under


31

compression (static) and sliding (dynamic) conditions, which have not previously been

explored. Since it is challenging to investigate the mechanical response using plant cell walls

directly, model hydrogel systems will be used to probe the role of microstructure on their

tribological behaviour. In this section of the literature review I will appraise the current

approaches to characterising the mechanical and friction properties of hydrogels.

2.3.1 Hydrogel Material Characterisation

The term hydrogel is used to describe and interconnected polymer network that is solvated

with water. The unique aspect of hydrogels is that they have the potential to exhibit so-called

poroelasticity, whereby under deformation the mechanical response is not only a function of

the elastic polymer network, but also the movement of solvent through that network. The

effect of water on the mechanics and friction properties of hydrogels depends on the

relaxation rate and compression rate. This is best explained by looking at shape of a

compression relaxation curve, an example of which is drawn in Figure 2.16. During

compression, the normal stress increases with strain as the hydrogel is deformed. This

increasing stress is due to a combination of interstitial fluid pressurisation in deformation of

the elastic network. The balance between these two things depends on the ability of the

solvent to escape the network. Once the hydrogel is kept at a constant strain, normal stress

relaxation is observed. The built up interstitial fluid pressure drives fluid flow out of the

hydrogel, and leads to structural rearrangement of the hydrogel network as the normal stress

decays.

Hydrogels with low permeability (effectively synonymous with porosity) are defined as

having a relaxation rate << compression rate. When hydrogels with relative low permeability

are compressed the solvent does not have time to flow such that the effect of poroelasticity is

negligible and the system behaves as an incompressible solid. For these systems the

compression curve in Figure 2.16 is linear and there is negligible normal stress relaxation.

The hydrogel mechanics can be adequately characterised by applying linear contact

mechanics models to the linear part of the compression profile.

Hydrogels with high permeability are defined as having a relaxation rate >> compression

rate. Modelling the non-linear mechanical response of the hydrogel, as in Figure 2.16, is

complex and involves the interplay between poroelastic behaviour of the fluid and the elastic


32

response of the matrix. In essence, the mechanism of stress build-up and relaxation in

unconfined compression is summarised in three steps:

(i) lateral expansion of matrix and interstitial fluid pressurisation,

(ii) contraction of matrix and fluid flow out of gel due to pressure gradient,

(iii) normal stress relaxation due to fluid redistribution125.

Figure 2.16. Typical stress-time curve for compression-relaxation of a hydrogel material.

During compression the normal stress increases as the sample is deformed (increasing strain).

Once the compression is stopped and the sample is held at a constant strain the normal stress

relaxes due to solvent flow out of the hydrogel and structural rearrangement of the network.

The compression-relaxation behaviour of hydrogels with high permeability has been

modelled using transversely isotropic linear biphasic theory126, 127. This model has been

successfully applied to experimental compression-relaxation profiles to determine material

parameters such as axial and radial modulus and permeability of articular cartilage126, 128, 129

as well as bacterial cellulose hydrogels127. Stress relaxation rate sets an important distinction

between mechanical properties of hydrogels with high and low permeability. Attempts to

relate the friction response and mechanical properties of hydrogels will require an appropriate

definition of ‘modulus’.


33

2.3.2 Relating Hydrogel Mechanics to Friction Response

In Table 2.2 I present a digest of what I perceive to be the most important and relevant

experimental studies on hydrogel friction. For each study the table catalogues the technique,

hydrogel, experimental and material parameters that affect friction, and the relationship

between the measured substrate modulus and the coefficient of friction. From Table 2.2 it is

clear that there is no consistent quantitative scaling relationship between the mechanics and

friction of the hydrogel systems. It is noted that different studies characterise the mechanics

of the hydrogel using different definitions of modulus. For example, Zhang et al.130 measure

the elastic modulus from indentation experiments and report an inverse relationship with the

coefficient of friction, whereas Chang et al.131 measure the dynamic modulus from oscillatory

shear measurements and report a positive correlation with the coefficient of friction. Another

point to make after analysing the studies in Table 2.2 is that often the mechanics of the

hydrogel are not varied in a controlled way. Comparing the same two studies from above,

Zhang et al.130 control hydrogel modulus through freeze-thawing cycles and composition, and

Chang et al.131 induce changes in the gel state by changing solvent composition. Thus any

relationships drawn with the modulus of the hydrogels are confounded by the variation in one

or more other factors.

To investigate the relationship between hydrogel mechanics and friction I will use a bacterial

cellulose system, because it provides superior control of the modulus compared to the studies

in Table 2.2. Lopez-Sanchez et al.127 demonstrate that the mechanical properties of bacterial

cellulose hydrogels can by varied by compressing the hydrogel. I am mindful that controlling

the hydrogel mechanics in this way also effects the network structure, and in particular the

solids concentration of the hydrogel. However, Lopez-Sanchez et al.127 and Bonilla et al.132

provide extensive mechanical modelling to accompany the experimental compression-

relaxation results, which makes it possible to interpret the contribution of microstructural

changes to the mechanical response of the hydrogels.

Instruments commonly used for friction measurements such as tribometers (sphere-plane),

surface force apparatus (SFA) (cross-cylinder), and colloidal probe AFM (sphere-plane) have

clearly defined areas of contact, which is pivotal for interpreting the surface friction.

However, the way bacterial cellulose is produced (detailed in Chapter 3) means that the

hydrogels cannot be fabricated in cylindrical or spherical shapes. For disk-shaped bacterial

34

Table 2.2. Summary of key findings from relevant studies on hydrogel friction.

Reference Technique Hydrogel Parameters varied Mechanics–Friction Relationship

Zang et al.130 Friction: Hydrogel against cartilage surface in

microtribometer.

Mechanics: compressive elastic modulus measured

with flat-head cylinder indenter.

Poly(vinyl

alcohol)/Hydroxylapatite

composite.

Freeze-thawing cycles and

HA content which change

hydrogel modulus.

An inverse relationship between

coefficient of friction and modulus.

Baykal et

al.128

Friction: pin-on disk tester with hydrogel pin against

ceramic disk.

Mechanics: confined compression (i.e. impermeable

side walls and permeable top wall) and unconfined

compression (i.e. no side walls and impermeable top

and bottom walls).

Proprietary hydrogel. Velocity, load, lubricant

(water and bovine serum),

hydrogel modulus and

permeability.

Positive correlation between

coefficient of friction and hydrogel

modulus.

Kozbial et

al.133

Friction: Nano-tribometer with stainless steel ball

against hydrogel surface.

Mechanics: Compression testing in a Brookfield

Texture Analyser to determine Young’s modulus.

-carrageenan hydrogel. External load, cross-

linking density, velocity,

and environment (water or

air).

Increasing cross-linking density

increases friction force and is

proportional to Young’s modulus.

Kurokawa et

al.134

Friction: Parallel plate rheometer with gel disks

attached to both plates.

Mechanics: Elastic modulus from applying Hertz

model to force maps using AFM with a triangular

tip.

Cross-linked poly(N,N’-

dimethyl acrylamide)

Elastic modulus. Negligible effect of modulus on the

coefficient of friction due to the

friction response being dominated by

the presence of loose polymeric

chains at the surface of the hydrogel.

Kagata et

al.135



Mechanics: Dynamic modulus from oscillatory shear

test in the rheometer.

Physically cross-linked

poly(vinyl alcohol),

chemically cross-linked

poly(2-acrylomido-2-

methylpropane-sulphonic

acid sodium salt.

Velocity, normal stress,

temperature

An inverse relationship between

coefficient of friction and modulus

whereby modulus changes with

temperature.

Chang et

al.131



Mechanics: Dynamic modulus determined by small-

amplitude oscillatory shear measurements in the

rheometer.

Poly(N-

isoproylacrylamide)

Angular velocity, normal

load, different gel state

(swollen and collapsed)

induced by changes in

solvent composition.

Positive correlation between the

coefficient of friction and dynamic

modulus.


35

cellulose hydrogels, a parallel plate rheometer is the most readily available technique to probe

hydrogel-hydrogel friction.

To investigate the behaviour at the interface between pairs of hydrogels a rotational

rheometer with parallel plate geometries has been used as shown in Figure 2.17. Pairs of

hydrogels are attached to parallel plates and brought into compressive contact at a constant

normal stress, after the system has equilibrated one of the plates is rotated at a specific

angular velocity while the frictional torque is recorded over time131, 134-136. In previous studies

using this technique, the elastic modulus of hydrogels is measured external to the friction test

by indentation tests134, or in situ using small amplitude oscillatory shear before friction

testing131, 135. The ability to measure the mechanics of hydrogel in situ is a major advantage of

using a parallel plate rheometer to investigate hydrogel friction. This powerful technique has

not previously provided insight into the mechanics of plant cell walls because it is not well

suited to plant material.

Figure 2.17. Gel-Gel friction experiment in a rotational rheometer (reproduced from Chang

et al.131).

The crucial challenge with using parallel plate geometry for friction measurements is the

unknown contact area. This is highlighted explicitly by Yamamoto et al.137, who capture

images of the contact between polyacrylamide hydrogels and glass in water. As shown in

Figure 2.18, there are regions of contact and regions of trapped water. The degree of contact

was found to be dependent on velocity and contact pressure. These observations are


36

consistent with an early study by Roberts138, who experimentally visualised the interfacial

film between rubber and glass with optical interference measurements. Elastic deformation of

the rubber surface leads to ready entrapment of liquid at the interface. Adhesive forces

between the rubber and glass lead to contact at the point where the opposing surfaces are

closest. The contact area then spreads to trap pockets of fluid at the interface, that is, wetted

regions are surrounded by areas of solid-solid contact. A decrease in lubricant viscosity

resulted in the fluid pockets disappearing at a rate inversely propositional to the viscosity.

Squeeze film lubrication theory has been applied to study the behaviour of a fluid film at the

interface between hydrogel surfaces when they approach each other in the normal direction.

The behaviour of the film is typically described by a modified Reynolds equation. The load

carrying capacity, film thickness, and squeeze time are predicted for hydrogel systems with

varying permeability and elastic modulus139-141. I will use this modelling approach in

combination with the well-defined model for the mechanics of bacterial cellulose systems to

Figure 2.18. An aerial image and corresponding side-view illustration of the contact between

a hydrogel and glass surface. There is a region of trapped water at the interface that causes

the area of contact to be less than the area of the hydrogel. (Reproduced from Yamamoto et

al.137).

predict the contact area between parallel hydrogel disks bought into compression in a

solvated environment. Findings from this study will have significant impact on the ability to

accurately interpret the friction response, and relate it to the mechanics of hydrogels.


37

2.3.3 Cellulose Hydrogels Mechanics and the Relevance to Plant Cell Walls

Bacterial cellulose hydrogels are compressible poroelastic gels that relax to near zero loads

even after compression to high strains (>50%)127, 142. The mechanical behaviour of these

systems during compression-relaxation has been previously characterised from both

experimental127, 142 and modelling approaches127, 132.

Bacterial cellulose hydrogel properties are modulated by creating composite hydrogels with

arabinoxylan (AX) and xyloglucan (XG). The effect of hemicelluloses on the mechanical

properties of cellulosic hydrogels have been studied using uniaxial143, 144 and biaxial49 tensile

testing, and under compression127. From uni-axial testing it was observed that

cellulose/xyloglucan composites have a lower modulus (decreased stiffness and increased

extensibility) compared to the pure cellulose network143. Deformation of cellulose/xyloglucan

composites via equi-biaxial tension, mimicking the effect of turgor pressure on the cell wall,

shows increased compliancy and time-dependent creep behaviour compared to pure

cellulose49. It is suggested that during the biosynthesis of bacterial cellulose, the adsorption of

XG onto the cellulose fibril surface reduces the number of fibre contacts within a network 124.

A reduced number of fibre entanglements in the presence of XG is a common hypothesis for

the observed increase in extensibility of cellulose-xyloglucan composites under tension,

compared to cellulose hydrogels49, 143. Moreover, this supports the biological interpretation of

the role of XG in the tethered network model of the plant cell wall. The presence of

hemicellulose cross-links prevents microfibril aggregation, resulting in a decreased

mechanical strength that facilitates turgor-mediated cell expansion/extension25, 143. The

increase in extensibility due to the presence of arabinoxylan in the cellulose composite is

modest compared to xyloglucan144.

Under compressive strain the presence of arabinoxylan and xyloglucan in cellulose

composites increases the modulus compared to pure cellulose, although this effect is

dependent on compressive strain rate142. At higher compressive strain rates (>10µm/s) the

effect of arabinoxylan and xyloglucan are similar, however at slower rates (1µm/s) the

arabinoxylan has little effect compared to xyloglucan. These results are contrary to those

from uni- and bi-axial tensile testing because the surfaces applying compression are

impermeable, limiting water flow to the radial direction which has lower porosity than in the


38

axial direction. These mechanical studies again highlight the important role of water

movement.

The lubricating role of water and other polysaccharides at fibril-fibril contacts has been

investigated by characterising the fibril orientation and interaction in three bacterial cellulose

composites (cellulose C, cellulose/pectin CP, and cellulose xyloglucan CXG) for an applied

uniaxial strain using FT-IR and dynamic 2D FT-IR spectroscopies145. On the molecular level,

the reorientation of cellulose fibrils is in the direction of the applied strain. ‘The cellulose-

network reorientation depends on the composition of the matrix, including water content,

which lubricates the motion of macromolecules in the network’145. Enhanced reorientation of

cellulose fibrils in systems with higher water content supports the role of water in lubricating

fibrillar surfaces in molecular motion. Results from dynamic 2D FT-IR experiments suggest

that the independent response of cellulose and pectin to a small amplitude strain could be a

result of few fibril contacts in the composite. Whereas cross-linked cellulose-xyloglucan

domains are uniformly strained along the direction of stretch and the alignment results in

greater extensibility. Pure cellulose networks contain the highest density of mechanically

relevant contact points which are more easily disrupted upon elongation compared to CXG

composites.

The findings from Kacurakova et al.145 provide a starting point for a more detailed

investigation into the role of cell wall components on the mechanics of hydrogel systems.

This section of the literature review has emphasised the need for a combined experimental

and modelling approach to illuminate the exact microstructural features that explain the

mechanics of bacterial cellulose hydrogels. For example, to evaluate the hypothesis that XG

reduces the number of contacts between cellulose fibres in the network, the number of cross

links in the model network can be varied in silico. The outputs of the model can then be

compared to the mechanical measurements of bacterial cellulose hydrogels and composites

with XG. These findings will contribute new knowledge in terms of the lubricating

mechanisms of wall components at intercellular contacts during plant growth.

2.4 Measurement of Fibre-Fibre Interactions

The mechanical properties of a range of fibrous materials have been studied using

compression, uni- and bi-axial tensile testing and small-amplitude oscillatory shear49, 127, 143,

146-153. The results from these studies indicate that the mechanics of random fibre networks is


39

defined by the intrinsic mechanical properties of nanofibres, surface interactions between

fibres, the network microstructure, and number and nature of entanglements and/or cross-

links, as well as the solvent properties.

The strength of adhesion between cellulose fibres and the surrounding polymer matrix is a

key factor that determines the mechanical properties of cellulose composites, including

natural cellulose fibre systems such as plant cell walls. The remarkable load bearing capacity,

in combination with mechanical toughness, makes such materials stand out amongst other

biocompatible hydrogels for material applications. Currently, the most reliable information

regarding inter-fibre adhesion can be deduced indirectly from analysis of macroscopic

mechanical properties of composites. Inputs into mechanical models of fibrous assemblies

include the network structure, mechanics of the fibres and fibre junctions. A review of the

fibre network models, experimental approaches for measuring mechanics of single fibres and

interactions between individual fibres is detailed here.

2.4.1 Fibre Network Models

The development of structural models of fibre networks provides predictive capabilities for

design and evaluation, as well as enhancing understanding of the underlying principles

controlling deformation processes in natural systems. In order to model fibre networks,

specific assumptions around the mechanics of fibre-fibre contacts have to be implemented.

Fibre network models commonly treat contacts between fibres as rigid junctions, which can

approximate elastic network deformation (i.e. no sliding at fibre contacts)154-157. However,

this is only appropriate when fibre interactions are very strong. Constitutive equations are

constructed such that the stress-strain response depends on orientation, density and fibre

properties. The assembly of fibres in the network strongly influences the overall network

mechanics. This is evidenced when comparing the mechanics of fibres and fibre network of

bacterial cellulose. The Young’s modulus of individual cellulose fibres is of the order of 100

GPa158, and is orders of magnitude greater than the modulus of bacterial cellulose which is of

the order of 1 MPa49, 127, 143. Moreover, bacterial cellulose hydrogels incorporating XG have a

modulus of the order 0.1 MPa49, 127, 143. I expect that XG has negligible effect on the

individual cellulose fibre modulus, or at least not a sufficient effect to account for the order of

magnitude reduction in the modulus at the hydrogel level. Instead, it is likely that XG reduces

the hydrogel modulus through its effect on fibre orientation, number fibre contact points, and

the mechanics of fibre contacts.


40

Mechanical testing of cellulose hydrogels shows plastic deformation127, which suggests that

fibre-fibre contacts are not rigid. Pan and Carnaby159 present a mechanical model of a fibre

network that incorporates fibre bending and slippage at contact points. A force balance based

on the applied contact forces and the fibre orientation is implemented to determine if contact

points are sliding (inter-fibre friction) or non-slipping (deformation through bending of fibre

segments) in response to an applied shear stress. For viscoelastic fibre networks, Chatterjee160

applied an energy penalty to the breaking of each fibre-fibre contact and related it to the

stored elastic energy of deformation. Heyden and Gustafsson161 include a slip criterion for

bonds in a network mechanics model whereby bonds show non-linear stick-slip facture

behaviour and slip leads to the degradation of stiffness and strength properties of the bond.

Using a finite element method of analysis, a comparison is made between 3D network

simulations and experimental results for dry-shaped cellulose fibre materials. The modelling

and experimental results are compared in terms of homogenised mechanical properties such

as stress versus strain performance under tensile deformation, initial anisotropic 2D and 3D

stiffness properties, strength and fracture energy. Reasonable agreement was observed up to

peak tensile stress, after which considerations around strain localisation and heterogeneity in

the material take effect161.

I recognise the need to build models that can predict the yield point at fibre-fibre contacts,

based on the plastic deformation behaviour of fibre networks. This would provide important

insights into the loosening of cellulose fibre contacts in the cell wall during extension and

plant growth. Accurate knowledge on the fibre mechanics and adhesive potential between

fibres at network junctions will be required to build and validate such a model, and this

information can only obtained through experimentation.

2.4.2 Fibre Mechanics

The mechanical properties of cellulose fibres have primarily been measured with the AFM

using nano-indentation techniques. Single cellulose microfibrils are horizontally suspended

over a trench, and the Young’s modulus is measured using a modified nano-scale three-point

bending test where the fibre is deflected by the AFM cantilever with a known force at several

points along the fibre158. A bacterial cellulose suspension was dispersed by sonication, placed

on a silicon-nitride coated grating with a pitch of 3 µm, then spin coated to disperse the fibres

as a uniform monolayer as seen in Figure 2.19.


41

Figure 2.19. Cellulose fibres suspended over grating (reproduced from Guhados et al.158).

For mechanical testing, force spectra were obtained by recording cantilever deflection as a

function of vertical sample displacement as shown in Figure 2.20158. The Young’s modulus is

determined from the slope of the force spectra according to Equation 2.1 where k is the

cantilever spring constant, E is the Young’s modulus, I is the area moment of inertia (I =

(πwh3)/64 for width, w and height, h of a fibre with elliptical cross-section), a is the distance

from one end of the fibre, and L is the length of the fibre.

𝑑𝑦

𝑑𝑧= [1 +

𝑘

3𝐸𝐼(

𝑎(𝐿 − 𝑎)

𝐿)

3

]

−1

(2.1)

The measured Young’s modulus was 78+/-17 GPa for fibres with diameters ranging from 35

to 90 nm. This experimental procedure, depicted in Figure 2.21, looks at only a small vertical

deflection from which only the elastic modulus can be determined. A slight modification to

this configuration has been used to pull the fibre laterally, allowing for a larger deflection162.

Investigating the mechanics of fibres under large deformations is more informative in terms

of characterising the stretching and bending of the fibre. This level of detail is required for

building a network model that can predict plastic deformation behaviour which is expected to

involve large deformation of the fibres before slippage or detachment at contact points.

Instead of vertical deflection, the lateral deflection of an AFM cantilever can be used as a

force sensor for measuring the tensile properties of individual electrospun polymer nano-

fibres suspended across trenches162. The fibres were electrospun and glued onto a parallel bar


42

TEM grid where the spaces between the bars act as trenches that are deep enough to allow the

AFM cantilever to hook onto the fibre and pull it laterally as shown in Figure 2.22. Using the

lateral motion of the cantilever to probe the mechanical properties of a suspended nano-fibre

increases the range of motion significantly, compared to the vertical geometry, enabling the

breaking strength and elongation at break to be measured.

Figure 2.20. Force-distance curve obtained near the middle of the suspended fibre (Solid

curve: approach. Dashed curve: retraction) (reproduced from Guhados et al.158).

Figure 2.21. Fibre suspended across a trench of distance L, deformed by a vertical force F

applied at a distance a from one end of the fibre (Reproduced from Guhados et al.158).

This three-point testing configuration deforms the fibre via tensile stretching rather than

bending due to the low modulus and high aspect ratio of the tested fibre. This assumption is

validated by the non-linear force-cantilever travel curve in the elastic region as seen in Figure

2.23. Assuming a tensile stretching model, the corresponding stress-strain curve is derived


43

using Equations 2.2, 2.3 and 2.4. σ and ε are the fibre tensile stress and strain respectively, Fl

is the cantilever lateral force, A is the cross-sectional area of the fibre, x is the cantilever

travel from the initial point of contact with the fibre, θ is the angle between the stretched and

initial fibre position and l0 is half the initial length of the fibre. The Young’s modulus, yield

stress/strain, and breaking stress/strain of the test fibre are obtained from the stress-strain

curves. In this thesis I use the large range of motion of the cantilever in the lateral

configuration to probe the yielding and friction behaviour at cellulose fibril junctions as a

single fibre is pulled out of cellulose and composite networks.

𝜎 = 𝐹𝑙

2𝐴𝑠𝑖𝑛(𝜃)

(2.2)

𝜀 =(

𝑥sin (𝜃)

) − 𝑙0

𝑙0

(2.3)

tan(𝜃) =𝑥

𝑙0 (2.4)

Figure 2.22. Schematic diagram of an AFM cantilever dragging a fibre laterally (reproduced

from Gestos et al.162).


44

Figure 2.23. Force-cantilever and stress-strain curves in the elastic region for single test

nanofibre (reproduced from Gestos et al.162).

2.4.3 Experimental Approaches for Fibre-Fibre Measurement

Direct measurement of fibre adhesion has been achieved for sub-micron (>100 nm)

electrospun fibres through a variety of elaborate experiments. This includes taping

freestanding fibres to cardboard mounts163, 164 or gluing between two microspheres on an

AFM cantilever165 as shown in Figure 2.24. Two fibres are arranged orthogonal to each other

at the midpoint in a cross-cylinder configuration and pressed into contact for a given time.

The applied load and vertical displacement are monitored as the fibres are pulled apart at a

constant speed and the pull-off force is measured. Shi et al. (2010, 2012) show that for

polycaprolactone and Nylon 6 fibers, the pull-off force increases linearly with radius of the

fiber. Stachewicz et al.166 also measure the adhesion force in parallel configurations by

attaching two individual fibres to AFM tips at one end and bringing the free fibre ends into

contact. The measured pull-off force critically depends on the contact area which changes

with fibre configuration. Despite the free fibre ends in the Stachewicz et al.166 assembly, the

degrees of freedom are still restricted to only enable the two extreme fiber orientations;

parallel and cross-cylinder as shown in Figure 2.25.


45

Figure 2.24. Experimental configurations for fibre-fibre measurements (Reproduced from

Shi et al.163 and Wang et al.165).

It is challenging to use the methods described above to assess all the possible fibre

orientations between parallel and orthogonal, that are observed in randomly assembled

fibrous networks. Another limitation of these techniques is the inability to measure the

potential for fibres to interact via mechanical entanglement. Xing et al.167 show that there is a

significant effect on adhesion if fibers are permitted to wrap around each other. In their

experiment an electrospun polystyrene nanofiber is observed to wrap around a nanoparticle

attached to an AFM tip.

The experimental techniques describe above that look at the contact between single

electrospun fibres have not been applied to cellulose fibres due to the difficulty isolation and

handling individual fibres. Gutsmann et al.168 attempt to measure the mechanical properties

of a highly organised hierarchical assembly of collagen fibres. Force-extension curves are

collected when pulling parallel substructures out of the assembly using an AFM cantilever

however it could not be confirmed whether the rupture events observed were between the tip

and the molecule or between the molecules. Yan and Li169 use the AFM with an –OH

functionalized cantilever tip to measure the inter- fibre bonding properties , including pull-off

forces and work of adhesion, of wet wood pulp fibre surfaces that are solid, swollen and

micro-fibrillated. The technique is limited by the fact that the inter-fibre bonding properties

are controlled by surface deformability of the pulp fibre. There is large scope for developing

a novel method that can be applied to measure the mechanics and forces at contact between


46

individual cellulose fibres that eliminates the effect bulk deformation of the fibre assembly.

This would have major implications for understanding the role of interactions between

cellulose and other cell wall components including expansins on plant cell wall mechanics

during growth processes.

Figure 2.25. Two fibre free ends arranged in parallel and cross-cylinder contacts (reproduced

from Stachewicz et al.166).

2.5 Future Perspective: Scope and Goals of Thesis

A significant amount of literature is presented that investigates the structure of plant cell wall

materials, and the physical processes underlying plant growth. The tribological contacts that

are essential for facilitating growth include the deforming interface between adjacent cell

walls in the plant tissue, and the shearing of conjoined cellulose fibres and surrounding

matrix polymers in an extending cell wall. I postulate that certain lubrication mechanisms are

controlling the friction response at these contacts, but these have not yet been substantiated.

Mechanical measurements on plant tissue and isolated wall fragments have shown that the

materials are poroelastic. This highlights the scope for systematically exploring plant cell


47

wall mechanics using model hydrogel systems, which are defined by their poroelasticity. The

mechanics of bacterial cellulose and composite hydrogels have been investigated. However

the reported findings are mostly limited to experimental observations, with no way to

interpret the microstructural components that determine the macro-scale material properties.

A step-change in the approach to investigating hydrogel mechanics is provided through the

use of modelling by Lopez-Sanchez et al.127 and Bonilla et al.132. I will extend the use of a

combined experiment-modelling approach to interrogate the role of cell wall components and

their assembly on the mechanics and friction behaviour of bacterial cellulose hydrogels.

In previous work on articular cartilage and other hydrogel systems, researchers have drawn

correlations between the hydrogel modulus and the coefficient of friction. However, results

from these studies cannot be distilled down to any universal material function that relates

hydrogel mechanics and friction properties. I have identified an opportunity to use a

rotational rheometer to measure the friction response and in situ mechanical properties of

bacterial cellulose hydrogels. Coupled with the existing mechanical model127, 132 for the

hydrogel system, I will construct a generalised relationship between mechanics and friction

properties. This study will provide a compelling case for the potential role of cell wall

mechanics in lubricating the intercellular contacts during plant growth.

The second major goal of this thesis is to directly measure the adhesive energy stored at

cellulose fibre contacts in the absence of, or mediated by other non-cellulosic wall polymers.

This study will be revealing in terms of the way cellulose fibres linkages are formed, and the

structural role of individual cell wall components. A primary motivation for this work is the

need to have specific information on the mechanics of fibres contact in order to build a fibre

network model. The direct measurement technique and fibre network model will be

invaluable for gaining new insight into the action of expansins that loosens fibre contact and

drives cell wall extension.

This thesis has significant impact for the eventual development of a working mechanical

model that predicts the multi-scale material properties of plant tissue, and the physical

processes that underlie cell wall extension and plant growth. The key distinction between this

thesis and previous studies is the use of model systems to systematically probe individual

structural features, coupled with finite element modelling to interpret the effect of structural

features on the overall mechanical properties. I provide unique perspectives through the


48

application of an engineering and physical sciences toolkit to investigate plant biological

processes.


49

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55

Chapter 3

Research Methods

The scope and goal statement from Chapter 1 Section 1.2 and Chapter 2 Section 2.5 is to

measure the interactive forces between cellulose fibres, and investigate the role of non-

cellulosic cell wall components at these fibre contacts. This thesis focuses on the direct

measurement of model systems to make inferences around the mechanics of plant cell walls

during growth and other deformations. From Chapter 2 Section 2.2.1, plant cellulose has a

crystalline core surrounded by a paracrystalline shell. The chemical and mechanical methods

of extracting plant cellulose disrupt the paracrytalline layer, which is the region that

facilitates cellulose interactions with the hemicellulose amorphous phase in plant cell walls.

Bacterial cellulose has a similar structure to plant cellulose in terms of the crystalline and

paracrystalline phases, and can be produced as a pure cellulose network or as a composite

with hemicelluloses (AX and XG). A tribo-rheological technique is developed in a rotational

rheometer in Chapter 4 to measure the shear forces between pairs of bacterial cellulose

hydrogels and composites that are brought into compressive contact whilst surrounded by

solvent. The influence of AX and XG on the interaction between cellulose fibres at the

interface is investigated. The other major cell wall component that is considered in this thesis

is pectin. Pectin is rich in the middle lamella layer and is hypothesised to play a role in

lubricating the contact between adjacent cell walls. This is tested in Chapter 4 by varying the

pectin concentration in the solvent as pairs of bacterial cellulose hydrogels are compressed

together, and measuring the shear forces at the interface. A dip-and-drag technique is

developed in an AFM to measure the adhesive force between individual nanofibres.

Electrospun polymer fibres and cellulose fibres extracted from plant sources are used to

validate the technique in Chapter 5. The influence of hemicelluloses on bacterial cellulose

fibre contacts is investigated using the dip-and-drag technique in Chapter 6. Finally, both the

CHAPTER 3. RESEARCH METHODOLOGY Grace Dolan, PhD Thesis

56

tribo-rheological and dip-and-drag techniques are used in Chapter 7 to assess the activity of

bacterial expansin on bacterial cellulose systems and elucidate the activity of plant expansins

on plant materials. Here, I detail the materials and measurements on bacterial cellulose

systems that are used in this thesis.

3.1 Materials

3.1.1 Electrospun Fibres

The dip-and-drag technique developed in Chapter 5 is validated by measuring the adhesive

force between electrospun polymer fibres. Polymer fibre adhesion is dominated by DLVO

interactions and thus the measured adhesive force can be compared to the theoretical

prediction from DLVO theory. The other advantage is that the fibre network density can be

varied easily through the electrospinning process to determine whether the bulk network

properties influence the measured adhesive force at single fibre contacts. Electrospun

Sulphonated Poly Ether Ether Ketone (SPEEK) fibre samples with varying fibre network

densities are supplied by Dr. George W. Greene from Deakin University. Electrospun

Polyvinyl Alcohol (PVA) fibres are supplied by Professor Darren Martin’s research group at

the Australian Institute for Bioengineering and Nanotechnology (AIBN), The University of

Queensland.

Electrospun Sulphonated Poly Ether Ether Ketone (SPEEK) fibres

SPEEK is prepared from Victrex polyether ether ketone 450PF (PEEK; Mw = 38,300)

following the protocols outlined by Huang et al.1. A solution of PEEK is prepared in

concentrated sulfuric acid (95-97 %) at room temperature under mechanical stirring at a

concentration ratio of 5/95 (w/v). Once complete dissolution of the PEEK is achieved, the

solution is sealed in a solution bottle and incubated in an oven at 36 °C for 15 hours. The

SPEEK is then precipitated from solution by the addition of deionised water from a Milli-Q

Advantage A10 system with a resistance of 18 Ω.cm at 25 °C. The precipitated SPEEK

powder is recovered using filtration and washed thoroughly with clean deionised water to

remove any residual acid. The recovered and washed SPEEK powder is then dried in a

vacuum oven at 50 °C for approximately 48 hours to remove any residual water.

For electrospinning, a solution of 15 wt % SPEEK is prepared in dimethylformamide on a

hotplate at 60 °C under mechanical stirring for 24 h. The SPEEK solution is loaded into a 1


57

ml Hamilton syringe which is fixed with a blunted 20 G x 1½ in. stainless steel syringe

needle. The syringe is loaded onto a syringe pump and the syringe needle is connected to a

high voltage power supply (Gamma High Voltage Research, USA). A clean glass

microscope slide is mounted to a grounded collection plate using double sided tape and the

collection plate and slide are covered with aluminium foil. A hole is cut out of the centre of

the aluminium foil to expose an approximately 1 cm x 1 cm area of the underlying glass slide.

The collection plate is then positioned 17 cm away from the tip of the syringe needle. The

electrospinning is done by pumping the SPEEK solution through the syringe under a constant

flow rate of 0.12 ml/hr and an applied voltage of 20 kV to the syringe needle. The SPEEK

nanofibres are electrospun onto the substrate for a given time ranging from 1 to 5 minutes,

resulting in fibre matts with varying network densities. The SPEEK nanofibre network is then

imaged using a NeoScope JCM-5000 SEM (JEOL) and the average fibre diameter, 127±9.3

nm, is obtained directly from the SEM micrographs analysed using ImageJ software.

Electrospun Polyvinyl Alcohol (PVA) fibres

PVA polymer (molecular weight of 85-124 kg/mol -Sigma-Aldrich, Castle Hill, Australia) is

firstly dissolved in deionised water at 80 °C for 4 hours. The solution is left to stand,

unstirred, for a few minutes in order to degas before electrospinning. For the electrospinning

process, polymer solution is loaded into a 5 ml syringe and a positive electrode is clipped

onto the syringe needle with a 0.5 mm diameter. The flow rate of the PVA solution is 0.5

mm/hour, at an applied voltage of 22 KV and tip to collector distance of 13 cm. PVA solution

is electrospun horizontally onto the target. After electrospinning, the collected nanofibre mat

is dried in a vacuum oven at 60 °C for 8 hours. The morphology of PVA nanofibres is

investigated using Scanning Electron Microscope (JEOL JSM-6460LA). From SEM images,

the average diameter of 50 individual nanofibres is 163 ± 42 nm.

3.1.2 Cellulose Nano-fibres Extracted from a Plant Source

In Chapter 5, the dip-and-drag technique is also applied to cellulose nano-fibres that interact

via hydrogen bonding. Cellulose Nanofibrils (CNF) and Cellulose Nanocrystals (CNC) are

supplied by Professor Darren Martin’s research group at the Australian Institute for

Bioengineering and Nanotechnology (AIBN), The University of Queensland.


58

Cellulose Nanofibres (CNF)

Cellulose nanofibres (CNF) from Triodia pungens, an Australian native grass, are produced

based on the method explained elsewhere2, 3. Briefly, water washed ground grass is

delignified using a 2 %(w/v) sodium hydroxide solution, followed by bleaching two times

with a 1 %(w/v) acidic solution of sodium chlorite. Cellulose nanofibrils are obtained by

passing a 0.3 %(w/w) dispersion of bleached pulp through the high pressure homogeniser

(Panda 2K NS1001L, GEA Niro Soavi S.p.A, Italy) at a pressure of 700 bar for two passes.

TEM images of nanofibrils are obtained using a JEOL 1011 TEM (JEOL Pty Ltd., Frenchs

Forest, Australia) at 100 KV. The dimensions of nanofibrils are measured using digital image

analysis (Image J) of several TEM images at the same magnification. Individual CNF

obtained from Triodia pungens have an average diameter of 4.5 ± 1.5 nm, and a length of

several microns.

Cellulose Nanocrystals (CNC)

Cellulose nanocrystals (CNC) of Triodia pungens are obtained by sulphuric acid hydrolysis

of bleached pulp. T.pungens bleached pulp is treated with 40 %(v/v) sulphuric acid at 45 °C

for 3 h, followed by centrifuging the hydrolysed fibre dispersion for 20 minutes at 4750 rpm.

The centrifugation step is repeated 4 times in order to remove excess acid and dissolved

extractable material. Hydrolysed fibres are dialysed against distilled water for a week, and

redispersed in deionised water using an ultrasonic probe (Q500 Sonicator, via QSonica,

Newtown, United States) at 25 % amplitude, a frequency of 20 kHz, and output energy of

500 W for 20 minutes. The diameter and length of CNC measured from TEM images are 3.5

± 0.8nm and 497 ± 106nm, respectively.

3.1.3 Bacterial Cellulose

Bacterial cellulose is considered to be a good model system for investigating cellulose-

hemicellulose interactions that are prevalent in the plant cell wall. The method for producing

cellulose hydrogels is based on the fermentation of Gluconacetobacter xylinus in liquid

media4, 5. The bacterium is aerobic and locates at the air interface. The synthesised cellulose

fibres form a self-assembled network that floats on the surface of the liquid fermentation

medium and takes the shape of the container in which it is grown. For the tribo-rheological

technique in Chapter 4, hydrogel disks are grown in a 41 mm diameter container. The

thickness of the hydrogel disks is somewhat controlled by the fermentation time. The


59

hydrogels used in this thesis are measured using calipers to have an average thickness of

approximately 2.5 mm.

Gluconacetobacter xylinus (ATCC 53524 American Type Culture Collection, Manassas, VA,

U.S.A) is stored in Hestrin and Schramm (HS) agar medium at -80 °C. The composition of

HS medium is given in Table 3.1. The frozen strain is revived by incubating on HS agar

plates at 30 °C for 72 hours. A loop of bacteria is transferred to 20 mL of liquid HS medium

with 50 %w/v glucose solution. The liquid medium is adjusted to pH 5 with 0.1 M HCl,

before incubating under static conditions for a further 72 hours at 30 °C. The cellulose

network that forms on the surface of the medium contains trapped bacteria. An orbital

platform shaker (KS 260 IKA-Werke, Staufen, Germany) is used at 350 rpm for 5 minutes to

dislodge the bacteria into the liquid medium. This forms the primary inoculum, of which 1

mL is aliquoted into sterile containers (41 mm diameter) with 9 mL of HS liquid medium.

The containers are then incubated under static conditions for 72 hours at 30 °C before being

agitated on the orbital platform shaker (350 rpm, 5 mins). The samples are harvested from the

liquid medium using metal forceps, and the surface in contact with the medium is scraped

gently along the rim of the container to remove loosely attached cellulose strings. The

hydrogels undergo six rinse treatments in ice cold ultrapure water (resistivity 18.2 MΩ.cm at

25 °C from Milli-Q water purification system) under agitation. The rinsing is carried out on

the orbital platform shaker with 3x30 min and 3x10 min steps at 100 rpm, replacing the water

at each step. Finally, the hydrogels are stored in 0.02 wt% sodium azide to prevent

microbiological contamination and growth.

Table 3.1. Composition of 300 mL of Liquid HS medium

Ingredient Amount

Peptone 1.5 g

Yeast Extract 1.5 g

Na2HPO4.2H2O 1.014 g

Citric acid 0.345 g

Glucose (50 %) 12 mL

Water 288 mL

Composite hydrogels are produced by dissolving polysaccharides (XG or AX) into solution

(1 g/100 mL) at 85 °C stirring at 250 rpm overnight. The polysaccharide solution is added to


60

a twice concentrated HS medium in a 1:1 ratio. Composites had a polysaccharide

incorporation of 41.2 % for the cellulose/AX composite (CAX) and 44.4 % for the

cellulose/XG (CXG). A comprehensive protocol for the production of cellulose and

composite hydrogels is provided in Appendix A.

Microarray moulds

To be compatible with the dip-and-drag technique, the dimensions of the bacterial cellulose

networks have to be much smaller than the hydrogels produced above. A

Polydimethylsiloxane (PDMS) microarray mould has been designed here to grow bacterial

cellulose micro-hydrogels within 50 µm diameter cylindrical wells, 50 µm in depth. The

design is etched onto a chromium mask which is then used for SU-8 master fabrication to

give a silicon wafer mould with an array of cylindrical pillars (50 µm diameter and height).

PDMS is cast onto the silicon wafer mould to create arrays of micro-wells that can be

inoculated with bacteria in liquid HS medium to grow cellulose micro-hydrogels. Detailed

procedures for the chromium mask, SU-8 fabrication, and PDMS casting are presented in

Appendices B – D.

To grow cellulose micro-hydrogels, the above procedure for fermenting Gluconacetobacter

xylinus is followed. The PDMS microarray is plasma treated on high for 38 seconds to make

the surface hydrophilic. The primary inoculum is pipetted onto the PDMS microarray, and

the hydrophilic nature of the surface promotes the spreading of inoculum and sedimentation

of bacteria into the individual wells. The surface of the microarray is blotted to remove

excess liquid medium, allowing micro-gels to grow as a thin layer on the surface of the

confined micro-wells. The micro-gels are harvested after 72 hrs incubation under static

conditions by washing the surface of the microarray with ice cold water. A comprehensive

protocol for producing cellulose micro-hydrogels is provided in Appendix A.

3.1.4 Pectin Solutions

The effect of pectin solutions on cellulose fibres interactions is tested using the tribo-

rheological technique in Chapter 4. Commercial pectin extracted from citrus peel with a

degree of esterification of 65 (GENU® pectin 150 USA-SAG type D slow set, CPKelco,

Atlanta, USA) was slowly added to reverse osmosis (RO) treated water with resistivity of

18.2 MΩcm (Satorius Stedim) at 0.5, 1, 2, 4 wt%. The pectin solutions are mixed for 2 hours

using an overhead stirrer, then transferred to a container and left overnight on a roller mixer.


61

To measure the viscosity of the pectin solution an AR-G2 (TA instruments) with cone and

plate fixture (40 mm diameter, 2° angle) was used to perform a shear rate continuous ramp

between 1 to 1000 s-1 (5 points per decade, 30 s per point).

3.1.5 Bacterial Expansins

Bacterial expansins were supplied by Professor Daniel Cosgrove’s research group at

Pennyslvania State University (PSU), USA. Wild type bacterial expansin (EXLX1 or YOAJ)

and 3 protein variants designated WWY, RKKQ and D82, are included in this study. Details

of the mutations to each of the protein variants are discussed in Chapter 7: Section 7.1. The

method of treating bacterial cellulose substrates with expansins is explained in Chapter 7:

Section 7.2.

3.2 Measurements

3.2.1 Tribo-rheological Technique in a Rotational Rheometer

In Chapter 2: Section 2.3.2 I review the use of a rotational rheometer to measure the friction

between hydrogels. In the literature, hydrogel pairs are brought into compressive contact at a

given normal load and the friction is measured for a controlled angular velocity. The major

difference between the bacterial cellulose hydrogels studied in this thesis and the hydrogels

studied in literature is that the cellulose hydrogels have a much higher permeability and relax

to near-zero loads after compression through a poroelastic mechanism. I build upon the

measurement technique in literature to include a comprehensive in situ mechanical

characterisation of the hydrogel system, coupled with computation modelling of the hydrogel

poroelasticity and squeeze flow of the solvent at the interface during compression. The

experimental protocol for the tribo-rheological technique is detailed here. The sensitivity of

the results to certain experimental parameters is explored in Chapter 4: Section 4.2.1. The

poroelastic mechanical model is detailed in Chapter 4: Section 4.2.2, and the computational

model for simulating the squeeze flow of solvent during compression is detailed in Chapter

4: Section 4.2.3.

A Haake MARS III stress controlled rheometer (Thermo Fisher Scientific, Karlsruhe,

Germany) is used to measure the friction behaviour between pairs of bacterial cellulose

hydrogel disks (~41 mm diameter) produced according to the procedure in Section 3.1.3. All

measurements are performed using a 60 mm titanium parallel plate (customised in the


62

RHEOWIN Job Manager software to have a diameter equivalent to the hydrogel) and a

titanium metal dish. Equivalent diameter circles of emery paper (P240/S85, 58 µm

roughness) are attached to the parallel geometries using double adhesive tape. The zero point

for the gap is set between the emery paper covered geometries. Pairs of hydrogels are fixed to

the emery paper, as illustrated in Figure 3.1, using cyanoacrylate adhesive (RS components,

NSW, Australia) and centred with the help of a stencil. The initial measurement gap is set at

8000 µm, that is, a distance of 8000 µm separates the two emery paper surface (not the

distance between the hydrogel surfaces). At this gap, the top geometry is below the edge of

the bottom dish but the hydrogels are not touching. The dish is then filled with water or

pectin solution to completely submerge the top geometry. The normal force is set to zero

before the top plate is lowered to a gap of 3000 µm at a constant axial ramp rate (33 µm/s),

following the previously published compression-relaxation procedure for bacterial cellulose

hydrogels6. After compression, the normal stress relaxes due to the poroelastic properties of

the samples and water transport out of the network6. The hydrogels are held at the constant

axial strain for 15 minutes to achieve an equilibrium normal stress. A small amplitude

oscillatory shear (SAOS) step at 1 Pa and 1 Hz is run for 60 seconds to determine the storage

and loss modulus (G’ and G”) of the system; these conditions are chosen to ensure that all

measurements are in the linear regime where the stress is linear with strain. After the

compression-relaxation and SAOS steps, a steady shear rate of 0.1 s-1 is applied for 2

minutes. This test procedure is illustrated in Figure 3.2. The torque is recorded and converted

to shear stress at the rim of the hydrogel using equation 3.1.

𝜏 =2𝑀

𝜋𝑅3

(3.1)

τ is the shear stress at the radius of the hydrogel, M is the torque, and R is the radius of the

hydrogel. The hydrogels are then further compressed in 500 µm steps and the above

procedure is repeated until a minimum gap of 1500 µm. The initial height (hi) of the hydrogel

pairs is taken to be 5000 µm, which is twice the average initial thickness of a single gel disk

prior to compression. The compression ratio (CR) is calculated in terms of the final height

after compression (hf) using equation 3.2.

𝐶𝑅 = ℎ𝑖 − ℎ𝑓

ℎ𝑖

(3.2)


63

Figure 3.1. Bacterial cellulose hydrogels adhered to emery paper covered geometries.

Figure 3.2. Test procedure for mechanical and friction characterisation of poroelastic

hydrogels: (1) Compression at a constant axial rate to a set compressive strain, followed by a

15 minute relaxation step. (2) Small amplitude oscillatory shear of the relaxed system. (3)

Constant angular velocity step.

3.2.2 Dip-and-drag Technique in the AFM

Techniques in literature for directly measuring the adhesive force between nanofibers are

reviewed in Chapter 2: Section 2.4.3. Due to the difficulty of isolating individual bacterial

cellulose fibres, I develop a technique that can be applied directly to fibre networks. In

Chapter 5 I validate the technique using model electrospun fibres that are produced according

to Section 3.1.1. The specific details for applying the dip-and-drag technique to the model

electrospun fibre mats are provided in Chapter 5: Section 5.2.2. In Chapter 6 I use the

validated technique on bacterial cellulose and composite networks with AX and XG produced

according to Section 3.1.3. The experimental protocol for applying the dip-and-drag

technique to bacterial cellulose systems is provided here.

Cellulose micro-hydrogels grown within the confined geometries of a PDMS microarray are

shown in Figure 3.3. The gels are stained with calcofluor white and imaged in the confocal


64

microscope with DAPI filter set for epifluorescence (wavelength 450-500 m). The array of

micro-hydrogels is placed face down onto a glass slide that has been plasma-treated on high

for 38 seconds. The plasma treatment removes contaminants and makes the surface

hydrophilic, which breaks the surface tension of the liquid in the micro-wells and draws to

micro-hydrogels onto the glass slide. The gels are left in contact with the substrate for

approximately 1 hour to allow this process to occur. The PDMS mould is then peeled off

leaving the micro-hydrogels deposited on the glass surface.

Figure 3.3. Cellulose micro-hydrogels grown in PDMS micro-array, stained with calcafluor

white and imaged with a confocal microscope using DAPI filter set for epifluoresence

(wavelength 450-500).

The micro-hydrogels are glued to the substrate using a JPK Nanowizard II AFM mounted on

an inverted optical microscope (JPK Instruments, Germany). The AFM is equipped with a

CellHesion® module that has a Z-piezoelectric translator range of 100 µm. First, a small

volume of 5 minute curing epoxy resin (UHU GmbH & Co. KG, Germany) (equal parts base

and curing agent) is deposited onto the substrate close to the micro-hydrogels. The droplet of

epoxy resin can be administered by hand using a fine glass rod with direction from

microscope. The AFM tip is then lowered into the epoxy resin droplet and subsequently

lowered onto the edge of the micro-gel. This is repeated for the opposite edge of the micro-

hydrogel so that it is adhered to the substrate at two points as illustrated in Figure 3.4. The

epoxy resin is given sufficient time to cure before the adhered micro-hydrogel is imaged.

The AFM was loaded with a stiff cantilever (HQ:NSC35/Cr-Au BS, Cantilever A) from

Mikromasch (Nano World AG, Germany) for imaging hydrogels in intermittent contact mode

in air. The imaging is performed at a scan rate of 2 Hz for a 60 x 60 µm scan size with 1024 x

1024 pixels. The set point and drive amplitudes are around 1 V and the drive frequency is


65

Figure 3.4. An image taken after adhering micro-gels to the glass substrate, and a confocal

image showing the micro-gels attached at two points by epoxy-resin.

around 200 kHz. The image is used to identify the edge of the micro-hydrogel. The micro-

gels are then rehydrated by pipetting reverse osmosis (RO) treated water with resistivity of

18.2 MΩcm (Satorius Stedim) around the cantilever. The manipulation control function in the

AFM software is then used to trace a cantilever path over the image as shown in Figure 3.5.

The cantilever is translated laterally outwards from the edge of the micro-hydrogel in order to

pull fibres out of the network.

Figure 3.5. AFM image of glued micro-gel showing the edge of the network and a

superimposed trace of the cantilever path for lateral force measurements.

Lateral force measurements are taken with a set point vertical deflection of 300 nN and a

cantilever travel speed of 0.3 µm/s. A cantilever of high stiffness is used in order to apply a

high lateral force for separating fibre contacts. In order to hook onto the loose fibre loops that

occur at the edge of the micro-hydrogel, as seen in the inset of Figure 3.5, the AFM tip is

engaged with the substrate several microns outside of the identified edge and dragged away


66

from the micro-hydrogel. Then the tip is disengaged from the surface and moved (without

touching the substrate) to the starting point of the subsequent trace which is incrementally

closer to the edge of the hydrogel. This “dip-and drag” procedure is repeated several times

until the first peaks in the lateral deflection curve are observed.

The vertical sensitivity of the cantilever is measured to be 3x10-7 N/V using the built-in

calibration manager in the JPK NanaWizard® software. For lateral calibration of the

cantilever, the Torsional Sader Method7 is used to find the torsional spring constant (5.16x10-

8 N m), and the lateral sensitivity (3.12x10-5 N/V) is calculated using a non-contact

calibration procedure8. To find the lateral sensitivity of the cantilever in water (2.35x10-5

N/V) the lateral sensitivity in air is multiplied by the ratio of the refractive index of air and

water. Analysis and interpretation of the lateral force distance curves is detailed in Chapter 5.


67


1. R. Y. M. Huang, P. H. Shao, C. M. Burns and X. Feng, Journal of Applied Polymer

Science, 2001, 82, 2651-2660.

2. N. Amiralian, P. K. Annamalai, P. Memmott and D. J. Martin, Cellulose, 2015, 22,

2483-2498.

3. N. Amiralian, P. K. Annamalai, P. Memmott, E. Taran, S. Schmidt and D. J. Martin,

RSC Adv., 2015, 5, 32124-32132.

4. E. Chanliaud and M. J. Gidley, Plant Journal, 1999, 20, 25-35.

5. D. Mikkelsen and M. J. Gidley, in Plant Cell Wall: Methods and Protocols, ed. Z. A.

Popper, Humana Press Inc, Totowa, 2011, vol. 715, pp. 197-208.



7. C. P. Green, H. Lioe, J. P. Cleveland, R. Proksch, P. Mulvaney and J. E. Sader,

Review of Scientific Instruments, 2004, 75, 1988-1996.

8. K. Wagner, P. Cheng and D. Vezenov, Langmuir, 2011, 27, 4635-4644.

68

Chapter 4

Friction, lubrication and in situ

mechanics of poroelastic cellulose

hydrogels.

4.1 Introduction and Background

Naturally occurring lubrication mechanisms in biological systems have largely motivated the

study of aqueous lubrication. The systems commonly studied involve polymeric networks

and surface films with solvent present throughout the polymeric network and at the

tribological interface. Solvated interconnected polymer networks are typically referred to as a

gel, or a hydrogel in the case where the solvent is water. The unique aspect of gels is that

they have the potential to exhibit so-called poroelasticity, whereby under deformation the

mechanical response is not only a function of the elastic polymer network, but also the

movement of solvent through that network. The mechanical properties that determine

whether a full or partial solvent layer can be supported at the interface between gel surfaces

and/or gelled surface films is still not fully understood.

The most commonly used example of biological soft material where poroelastic effects are

potentially important to their tribological performance is articular cartilage. In this example,

under compressive forces, the interstitial solvent supports a significant proportion of the

normal load1. This load support from the solvent reduces the load on the polymeric matrix

that contributes to friction. For two surfaces in relative lateral motion, the coefficient of

friction is defined as the ratio of tangential force resisting the motion and an applied normal

CHAPTER 4. RESULTS Grace Dolan, PhD Thesis

69

load. Controlled normal load tests are challenging to perform for highly permeable hydrogels

because they compress under load as the interstitial solvent moves out of the network. When

compressing two poroelastic gels to a fixed gap, the normal force may relax to near-zero

values. However, provided there is contact between the gels, lateral movement under this

condition is expected to provide quantifiable information on adhesive forces between the gels

as an assessment of their tribological properties.

The primary motivation of this thesis is to elucidate potential interactions occurring between

plant cell walls that undergo wall stress relaxation during plant growth and other

deformations experienced at the cellular level. I consider that studying the physics of

hydrogel tribology is relevant because plant cell walls are essentially hydrogel composites of

cellulose fibrils within a matrix of biopolymers (e.g. hemicelluloses, pectin) and water.

During dynamic growth processes, the load-bearing cross-links in the wall structure are

biochemically loosened, which leads to wall stress relaxation that drives cell expansion2, 3.

As cells expand within the tissue structure, I consider there to be a sliding contact between

adjacent extending walls. Thus plant cell walls, like articular cartilage, require modes of

lubrication under compression (static) and sliding (dynamic) conditions, which have not

previously been explored. Since it is challenging to investigate the mechanical response using

plant cell walls directly, I use bacterial nano-fibrillar cellulose hydrogels to probe the role of

microstructure on their tribological behaviour. A mechanical study on the poroelasticity of

these bacterial nano-fibrillar cellulose hydrogels and composites with arabinoxylan (CAX)

and xyloglucan (CXG) shows that they are highly permeable and fully relax after

compression4.

The sliding friction behaviour between two hydrogels in a loaded contact is distinctly

different from non-porous solid materials. Hydrogel tribopairs have a significantly lower

friction coefficient compared to non-porous solids and they do not conform to Amonton’s

law for solid friction5. The non-linear relationship between frictional force and load has been

investigated for a variety of hydrogels using a rotational rheometer with parallel plate

geometries. Pairs of hydrogel disks are attached to the plates, and under constant compressive

load, one plate is rotated at a specific angular velocity while the torque is recorded over time6-

9. The mechanism of gel-gel friction is explained by Gong et al using a repulsion-adsorption

model10. Gong’s model states that between two repulsive surfaces, friction is determined by

the hydrodynamic lubrication of the solvent layer at the interface. For the case of two


70

attractive surfaces, friction is due to elastic deformation of the polymer chains that are

interacting at the interface.

Experimental tribology studies involving hydrogel substrates, and soft contacts generally,

find that the friction coefficient depends on the velocity and load condition, as well as

material properties including elastic modulus, permeability, relaxation rate, and residual force

after relaxation11-15. Therefore, in addition to chemical structure and surface properties of the

hydrogels that are explained through Gong’s repulsion-adsorption model, the mechanical

response to compression and relaxation is also likely to play a role in the tribological

behaviour. The compression-relaxation response of hydrogel materials is determined by the

interplay between the viscous behaviour of the solvent throughout the porous network and the

elastic response of the porous network.

In essence, the mechanism of stress build-up and its relaxation during unconfined

compression of gels can be summarised in three steps:

(i) lateral expansion of the matrix and interstitial fluid pressurisation,

(ii) contraction of the matrix in combination with fluid flow out of the gel due to a

pressure gradient,

(iii) normal stress relaxation of the gel due to fluid redistribution16.

The compression-relaxation behaviour of hydrogels has been modelled using transversely

isotropic linear biphasic theory17, 18. This model has been successfully applied to

experimental compression-relaxation profiles to determine material parameters such as axial

modulus, radial modulus, and permeability of articular cartilage11, 17, 19 and bacterial nano-

fibrillar cellulose hydrogels18.

Squeeze film lubrication theory has been applied to study the behaviour of a fluid film at the

interface between hydrogel surfaces when they approach each other in the normal direction.

The behaviour of the film is typically described by a modified Reynolds equation. The load

carrying capacity, film thickness, and squeeze time are predicted for hydrogel systems with

varying permeability and elastic modulus20-22. Carbone and Persson theoretically show that

for soft materials (e.g. rubber), the viscoelastic losses slow down the dewetting of an

interface. When the spreading velocity approaches zero, the interface has a dry zone in the

centre and a trapped liquid region around the rim23. This description of the interface is in

contrast to the experimentally visualised interfacial film between rubber and glass from


71

optical interference measurements24. Adhesive forces between the rubber and glass lead to

contact at the point where the opposing surfaces are closest. The contact area then spreads

and traps pockets of fluid at the interface, that is, wetted regions are surrounded by areas of

solid-solid contact. A decrease in lubricant viscosity resulted in the fluid pockets

disappearing at a rate inversely propositional to the viscosity. Yamamoto et al.25 visualise the

heterogeneous contact between polyacrylamide hydrogels and glass, and relate the

macroscopic contact area to the frictional stress measured for a range of sliding velocities.

Under the dynamic conditions of the friction experiments, increasing the velocity drives the

spreading process of trapped water.

In this chapter, I aim to uncover the underlying physics for the tribological contact between

poroelastic hydrogels. I use a tribo-rheological test procedure where pairs of cellulose

hydrogels are squeezed into contact in a series of compression-relaxation steps on a

rheometer. After the gels are pressed into contact and the relaxing normal force is allowed to

equilibrate, a constant rotation rate is applied to evaluate the apparent friction between

surfaces. I investigate the effect of substrate modulus and solvent viscosity on the tribological

response. Scaling relationships between the apparent static friction, substrate modulus, and

solvent viscosity are then interpreted using simulations that predict the interfacial contact area

between gels. Results presented here provide insight into the static and dynamic lubrication

modes for poroelastic hydrogels.

4.2 Experimental Section

4.2.1 Physical characterisation of hydrogel mechanics and friction

Bacterial cellulose hydrogels and composites with AX and XG are prepared according to the

method in Chapter 3: Section 3.1.3. The hydrogel mechanics and friction behaviour are

measured in a rotational rheometer and the steps are detailed in Chapter 3: Section 3.2.1. In

summary, hydrogel pairs attached to the parallel geometries are brought into compressive

contact at a given CR (refer to equation 3.2 in Chapter 3: Section 3.2.1). After the normal

force relaxes to an equilibrium value, a SAOS test is used to measure the G’ and G” of the

system. Finally the top plate is rotated at a controlled angular velocity to assess the friction

response of the hydrogel pair. These three steps are illustrated in Figure 4.1. The bottom

geometry is in fact a dish that holds either water or pectin solution, such that there is solvent

at the interface between hydrogels during the measurements.


72

Figure 4.1. Schematic showing the steps for characterising the mechanics and tribological

behaviour of hydrogel pairs.

Lopez-Sanchez et al.18 perform compression-relaxation steps on single bacterial cellulose

hydrogels and show that the network microstructure and mechanics are influenced by the

speed of compression. Here I test whether the friction response between a pair of cellulose

hydrogels is sensitive to the compression speed. Cellulose hydrogel pairs with water as a

solvent are compressed to a CR value of 0.6 at a compression speed of 10, 100, and 1000

m/s. The shear stress curves measured between the hydrogels at a controlled rotation rate of

1rad/s are presented in Figure 4.2. The compression-relaxation steps establish the contact

between the hydrogels prior to the rotation step. However, there is no substantial influence of

the compression speed on the shear stress measured at a constant angular velocity. The

mechanics during the compression-relaxation steps are used to predict the contact area at the

interface prior to shearing with the model described in Section 4.2.3. In this thesis, a

compression speed of 33 m/s is selected to be consistent with the previous work by Lopez-

Sanchez et al.18. This compression speed is kept constant for all future measurements to

ensure that its influence on the microstructure is controlled across all samples.

There are two potential contributions to the shear stress measured at the interface between

two hydrogels. The first is the adhesion between the hydrogel surfaces that are in contact,

which is proportional to the contact area. The second is the viscous stresses from any solvent

present at the interface between the hydrogels. The viscous stress, τv, depends on angular

rotation rate ω, based on Newton’s law of viscosity in equation 4.1, where a Newtonian fluid

with viscosity, η, is present between two parallel plates with radius R and separated by a

distance, H.

𝜏𝑣 = 𝜂𝜔𝑅

𝐻

(4.1)

According to equation 4.1, the friction stress increases with angular rotation rate. This

relationship applies to any pockets of solvent that may be present at the interface between the


73

Figure 4.2. Sensitivity analysis of the compression speed on the friction response of bacterial

cellulose hydrogel pairs tested in water at a CR of 0.6 and rotation rate of 1 rad/s. The curves

are representative examples of the compressions speeds, which are labelled in the legend.

hydrogels. Figure 4.3 shows the friction response at different angular rotation rates for

cellulose hydrogels in water. There is no substantial effect of the angular rotation rate on the

shear stress measured. Thus there is apparently negligible viscous stress generated by the

solvent at the interface. The measured shear stress must be dominated by the adhesion

between surfaces in contact at the interface, which is the basis of detailed analysis in the

coming sections of this chapter.

Figure 4.3. Sensitivity analysis of the rotation rate on the friction response of bacterial

cellulose hydrogel pairs in water, compressed at speed of 1000 m/s to a CR of 0.6. The

curves are representative examples of the rotation rates, which are labelled in the legend.

Shear Strain (-)

0.0 0.5 1.0 1.5 2.0

Sh

ea

r S

tre

ss (

kP

a)

0.0

0.1

0.2

0.3

10 m/s

100 m/s

1000 m/s

Shear Strain (-)

0.0 0.5 1.0 1.5 2.0

Sh

ea

r S

tre

ss (

kP

a)

0.0

0.1

0.2

0.3

0.01 rad/s0.1 rad/s1 rad/s


74

4.2.2 Modelling the hydrogel mechanics during compression-relaxation

The micromechanical behaviour of bacterial cellulose hydrogels has been modelled by

Lopez-Sanchez et al.18 using poroelastic theory. The hydrogel is treated as a linear

transversely isotropic material, with the plane of isotropy depicted in Figure 4.4. The material

parameters that describe the mechanics, and their description, are summarised in Table 4.1.

Figure 4.4. Representation of a cellulose hydrogel disk showing that the 1-2 plane is

transversely isotropic, that is, the material is isotropic in the radial direction. The image is

reproduced from Lopez-Sanchez et al.18.

Table 4.1. Material functions in the mechanical model.

Material Function Description

E1 Radial modulus or Young’s modulus in the 1-2 plane

ν21 Poisson’s ratio in the 1-2 plane

E3 Axial modulus or Young’s modulus perpendicular to the 1-2

plane

ν31 Poisson’s ratio perpendicular to the 1-2 plane

G31 Shear modulus perpendicular to the 1-2 plane

The results from the compression-relaxation experiment are recorded as the normal stress

measured with time. The sample is compressed for t0 seconds, followed by normal stress

relaxation at a constant axial strain. The normal stress predicted by the model during

compression and relaxation is given as equation 4.2 and 4.3, respectively18.

𝜎𝑛(𝑡) = 𝐸3𝜀0̇𝑡 + 𝐸1𝜀0̇𝑅

2

𝐶11𝑘∆3 {

1

8−∑

exp(−𝛼𝑛2𝐶11𝑘𝑡/𝑅

2)

𝛼𝑛2[𝛼𝑛2∆22 − ∆1/(1 + 𝜈21)

∞

𝑖=1

} ; 0 < 𝑡 < 𝑡0 (4.2)


75

𝜎𝑛(𝑡) = 𝐸3𝜀0̇𝑡0

+ 𝐸1𝜀0̇𝑅

2

𝐶11𝑘

×∆3 {∑exp(−𝛼𝑛

2𝐶11𝑘𝑡/𝑅2) − exp[−𝛼𝑛

2𝐶11𝑘(𝑡 − 𝑡0)/𝑅2]

𝛼𝑛2[𝛼𝑛2∆22 − ∆1/(1 + 𝜈21)

∞

𝑖=1

} ; 𝑡 > 𝑡0

(4.3)

𝜎𝑛(𝑡) is the normal stress at time t, 𝜀0̇ is the compression speed, R is the radius of the

hydrogel, C11 is given by equation 4.4, k is the ratio of the intrinsic permeability and fluid

viscosity. ∆1, ∆2, and ∆3 are given in equations 4.5, 4.6, and 4.7, respectively. 𝛼𝑛

corresponds to the roots of the transcendental equation 4.8, of which J1 and J0 are Bessel

functions of the first kind. The MATLAB files for solving the series of equations 4.2 to 4.8

are provided in Appendix E, and an example of the input data is given in Appendix F. The

model fit of experimental data is provided in Section 4.3.1. This model is referred to as the

‘poroelastic mechanical model’ throughout the chapter.

𝐶11 = 𝐸1(1 − 𝜈312𝐸1/𝐸3)/[(1 + 𝜈21)Δ1]

(4.4)

Δ1 = 1 − 𝜈21 − 𝜈312𝐸1/𝐸3

(4.5)

Δ2 = (1 − 𝜈312𝐸1/𝐸3)/(1 + 𝜈21)

(4.6)

Δ3 = Δ2/Δ1

(4.7)

𝐽1(𝑥) − (1 − 𝜈31

2𝐸1/𝐸31 − 𝜈21 − 2𝜈312𝐸1/𝐸3

) 𝑥𝐽0(𝑥) = 0 (4.8)

4.2.3 Simulating the interface between hydrogels during compression-

relaxation

The poroelastic cellulose hydrogels are surrounded by solvent and are brought into

compressive contact at a constant speed. Variation in the thickness h of the solvent film

during compression is predicted using the Reynolds equation, given by equation 4.9 where p

is the pressure in the solvent film and r the radial coordinate shown in Figure 4.5.


76

Figure 4.5. (a) Equivalent simulation system to the double hydrogel contact. The modulus of

the soft substrate must be corrected as described by Szeri26. (b) Pressure distribution on the

interstitial film at maximum compression.

1

𝑟(𝑟ℎ3

𝑑𝑝𝑓𝑖𝑙𝑚

𝑑𝑟) = 𝜋𝑟2

(4.9)

Under quasistatic conditions, the film pressure must be equilibrated by the axial stress at the

solid boundaries, 𝜎𝑔𝑒𝑙, which is in turn governed by the poroelastic constitutive equation

4.1017:

𝜎𝑔𝑒𝑙 =−𝑝𝑔𝑒𝑙𝐈 + 𝜎𝑠 (4.10)

I is the identity matrix, 𝑝𝑔𝑒𝑙 is the pressure of the fluid within the hydrogel pore space, and

𝜎𝑠is the stress tensor of the solid matrix, which is assumed to be linear elastic and

transversely isotropic. In such a case, the solid matrix is described by five parameters from

the poroelastic mechanical model above: E3, E1, 21, 31, and the permeability k.

The actual system reduces to an equivalent model system in which the top hydrogel is rigid

and the bottom substrate has an equivalent Young’s modulus26, E* = E/(1 - 2). For bacterial

cellulose, E1 is much larger than E3, and the axial force during compression is much larger

than the residual force after relaxation18, 27. Taking 31 0 and 21 0.518, 27, the equivalent

moduli are given by E21* = 1.3E21 and E31

* = E31. The current simulation assumes a perfectly


77

poroelastic sample. This assumption affects the transient evolution of the film thickness but

does not affect the final thickness upon relaxation, since that depends solely on the axial

modulus. In order to obtain the curves, typical values for bacterial cellulose were assumed:

E21 = 200 kPa, E31 = 10 kPa and k = 110-13 m2 18. The model also requires a pre-set initial

film thickness which we take to be 20 µm; however, order of magnitude changes in this value

do not significantly affect the equilibrium film thickness after compression-relaxation.

For purely elastic gels, equations (4.9) and (4.10) can be solved analytically. For poroelastic

gels, an accurate solution can only be reached numerically. To this end, a finite element

package Comsol™ Multiphysics is used, which enables the prediction of the normal force

and film thickness, and the sensitivity of these parameters to solvent viscosity and axial

modulus of the hydrogels. It is assumed that there is no mixing between the solvent and the

interstitial fluid in the hydrogel, either inside or outside the simulation box. This means that

solvent under pressure escapes the film boundaries and can be reabsorbed back into the film

without affecting the pectin concentration. For the simulation, a 2D axisymmetric geometry

is used with triangular elements as shown in Figure 4.5. The mesh size was refined until the

results were seen to be size independent. The simulation of the interface between poroelastic

surfaces is referred to as the ‘ComsolTM Multiphysics model’ throughout this chapter.

4.2.4 Pectin solution and viscosity measurements

The lubricating effect of solvent viscosity is tested by increasing the pectin concentration in

the solution surrounding the hydrogel pair. Pectin solutions (0.5, 1, 2, 4 wt%) are prepared

and their viscosity measured according to the procedure in Chapter 3: Section 3.1.4. The

viscosity curves are shown in Figure 4.6 below.

The binding of pectin to cellulose is largely through the neutral sugar side chains28.

Furthermore, the binding of pectin to cellulose is weak and reversible with water washing.

The crystallinity of bacterial cellulose and the assembly of cellulose fibres into a network are

not influenced by the presence of pectin in the fermentation medium28. The commercial

pectin used here is debranched and is therefore expected to act as a viscosifier and have

negligible interaction with the cellulose fibres in the hydrogel.


78

Figure 4.6. Viscosity of pectin solutions (0.5, 1, 2, and 4 wt%) across the range of shear rate

from 1 to 100 s-1.

4.3 Results and Discussion

4.3.1 Mechanical properties of poroelastic hydrogels

The measured mechanical responses of bacterial cellulose and composite hydrogels during

compression-relaxation steps are shown by the lines in Figure 4.7. During compression, the

top plate is lowered at a constant rate, so the time-axis is proportional to axial strain. For the

relaxation step, the axial strain is held constant over time. The SEM image inserts in Figure

4.7 show differences in network structure (images provided by Dr Patricia Lopez-Sanchez

and Dr Dongjie Wang, 2014). The curves are non-linear during compression and the normal

stress relaxes to near-zero loads as water moves out of the hydrogel; this response is

characteristic of poroelastic hydrogels. The experimental data is fitted with the poroelastic

mechanical model published by Lopez-Sanchez et al.18 and detailed in Section 4.2.2. The

experimental data and corresponding model fits are shown in Figure 4.7.

The poroelastic mechanical model assumes that the pair of hydrogels behaves as a continuous

system, that is, that the two hydrogels are in contact and no solvent is present between them.

This assumption is valid based on the results in Figure 4.3 in Section 4.2.1. The exact amount

of solvent present at the interface is investigated in Section 4.3.2, but the fit of the poroelastic

model to the experimental data in Figure 4.7 is considered to be good enough to approximate

the material properties of the hydrogels. The model does not track the data well during the


79

relaxation step, however the material properties are determined by the poroelastic model from

the linear slope during compression and the residual force after relaxation and at these points

the measured data and model fit are in good agreement.

The axial modulus, radial modulus, and permeability of the hydrogel are described in Table

4.1 in Section 4.2.2, and are obtained from fitting the experimental data with the poroelastic

model. The fitted values are presented in Table 4.2 and the raw data for the compression-

relaxation of cellulose, CAX, and CXG hydrogels at all CRs are included in Appendix G.

Figure 4.7 shows that for the same axial strain, the peak normal stresses on compression of

CXG and CAX are larger than cellulose hydrogels. The higher resistance to compression for

CXG and CAX is consistent with the lower permeability and higher axial modulus in Table

4.2. As the hydrogels are further compressed, water is squeezed out in the absence of lateral

expansion. This leads to an increase in cellulose concentration and changes in the network

structure. Fibre aggregation of compressed cellulose and composite hydrogels has been

shown when comparing SEM images before and after compression4, 18. The effect of fibre

aggregation is highlighted in Table 4.2 where the axial and radial moduli of all gel pairs

increase, while the permeability decreases with increasing CR. Results are not included for a

CR value of 0.4 because of the difficulty modelling the non-linearity of parameters during

this first compression step. Experimentally, the bacterial cellulose hydrogels are relatively

inhomogeneous in the axial direction. This arises because of the way the bacterial cellulose

grows on the surface of the liquid culture medium. The bacteria are aerobic and preferentially

locate at the air interface. As a result, the network is visibly denser at the air interface and

‘looser’ toward the surface that faces the liquid medium during fermentation. The denser

surfaces of the hydrogels are positioned at the interface during measurement. Upon

compression the network becomes more concentrated and the overall concentration gradient

within the hydrogel is reduced, which leads to much better agreement with the assumptions

of the poroelastic model.

During compression, there is an initial linear response up to a critical value of strain. This

linear region characterises the deformation that can be sustained without water moving out of

the network, and the system behaves elastically. The transition to non-linear behaviour occurs

when the forces applied during compression are sufficient to overcome the resistance to water

displacement, which is a function of the network permeability. In order to compare the

compression mechanics of the different hydrogels, the compression curves are normalised


80

a

b

c

Figure 4.7. Compression-relaxation profiles of pairs of (a) cellulose, (b) CAX, and (c) CXG

hydrogels showing experimental data (symbols) and the model fit (lines). Representative

curves are at a CR value of 0.7.


81

against the peak normal stress and plotted together in Figure 4.8. Non-linearity of the

cellulose stress-strain curve occurs at a much lower strain compared to CAX and CXG.

Lopez-Sanchez et al.18 report purely elastic behaviour of CXG and CAX composites at a

large compression rate (33 m/s), whereas Cellulose displayed elastic behaviour only up to

strains of ca 1%. This is in good agreement with the results in Figure 4.8 and suggests that for

the given compression rate, pairs of hydrogels behave similarly to a single hydrogel. The

highly non-linear response of cellulose hydrogels is consistent with ca. 4-fold higher

permeability compared to CAX and CXG. That is, water movement within the hydrogel has

more influence on the mechanics during the compression of Cellulose hydrogels compared to

CAX and CXG.

Table 4.2. Mechanical parameters of pairs of cellulose and composite hydrogels at different

CR

CR Axial modulus, E3

(kPa)

Radial modulus, E1

(kPa)

Permeability, k x 1010

m2

Cellulose CAX CXG Cellulose CAX CXG Cellulose CAX CXG

0.5 7.5 16 24 240 290 190 4.4 1.3 1.9

0.6 12 39 41 340 420 320 3.7 1.1 1.1

0.7 22 64 73 440 550 400 3.7 0.7 0.9

Figure 4.8. Compression profiles of cellulose, CAX, and CXG hydrogel pairs normalised for

peak normal force. Representative curves at CR 0.7.

Compressive Strain (%)

0 2 4 6 8 10 12 14 16 18

Norm

al S

tress/P

eak N

orm

al S

tress

0.0

0.2

0.4

0.6

0.8

1.0

CelluloseCAXCXG


82

The irreversible (within the allowed recovery time) water displacement during compression

can be quantified by looking at consecutive compressions. Cellulose, CAX, and CXG

hydrogels are compressed to 50% strain in a single step then unloaded for 30minutes before

repeating the compression. The areas between the consecutive compression curves in Figure

4.9 represent the mechanical energy that is not recovered after the first compression, and the

values are presented in Table 4.3. From these results the cellulose hydrogel has a 3-fold

higher irreversible deformation, which is attributed to greater water displacement and

concomitant fibre aggregation during compression.

The potential for fibre aggregation is further assessed by measuring the ability of a

compressed hydrogel to re-swell after the compression force is removed. This experiment

was completed by Kevin Setiadi who was a Masters student co-supervised by myself and Dr

Patricia Lopez-Sanchez. A single hydrogel (initial thickness ~2500 m) is compressed to

three different thicknesses; 2000 m, 1000 m, and 100 m. The compressed hydrogels are

then placed in a water dish. The hydrogel is removed after a given period of time using metal

forceps so as to not squeeze the material substantially. As the hydrogel is being removed it is

dragged along the edge of the dish to remove surface water as best as possible. The hydrogel

is then weighed before being returned to the water dish for another length of time. The weight

of the hydrogel is recorded over the cumulative time. The weights of the hydrogels

compressed to different thickness are compared to the uncompressed weight in Figure 4.10.

The results show that the hydrogels do not completely recover their water content after

compression, and the re-swelling ability decreases with increasing compression. This result

strongly suggests that cellulose fibres form new adhesive contacts and irreversibly change the

network microstructure, preventing complete water uptake which would be required for

restoring the original hydrogel weight after the compression force is removed. Increasing the

compression leads to an increase in the probability that cellulose fibres will adhere together.

The aim of this Chapter is to investigate the relationship between hydrogel mechanics and the

friction response. I therefore identify a key issue with characterising the mechanics using the

parameters in Table 4.2. The axial modulus is strongly influenced by the permeability of the

hydrogel. The presence of AX and XG restricts water movement during compression, which

leads to a higher axial modulus. However, only shear deformation is applied during the

friction measurement, during which fluid pressurisation is not as substantial compared to

compression. The radial modulus is expected to provide a more accurate representation of the


83

a

b

c

Figure 4.9. Two consecutive compressions of a single (a) Cellulose, (b) CAX, and (c) CXG

hydrogel to a CR of 0.6. The circles symbols are for the first compression and the square

symbols are second compression. The difference between the two curves for each hydrogel

shows the degree of plastic deformation.

Gap ( m)

1000 2000 3000 4000

Norm

al S

tress/P

eak N

orm

al S

tress

0.0

0.2

0.4

0.6

0.8

1.0

Gap ( m)

1000 2000 3000 4000

Norm

al S

tress/P

eak N

orm

al S

tress

0.0

0.2

0.4

0.6

0.8

1.0

Gap ( m)

1000 2000 3000 4000

Norm

al S

tress/P

eak N

orm

al S

tress

0.0

0.2

0.4

0.6

0.8

1.0


84

network’s mechanical response to shear deformation during the friction measurement. The

radial modulus is measured indirectly from the poroelastic model fitted to compression-

relaxation data. After the compression and normal stress relaxation steps, the hydrogel

mechanics are characterised by the G’ and G” from SAOS measurements, and the values are

presented in Table 4.4.

Table 4.3. Hysteresis areas for consecutive compressions of Cellulose, CAX, and CXG

hydrogel pairs

Hydrogel Pair Hysteresis Area (×10-4, N.m)

Cellulose 2.9

CAX 1.1

CXG 1.0

Figure 4.10. Recovery of the weight of a single bacterial cellulose hydrogel over time after

compression. The dotted line shows the original weight of an uncompressed hydrogel. The

three data sets are for cellulose hydrogels compressed to the different thicknesses that are

labelled (initial thickness ~ 2500m).

When comparing the moduli in Table 4.2 and 4.4 it is observed that the presence of AX and

XG substantially increases the axial modulus, has little effect on the radial modulus, and

substantially decreases the G’. AX and XG increase the resistance to water displacement

which is measured as a high axial modulus of the hydrogel. Bonilla et al.27 describe in detail,

the application of the poroelastic mechanical model to cellulose composite hydrogels and

states that ‘radial strains arising as a consequence of internal pressure gradients are

Time (s)

0 20 40 60 80 100 120

We

igh

t (g

)

0

1

2

3

4

5uncompressed

2000 m

1000 m

100 m


85

infinitesimal’. Thus the radial modulus in Table 4.2 is a measure of the mechanical response

of the cellulose fibre network to small deformations applied by fluid pressure within the

hydrogel. SAOS measurements apply a finite oscillating shear strain on the hydrogel, thus the

measured G’ reflects the hydrogel’s mechanical response to deformation on a much larger

length scale compared to the radial modulus. AX and XG do not appear to influence the

networks response to the small deformations which are measured by the radial modulus in

Table 4.2. However, the reduction in the measured G’ for CAX and CXG compared to

cellulose hydrogels in Table 4.3 suggests that AX and XG influence the networks response to

large deformation. The effect of AX and XG could be through one or a combination of the

network orientation, fibre contact density, and the nature of fibre contacts. The role of AX

and XG on fibre contacts is investigated in Chapter 6. This Chapter investigates whether any

relationships exist between the friction behaviour and the axial modulus, radial modulus, or

G’.

Table 4.4. The apparent linear viscoelastic moduli (G’, G’’ in kPa) of the hydrogels obtained

by performing SAOS immediately prior to tribological measurement.

CR Cellulose CAX CXG

G’ G” G’ G” G’ G”

0.4 5.0±0.0 0.6±0.0 1.3±0.2 0.2±0.0 0.8±0.0 0.1±0.0

0.5 11.0±0.1 1.4±0.1 2.2±0.0 0.4±0.0 1.4±0.0 0.2±0.0

0.6 23.7±0.1 2.9±0.3 3.8±0.1 0.7±0.0 2.4±0.0 0.4±0.0

0.7 73.9±1.3 11.3±1.6 8.3±0.2 1.6±0.1 5.3±0.0 0.9±0.0

4.3.2 Contact area between poroelastic hydrogels

Chapter 2: Section 2.3.1 highlights on of the key challenges in measuring the friction

between hydrogel disks in a rotational rheometer as the unknown contact area. The interface

between two hydrogels is visualised as a region of fluid in the centre, surrounded by an

annulus region of surface contact. I hypothesise that the contact area is a function of the axial

modulus of the hydrogel that is a measure of the ability of the surfaces to deform during

compression, and the viscosity of the solvent that determines its resistance to flow out of the

interface. The ComsolTM Multiphysics model described in Section 4.2.3 is used to simulate

the compression-relaxation of two poroelastic surfaces in a solvated environment (prior to

sliding). The model is used to predict the film thickness between surfaces with water as a

solvent, and the sensitivity to substrate axial modulus and solvent viscosity.


86

Due to the poroelasticity and the potential for substrate deformation during compression, as

well as squeeze flow of fluid out of the contact, the pressure at the interface varies with

spatial position and the compression stress or strain. The film thickness at the centre (r=0)

and edge (r=R) of the interface is plotted against time in Figure 4.11, where compression

takes place in the first 12 seconds and then the system relaxes. Across the entire interface, the

film thickness decreases with increasing compressive strain, which is proportional to time up

to 12 s. The model predicts that the film thickness between the hydrogels is initially larger at

the outer edge than in the centre. With increasing compression, the film thickness at the edge

decreases more rapidly than in the centre and becomes negative. Note, due to how the model

is formulated, film thickness values below zero merely indicate that the surfaces are in

contact and have deformed. The model predicts that a finite film thickness is maintained at

the centre of the interface, and the surfaces are in contact in the outer annular region. The

final film thickness is shown as a function of radial position together with a depiction of the

contact in Figure 4.12.

Figure 4.11. Simulated film thickness at the centre, i.e. r = 0 (filled symbols), and edge, i.e. r

= R (open symbols) of the interface against time. The hydrogels (axial modulus, E3 = 5kPa)

are compressed in water (viscosity 0.001 Pa.s) at a constant rate (33 µm/s) from 0 – 12 s

followed by relaxation at a constant CR.

The radial position when the film thickness equals zero in Figure 4.12 marks the start of

surface contact, which extends to the edge of the surface. Thus the annular surface contact

area can be determined. Figure 4.13 shows that the power law exponent is 0.3 for the

relationship between ‘contact area/total area’ and hydrogel axial modulus across the range of

Time (s)

0 10 20 30 40 50

Thic

kn

ess (

m)

-10

0

10

20

r = 0

r = R


87

5-30 kPa. The range of axial modulus in Figure 4.13 is of the order of the axial modulus in

Table 4.2. For hydrogels with a low axial modulus, the balance between squeeze flow forces

and substrate deformation drives substrate deformation, which leads to a larger wetted area in

the centre of the contact.

a

b

Figure 4.12. (a) The variation in film thickness with radial position in the interface at the

final time (t = 48s) from Figure 4.11. The graph shows a film of finite thickness at the centre

of the interface, and gel-gel contact beyond r = 15mm. (b) shows a depiction of the contact at

the interface between poroelastic hydrogels (not to scale).

Figure 4.13. Logarithmic plot of the fraction of the interface that is in contact, predicted from

the simulations, against the axial modulus of the hydrogels. The linear curve fit has a slope of

0.3.

Radial position (mm)

0 5 10 15 20

Film

Thic

kn

ess (

m)

0.0

0.5

1.0

1.5

2.0

Log (axial modulus)

3.5 4.0 4.5 5.0

Log

(C

on

tact

/ to

tal a

rea)

-0.3

-0.2

-0.1

0.0

0.1


88

The ComsolTM Multiphysics model is used to investigate the influence of solvent viscosity on

the contact area. The thickness of the solvent layer between poroelastic hydrogels during

compression is simulated for Newtonian solvents with viscosity values ranging from 0.001 to

0.5 Pas. The results from the simulations are used to predict the scaling relationship between

solvent viscosity and contact area. In Figure 4.14, the film thickness at the centre of the

interface is plotted against time for a solvent viscosity of 0.01 and 0.1 Pa.s. The important

observation is that the final film thickness, and consequently the area of the wetted region in

the centre, increases with increasing solvent viscosity. Figure 4.15 presents a logarithmic plot

of the fraction of the interface that is in contact, against the solvent viscosity. The model

shows that increasing the solvent viscosity reduces the contact area at the interface according

to a power law scaling with an exponent of -0.16.

Figure 4.14. Simulated film thickness at the centre of the interface, i.e. r = 0, against time.

The hydrogels (axial modulus, E3 = 5kPa) are compressed at a constant rate (33µm/s) from 0

– 12 s, followed by relaxation at a constant CR. The solvent viscosity (η) is labelled for each

curve.

4.3.3 Tribological response between hydrogels

The shear forces between cellulose hydrogels are measured after compressing two gels into

“contact” to different CR values and rotating the upper surface. The torque required to rotate

the upper disk at a constant velocity is converted to shear stress and plotted against shear

strain to evaluate the tribological behaviour. Figure 4.16 presents two characteristic

tribological responses; (4.16a) stick-slip and (4.16b) stiction, which are observed at the same

CR value of 0.6 for different hydrogels in water.

Time (s)

0 10 20 30 40 50

Thic

kness (

m)

0

5

10

15

20

25

30

= 0.1 Pa s

= 0.01 Pa s


89

Figure 4.15. Logarithmic plot of the fraction of the interface that is in contact, predicted from

the simulations, against the solvent viscosity. The linear curve fit has a slope of -0.16.

Figure 4.16. Characteristic tribological responses for hydrogels tested in water at CR 0.6.

stick-slip sliding (Cellulose) and stiction (CXG).

“Stick-slip” refers to the situation where the interface cycles between adhesive contact and

relative sliding, and is observed with a peak and a distinctive zig-zag pattern in the shear

stress-strain curve; this is observed for the cellulose hydrogels in water in Figure 4.16a.

Starting from rest, the measured shear stress is linear with strain up to a critical value,

hereafter referred to as an interfacial yield stress that I consider to be a measure of apparent

“static friction” between the hydrogels. The initial linear region at low strains is characteristic

Log (Viscosity)

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5

Log

(C

on

tact

/ to

tal a

rea)

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

Strain (-)

0 1 2 3 4 5

Sh

ea

r S

tre

ss (

kP

a)

0.0

0.1

0.2

0.3

0.4

0.5Cellulose

CXG


90

of bulk elastic deformation. Due to the potential for cellulose fibre adhesion within a

network, shown by the results of consecutive compressions and re-swelling ability of

hydrogels in Figures 4.9 and 4.10, it is hypothesised that hydrogels brought into compressive

contact interact through adhesion between fibres at the surfaces. Furthermore, it is

hypothesised that fibre adhesion at the interface results in the pairs of hydrogels being

conjoint and hence behaving as a continuous bulk gel at low strains. This is supported by

comparing the mechanics of a single hydrogel and pair of hydrogels under shear deformation,

after being compressed to the same CR. The single hydrogel is attached to both rheometer

plates, whereas one hydrogel surface is attached to each rheometer plate for the hydrogel

pairs. The similarity of the initial linear slope of the stress-strain curves in Figure 4.17

indicates that the system’s shear modulus is the same, regardless of whether a single or pair

of hydrogels is being deformed.

Figure 4.17. Stress-strain curve of single Cellulose hydrogel glued to both rheometer plates

(line) and a pair of Cellulose hydrogels with one surface of each gel glued to a rheometer

plate (symbols). Samples are compressed to a CR of 0.5.

Hydrogel pairs can be treated as a continuous system up until the yield point. A yield point is

not observed for the single hydrogel within the range of stress tested. Thus the interfacial

yield stress is characteristic of the interface rather than failure of the adhesion of the

hydrogels to the rheometer plates, or failure of the hydrogels themselves. During the stick

cycle, the surfaces are adhered together and the shear stress increases with strain as the gels

undergo shear deformation. When the applied shear stress is sufficient to overcome the static

friction between the gels, the “slip” cycle is initiated and the surfaces move relative to each

Shear Strain (-)

0.001 0.01 0.1 1

Shear

Str

ess (

kP

a)

0.01

0.1

1


91

other. The rotating surface undergoes rapid acceleration-deceleration to try to maintain the set

rotation rate. During the slip cycle, the shear stress decreases with strain until it reaches the

kinetic friction stress and the surfaces adhere again.

Figure 4.16b shows the shear response for CXG composite hydrogels with water; the

measured shear stress increases linearly with strain up to the interfacial yield stress, which is

followed by a decrease to a relatively constant shear stress value required to maintain the

controlled rotation rate. This is characteristic of “stiction”, which is the situation where the

stress increases until a static friction is overcome, followed by a decrease to a steady “kinetic

friction” value29. A very weak dependence of shear stress on strain is apparent beyond the

peak stress. I consider that during shearing the hydrogel surfaces are prevented from coming

into adhesive contact again, which may be governed by the hydrodynamic drag of the solvent

phase or the restructuring of the hydrogel network at the interface between the two surfaces.

These two phenomena (stick-slip and stiction) have been observed for model hydrogel

systems and articular cartilage surfaces in sliding contacts at a range of length scales;

including those obtained using a similar tribo-rheological technique6, colloidal probe AFM6,

13, micro-tribometer12, Surface Force Apparatus (SFA)29 and a SFA-type experiment where

two glass tubes coated with a gel layer are in cross-cylinder orientation30. The fact that stick-

slip and stiction responses are observed between hydrogel surfaces in a range of experimental

set ups suggests that these friction phenomena are a material/system property rather than an

instrumental artefact, and that the measured interfacial yield stress is related to adhesive

contact forces between the hydrogel surfaces. The stick-slip and stiction behaviours will be

explored later in Section 4.3.7.

Sections 4.3.4 to 4.3.6 focus on the interfacial yield stress as a measure of the static friction

between hydrogel surfaces. The hydrogel tribology is considered in terms of the contribution

of any solvent layer present between the surfaces and/or interactions occurring at the

interface, which may also be a function of the mechanical properties of the substrates.

4.3.4 Influence of substrate mechanics on interfacial friction

Cellulose, CAX, and CXG hydrogel pairs measured at all CRs with water as the solvent

display either stick-slip or stiction behaviour; these are considered to be at least partially

adhesive contacts. Representative friction curves for the two phenomena are shown in Figure

4.16a and 4.16b. The friction curves for all samples (cellulose, CAX, CXG) at all CRs are


92

included in Appendix H. The accuracy of the recorded friction response is quantified by

repeating the controlled rotation rate step at a given CR three consecutive times and

comparing the interfacial yield stress, which is found to have an associated error of 16%. The

variation between different hydrogel pairs is quantified by measuring the interfacial yield

stress at the same CR for 3 different pairs of cellulose hydrogels and is found to be 14%.

The mechanical properties of bacterial cellulose hydrogels are shown to be time- and strain-

dependent due to poroelastic effects. A key objective of this study is to determine which

material properties determine the friction response between hydrogels. Relationships between

the interfacial yield stress and the axial modulus or radial modulus from the poroelastic

model in Table 4.2 are presented in Figure 4.18. There is a positive correlation between

interfacial yield stress and both the radial and axial modulus. From both graphs in Figure

4.18, AX and XG appear to reduce the interfacial yield stress compared to cellulose

hydrogels with equivalent axial or radial modulus. AX or XG either change the interaction

between hydrogel surfaces by reducing adhesion, or the axial and radial moduli do not

capture the mechanics of the hydrogel that influence the contact area at the interface.

In Figure 4.18, the data points for the composite hydrogels (CAX and CXG) are shifted

towards the right hand side of the x-axis, relative to the cellulose hydrogels. This could

suggest that the axial and radial modulus from poroelastic mechanical model overestimate the

material property that more generally determines the friction response of poroelastic

hydrogels. Water movement is more restricted in CAX and CXG compared to cellulose,

resulting in an increased modulus measured during compression. After compression the

systems relax to an equilibrium normal stress prior to the interfacial yield stress being

measured. Material characterisation of the fully relaxed networks is achieved with SAOS, and

the G’ of the hydrogel pairs from Table 4.4 is plotted against the interfacial yield stress in

Figure 4.19.

From Figure 4.19, the tribological response of the poroelastic hydrogels has a strong

dependency on the substrate’s G’, with a power law exponent of 0.8. The generality of the

relationship for all hydrogel compositions (Cellulose, CAX, and CXG) and compression

ratios confirms that the G’ measured after normal stress relaxation characterises the

mechanics of the system that determine tribological behaviour. Very few studies in literature

measure the G’ of hydrogels, instead relating the elastic modulus during compression to the

friction response. For the cellulose hydrogels used in this study, their high permeability


93

means that the normal stress relaxes to near-zero values when the system is at a constant axial

strain. Thus the system in not under load as it is being sheared.

a b

Figure 4.18. (a) Axial and (b) Radial modulus from biphasic modelling of compression-

relaxation data plotted with the interfacial yield stress. Dashed lines are the curve fits of

cellulose data with a power law exponent of 1.5 and 3.3 for axial and radial modulus,

respectively.

The CXG data in Figure 4.19 appears to have a slightly lower interfacial yield stress

compared to the CAX hydrogels at the same G’. This suggests that XG may have an effect on

the adhesive interactions between the hydrogels. However, we cannot assume that the contact

area between the gels is governed by their diameter because of the presence of a fluid film

during the compression. To assess the inherent adhesiveness between the gels, it is thus

necessary to deconvolute the influence on the interfacial yield stress from surface contact

area and substrate modulus. The ComsolTM Multiphysics model predicts the contact area for a

given axial modulus of the hydrogel in Figure 4.13. In Figure 4.20, the G’ from Table 4.4 is

plotted against the axial modulus from Table 4.2. The two moduli are proportional, with a

different proportionality constant for cellulose, CAX, and CXG. This means that the scaling

relationship in Figure 4.13 can be used to factor out the effect of contact area on the measured

friction response for hydrogels with different G’. The ComsolTM Multiphysics model also

shows a scaling relationship between solvent viscosity and the contact area. In the next

section I experimentally investigate the influence of solvent viscosity on the interfacial yield

stress between cellulose hydrogels.

Axial Modulus (kPa)

1 10 100

Inte

rfacia

l Y

ield

Str

ess (

kP

a)

0.001

0.01

0.1

1

10CelluloseCAXCXG

Radial Modulus (kPa)

100 1000

Inte

rfa

cia

l Y

ield

Str

ess (

kP

a)

0.001

0.01

0.1

1

10CelluloseCAXCXG


94

Figure 4.19. Logarithmic plot of the interfacial yield stress against G’ of cellulose and

composite hydrogels in water. The linear curve fit has a slope of 0.8.

Figure 4.20. Linear relationships between G’ and axial modulus, showing different

proportionality constants for Cellulose, CAX, and CXG.

4.3.5 Influence of solvent viscosity on interfacial friction

The viscosity of the solvent is varied experimentally using pectin in water. The pectin

solutions included in this study are Newtonian (within the measured shear rates) with a

viscosity range from 0.001 to 0.5 Pa.s and all the friction curves are provided in Appendix H.

Figure 4.21 presents the measured tribological response between cellulose hydrogels at a

Log(G')

2 3 4 5

Log(I

nte

rfacia

l Y

ield

Str

ess)

1

2

3

4CelluloseCAX CXG

Axial modulus (kPa)

0 10 20 30 40 50 60 70 80

G' (

kP

a)

0

20

40

60

80CelluloseCAX CXG


95

representative CR value of 0.5 with varying solvent viscosity. Except for the system with the

highest viscosity, stick-slip behaviour is prevalent, consistent with intimate contact between

the surfaces and high adhesion. At a critical viscosity there is a transition in tribological

response marked by a stress-strain curve that initially shows a stiction response which

evolves into stick-slip sliding at large strains. Further increasing the viscosity of the solvent

leads to stiction behaviour, where the shear stress is maintained at a roughly constant value at

high strains. In this case, I propose that the viscosity increases the interfacial separation and

leads to only a small region of contact at the interface.

Figure 4.21. Tribological response of pairs of cellulose hydrogels at CR 0.5 with solvent

viscosity in the range of 0.001 to 0.5 Pa.s.

A logarithmic plot of the interfacial yield stress against the solvent viscosity for cellulose

hydrogel pairs at all compression ratios is shown in Figure 4.22. The data set for each CR is

fitted with a power law model with set exponent of -0.16, which is the predicted exponent for

the relationship between solvent viscosity and contact area in Figure 4.15. Remarkably, this

exponent is entirely compatible with the experimental results for CR values of 0.5 to 0.7, and

suggests that the dependence of the measured interfacial yield stress on viscosity arises

because of the varying degree of contact between the hydrogels. The predicted power law

model does not fit the measured data set with a CR of 0.4.

At this CR value, the substrates have the lowest modulus and the smallest contact area. I thus

suggest this higher exponent arises because of a greater potential for viscous stresses to

influence the tribology, beyond the influence on contact area during squeeze flow. That is,

equation 4.1 in Section 4.2.1 has a non-negligible contribution to the measured shear stress. It

Strain (-)

0 1 2 3 4 5

Sh

ea

r S

tre

ss (

kP

a)

0.0

0.1

0.2

0.3

0.4

0.5

0.6 = 0.001 Pa.s

= 0.5 Pa.s


96

is worth reinforcing here that there is a higher degree of uncertainty in the fitting of the

poroelastic mechanical model to the experimental data for hydrogels at CR 0.4, which is

explain in Section 4.3.2. Furthermore, the assumption of the poroelastic mechanical model is

that the pairs of hydrogels behave as a continuous material, which is no longer valid if there

is a contribution of viscous stresses from the solvent. The results for CR 0.4 will be left out of

all further analysis.

Figure 4.22. Logarithmic plot of the interfacial yield stress against the lubricant viscosity for

cellulose hydrogels. The different symbols represent different CR, as listed in the legend. The

data set for a given CR is fitted with a slope of -0.16.

4.3.6 Interfacial friction at the true contact area

The findings from the ComsolTM Multiphysics model illustrate how the interfacial contact

between poroelastic hydrogels is modulated through the substrate mechanics and solvent

viscosity. The scaling relationships between the area of contact and substrate modulus or

solvent viscosity in Figures 4.13 and 4.15 respectively, provide an approach to factor out any

differences in the measured friction response that are due to differences in contact area.

Firstly, the measured G’ (G’m) is corrected for contact area according to equation 4.12. G’c is

the corrected G’, At is the total area, and Ac is the area of contact.

𝐺′𝑐 =𝐺′𝑚𝐴𝑡𝐴𝑐

(4.12)

Log(Viscosity)

-3 -2 -1 0

Log(I

nte

rfacia

l Y

ield

Str

ess)

0

1

2

3

4

0.40.50.60.7


97

From Figure 4.13, the area of contact as a fraction of the total area is related to G’ according

to equation 4.13.

𝐴𝑐𝐴𝑡

= 0.037𝐺′𝑐0.32

(4.13)

Combing equation 4.12 and 4.13 gives equation 4.14.

𝐺′𝑐 = (𝐺′𝑚0.037

)

11.32

(4.14)

Then the measured interfacial yield stress (τm) is corrected for contact area according to

equation 4.15. τc is the corrected interfacial yield stress and η is the solvent viscosity. The

exponents are taken from the relationships in Figure 4.13 and 4.15.

𝜏𝑐 =𝜏𝑚𝜂

0.16

𝐺′𝑐0.3

(4.15)

τc is plotted against G’c in Figure 4.23 for all hydrogels, solvent viscosities, and all

compressions except for CR = 0.4 which did not fit the model in Figure 4.22. Applying the

corrections in equation 4.14 and 4.15 accounts for the influence of viscosity on the contact

area during the compression process prior to shearing. The data for different pectin solutions

collapse onto the power law relationship that is fitted to the cellulose and CAX hydrogels in

water in Figure 4.23. The power law regression has an exponent of 2/3. The CXG data does

not appear to fit the regression well and reasons for this will be discussed separately.

I postulate that the dependence of the corrected interfacial yield stress on the substrate

modulus is due to increased adhesion between cellulose fibres at the contact area. In Section

4.3.1 I show that cellulose fibres within a network have the potential to adhere together

during compression, and the formation of new cellulose contacts in the network increases

with increasing compression. Therefore, when pairs of hydrogels are brought into

compressive contact, it is expected that cellulose fibres from opposing surfaces have the

potential to adhere together. The G’ of the hydrogel increases with CR because water is

squeezed out of the network and the solids concentration increases. Thus with increasing

compression, which translates to increasing G’, there is a higher probability of adhesive

contacts forming at the area of contact.


98

Figure 4.23. The corrected interfacial shear stress (τc) plotted against the corrected G’ (G’c)

for all hydrogels and all solvent viscosities. Symbols with a white cross inside represent the

cellulose hydrogels tested in water; all other black symbols are in pectin solutions with

different concentration. The grey circles are CAX and the open circles are CXG hydrogels in

water at all compression ratios. The solid line is a linear fit of the Cellulose and CAX

hydrogels in water, with a slope of 0.67.

Lopez-Sanchez et al.18 show a positive relationship between G’ and concentration for

bacterial cellulose hydrogels, their raw data is included in Appendix I and is used to predict

the cellulose concentration of hydrogel samples in this study from their G’. I interpolate

between the data points in Appendix I to find the cellulose concentration for the G’c of my

systems; values of G’c outside the range of the provided data are omitted. The τc is plotted

against cellulose concentration for cellulose, CAX and CXG hydrogels in Figure 4.24. For

cellulose and CAX, the τc scales linearly with cellulose concentration. This is consistent with

the proposed mechanism, where increasing the number of fibres at the interface

proportionally increases the adhesion between the surfaces.

Revisiting Table 2.2 from Chapter 2, a positive correlation between friction and hydrogel

modulus is observed for proprietary hydrogels 11, hydrogels with different crosslinking

density 14, and different gel states (swollen/collapsed) 6. The hydrogels tested in each study

have varying microstructure, which may lead to a different concentration of polymer at the

interface driving adhesive interactions. Inverse relationships between friction and hydrogel

modulus were observed with changing hydrogel composition 15 and temperature 8. For

example, increasing the content of a polymer that is rigid and not particularly adhesive could

Log (G'c)

3.0 3.5 4.0 4.5 5.0

Log

c

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4Cellulose, CR=0.5Cellulose, CR=0.6Cellulose, CR=0.7CAX, all CRCXG, all CRCellulose, CR=0.5, waterCellulose, CR=0.5, waterCellulose, CR=0.5, water


99

reduce the friction and simultaneously increase the hydrogel modulus. The temperature will

affect the kinetics of the polymers at the interface, and thus the rate at which they can form

adhesive bridges between the hydrogel surfaces that determine friction. Thus, the mechanism

I propose for the relationship in Figure 4.23 is consistent with the relationships observed for

other hydrogel studies in literature.

Figure 4.24. Interfacial yield stress versus the cellulose concentration calculated from the

measured G'. The power law regression fitted to the Cellulose and CAX data has an exponent

of 1.

From Figure 4.24, XG reduces the τc compared to cellulose and CAX hydrogels for

equivalent cellulose concentration. The presence of XG presumably reduces the adhesion

between cellulose fibres at the interface, whereas AX has no influence. An alternative

explanation is that the XG changes the microstructure in a manner that reduces the presence

of cellulose fibres at the interface, or orients the fibres such that they are less likely to come

into contact with another fibre from the opposing surface. The effect of AX and XG on

cellulose fibre-fibre adhesion will be measured directly in Chapter 6 and all further

discussion around the mechanism of interaction between cellulose, CAX and CXG can be

found there.

4.3.7 Stick-slip and stiction behaviour

The two characteristic tribological responses observed between hydrogels in this study are

introduced in Section 4.3.3 as stick-slip and stiction. Representative shear stress curves for

Cellulose Concentration (%)

1

c (

kP

a)

0.001

0.01

CelluloseCAXCXG


100

these two phenomena are presented in Figure 4.25. Cellulose and CAX hydrogels across the

range of CR in water show a relatively consistent zig zag pattern in the shear stress after the

interfacial yield stress (τm), indicative of stick-slip sliding. For CXG hydrogels across the

range of CR in water, and cellulose hydrogels at low CR and high solvent viscosity, stiction

behaviour is observed where the measured shear stress peaks at τm and then decreases to a

lower equilibrium value τk.

a b

Figure 4.25. Characteristic friction behaviours during the constant rotation rate step showing

static (m) and kinetic (k) shear stresses: (a) stick-slip sliding for Cellulose/water at CR 0.6,

and (b) stiction behaviour for CXG/water at CR 0.6.

The terms characterising stick-slip behaviour are labelled in Figure 4.26. Prior to τm the

surfaces are adhered together and the initial slope of the shear stress-strain curve is a measure

of the bulk shear modulus, G, of the system. If the surfaces are adhered together during

subsequent stick cycles, the slope during stick, kst, should also be a measure of the system’s

shear modulus. In Figure 4.27a, time is proportional to strain and the G is measured at low

strain values for comparison to the mechanics of the stick cycle, where similarly low strains

are applied. In Figure 4.27b, kst is plotted against G with a line fit of kst = G, which shows

that the two moduli are in fact equal for comparable deformation strains.

Klein31 investigated the frictional dissipation in stick-slip sliding between two surfaces,

where the top surface is subject to a lateral force via the attached spring being pulled at a

constant velocity. During the stick cycle the spring extends and applies and increasing force

on the surface until the adhesion is overcome and the top surface slips past the bottom one.


101

Klein31 highlights that the elastic energy stored in the spring during the stick cycle must be

dissipated during the slip cycle. This is true of a system that is controlled by a passive spring.

However, for my friction experiments the rheometer uses embedded feedback equations to

actively control the angular velocity at the set point value.

Figure 4.26. Characterisation of stick-slip behaviour showing the elastic modulus, kst, during

the stick cycle, the slope of the slip cycle, ksl, the energy of the stick and slip cycles, Est and

Esl, the static friction stress, τm, kinetic friction stress, τk, and the length of the stick, γst, and

slip, γsl, cycles.

a b

Figure 4.27. (a) Shear stress over time for constant rotation (CAX at CR 0.7 in water); the

shear modulus, G, is taken as the slope of the linear region at low strains and kst is the slope

of the stick cycle. The standard deviation of the kst measured for each peak in a given shear

stress-strain curve is approximately 15%. (b) Scatterplot of the slope of kst against G with a

line fit of kst = G. Data for cellulose and CAX hydrogels at all CR in water are included.

G (Pa/s)

10

kst

(Pa

/s)

10

CelluloseCAX kst = G


102

For the cellulose hydrogels in the rotational rheometer, when the applied shear stress is

greater than τm, the slip cycle is initiated and the rotating surface rapidly accelerates. This is

followed by a deceleration and corresponding decrease in the applied shear stress as the

systems adjusts to the set rotation rate. After deceleration the surfaces stick again because the

applied stress is now less than τm. τk is expected to be the point at which the top surface has

decelerated enough to allow the fibres and the interface to adhere again. This acceleration-

deceleration during the slip cycle can be observed in the measured angular velocity during the

friction test in Figure 4.28. The sharp peaks in angular velocity are aligned to the slip cycle,

where the surface accelerates along the first half and decelerates along the second half of the

slip length in Figure 4.28. The friction curves with corresponding angular velocity for

hydrogel pairs (cellulose, CAX, CXG) at all CRs are included in Appendix J.

Figure 4.28. Shear stress () and angular velocity () measured over time during constant

rotation rate step for cellulose hydrogels at a CR of 0.6 in water. Inset shows a close up of a

single angular velocity peak (m to show how it aligns to the slip cycle.

Typically the angular velocity at the beginning and end of the slip cycle is comparable, which

indicates that the slip length is determined by the ability of the instrument to bring the

rotation rate back to the set point value. The magnitude of the angular velocity during the

acceleration-deceleration is expected to be controlled by the torsion that was being applied at

the point of slipping, and the feedback system of the instrument for correcting the rotation

rate which is constant for all samples. From Figure 4.25a, τm is the measured shear stress

applied at the point of slipping. As expected, the peak angular velocity (m) during the slip


103

cycle is shown to increase with τm in Figure 4.29. The m then controls the slope of the slip

cycle, whereby the time taken to correct the angular velocity scales with the magnitude of the

increase in angular velocity above the set point value. The slope of the slip cycle, ksl, is

shown to increase with m in Figure 4.30. Thus the stick-slip response is due to the adhesive

nature of the interface that prevents the rheometer from being able to accurately control the

set point rotation rate.

It is anticipated that reducing the adhesion or contact area between the hydrogel surfaces will

eliminate the stick-slip response. The findings from the ComsolTM Multiphysics model in

Section 4.3.5 show that the contact area at the interface is reduced with decreasing G’ and

increasing solvent viscosity. A map of the G’ and solvent viscosity for the cellulose hydrogel

pairs across the range of CR and pectin concentrations is presented in Figure 4.31, with the

tribological behaviour labelled as either stiction or stick-slip. The clustering of the different

responses in Figure 4.31 follows the contact area model of adhesion. Stick-slip is observed

for a large contact area, whereas stiction behaviour is observed when the contact area at the

interface is low. The presence of a viscous layer at the interface after the τm is overcome is

proposed to prevent the cellulose fibres from coming into contact again. Thus the set rotation

rate can be maintained at a constant stress value τk.

Figure 4.29. The peak in angular velocity (m during the slip cycle over the torque applied

to the rotating surface at the point of slipping (m).

From Figure 4.24 in Section 4.3.6, the adhesion between surfaces is reduced due to the effect

of XG on the interaction between cellulose fibres at the interface. The stiction curve and

m (kPa)

0.01 0.1 1

m (

rad

/s)

0.01

0.1

1

CelluloseCAX


104

corresponding angular velocity for CXG at CR = 0.7 is presented in Figure 4.32. The angular

velocity in Figure 4.32 confirms that stiction occurs when the adhesion between surfaces is

sufficiently reduced such that the rheometer is able to maintain the set point rotation rate by

applying a constant stress τm.

Figure 4.30. The slope of the slip cycle, ksl, plotted against the peak in angular velocity (m)

during the slip cycle. The standard deviation of the ksl measured for each peak in a given

shear stress-strain curve is approximately 15%.

Figure 4.31. Scatterplot of the G’ against viscosity for the different sliding behaviours

labelled in the legend.

m (rad/s)

0.0 0.1 0.2 0.3 0.4

ksl (P

a/s

)

-140

-120

-100

-80

-60

-40

-20CelluloseCAX

Viscosity (Pa.s)

0.0001 0.001 0.01 0.1 1

G' (

kP

a)

1

10

100

StictionStick-Slip


105

Figure 4.32. Shear stress and angular velocity measured over time for a set rotation rate. This

curve is for CXG at CR = 0.7 but is representative of all friction curves that display a stiction

response.

4.4 Concluding remarks

Tribological interactions occurring between pairs of poroelastic cellulose hydrogels are

determined using a torsionally driven parallel plate rheometer. After compressing cellulose

gels into contact, the measured shear stress increases with strain to an interfacial yield stress,

which is followed by either a stick-slip pattern or a decrease in stress to a steady value to

indicate sliding friction between the gels. The measured interfacial yield stress is found to be

dependent on the hydrogel modulus and the viscosity of the fluid medium. However, this

observation doesn’t consider the influence of the true contact area between the gels. To

overcome this issue with the parallel plate geometry, compression-relaxation and SAOS are

performed prior to torsional sliding. When the results are combined with a computational

model that utilises a poroelastic model for the compressible substrates in association with

squeeze flow of Newtonian fluid between the gels, the area of contact between the gels is

predicted. Strong evidence is found for the presence of contact between the cellulose

hydrogels in an annular region at the outer edge of the disks, and an inner region of entrapped

solvent at the centre of the interface; in particular, the area of contact between the gels

following compression reduces with increasing solvent viscosity. This is in agreement with

work by Yamamoto et al.25 using a rotational rheometer to measure the friction between

hydrogel surfaces; direct visualisation of the contact reveals a region of trapped water in the

Time (s)

0 10 20 30 40

Shear

Str

ess (

, kP

a)

0.00

0.05

0.10

0.15

Angula

r velo

city (

, ra

d/s

)

0.00

0.01

0.02

0.03

0.04

0.05


106

centre surrounded by an area of surface contact. The authors are able to relate the measured

friction to the true contact area at the interface. In the present study, when factoring in true

contact area, the interfacial yield stress scales with the storage modulus of the hydrogels with

a power law exponent of 0.67. The scaling of interfacial yield stress with modulus is

associated with its direct relationship to the cellulose fibre concentration. I postulate that the

interfacial yield stress at the true contact area is an indicator of the static friction between

gels, and that it is a function of contact forces between cellulose fibres in opposing surfaces.

With the approach presented in this chapter, the surface interactions between hydrogel pairs

with different composition can be measured. The presence of xyloglucan is shown to reduce

the static friction between hydrogels, whereas arabinoxylan does not. The cellulose

hydrogels studied have a water-filled fibrous network that is akin to the microstructure of

plant cell walls. Thus results provided here give insights into the potential role of wall

components on cell-cell friction.


107


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109

Chapter 5

Method development for measuring

the adhesive forces between

individual nano-fibres


Inter-fibre adhesion is a key factor in the functionality of naturally occurring fibrous

assemblies, which includes plant cell walls. The ubiquity of fibrous structures in nature calls

for the development of techniques enabling the direct measurements of adhesion between

nanofibres. These techniques are set to play an important role in biomimetic design since

fibre-fibre interactions are of fundamental importance to the overall network mechanics and

material performance.

The mechanical properties of a range of fibrous materials have been studied using

compression, uni- and bi-axial tensile testing and small-amplitude oscillatory shear1-12. The

results from these studies indicate that the mechanics of random fibre networks is defined by

the intrinsic mechanical properties of nanofibres3, 7, surface interactions between fibres1, 9, 12,

the network microstructure1, 4, 5, 9-12, and number and nature of entanglements and/or cross-

links1, 4, 5, 7-12.

The development of structural models of fibre networks provides predictive capabilities for

design and evaluation, as well as enhancing understanding of the underlying principles


110

controlling natural systems. The common approach to account for the adhesive potential is to

simply treat contacts between fibres as rigid junctions13-16, which is only appropriate when

fibre interactions are very strong. To estimate the yield strain of a fibre networks, that is the

strain corresponding to the limits for linear and elastic deformations, Chatterjee17 applies an

energy penalty for breaking the fibre contact points that equals the stored elastic energy of

deformation. However, a reliable model for any particular system requires accurate

knowledge of the adhesive potential between fibres at network junctions, which requires

validation through experiments.

Current experimental approaches for direct measurement of fibre adhesion for sub-micron

(>100nm) electrospun fibres are reviewed in Chapter 2: Section 2.4.3. In summary, the

existing techniques require isolation and handling of individual fibres. The ends of an

individual fibre are attached to two points such that the length of the fibre is suspended. The

suspended midsections of two fibres are brought into contact in a cross-cylinder or parallel

configuration. A pull-off force is measured as the fibres are pulled apart at a constant

velocity. Here I develop a novel method for measuring the adhesive-detachment forces

between nano-fibres in situ, that is, within the fibre network. The technique captures the

native fibre contact configurations of self-assembled networks, and eliminates the need for

isolation and handling of nano-fibres. The method uses an AFM to perform what is referred

to as a ‘dip-and-drag’ test, which involves inserting an AFM tip into the network and

dragging it laterally. The forces measured are related to detachment events between fibres as

they are pulled apart from each other by the AFM tip. The technique is explained in detail in

Chapter 3: Section 3.2.2.

In the ideal scenario, the dip-and-drag technique pulls a single fibre and probes a single

contact zone to measure the detachment force. This cannot be practically and consistently

achieved, and often multiple fibres are pulled out of the network simultaneously leading to

large-scale network deformation. The fibre network density cannot be controlled for bacterial

cellulose systems, so model fibrous systems are first used to investigate the effect of network

deformation on fibre detachment. I validate the method using well-characterized electrospun

polymer fibres fabricated from sulphonated polyether ether ketone (SPEEK) and polyvinyl

alcohol (PVA). In these systems the adhesive forces are dominated by DLVO interactions,

making them suitable for testing the novel technique. I also test the ability of the technique to

measure hydrogen bonding interactions using fibre mats of Cellulose Nanocrystals (CNC)

and nano-fibrillated cellulose (CNF). The hydrogen bonding energy between the cellulose


111

fibres is different in water and air, and both environments are tested to confirm the ability of

the technique to measure these differences. This chapter is focussed on the rigorous

validation of the dip-and-drag method. In Chapter 6 the technique is applied to bacterial

cellulose systems to investigate the effect of individual cell wall components on cellulose

fibre interactions.


5.2.1 Model fibre Systems

Fibre samples are prepared according to the fabrication procedures in Chapter 3: Sections

3.1.1 and 3.1.2. Images of the SPEEK, PVA, CNC and CNF fibres are presented in Figure

5.1. SPEEK fibres are electrospun directly only a glass substrate, whereas for PVA, CNC and

CNF samples, preformed fibres network are glued onto a glass substrate with 5-minute curing

epoxy resin (UHU GmbH & Co. KG, Germany) (equal parts base and curing agent). The

epoxy resin is applied delicately using a narrow glass rod. A section of the network

approximately 5mm x 5mm is glued around the edges leaving a small gap through which the

AFM tip can pull fibres out of the network.

5.2.2 Dip-and-drag technique

The dip-and-drag technique applied to bacterial cellulose micro-hydrogels is explained in

Chapter 3: Section 3.2.2. The sample principle is applied to the model fibre systems (SPEEK,

PVA, CNC, and CNF). Briefly, the JPK Nanowizard II AFM was mounted on an inverted

optical microscope (JPK Instruments, Germany). The AFM was loaded with a stiff cantilever

(HQ:NSC35/Cr-Au BS, Cantilever A) from Mikromasch (Nano World AG, Germany). The

networks were first imaged in intermittent contact mode in air to identify the exposed edge.

The imaging is performed at a scan rate of 2 Hz for a 60 x 60 µm scan size with 1024 x 1024

pixels. The set point and drive amplitudes are around 1 V and the drive frequency is around

200 kHz. Using manipulation control in contact mode, the path of the AFM tip was traced

over the image such that the tip was engaged around the exposed edge of the network for

PVA, or anywhere inside the homogeneous network for SPEEK samples, and then dragged

outward to measure fibre detachment events as illustrated in Figure 5.2.


112

Figure 5.1. Microscopy images of nano-fibrous networks. (a) SEM micrograph of

electrospun SPEEK nanofibre network. The inset shows a single SPEEK fibre with the

corresponding diameter measurement. (b) SEM micrograph of electrospun PVA nanofibre

network. (c) TEM image of Triodia pungens nanofibrils obtained via high pressure

homogenizer (CNF). (d) TEM image of Triodia pungens nanocrystal network obtained via

acid hydrolysis (CNC).

For lateral force measurements the set point vertical deflection was 300 nN and the AFM tip

travel speed was 0.3 µm/s. This lateral force measurement was repeated several times on

different parts of the network. The initial placement of the AFM tip inside the network is

random and in some cases may land on a fibre rather than the substrate. Force-distance curves

with an initial constant baseline force, where the lateral force is equal to the substrate friction

as depicted in Figure 5.2, are selected for analysis to ensure that a set point vertical force is

established between the AFM tip and the substrate. The test was repeated for a given SPEEK


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Figure 5.2. The AFM tip is engaged with the substrate at a constant normal force and moved

in a lateral pulling direction. The initial lateral force is due to friction between the AFM tip

and substrate. When the tip engages with a fibre the lateral force increases due to fibre

deformation until a detachment event occurs at a fibre-fibre contact in the network.

fibre sample with aniline (Sigma) as a solvent. Aniline has a refractive index between that of

glass and SPEEK causing negative van der Waals interactions that substantially reduce the

adhesion between the fibres and substrate 18. By contrast, aniline has only a marginal effect

on adhesive forces between SPEEK fibres, because van der Waals interaction between

surfaces of the same material is always attractive 19. Subsequently, the results are compared

to those obtained from the measurement in air to confirm that the recorded forces are due to

fibre-fibre interactions and not influenced by fibre-substrate adhesion.

The lateral deflection data was recorded during the AFM tip trace and converted to lateral

force according to the procedure discussed in Chapter 3: Section 3.2.2. Measurements are

completed in ambient air for all samples as well as in water for CNC and CNF.


5.3.1 Dip-and-Drag Lateral Force Spectroscopy of SPEEK electrospun

mats of varying network density.

Figure 5.3 presents lateral force-distance measurements obtained for SPEEK fibre samples at

two extremes of network density (force-distance data for all SPEEK samples can be found in


114

Appendix K). The AFM tip is engaged with the substrate and translated laterally whilst

maintaining a constant normal force. During dragging, the baseline force is due to a

combination of friction between the tip and substrate, and elastic deformation of the network.

For low network density, it is suggested that the fibres are sufficiently far apart that a single

fibre is pulled without deforming large sections of the network. Thus the relatively constant

baseline force (designated ‘bf’) in Figure 5.3a is anticipated to be dominated by tip-substrate

friction. In contrast, the lateral force measured for the dense fibre network in Figure 5.3b is

steadily increasing, suggesting a baseline force that is dependent on degree of network

deformation. The baseline force in Figure 3b is initially constant, confirming that the AFM

tip first comes into contact with the substrate at the set point vertical force before contacting

fibres with lateral movement. The overall increase in lateral force is suggested to correspond

to the AFM tip dragging a number of fibres collectively, which leads to a large and

cumulative contribution of network deformation to the measured force.

In the force-distance profiles of SPEEK samples with low network density, consistent peaks

above the baseline force are observed (designated by * in Figure 5.3a). I propose that the

observed sharp increase in lateral force (above the baseline) corresponds to the AFM tip

engaging with a fibre and bringing it into tension. The abrupt decrease in lateral force is thus

associated with a detachment event at a fibre-fibre contact, such that the fibre is no longer in

tension and the signal returns back to the baseline value. Figure 5.3a indicates where I take

the height of the peak force (designated by ‘h’) to be a measure of the force required for

detachment at a fibre contact, which is akin to a ‘pull-off’ force between fibres. Figure 5.4a is

an SEM image of the SPEEK fibre substrate superimposed with a white line to represent a

potential 2 micron length pathway for the lateral movement of the AFM covered in Figure

5.3a. Whilst this particular image does not necessarily correspond to the section of the fibre

network that is measured, it provides an indication that the fibre detachment events occur in

line with the density of fibre interactions (designated by * in Figures 5.3a and 5.4a). The

image shows that it is plausible that 4 contacts are probed during measurement over the 2µm

lateral distance whilst maintaining a stable baseline force.

For high network density samples, a sharp drop in the lateral force is observed relative to the

deformation-dependent baseline force (Figure 5.3b). In this case, the measured force is

expected to be distributed across a number of fibre contact points. I suggest that when the

local force at a single contact point exceeds the adhesion force, fibre-fibre detachment occurs,

seen as a sharp drop in the measured lateral force. The peak height or pull-off force is


115

labelled ‘h’ in Figure 5.3b. In Figure 5.4b a 7µm trace is marked that corresponds to 7 fibre

contacts being disrupted. The fibres that are pulled during the trace have remaining

connections to the network leading to large scale deformation and an increasing baseline

force. This proposed trace is consistent with the observations in Figure 5.3b.

a

b

Figure 5.3. Typical lateral force-distance curves for SPEEK samples with (a) constant and

(b) increasing baseline force (bf). (*) denotes the peak events identified during data

processing. The peak height (h), calculated as the distance between the maximum and

subsequent minimum of the peak is labelled. The z-piezo position of the cantilever holder

relative to the substrate is plotted on the right-hand y-axis.

In Figure 5.3 there is an initial decrease in the z-piezo position of the cantilever (right axis in

Figure 5.3a and 5.3b) which corresponds to an overshoot of the vertical deflection before


116

settling to the set point with changing height. The overall drift in the height, particularly in

Figure 5.3b, is attributed to optical crosstalk between the photodetector signals related to

normal and torsional deflections of the cantilever. Due to rotational misalignment of the

photodetector during lateral force measurements, the vector representing the lateral shift of

the laser has a non-zero vertical shift 20. A substantial height change is observed in Figure

5.3b at a distance of around 6.5µm, which we suggest is due to fibre breakage. The frequency

of these types of events can be determined by histogram analysis of the population of peak

heights.

The entire set of force-displacement curves is analyzed using a semi-automated MATLAB

routine, for which the code is included in the Appendix L. The code identifies a peak if the

average force of x number of consecutive points on either side is less than the force at the

point of interest. The value of x is adjusted for the background noise frequency. The local

maximum and minimum of the identified peaks are found. The peak height is taken as the

distance between the maximum and subsequent minimum.

a

b

Figure 5.4. (a) and (b) show SEM images superimposed with proposed AFM tip traces

corresponding to the lateral distances measured for respective SPEEK samples in Figure 5.3

(a) and (b).


117

Figure 5.5a shows a representative force-distance curve for the lowest network density

SPEEK sample with the baseline force subtracted. The peak heights extracted from the set of

fibre pulling measurements are presented in a histogram in Figure 5.5b. The tail of the

distribution at large peak heights is attributed to the situations where the AFM tip cuts

through the fibres, which are shown to occur with low frequency.

Figure 5.5. Analysis of example force distance curve for SPEEK sample showing (a)

representative force-distance curve and (b) histogram of peak heights obtained from an entire

series of curves.

Peak heights correspond to fibre detachment events when a fibre under tension is released

from the network either by the fibre breaking or the adhesion between fibres at a contact zone

being overcome. SEM images of the different SPEEK samples after testing, labelled A

through to E, are shown in Figure 5.6. There is evidence of broken fibres, however some

broken fibres are also observed for SPEEK samples that have not been measured using the

dip-and-drag technique. Furthermore, the broken fibres seem to largely occur around the

globular structures, as seen in Figure 5.6, and could be an artefact of the electrospinning

process. Whilst fibre breakage may be occurring, the overall increasing baseline force in

Figure 5.3b suggests that for the most part fibres remain in tension. The experimental results

are compared to theoretical adhesion energies in the next section to support the interpretation

of the peak heights as a measure of the adhesion between fibres.

The shape of the distribution is largely influenced by the fibre network density and the

number of contacts that are in tension just prior to a detachment event occurring. To illustrate

this point, two scenarios of dragging a fibre are considered. As depicted in Figure 5.7a, either

the pulling force is applied at a single fibre contact or divided between two fibre contacts. For


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the first scenario, the pulling force (FTOTAL) is equal to the adhesion force (Fadh) at the single

contact zone. For the second scenario the AFM tip can pull from any point along a fibre

connecting two contact zones, where the two distances are designated L1 and L2. The pulling

force stretches the fibre by the distance 2, and hence the strain applied to each segment of

the fibre is δ/L1 and δ/L2. The detachment at the weakest contact zone, either 1 or 2, occurs

when the resulting elastic force applied to the respective segment, 𝐹𝑖, is equal to the adhesive

force, 𝐹adh𝑖 as in equation 5.1.

𝐹𝑖 = 𝜋𝑅2𝐸𝛿𝑖

∗

𝐿𝑖= 𝐹adh𝑖

(5.1)

Figure 5.6. SEM micrographs at 10 000 x magnification of electrospun SPEEK nanofibre

networks with different electrospinning times labelled A through to E (scale bar is 1 µm). A2

is an SEM micrograph of substrate A at 2000 x magnification showing the breakages of

fibres around the globular-like structures.


119

R is fibre radius, E is Young’s modulus. Consequently, the strain at the pull-off, 𝛿𝑖∗ is given

by equation 5.2.

𝛿𝑖∗ =

𝐿𝑖

𝜋𝑟2𝐸𝐹adh𝑖

(5.2)

Here, the stretching force is assumed to be linear with deformation, and the pull-off force is

independent of elastic parameters of the fibre. The resulting force, FTOTAL, is the sum of the

forces applied to both segments of the fibre and is a function of the ratio of L1 and L2. The

expression for FTOTAL in equation 5.3 uses the Heaviside function as a convenient operator

which ‘selects’ whether the detachment occurs at contact 1 or 2. It can be seen from equation

5.3, that the total pulling force at the point of detachment is independent of elastic parameters

of the fibre and depends only on the ratio of fibre segment lengths, 𝑙 =𝐿1

𝐿2 , and the force of

adhesion (𝐹adh𝑖).

FTOTAL = 𝐹1 + 𝐹2 = [𝐻(𝛿2∗ − 𝛿1

∗) ∙ 𝐹adh1𝑙 + 𝐻(𝛿1

∗ − 𝛿2∗) ∙ 𝐹adh2

] ∙1 + 𝑙

𝑙

(5.3)

H() is the Heaviside function. Each detachment event depends on the three random variables

that contribute to the value of the force, Fadh1 , Fadh2 , and l. If Fadh1 and Fadh2 are assumed to

be part of the same distribution {𝐹adh} then FTOTAL is given by equation 5.4.

𝐹TOTAL = {𝐹adh} ∙ (1 + 𝑙) ∙ {1

𝑙, 𝑙 > 1

1, 𝑙 ≤ 1

(5.4)

Further, if a uniform distribution of the random variable l is assumed, then the ensemble

average force can be calculated using equation 5.5.

⟨𝐹TOTAL⟩ =1

𝑙∫ 𝐹TOTAL𝑑𝑙 ≈ 1.2773 ∙ {𝐹adh}

𝑙

0

(5.5)

Therefore, for the contact where the pulling force is divided between two fibres the measured

force is expected to have a similar distribution to the adhesive force of a single junction with

a correction coefficient of 1.3, as shown in Figure 5.7b. Amongst many peak force

distributions recorded, all of them feature a wide distribution of forces similar to the example

shown in Figure 5.5b. Due to the breadth of the distributions, both scenarios are captured

within the range of the most frequent event. Further refinement can be achieved by applying


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Jarzynski’s averaging 21, 22 to the data according to equation 5.6. This exponential averaging

gives more weight to more frequent events that occur at low peak height values.

𝑒𝑥𝑝[−∆𝑄] = lim𝑛→∞

⟨𝑒𝑥𝑝[−ℎ𝑖]⟩𝑁 (5.6)

Q is the exponentially averaged peak height, <>N denotes arithmetic averaging of N peak

events, and hi represents the peak height of the ith event.

The average peak heights for SPEEK samples from the Jarzynski equality in equation 5.6 are

presented in Table 5.1. Remarkably, there is no dependence of the peak height on the network

density when comparing the SEM images in Figure 5.6 with the values in Table 5.1; in

particular samples D and E show the lowest fibre network density but not necessarily the

lowest peak height. This provides evidence that regardless of whether the baseline force is

deformation-dependent or not, the origin of the sharp decrease or peak in lateral force is the

same and likely to be a fibre-fibre detachment event. This supports the peak height

representing a ‘pull-off’ force between two fibres in contact. Elastic deformation of the fibre

network thus has little influence on the pull-off force, and the average for all samples is

8.4±1.4µN.

Table 5.1. The exponentially averaged peak height values from a set of force-distance curves

measured for SPEEK samples referenced A-E for increasing network density. Total number

of peak events is 280.

Sample

Reference

Peak Height

(µN)

A 6.8

B 6.9

C 11

D 7.3

E 10

To confirm that the measured detachment events are not due to fibre-substrate interactions,

the dip-and-drag technique is used to measure the forces for one of the SPEEK samples (E)

with aniline as a solvent. Aniline has a refractive index between glass and SPEEK, giving rise

to repulsive van der Waals interactions between the fibre and substrate whilst maintaining

attractive van der Waals interactions between fibres. There was found to be no statistically

significant difference between the population of peak heights measured in air and aniline with


121

a

b

Figure 5.7. (a) Illustrations of two possible scenarios for pulling a fibre and probing either 1

or 2 contact points. The insets show the SEM images of the SPEEK networks that may

illustrate the microscopic representation of such scenarios. (b) A theoretical model of a pull-

off experiment based on 10 000 junctions with normally distributed inter-fibre adhesive

energies. Open circles represent the frequency distribution of pull-off forces for Scenario 1.

Open diamonds represent the corresponding distribution of pull-off forces for Scenario 2,

calculated based on equation 5.3 and a uniform distribution of the parameter 𝑙 = 𝐿1 𝐿2⁄ ,

which corresponds to the random position of the AFM tip with respect to the contact points.

Solid lines are best fits using a Gaussian function. Dash lines mark the most frequent value of

pull-off force for each scenario. The dash-dot line marks the force value for the case of a

symmetric pull, i.e., l = 1


122

a p-value of 0.96. Thus the detachment events measured are attributed to the interactions

between fibres.

5.3.2 Dip-and-Drag Lateral Force Spectroscopy of PVA network

The developed technique is further tested on a network of electrospun PVA fibres with an

average diameter of 163 ± 42 nm. The force-distance curves for the PVA sample, an example

of which is in Figure 5.8a, shows a large contribution of network deformation to the baseline

force that is consistent with a highly dense network. The histogram of peak heights in Figure

5.8b is characterized by the Jarzyski’s averaged peak height of 6.1µN which I take as the

PVA pull-off force for further analysis.

Figure 5.8. (a) Representative force-distance curve for PVA and (b) histogram of peak height

values for the entire set of curves.

5.3.3 Analysis of adhesive forces between fibres

It is appropriate to consider electrospun polymer fibres in the network to be interacting

through van der Waals forces. The electrospinning procedure gives reasonably cylindrical

fibres and capillary forces are expected to be negligible for the contact angles created by two

cylinders. I examine whether the order of magnitude of the measured pull-off forces for

SPEEK and PVA fibres is comparable to the forces (FvdW) predicted from van der Waals

interaction energy between two cylindrical bodies in parallel configuration according to

equation 5.7 23. For a parallel configuration the length (L) of fibre-fibre contact needs to be

specified. The L used for the calculation is the contact length of two fibres interacting with an

orientation at the midpoint between parallel and orthogonal, that is, a 45° angle between

longitudinal axes of fibres.


123

𝐹vdW = 𝐴H𝐿√𝑅

16𝐷5

2⁄

(5.7)

AH is the Hamaker constant, R is the fibre radius and D is the separation distance which is

reported to be of the order of 1 Å for strong van der Waals interaction 23. There is uncertainty

around the values of the Hamaker constants for SPEEK and PVA. Therefore I will use

equation 5.7 to predict the Hamaker constant from the experimental pull-off forces 8.4 µN

and 6.1 µN as FvdW for SPEEK and PVA, respectively. Additionally, to test the effect of the

pulling configuration on the measured force, the experimental pull-off forces are adjusted by

applying the factor 1.3 in accordance with equation 5.5. The Hamaker constant for these

corrected values is again predicted from equation 5.7. The Hamaker constants computed this

way correspond to the scenario where the dragging force is predominantly divided between

two fibre contacts. I will then compare the experimentally determined values to the

theoretically calculated Hamaker constants using a number of different approaches.

The theoretically predicted Hamaker constants are calculated using two methods. Firstly, a

method based on extracting the surface energies from the wetting data is employed, which

gives 𝐴HSE = 5.81 x10-20 J and 10.5 x10-20 J for SPEEK and PVA, respectively 24, 25.

Secondly, a full calculation based on the Lifshitz’ theory of van der Waals forces is

performed 19, which gives 𝐴HL = 12.9 x10-20 J and 10.5 x10-20 J for SPEEK and PVA,

respectively. These calculations use the integrated form of the equation for the free energy of

interaction developed by Parsegian and Ninham 26. The permittivity spectra are calculated

using the method of Hough and White 27 in equation 5.8, which is based on the representation

of the material’s dielectric response 휀(𝑖) at the imaginary frequency (𝑖) as a sum of two

damped Lorentz oscillators 28.

휀(𝑖) = 1 +𝐶UV

(1 + (

𝜔UV⁄ ))

+𝐶IR

(1 + (

𝜔IR⁄ ))

(5.8)

All constants, CUV, UV, CIR, IR, are determined from the experimental data available in the

literature. The CUV and UV values are extracted from the Cauchy equation (equation 5.9) and

the refractive index spectra available for SPEEK 29 (CUV = 1.6, UV =1.24×1016 rad/s) and

PVA 30 (CUV = 1.5, UV =1.36×1016 rad/s).


124

𝑛2(𝜔) − 1 = 𝐶UV + (𝑛2(𝜔) − 1)𝜔2

𝜔UV2

(5.9)

The IR frequencies are evaluated based on FTIR spectra for SPEEK 31 and PVA 30. The

maximum absorption in the IR are found at 3451 cm-1 (IR = 6.50×1014 rad/s) and 2044 cm-1

(IR = 3.85×1014 rad/s) for SPEEK and PVA, respectively. The CIR is determined based on

the approximate equation 5.10 28.

𝐶IR = 휀0 − 𝐶UV − 1 (5.10)

0 is the static dielectric constant, which was determined from the electrical impedance

measurements for SPEEK (0 = 5, CIR = 2.4) 32 and PVA 33 (0 = 3, CIR = 0.5).

From Table 5.2, the AH values for PVA calculated using wetting data and the Lifshitz’ theory

show an excellent agreement, and highlight the fundamental equivalency of both approaches.

For SPEEK, the discrepancy is somewhat larger, which may be associated with changes in

the SPEEK material in the presence of water that impact the wetting studies 25. The

experimentally determined values of the Hamaker constant are found to be in a good

agreement with theoretical predictions. In particular, a very good agreement is observed for

SPEEK when 𝐴HL is compared to the experimental Hamaker constant calculated using

equation 5.7 and 5.5, i.e. for the scenario where the dragging force is divided between two

fibre contacts. In contrast, for PVA we observe a very good agreement for the case of a single

contact model, i.e. ⟨𝐹TOTAL⟩ ≈ {𝐹adh}. Although these values should be taken as an order of

magnitude approximation, it is plausible that the structure of the network may play a role in

determining the probability of pulling configurations. From Figure 5.1, fibres in the SPEEK

electrospun mat are more regularly aligned compared to PVA, where many fibres are being

curled and entangled into bundles containing more than two fibres. Thus, a more grid-like

configuration of SPEEK fibre mats may favor configurations that involve two-fibre contacts.

5.3.4 Dip-and-Drag Lateral Force Spectroscopy of CNC and CNF networks

in air and water

The dip-and-drag technique is also applied to CNC and CNF fibre mats. CNF has regular

hydroxyl groups which retain their hydrogen bonding potential, whereas the sulphuric acid

used for hydrolysis changes some hydroxyl groups to sulphate groups on the surface of CNC.


125

Table 5.2. The experimental and theoretical values of the Hamaker constant (𝐴H) for SPEEK

and PVA. The theoretical values are calculated using the surface energy approach (𝐴HSE), and

the full Lifshitz’ theory calculation using the integrated form of the equation for the free

energy of interaction developed by Parsegian and Ninham (𝐴HL) (see text for details of the

calculation). The experimental values are calculated using eq 7 and (i) the average

experimental values of pull-off forces (𝐴Hexp), (ii) the average experimental values of pull-off

forces adjusted using a correction factor from eq 5 that corresponds to the scenario where the

dragging force is divided between two fibre contacts (𝐴Hexp°).

𝑭𝐩𝐮𝐥𝐥−𝐨𝐟𝐟 [𝝁𝑵] 𝑨𝐇𝐒𝐄 [J 10-20] 𝑨𝐇𝐋

[J 10-20] 𝑨𝐇𝐞𝐱𝐩 [J 10-20] 𝑨𝐇𝐞𝐱𝐩° [J 10-20] L [nm]

SPEEK 8.4 5.8 12.9 16.07 12.6 331

PVA 6.1 10.5 10.5 9.4 7.4 362

The average diameter and length of individual CNC is 3.5±0.8 nm and 500±100 nm,

respectively, while the average diameter of CNF is 4.5±1.5 nm with a length of several

microns. In both cases the nanofibres agglomerate upon drying to give fibre diameters of the

order of 300nm. There are certain challenges with verifying the experimental pull-off force

from the dip-and-drag technique against theoretical predictions for hydrogen bonding. The

hydrogen bonding energy can be used to predict the adhesive energy between fibres if the

number of hydrogen bonding sites at the contact area is approximated. However, the

experimental pull-off force would need to be converted to an adhesive energy for

comparison. It is not clear how the fibres are separated during the dip-and-drag test, for

example, they could be peeled apart. Information about the mechanism of fibre detachment is

required to choose an appropriate model for converting the pull-off force to adhesion energy.

In Chapter 6: Section 6.3.2 I include simulations from a ComsolTM Multiphysics model to

relate the pull-off force and adhesion energy at the fibre contact. In this chapter, I assess

whether the dip-and-drag technique is able to measure pull-off forces between CNC and CNF

fibres that interact through hydrogen bonding. I can validate this by testing the fibre samples

in air and water and comparing how the experimental values scale with the hydrogen bonding

energies in air and water.

The force-distance curves for CNC and CNF in air, for which representative curves are in

Figure 5.9a and 5.9b, show large peaks in lateral force at the beginning of the AFM tip path.

The maximum lateral force is reached and the sharp drop is followed by stepped decreases in

the successive peaks. A similar profile is observed for CNC and CNF in water, shown in


126

Figure 5.9c and 5.9d, although the peaks appear smoother/rounder than in air. The curves are

analysed and the Jarzynski’s average of peak heights are presented in Table 5.3.

Figure 5.9. Representative force-distance curves for (a) CNC in air, (b) CNF in air, (c) CNC

in water, and (d) CNF in water.

Table 5.3. The Jarzynski’s average peak height value for CNC and CNF samples in air and

water. Sample size for each is approximately 50 peak events.

Sample Peak Height

(µN)

CNC in air 11

CNC in water 2.7

CNF in air 9.1

CNF in water 3.4

The peak heights, or pull-off forces, are comparable for CNF and CNC suggesting that the

slight changes to surface chemistry and the different aspect ratios of the fibres do not

significantly affect the interactions between fibres. The pull-off forces in air are larger than

those measured for SPEEK and PVA fibres. This is likely to be due to a combination of the


127

larger fibre diameter of the aggregated CNC and CNF compared to the electrospun fibres,

and the higher adhesion energy associated with hydrogen bonding compared to van der

Waals interactions which dominate for the polymer fibres. The differences between the pull-

off forces in air and water in Table 5.3 roughly scale with the difference between hydrogen

bonding energy in air (20kJ/mol) compared to water (6.6kJ/mol) 34. This finding strongly

supports the ability of the technique to measure the hydrogen bonding interactions between

fibres. The relationship between the pull-off force and adhesion energy for cellulose fibre

contacts will be investigated in Chapter 6.

5.4 Concluding Remarks

I have developed a novel technique for measuring the adhesion between individual nano-

fibres. Currently, there are technical challenges associated with isolating and handling

individual nano-fibres for measuring the adhesion between them in cross and parallel

configurations. In this study, an AFM cantilever tip is used to drag fibres out of a network

and measure the pull-off force. This technique has the unique advantage of working directly

with fibrous networks which inherently have a distribution of fibre diameters and

orientations. I consider the Jarzynski’s average of the distribution of detachment forces to

represent the pull-off force corresponding to the event where a single fibre contact is probed.

The experimental results are in good agreement with theoretical adhesion for the nanofibres

(electrospun SPEEK, electrospun PVA) which interact through van der Waals forces. CNC

and CNF fibre mats in air and water are used to demonstrate the applicability of the technique

for measuring the pull-off force for fibres interacting through hydrogen bonding. The

validated dip-and-drag technique will be used to measure the effect of important cell wall

components on the adhesive interactions between bacterial cellulose fibres. This will be done

in combination with a computational study that relates the measured pull-off force from the

dip-and drag technique to the adhesive energy at fibre contacts.


128



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130

Chapter 6

Measuring the effect of

hemicelluloses on the adhesive forces

between cellulose fibres


Based on the results in Figure 4.23 in Chapter 4: Section 4.3.6, I hypothesise that XG reduces

the adhesion between cellulose fibres, whereas AX has no effect. The main objective of this

chapter is to test this hypothesis. In Chapter 5 a dip-and-drag technique is developed to probe

the interactive forces at individual fibre contacts. The lateral force is recorded as an AFM tip

is dragged through a fibre network. Peaks in the recorded force-distance curves are

interpreted to represent fibre detachment events. Here, the dip-and-drag technique is applied

to bacterial cellulose networks and composites with AX and XG. These polymers interact

with the surface of cellulose fibres and mediate cellulose fibres contacts. The force-distance

curves obtained for cellulose and composite networks are compared, to determine the

influence of AX and XG. A model of fibre detachment is constructed in ComsolTM

Multiphysics to interpret and validate the experimental force-distance curves, and elucidate

the precise effect of AX and XG on the physical properties of cellulose fibre contacts.

Cellulose fibres are described as having a paracrystalline surface layer and a crystalline

domain in the core1, 2. The paracrystalline state has intermediate mechanical properties

between crystalline (high modulus) and amorphous (low modulus) phases. The partially

ordered structure of the paracrystalline surface layer is thought to permit an association


131

between the crystalline cellulose core and the semicrystalline hemicellulose in the cell wall1.

The hierarchical structure of bacterial cellulose has been investigated using small angle

scattering techniques with XRD and SEM3. Bacterial cellulose ribbons are approximated by a

core-shell model similar to plant cellulose where the outer region (shell) consists of solvent

accessible hydrated paracrystalline cellulose and the core is composed of cellulose

crystallites. Thus it is expected that the nature of interactions between bacterial cellulose and

hemicelluloses is representative of the associations in plant cell walls.

AFM imaging of onion epidermis shows that the cellulose fibres come into close proximity

with one another over short distances4. It is difficult to use this direct visualisation technique

to investigate the nature of interaction between cellulose fibres because the contact points are

obscured by matrix material. However, due to the prevalence of matrix material around the

contact points it is suspected that the polymers interact with cellulose and influence the nature

of the fibre contacts. Park and Cosgrove5 investigate the biomechanical changes in cucumber

and Arabidopsis hypocotyl walls induced by substrate-specific endoglucanases. They find

that endoglucanases that hydrolyse both XG and cellulose are required to induce creep. Park

and Cosgrove5 postulate that there is a minor, relatively inaccessible XG compartment that

may be intertwined or otherwise complexed with cellulose at fibre contact points. There are a

number of hypotheses for the nature of interaction between XG and cellulose, including;

entanglement with the amorphous glucans on the fibril surface5, 6, physical entrapment inside

the microfibril during synthesis5, 7, covalent bonding via a transglycosylation reaction8, or

non-covalent bonding5. In vitro cellulose binding experiments on the walls of barley aleurone

cells, containing 85% arabinoxylan (AX), indicate strong non-covalent bonds between the

AX chains themselves and with cellulose fibres9. XG and AX are the most abundant

hemicelluloses across plant species and their interaction with the surface of cellulose fibres is

investigated in this chapter.

Currently, the most reliable information regarding inter-fibre adhesion is inferred indirectly

from the analysis of macroscopic mechanical properties of cellulose networks. The

mechanical properties of bacterial cellulose and composite hydrogels (with AX and XG) have

been probed using small deformation oscillatory rheology tests and large deformation

uniaxial tensile testing10, equi-biaxial tensile testing11, and under compression12. From these

tests, the modulus of cellulose hydrogels and cellulose composites are measured to range

from 0.1 to 1 MPa10-12. The mechanical properties of fibre networks are vastly different to

individual bacterial cellulose fibres, which are reported in Chapter 2: Section 2.4.2 to have a


132

Young’s modulus of the order of 100 GPa13. From these multi-scale measurements, and

based on fibre network models reviewed in Chapter 2: Section 2.4.1, it is implicit that the

mechanical properties of cellulose-based composites are largely driven by interactions

between cellulose fibres, matrix polymers, and the assembly of these components into a

network.

The AFM has enabled direct measurement of the friction and adhesion forces between model

cellulose surfaces including pulp fibres14, 15, spherical cellulose particles16-18, and cellulose

thin films18-21. All of these attempts to measure cellulose friction and adhesion probe contacts

between large aggregates of cellulose fibres of the order of 10 m. This length scale is

relevant for biomaterials that use commercial sources of cellulose, but is not representative of

interactions between individual cellulose fibres that are important for plant cell wall

mechanics. Hence, the dip-and-drag technique provides new insights in to the interactions

between cellulose fibres, AX, and XG at individual fibre contacts.


Bacterial cellulose and composite networks are grown in confined 50 µm wells and deposited

onto a glass slide for measurement. The complete steps for producing these substrates are

detailed in Chapter 3: Section 3.1.3. The dip-and-drag technique is explained in Chapter 3:

Section 3.2.2. All measurements are carried out in deionised water from a Milli-Q Advantage

A10 system with a resistance of 18 Ω.cm at 25 °C.


6.3.1 Probing contacts between individual cellulose fibres

The structure of cellulose fibres synthesised by Gluconacetobacter xylinus is hierarchical.

Firstly, cellulose chains synthesised and extruded out of the pores in the bacteria’s plasma

membrane. These cellulose chains assemble into protofibrils with a diameter of ca. 2-4nm

(Iguchi, Yamanaka et al. 2000). Subsequently, protofibrils aggregate into ribbon-shaped

fibres with dimensions of the order of tens of nm. The morphology of bacterial cellulose

ribbons and fibre contacts are show in Figure 6.1a and 6.1b. Using this bacterium, cellulose

can be produced to form a very thin 3D-network. The vertical dimension of the network is

required to be smaller than the height of the AFM tip so that the tip can penetrate the network


133

and contact the glass surface underneath to establish a baseline force during the dip-and-drag

experiments. Single fibre loops around the edge are pulled away from the network to probe

the interactive forces at fibre contact points, as seen in Figure 6.1c.

a

b

c

Figure 6.1. (a) and (b) AFM images of an air-dried cellulose network showing fibres and

fibre contacts. The scale on the left hand side is the vertical dimension, and the scale on the

right hand side is the horizontal dimension. (c) AFM image of the edge of cellulose network

showing a loose fibre loop that is pulled with the AFM tip. The arrow represents the desired

path of the AFM tip, where is engages with the glass substrate at a vertical force of 300nN


134

and is then dragged outward from the network to bring the fibre into tension and drive a fibre

detachment event. The scale on the right hand side is the verticle dimension and the

coordinates in a horizontal plane are marked on the left and bottom axes.

The dip-and-drag technique and analysis methods in Chapter 5: Section 5.3.1 are applied to

bacterial cellulose composite systems to determine the role of cell wall components on

cellulose fibre interactions. Peaks in the recorded lateral force-distance curves are observed in

a relatively consistent manner. I postulate that these peaks, an example of which is shown in

Figure 6.2, correspond to detachment events at contact points between individual cellulose

fibres. I interpret the observed sharp increase in force (above the noise) as corresponding to

the AFM tip engaging with a cellulose fibre in tension. This is followed by a detachment

event at a fibre contact point. Thus, the fibre being pulled by the AFM tip is no longer in

tension and the signal returns back to the moving baseline. For these systems, the baseline

force is not constant and is a function of the network mechanics, as described in Chapter 5:

Section 5.3.1. The lateral force-distance data for a set of experiments is processed to identify

peaks that represent the detachment at a fibre contact. An example force-distance curve for

the cellulose network is presented in Figure 6.3a. The peaks are denoted with ‘*’, and the

peak height for one of the detachment events is labelled ‘h’ in Figure 6.3a. A histogram of the

entire population of peak heights is included in Figure 6.3b.

In order for a detachment event to occur, the force applied directly at the contact must be

greater that then adhesive force between the fibres. To assist in interpreting these results, an

example of a force balance across a section of the network during a pulling experiment is

considered in Figure 6.4. The critical observation from this scenario is that the pulling

configuration is an important factor in determining which fibre contact is most likely to

detach. The AFM tip applies a force directly to the fibre that it is in contact with, and this

force gets divided between a number of fibres as you move further into the network. For

example, the 7 fibres at the bottom system boundary experience approximately a seventh of

the pulling force applied to the single fibre at the top system boundary. Thus, if the adhesive

force at all the fibres contacts is comparable, fibre detachment is most to likely occur at the

encircled contact in Figure 6.4 as it experiences the largest direct pulling force. In Figure 6.4

the pull-off force at the encircled contact is assumed to be equal to the pulling force measured

by the AFM tip at the point of detachment.


135

Figure 6.2. Lateral force-distance curve showing a typical peak that is representative of a

detachment event at a fibre contact point.

a

b

Figure 6.3. (a) Example force-distance curve for cellulose fibre network, * denotes the peaks

in the curve that represent detachment events at fibre contacts and h is an example of the peak

height. (b) Histogram of complete data set of peak heights (n = 100).

Peak Height (µN)

0 5 10 15 20 25 30 35

Count

0

5

10

15

20

25


136

Jarzynski’s equality in equation 6.1 is used to characterise the pull-off force required to

detach a single fibre contact, and gives a value of 4.12 µN.

𝑒𝑥𝑝[−∆𝑄] = lim𝑛→∞

⟨𝑒𝑥𝑝[−ℎ𝑖]⟩𝑁 (6.1)

Q is the exponentially averaged peak height, <>N denotes arithmetic averaging of N peak

events, and hi represents the peak height of the ith event.

6.3.2 Simulating fibre-fibre detachment events

In order to simulate the scenario portrayed in Figure 6.4, a simplified model is implemented

in ComsolTM Multiphysics using the beam mechanics interface. The model setup is depicted

in Figure 6.5. Contacts 1 and 2 in Figure 6.4 are assumed to be fixed in the simulation. The

cross section of the fibrils is assumed to be rectangular (30 nm width × 15 nm height) and the

fibril modulus is taken as 78 GPa13. The contact is modelled as a collection of ten beams

separated by 1 nm, each with an equilibrium length, 𝑙0. The mechanics of the contact are set

up to follow a simplified cohesive zone model (CZM) structure22, with the contact strength K

following equation 6.2. The CZM describes the cohesive forces that occur as material

elements are separated. During separation, the overall cohesive force reaches a maximum,

which subsequently reduces to zero when the surfaces are completely separate. This is

consistent with the experimentally measured peaks in the force-distance curves and thus

provides a good model of the detachment at fibre contacts.

𝐾 = 𝐾0𝐻(𝜀𝑐 − 𝜀) + 𝐾0𝑒−𝛼(𝜀−𝜀𝑐)𝐻(𝜀 − 𝜀𝑐) (6.2)

𝐾0 is the contact strength of the unstretched contact beams, 𝜀 is contact strain, 𝜀𝑐 is the

critical contact strain, and H(x) is the Heaviside function which takes the value of zero for x <

0 and unity for x ≥ 0. Hence, the contact beams weaken exponentially when 𝜀 > 𝜀𝑐 with a

decay constant . This is a departure from the usual formulation of the CZM, which is

written in terms of contact displacement rather than strain and assumes a weakening law for

𝐾 that leads to a finite detachment displacement. For the present system, incorporating a

finite detachment displacement adds an additional parameter which is highly dependent on

the type of polymer (AX or XG) mediating the fibre contact and cannot be easily extracted

from the experimental data. Expressing K in terms of strain separates the calculated force

from the influence of 𝑙0. What the modified version of the CZM in equation 6.3 physically


137

describes is that after the critical strain is reached, softening of the contact occurs and the

stiffness tends to zero at a rate governed by α. A small value of α leads to quick detachment;

this creates instability in the ComsolTM Multiphysics simulation because it means that there is

a fibre freely “floating” in space. Therefore, is fixed ( = 15) for numerical stability. It is

possible to set up a model in which complete fibre detachment occurs, but I am examining

the pull-off force and not detachment length so this refinement of the model is not required.

Figure 6.4. Force balance across a section of the fibre network to illustrate that the pulling

force recorded by the AFM tip is a good estimate of the force acting at the (encircled) fibre-

fibre contact, where the detachment event occurs. The dashed line marks the system

boundary over which the force balance is applied.

Parametric sweeps are performed over K0, 𝜀𝑐, and the ratio between beam lengths (b = L1/L2)

that are labelled in Figure 6.5. While apparently restrictive, the constructed scenario is

representative of the fact that only the encircled contact will, on average, detach upon pulling.

In reality, contacts 1 and 2 can translate in the pulling direction without detaching, which

increases the pulling distance at the point of detachment. However, I am investigating the

pull-off force which is found below to be independent of the structural factor b, and is

exclusively related to the parameters of the encircled contact in Figure 6.5. This means that


138

the force applied to the contact is constant as the fibres are being pulled apart, up until the

time that the contact is separated.

Figure 6.5. Simplified setup of the system depicted in Figure 6.3 implemented in ComsolTM

Multiphysics. Due to their large aspect ratio, the cellulose fibres can be modelled as ideal

beams. ComsolTM Multiphysics does not allow the use of its adhesion features in this kind of

system, so the contact is modelled as a collection of beams (which are shown in the inset) that

soften when a critical strain is reached. Contacts 1 and 2 in Figure 6.4 are assumed to be

fixed.

Some sample curves from the parametric sweeps are presented in Figure 6.6. The simulated

pulling force increases linearly with distance until a peak force is reached, beyond which the

pulling force decreases as the contact strength decays and the fibres are separated. This does

not follow the shape of the experimental peaks in force-displacement, for example in Figure

6.1d; however it is found that varying the decay constant α had no influence on the peak

pulling force, and the selected value of α = 15 simply allowed for stable simulations. The


139

peak pulling force is equivalent to the experimentally measured peak heights and is taken as

the pull-off force between fibres under the specific conditions. When comparing the

respective force-distance curves with black and grey symbols in Figure 6.6, it is clear that b

changes the initial linear slope but does not affect the pull-off force. This result is

fundamentally important because it confirms that, on average, the pull-off force is

independent of the system configuration. Moreover, comparing curves with the same K0 and

b but different c reveals that c does not modify the initial slope of the curve. Increasing c

leads to an increase in the pull-off force. The slope and the pull-off force increase with K0.

The curves in Figure 6.6 are sample curves to illustrate the effect of changing system

parameters. From these results, it can be concluded that the initial slope, s, of the force-

distance curve depends on the contact strength K0 and the structural factor b, and is

independent of the critical strain c. The peak force, Fpull-off, depends on the contact strength

K0 and the critical strain c, and is independent of the structural factor b. These conclusions

are summarised in equation 6.3 and equation 6.4.

𝑠 = 𝑓(𝐾0, 𝑏) (6.3)

𝐹𝑝𝑢𝑙𝑙−𝑜𝑓𝑓 = 𝑓(𝐾0, 𝑐) (6.4)

Figure 6.6. Predicted force curves for combinations of 2 different values of b, K0 and c. The

values of K0, c, and b are labelled in the legend.

Distance ( m)

0.0 0.1 0.2 0.3

Pulli

ng f

orc

e (

N)

0.00

0.04

0.08

0.12

0.16K0 = 10 MPa; c = 0.2; b = 0.5

K0 = 10 MPa; c = 0.2; b = 1

K0 = 10 MPa; c = 0.4; b = 0.5

K0 = 10 MPa; c = 0.4; b = 1

K0 = 20 MPa; c = 0.2; b = 0.5

K0 = 20 MPa; c = 0.2; b = 1

K0 = 20 MPa; c = 0.4; b = 0.5

K0 = 20 MPa; c = 0.4; b = 1


140

Figure 6.7 presents 3-D plots of the functions in equation 6.3 and equation 6.4, and the

equations of the best curve fits are given in equation 6.5 and 6.6, respectively.

𝑠 = 𝑒𝑥𝑝[436.51 − 0.017𝐾00.5 ln(𝐾0) + 1.05 ln(𝐾0) − 130.2𝑏 + 24.86𝑏 ln(𝑏)

− 434.64exp(−𝑏 11.67) + 25.95𝑏0.5 ln(𝑏) + 87.97𝑏0.5⁄ ]

(6.5)

𝐹𝑝𝑢𝑙𝑙−𝑜𝑓𝑓 = 10𝑒𝑥𝑝 [−5.21 −0.088

𝜀𝑐− 2.67 exp(−𝜀𝑐) − 6×10−4𝐾0

+ 6×10−3𝐾00.5 + ln(𝐾0)]

(6.6)

a

b

Figure 6.7. Best surface fit describing the functional relationship between a) slope s, contact

strength K0, and the structural parameter b; and b) peak force Fpull-off, contact strength K0, and

critical contact strain c.

The system is underdetermined with two equations, equation 6.5 and equation 6.6, and three

unknowns; K0, b, and εc. One way to circumvent this issue is by including a third equation for

the adhesion energy, which is approximated for cellulose fibres based on the theoretical

hydrogen bonding energy. The expression for adhesion energy, A, is given in equation 6.7.

The adhesion energy due to hydrogen bonding between cellulose surfaces is estimated from

information about the cellulose structure. Ding et al.23 use the AFM to directly image

different types of cell walls in maize. From the results, the authors propose a model of plant

cellulose fibres with 36-chain cellulose elementary fibres (CEFs) associated through

hydrophilic faces to create ribbon-like bundles. In this model, the CEFs are hexagonal shape

with four hydrophilic faces showing 8 cellulose chains involved in hydrogen bonding over a

height of 3.2nm. The repeating unit of cellulose, two glucose monomers, is approximately


141

1nm in length24, and provides sites for 4 hydrogen bonds25. For cellulose chains on the

surface of cellulose ribbons, 2 sites will be available for hydrogen bonding with an adjacent

ribbon at a contact point. Therefore an area of 3.2nm x 1nm has a potential for 16 hydrogen

bonds. In water, the hydrogen bond energy is 6.6kJ/mol26, giving a value of 0.055 J/m2 for A

between cellulose fibres. This value provides a good estimate for comparing the influence of

AX and XG at fibre contacts. The value for 𝑙0, between cellulose fibres is taken to be 0.3nm,

which is of the order of the distance between two water molecules.

𝐴 =𝐾0𝑙0𝑐

2

2

(6.7)

Now the system comprises 3 equations and 3 unknowns. The experimental Fpull-off for

cellulose is found above to be 4.12 µN. The slope of the experimental force-distance curves

prior to each Fpull-off is extracted using the MATLAB file in Appendix M. The distribution of

the experimental slope, s, for cellulose is plotted as a histogram in Figure 6.8. The most

frequent value of the slope is 0.36 µN/µm. These two values (s = 0.36 µN/µm and Fpull-off =

4.12 µN) are subbed into equations 6.5 and 6.6. Solving the simultaneous equations 6.5-6.7

using a MATLAB code in Appendix N gives the following values: K0 = 134 MPa, b = 1.45,

and εc = 1.65.

Figure 6.8. The slope, s, of the experimental force-distance curve is measured before each

peak event. The histogram presents the distribution of experimental values of s for cellulose.

(n = 100).

Slope, s ( N/ m)

0.0 0.4 0.8 1.2 1.6 2.0

Count

0

4

8

12

16


142

6.3.3 The role of hemicellulose at contacts between cellulose fibres

The role of hemicelluloses, AX and XG, on the interactions between cellulose fibres is

examined using the dip-and-drag technique on composite networks. The bacterial cellulose

was grown in liquid culture medium with the dissolved polysaccharide, which may influence

the assembly of individual fibres and the fibre network. Example force-distance curves and

histograms of the population of measured peak heights are presented in Figure 6.9 for CAX

and CXG networks. From Jarzynski’s equality, the values of Fpull-off are 3.04 µN and 1.79 µN

for CAX and CXG respectively. Comparing these values to the pull-off force for a cellulose

network (4.12 µN) indicates that AX reduces the adhesion energy between cellulose by 25%

(One way ANOVA, P-Value 0.005) and XG reduces the adhesion energy by more than 50%

(One way ANOVA, P-Value 0.001).

SEM images of the cellulose, CAX, and CXG networks in Figure 6.10 show that the presence

of hemicelluloses does not substantially change the network structure in terms of fibre

orientation and the length of fibre segments spanning two contact points. This means that

when applying the system of equations 6.5 to 6.7, the b calculated for cellulose is a good

estimate for CAX and CXG networks also.

Histograms of the experimental values of s for CAX and CXG are presented in Figure 6.11.

The slope for CXG (s = 0.15N/m) is notably less than CAX and cellulose, which is

reflected in the example force-distance curve in Figure 6.8c. From the distribution of slopes

for CAX in Figure 6.11a, the slope is taken to be the same as cellulose (s = 0.36N/m). The

experimental values for s and Fpull-off are input into equations 6.5 – 6.7 to extract K0, εc, and

A. The values are presented in Table 6.1.

From Table 6.1, K0 is lower for CXG compared to cellulose and CAX. This means that the

initial contact strength is reduced when a cellulose fibre contact is mediated by XG. From

Figure 6.10c, XG coats the surface of the cellulose fibres and is prevalent at fibre-fibre

contacts. It is reasonable to suggest that XG reduces K0 by forming a layer at the interface

between cellulose fibres that has a lower modulus (less crystalline) than the cellulose fibres

themselves. The value of εc is reduced in the presence of AX and relatively unchanged in the

presence of XG. Therefore, the strain required to initiate fibre detachment via a softening of

the contact strength is smallest for a cellulose fibre contact mediated by AX and largest for


143

a

b

c

d

Figure 6.9. (a) Example force-distance curve for CAX network, (b) histogram of peak

heights measured for CAX networks, (c) example force-distance curve for CXG network, (d)

histogram of peak heights measured for CXG networks.

a b C

Figure 6.10. SEM images of (a) cellulose, (b) CAX, and (c) CXG networks with a scale bar

of 1m. Images were provided by Dr. Patricia Lopez-Sanchez.

Lateral Distance (µm)

0 1 2 3 4 5 6

Late

ral F

orc

e (

µN

)

0

10

20

30

40

Peak Height (µN)

0 5 10 15 20 25 30 35

Cou

nt

0

5

10

15

20

25

Lateral Distance (µm)

0 1 2 3 4 5 6

Late

ral F

orc

e (

µN

)

0

10

20

30

40

Peak Height (µN)

0 5 10 15 20 25 30 35

Count

0

5

10

15

20

25


144

XG. εc is a function of the pulling distance and 𝑙0, and the effect of AX and XG structure on

𝑙0 is discussed below. The adhesion energy for CAX and CXG is substantially reduced

compared to cellulose for the same value of 𝑙0. If the adhesion energy is kept constant at the

value for a cellulose-cellulose contact (with𝑙0 = 0.3 nm), the 𝑙0for CAX and CXG is 0.6 nm

and 1 nm, respectively.

a

b

Figure 6.11. Distribution of experimental values of the slope, s, for (a) CAX and (b) CXG.

Table 6.1. Model parameters extracted from equations 6.5 - 6.7 using experimental values of

slope, s, and pull-off force, Fpull-off.

Cellulose CAX CXG

b 1.5 1. 5 1.5

K0 (MPa) 130 130 32

εc 1.7 1.2 1.8

A (J/m2)

𝑙0= 0.3nm 0.06 0.03 0.02

𝑙0= 0.6nm - 0.06 0.03

𝑙0= 1nm - - 0.06

Arabinoxylans consist of a linear chain backbone of β-D-xylopyranosyl residues linked

through (14) glycosidic linkages, with α-L-Arabinofuranosyl (Araf) residues attached to

some of the backbone27. The backbone of XG is chemically identical to cellulose with β-

(14)-linked D-glucopyranose residues28. In XG from Dicotyledons and onions, D-

xylopyranose (Xlyp) residues are attached to about 60-75% of the backbone. AX and XG

Slope, s ( N/ m)

0.0 0.4 0.8 1.2 1.6 2.0

Count

0

2

4

6

8

10

Slope, s ( N/ m)

0.0 0.4 0.8 1.2 1.6 2.0

Count

0

4

8

12

16

20


145

chains on the surface of cellulose fibres are thus expected to influence the contact length, 𝑙0.

At a minimum, one glucose residue (0.5 nm)28 and one Xlyp residue (0.5 nm)29 is expected to

be separating cellulose fibres mediated by XG, giving a value of 1nm for 𝑙0 which is in good

agreement with Table 6.1. The relative amount and sequence distribution of side chain

residues of AX molecules vary depending on the source27. At a minimum, a single Xlyp

residue is expected to separate cellulose fibres mediated by AX. This is consistent with the

value of 𝑙0 around 0.6nm in Table 6.1. The equilibrium lengths of the cellulose fibre contacts

mediated by the different polymers are illustrated in Figure 6.12. The results suggest that the

adhesion energy between the cellulose fibres remains roughly constant in each case, with the

role of AX and XG instead being to change the equilibrium contact length. The contact is

modelled in ComsolTM Multiphysics as effective springs where the spring constant decays

with strain. This is equivalent to the surface energy potential decaying with separation

distance. Thus the presence of AX and XG increases the separation distance and

consequently decreases the surface interaction between cellulose fibres.

The values of the pull-off force between individual cellulose fibres in the presence of AX and

XG are consistent with the macro-scale network mechanics. The cellulose and CAX networks

Figure 6.12. Depiction of the contact between two cellulose fibres and two cellulose fibres

mediated by arabinoxylan or xyloglucan with an estimate of the respective equilibrium

contact length, 𝑙0.

behave similarly under uni-axial tension30 whereas the CXG network displays decreased

stiffness and increased extensibility10. Gu et al.31 speculate that during the biosynthesis of


146

bacterial cellulose the adsorption of XG onto the cellulose surface reduces the number of

network entanglements. However, the results from the dip-and-drag technique strongly

suggest that XG changes the interaction between cellulose fibres and reduces the modulus of

the network by reducing the adhesive force between fibres. One possible explanation for the

reduced pull-off force between cellulose fibres in the presence of XG is that the

polysaccharide forms an amorphous layer sandwiched between the cellulose fibres that leads

to a reduced contact modulus; if this is the case, a smaller force is required to separate the

fibres. In Chapter 4: Section 4.3.6 I postulate that the static friction between two cellulose

hydrogel surfaces is driven by the adhesion between individual cellulose fibres at the

interface. The static friction between pairs of cellulose hydrogels is shown to be reduced by

approximately half in the presence of XG. This follows the close to 50% reduction in the

pull-off force between individual cellulose fibres in the presence of XG.


The Dip-and-drag technique is successfully applied to extract information about the

interactive forces between cellulose fibres, and the influence of important cell wall

components at these contacts. The measured peaks in lateral force-distance curves are

interpreted as representing fibre-fibre detachment events, where the Jarzynski’s average peak

height is taken as a pull-off force. The sensitivity of this pull-off force to uncontrolled

variables in the fibre network is investigated using ComsolTM Multiphysics to simulate fibre-

fibre detachment based on a cohesive model. The variables include; network structure,

equilibrium contact length, contact strength, and critical strain. The model indicates that XG

reduces the pull-off force by decreasing the contact strength and increasing the critical strain.

This result is consistent with the increased extensibility of macro-scale CXG networks under

tensile testing, and the reduced static friction between CXG networks measured in Chapter 4:

Section 4.3.6. Based on the ComsolTM Multiphysics model and adhesion energy equation, the

presence of XG and AX increases the separation between cellulose fibres to distances that are

in good agreement with the structure (residue lengths) of the molecules. Insights into the

interactions between cellulose, AX, and XG are critical for building a 3-D mechanical model

of the plant cell wall structure and assembly.


147


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149

Chapter 7

The effect of bacterial expansins on

cellulose fibre interactions

7.1 Introduction

The key hypothesis in this thesis is that plant growth is influenced by the interactive forces

(including friction) occurring between cellulose fibres and between cells. Uncovering

potential mechanisms for these interactions provides a framework to include in multi-scale

mechanical models of the plant cell wall. A significant step towards building a multi-scale

mechanical model of plant growth is elucidating the activity of expansins. Expansin is a

protein that is implicated in initiating cell wall elongation. In Chapter 2: Section 2.2.3, I

review expansins in terms of their binding specificity and subsequent effect on the

mechanical and structural properties of plant cell walls and other cellulose substrates.

To date, the most probable mechanism of action of expansins is the disruption of cellulose

fibre contacts to promoting slippage; this is represented pictorially in Figure 7.1. Firstly,

expansins bind to cellulose and are purported to slide along the length of the cellulose fibre.

Secondly, a bound expansin is able to locally disrupt cellulose fibre contact. The final step is

that cellulose fibres and surrounding matrix polysaccharides are able to slide relative to each

other. Recent advances in our understanding of how expansins are able to achieve steps 1 and

2 in Figure 7.1 are discussed in Section 7.2. Due to the important role of expansins in cell

wall remodelling, they are required in almost all plant physiological development aspects

from germination to fruiting1. Marowa et al.1 state that “expansins, combined with other

(breeding) tools can be useful in manipulating many plant physiological aspects such as


150

germination, stem development, yield and plant’s ability to withstand biotic and abiotic

stress”. In order to use expansins for crop improvement, it is important to be able to predict

how the molecular interactions between expansins and the plant cell wall influence the cell

wall mechanics. Chapter 4 and Chapter 6 highlight the capacity of the tribo-rheological and

dip-and drag techniques to measure the interactions between cellulose fibres, AX, and XG.

The goal of this chapter is to use both techniques to investigate the effect of expansins on

cellulose fibre interactions, and at cellulose fibre contacts mediated by AX and XG.

Figure 7.1. (1) Expansin (red pacman) binds to cellulose fibres (brown lines) and slides along

the length of the fibres as shown by the arrow. (2) Expansins disrupt cellulose fibre contact

points. In Chapter 2: Section 2.2.3 there are a number of hypotheses for the action of

expansin that is depicted by the lightning bolt in this Figure. (3) Disruption at cellulose fibre

contacts leads to relative movement of fibres, as shown by the arrows, and elongation of the

cell wall.

7.2 Background on the ‘wall-loosening’ activity of expansins

In Figure 7.2, expansins are shown to consist of two compact domains (D1 and D2). There

are highly conserved surface residues spanning across both domains that make up what is

referred to as the putative polysaccharide binding site (PPBS)2. It is difficult to assess the

function of the two domains and the residues at the PPBS due to the poor heterologous

expression of plant expansins. Thankfully, bacterial expansin (YOAJ) has high structural

similarity to plant expansins and can be easily expressed in Escherichia coli to generate

protein variants (mutants)2. Key amino acid residues are modified by site-directed

mutagenesis to assess their role in the binding and wall loosening activity of the protein.


151

Georgelis et al.2 use two mechanical assays for expansin activity; the breaking force of filter

paper in Figure 7.3, and the creep rate of alkali–pre-treated wheat coleoptiles in Figure 7.4.

Figure 7.2. Protein structure of expansin, showing two distinct domains (D1 and D2), that is

interacting with a cellulose elementary fibril. Image is reproduced from Silveira and Skaf3.

Figure 7.3. Activities of selected variants of bacterial expansin protein on Whatman filter

paper measured as a breaking force. The breaking force of the control (buffer with no

expansin) and native expansin (labelled EXLX1 and equivalent to YOAJ) are marked with

horizontal lines for comparison. Reproduced from Georgelis et al.2.

The substantial decrease in the breaking force of filter paper when treated with YOAJ in

Figure 7.3 suggests that bare cellulose is a key target for wall loosening activity. The activity

of various mutant expansins in Figure 7.3 and 7.4 is found to be closely linked to their


152

measured binding affinity to cellulose substrates (cotton fibres, Avicel, and filter paper)2. Key

protein variants that assess the role of binding on wall loosening activity include:

• WWY (labelled triple in Figure 7.3 and W125A-W126A-Y157A in Figure 7.4) –

substitution of the three aromatic amino acid residues on D2 that are part of the PPBS.

• D82A – substitution of the Asp-82 residue on D1 which is part of the PPBS.

• RKKQ (labelled R173Q-K180Q-K183Q in Figure 7.4) – three positively charged

residues in D2 are replaced by neutral glutamine.

Figure 7.4. Activities of variants of bacterial expansin protein on alkali-pretreated wheat

coleoptile measured as a relative creep rate. The activity of the native expansin (YOAJ) is

marked with a horizontal line at relative creep rate of 1. Reproduced from Georgelis et al.2.

The WWY and D82A mutants show no activity for either of the assays in Figure 7.3 and 7.4.

On the other hand, the RKKQ mutant is shown to increase the creep rate of a cell wall

substrate. The replacement of 3 positive residues to neutral ones reduces the interaction

between the RKKQ expansin and pectin in the cell wall, and thus allows the expansin to


153

diffuse through the wall and bind to cellulose more freely2. This is supported by the results of

a binding assay for expansin variants in which 1, 2, or 3 positively charged residues are

replaced with neutral ones. The variants’ binding to wheat coleoptile cell walls decreased

proportionally to the number of positive charges that were replaced.

According to Georgelis et al.2, the YOAJ structure (Protein Data Bank code 3D30) reveals

that the side chains of the three residues mutated in WWY are twisted in a clockwise

direction, which suggests that D2 binds to a single glucan chain on the surface of the

cellulose fibre. The authors postulate that YOAJ “may induce wall creep when these residues

bind a glucan that is part of the load-bearing network in the cell wall, distorting its shape and

allowing physical slippage at the junction if the wall is in tension”2. This interpretation of the

structure of the PPBS is supported by Silveira and Skaf3 who use molecular dynamics

simulations to show that YOAJ can “hydrogen bond a free glucan chain in a twisted

conformation and that the twisting is chiefly induced by means of residue Asp82 located on

D2”. Furthermore, their results suggest that YOAJ can slide along the hydrophobic surface of

crystalline cellulose via D2 and simultaneously disrupt hydrogen bonds by twisting glucan

chains through D13.

The structure of the cellulose used for mechanical assays is critical because the action of

expansin is likely to be through the binding to a single glucan chain rather than the flat,

highly crystalline cellulose surface. Part of the amorphous or paracrytalline phases of

cellulose may be removed for substrates that have been mechanically or chemically treated,

such as Avicel and filter paper. Chapter 6: Section 6.1 compares the structure of plant and

bacterial cellulose fibres and highlight that bacterial cellulose is a good model system for

plant cellulose as it possesses the same paracrystalline surface layer surrounding the

crystalline core. Moreover, in this thesis I have developed two techniques that measure the

interaction between bacterial cellulose fibres. The first is the tribo-rheological technique that

is detailed in Chapter 3: Section 3.2.1 and measures the static friction between two cellulose

hydrogels that is driven by cellulose fibres interacting at the interface. The second is the Dip-

and-drag technique in Chapter 3: Section 3.2.2 which is applied to measure the pull-off force

between individual bacterial cellulose fibres and at contacts mediated by AX and XG. In this

chapter, both of the techniques are used as mechanical assays to gain insight into the activity

of bacterial expansins on bacterial cellulose substrates. The native expansin and the protein

variants denoted WWY, D82, and RKKQ, are included in this study for a comprehensive


154

structure-function analysis. Key findings from the bacterial system provide insights into the

mechanism of action of plant expansins during plant growth.


7.3.1 Pre-treatment of bacterial cellulose hydrogels

Bacterial cellulose hydrogels are grown by the Cosgrove lab at Pennsylvania State University

using a similar procedure to that described in Chapter 3: Section 3.1, and cultivated in 12-

well plates to give 25mm diameter hydrogels. The harvested hydrogels are then boiled in

deionised water for 1 hour and rinsed repeatedly to ensure all bacteria is removed from the

cellulose network and is not available as a substrate for expansins. Due to the high water

content (> 99%), the average weight of the hydrogels is measured and taken, based on

density, as the volume of water (~ 2 mL). The native and variant expansins are stored as

concentrated solutions (order of 10 g/L) in 20mM Hepes buffer (pH 7.5). Therefore, the

large volume of water in the hydrogels means that an impractically small volume of the stock

solution is required to be added to give a working concentration of expansin in 20 mM Hepes

buffer (pH 7.5) of 200 g/mL. Pipetting a small volume of concentrated expansin solution

directly onto the hydrogel surface means that it would take a long time for the expansin to

diffuse and reach a constant concentration throughout the hydrogel. Therefore, the bacterial

cellulose hydrogels are compressed to remove a fraction of the water so that the expansin

solution can be diluted and added to the hydrogel in larger volumes. Four hydrogels were

placed between 2 perspex plates under a load of 70 g for 4 hours. The compressed hydrogels

weigh ~ 400 mg, so the volume of water in the hydrogels is ~0.4mL. The compressed

hydrogels are then placed in a 12-well plate, one hydrogel per well. The stock solutions of

expansin are accordingly diluted up to a volume of 1.6 mL (uncompressed – compressed

volume) to give a final concentration of expansin in 20mM Hepes buffer (pH 7.5) of 200

µg/mL once added to the compressed hydrogels. The larger volume of diluted expansin

solution is added to the wells to imbibe the hydrogel. The 12-well plate with the lid on is

wrapped in Parafilm to prevent evaporation, and left on a see-saw platform shaker in a 4°C

cold room overnight. The hydrogels are observed to re-swell to approximately 75% of the

initial hydrogel thickness (prior to compression) as the surrounding expansin solution is

absorbed.


155

7.3.2 Mechanical assay of expansin activity using the tribo-rheological

technique

The tribo-rheological technique is carried out using a Discovery Hybrid Rheometer HR-3

(TA Instruments) with a 25mm parallel plate and the bottom peltier plate. 25mm discs of

emery paper are attached to the plates with double sided tape and the hydrogels are glued to

the emry with cyanoacrylate glue. The procedure outline in Chapter 3: Section 3.2.1 is

followed, with the only modification being an axial ramp distance of 250 µm rather than 500

µm. For these experiments the hydrogels are not surrounded by water because the

concentration gradient would drive expansins to diffuse out of the hydrogel. However, during

compression fluid is squeezed out of the gels and surrounds the interface, and evaporation is

not expected to change the concentration of expansins within the measurement time. All

expansins (YOAJ, WWY, D82, and RKKQ) treatments are tested on different cellulose

hydrogel pairs in triplicate, and a control hydrogel pair treated with buffer and no expansin is

tested on each day of experimentation.

7.3.3 Mechanical assay of expansin activity using the Dip-and-drag

technique

The dip-and-drag technique is applied to bacterial cellulose networks as described in Chapter

3: Section 3.2.2. The only deviation from these detailed steps is that instead of water, the

measurements are carried out in either 20 mM Hepes buffer (pH 7.5) for the control, or 200

g/mL of YOAJ in 20 mM Hepes buffer (pH 7.5).

7.4 Results

7.4.1 The effect of bacterial expansins on the mechanics of bacterial

cellulose hydrogels

The first step of the tribo-rheological technique is to compress the hydrogel pair to a constant

axial strain, which is calculated as a compression ratio and denoted CR. The volume of the

hydrogel is decreased during compression, leading to an increase in the interstitial fluid

pressure that drives the flow of water out of the network. Thus the mechanics of the hydrogel

during compression is determined by the poroelasticity, or the interplay between the

interstitial fluid and the solid matrix as discussed in Chapter 4: Section 4.3.1. In Figures 7.5a


156

and 7.5b, the compressive mechanics of cellulose hydrogels treated with native (YOAJ) and

mutant (WWY, RKKQ, D82) expansins are presented with the control (buffer, no expansins)

hydrogels grown from the same batch of fermentation medium. In Figures 7.5c and 7.5d, the

measured normal stress during compression is divided by the peak value for a given sample

from Figures 7.5a and 7.5b so that the shape of the curves can be accurately compared. There

is no observable difference in the compression behaviour, which indicates that expansins

don’t influence the poroelasticity of the cellulose network. In Chapter 4: Section 4.3.2 I show

that the area of contact between hydrogels is determined by their axial modulus. From Figure

7.5, the axial modulus of all samples is the same, so the true contact area for all samples is the

same and the results can be directly compared to investigate the effects of native and mutant

expansins on the surface interactions. After the hydrogel pairs are brought into compressive

contact and the normal stress is allowed to relax to its equilibrium value, the viscoelastic

moduli of the system are measured using SAOS. The G’ and G” measured at 1 Pa and 1Hz

for different CR are presented in Tables 7.1 and 7.2. Table 7.1 includes the results for a

hydrogel pair treated with YOAJ expansin and an untreated hydrogel pair from the same

formation batch, compressed through a range of CRs. Table 7.2 includes the results for

hydrogel pairs treated with WWY, RKKQ, D82, and an untreated hydrogel pair from the

same formation batch, compressed through a range of CRs. Each treatment (YOAJ, WWY,

RKKQ, D82) is tested in triplicate and the results for only one replicate are included in

Tables 7.1 and 7.2. From the results in Tables 7.1 and 7.2 there is no substantial difference in

the G’ and G” between the hydrogels treated with expansins and the untreated controls, above

what could be attributed to variation between sample replicates.

In Chapter 4: Section 4.3.1 I show that compression leads to the formation of new fibre

contacts within the cellulose network. Furthermore, I show that G’ scales with cellulose

concentration, and postulate that an increase in the cellulose concentration directly increases

the probability that fibres in the network will come into contact and adhere together. From the

results in Table 7.1 and 7.2, expansins do not appear to influence G’ and therefore are not

expected to effect the cellulose network architecture. Note, the hydrogels are pre-compressed

under a fixed weight before re-swelling in expansin solution. Therefore, some cellulose fibre

contacts may be formed during the pre-compression step in the absence of expansin. After the

pre-compression step, expansins are added and the hydrogels are compressed again before the

G’ is measured. Expansin are shown to have negligible influence on the compression


157

mechanics in Figure 7.5. Thus it is expected that the cellulose network structure after the pre-

compression step dominates the G’ measured in Tables 7.1 and 7.2.

a

b

c

d

Figure 7.5. Compression curves of (a) cellulose hydrogel pair treated with the native (YOAJ)

expansin and, (b) cellulose hydrogel pairs treated with mutant expansins (WWY, RKKQ, and

D82). In (a) and (b) the compression curve for untreated hydrogels from the same batch of

fermentation medium is included as the control. (c) The compression curves in (a) are

normalised against their peak normal stress value. On the y-axis the measured normal stress

is divided by the peak value of the respective curve from (a). (d) The compression curves in

(b) are normalised against their peak normal stress value. On the y-axis the measured normal

stress is divided by the peak value of the respective curve from (b).

Time (s)

0 2 4 6 8

Norm

al S

tress (

kP

a)

0

2

4

6

ControlYOAJ

Time (s)

0 2 4 6 8

Norm

al S

tress (

kP

a)

0

2

4

6

Mutants ControlWWYRKKQD82

Time (s)

0 2 4 6 8

Norm

al S

tress/P

eak N

orm

al S

tress

0.0

0.2

0.4

0.6

0.8

1.0ControlYOAJ

Time (s)

0 2 4 6 8

No

rma

l S

tre

ss/P

ea

k N

orm

al S

tre

ss

0.0

0.2

0.4

0.6

0.8

1.0

Mutants ControlWWYRKKQD82


158

Table 7.1. The storage (G’) and loss (G”) moduli of hydrogel pairs that are untreated or

treated with YOAJ expansin are measured using SAOS at 1 Pa and 1 Hz. G’ and G” are

measured across a range of CR.

CR Control (no expansins) YOAJ

G’ G” G’ G”

0.08 380 ± 6 50± 0.4 310 ± 4 50 ± 0.2

0.15 420 ± 3 50± 0.7 340 ± 2 50 ± 0.5

0.23 430 ± 2 50± 0.6 390 ± 2 60 ± 0.7

0.31 480 ± 4 60± 0.5 470 ± 3 70 ± 0.6

0.38 550 ± 3 70± 1 590 ± 4 90 ± 1

0.46 680 ± 3 90± 0.7 770 ± 5 120 ± 1

0.54 910 ± 5 130± 3 1100 ± 7 180 ± 2

Table 7.2. The storage (G’) and loss (G”) moduli of hydrogel pairs that are untreated or

treated with expansin variants (WWY, RKKQ, D82) are measured using SAOS at 1 Pa and 1

Hz. G’ and G” are measured across a range of CR.

CR Control (no

expansins)

WWY RKKQ D82

G’ G” G’ G” G’ G” G’ G”

0.1 210 ± 3 40 ± 0.4

0.2 340 ± 3 50 ± 1 260 ± 3 40 ± 1 320 ± 6 50 ± 0.4

0.3 480 ± 3 80 ± 1 520 ± 3 80 ± 1 460 ± 4 90 ± 1 650 ± 7 100 ± 1

0.4 810 ± 5 130 ± 1 810 ± 4 120 ± 2 730 ± 5 140 ± 1 930 ± 9 140 ± 2

0.5 1400 ± 7 230 ± 2 1300 ± 9 190 ± 4 1000 ± 7 200 ± 2 1400 ± 12 200 ± 2

0.6 2500 ± 12 380 ± 6 2000 ± 15 380 ± 8 2300 ± 18 340 ± 7

7.4.2 The effect of bacterial expansins on the friction response between

pairs of bacterial cellulose hydrogels

After the compression and SAOS steps the hydrogel pairs are sheared at a constant rotation

rate. For approximately equivalent G’, which is a measure of cellulose concentration, the

shear stress curves in the presence of expansins are compared in Figure 7.6. The initial slope

of the curves show non-linear behaviour, but the shape of the curves for expansin treated

hydrogels is similar to the respective control. Thus the shear mechanics of the system appear

to be unaffected by expansins. The shapes of the curves also display either stick-slip or


159

stiction behaviour as discussed in Chapter 4: Sections 4.3.3 and 4.3.7. The stick-slip peaks

are less pronounced and consistent in Figure 7.6 compared to those in Figure 4.26a. In

Section 4.3.7, the parameters of the stick-slip peaks are shown to be related to the ability of

the rheometer to control the angular velocity around the set point. The Haake Mars III

rheometer used in Chapter 4 is a controlled stress machine, whereas the Discovery HR-3

rheometer used in this chapter can operate as a controlled stress or controlled strain machine.

The Discovery HR-3 machine in controlled strain mode is expected to be able to control the

angular velocity at the set point better than the Haake Mars III, which explains the less

pronounced stick-slip response in Figure 7.6 compared to Figure 4.26a. During the stick cycle

the cellulose fibres at the interface between the hydrogels are purported to adhere together

and during the slip cycle it is expected that the fibres are separated. Stiction behaviour is

observed for CXG composite hydrogels in Section 4.3.3, and is proposed to be due to the XG

coating the surface of the cellulose fibres reducing re-adhesion between cellulose fibres at the

interface under dynamic conditions. With this interpretation in mind, the results in Figure 7.6

indicate that the presence of expansins (YOAJ, RKKQ, and D82) reduces re-adhesion of

cellulose fibres at the interface during sliding.

a

b

Figure 7.6. Shear stress over time for a constant rotation rate for the (left) native and (right)

variant expansin proteins with the corresponding controls for samples with comparable G’

(cellulose concentration).

The interfacial yield stress is taken as the peak in the shear stress curve measured during the

constant rotation rate step of the tribo-rheological procedure, as in Chapter 4: Section 4.3.3.

In Figure 7.7, the interfacial yield stress is plotted against G’ for representative cellulose

Strain (-)

0.0 0.5 1.0 1.5

Shear

Str

ess (

Pa)

0

50

100

150

ControlYOAJ

Strain (-)

0.0 0.5 1.0 1.5

Shear

Str

ess (

Pa)

0

50

100

150

ControlWWYRKKQD82


160

hydrogels treated with YOAJ, WWY, RKKW, D82, and controls. The interfacial yield stress

and G’ for the triplicate samples of each treatment are included in Appendix O. The control

data is fitted with a power law regression with exponent 0.8, which is equivalent to the linear

scaling of the interfacial yield stress at the true contact area with cellulose concentration

based on Chapter 4: Figures 4.19 and 4.24. For an equivalent G’ (cellulose concentration),

the presence of expansins reduces the interfacial yield stress between hydrogels. This means

that expansins either reduce the probability that fibres at the interface form adhesive contacts,

or reduce the adhesive force between cellulose fibres interacting at the interface.

a

b

Figure 7.7. Interfacial yield stress against G’ for pairs of bacterial cellulose hydrogels treated

with (a) native (YOAJ) and (b) mutant expansins (WWY, RKKQ, D82). The data for the

respective control (buffer, no expansins) samples is included in each graph. Each data set is

for a single pair of hydrogels that is representative of the behaviour of the replicates. The line

in each graph is a power law regression fitted to the control data with a fixed exponent of 0.8.

The control data in Figure 7.7a is interpolated to approximate the interfacial yield stress at the

same discrete values of G’ as the YOAJ data. The measured interfacial yield stress (τm) for

YOAJ treated samples is then divided by the interfacial yield stress approximated for the

control (τcontrol) at the same G’, to give a relative interfacial yield stress (IYSR) as in Equation

7.1. This process is repeated for the WWY, RKKW, and D82 using the control data in Figure

7.7b. The IYSR values for each expansin are averaged across the triplicate samples and range

of CR, and are presented in Figure 7.8. All expansins appear to reduce the interfacial yield

stress compared to the respective control, as shown by an IYSR is less than 1. Based on a

One-way ANOVA test, YOAJ, RKKQ, and D82 give a statistically significant decrease in the

interfacial yield stress compared to the control (marked with an * in Figure 7.8). Importantly,

G' (kPa)

1

Inte

rfacia

l Y

ield

Str

ess (

Pa)

100

ControlYOAJ

G' (kPa)

0.1 1

Inte

rfa

cia

l Y

ield

Str

ess (

Pa

)

10

100

ControlWWYRKKQD82


161

the results presented in Figure 7.8 highlight that the activity of YOAJ, RKKQ, and D82 lead

to a decrease in the apparent static friction between cellulose hydrogels that is not due to

relative differences in the G’. Thus, these expansins are expected to influence the interfacial

properties by reducing the probability that fibre contacts form at the interface, or by reducing

the adhesion between fibre contacts at the interface. It is noted here that putatively effective

(YOAJ, RKKQ) and ineffective (D82) expansins both have an effect and there is no clear

pattern in their activity.

𝐼𝑌𝑆𝑅(𝐺′) =𝜏𝑚(𝐺

′)

𝜏𝑐𝑜𝑛𝑡𝑟𝑜𝑙(𝐺′)

(7.1)

Figure 7.8. IYSR is the interfacial yield stress measured in the presence of expansin (YOAJ,

WWY, RKKQ, D82) divided by the interfacial yield stress for the control sample at the same

G’, which is approximated by interpolating the measured control data. The results are

averaged across the triplicate samples and the range of CR and the standard deviation is

included as an error bar. * denotes the samples for which the measured interfacial yield stress

is statistically different from the control from a One-Way ANOVA test with a significance

value of p < 0.05.

7.4.3 The effect of bacterial expansins on adhesion between cellulose fibres

In Chapter 6: Section 6.3.3 the Dip-and-drag technique is used to measure the adhesion

between cellulose fibres mediated by XG. The presence of XG is found to reduce the

adhesion between cellulose fibres by approximately half. The same experiments are carried

out on cellulose and composite (CAX, CXG) networks in the presence of YOAJ expansin,

following the method in Section 7.2.3. The pull-off force between fibres is calculated from


162

the Jarzynski’s average of the distribution of peaks as described in Chapter 5: Section 5.3.1.

The pull-off force in the presence of YOAJ is divided by the value in the absence of

expansins to give a relative pull-off force, and is presented in Figure 7.9. Raw data from the

dip-and-drag experiments on Cellulose, CAX and CXG networks with and without YOAJ

expansin are included in Appendix P. The histograms of peak heights from the raw data for

Cellulose, CAX and CXG networks with and without YOAJ expansin are included in

Appendix Q. YOAJ expansin is observed to have no activity in reducing the adhesion

between cellulose fibres or a cellulose fibres contact mediated by AX, whereas a small

decrease in the pull-off force is observed in the presence of YOAJ for CXG. In Figure 7.9,

the present of YOAJ seems to increase the pull-off force measured for a cellulose network. It

is unclear why this would be the case and complex statistical analysis of the distribution of

peak heights may be more revealing than the Jarzynski’s averaging method from Chapter 5:

Section 5.3.1. However, changing the type of analysis would require validation using model

systems similar to the level of detail in Chapter 5 and this is outside of the scope of this

thesis. One-way ANOVA of the population of the different networks (cellulose, CAX, and

CXG) are compared in the presence and absence of YOAJ, and no statistical difference in the

means is observed (with significance value of 0.05).

From the results in Figure 7.9, there is no evidence that YOAJ expansin reduces the adhesion

between cellulose fibres. This supports the mechanism of action whereby YOAJ reduces the

probability that cellulose fibres form contacts. However, there are limitations with comparing

the results from the dip-and-drag technique to the tribo-rheological technique for measuring

the friction between hydrogels. The dip-and-drag technique investigates the effect of

expansin on cellulose fibre contacts in a preformed network, whereas the tribo-rheological

technique measures the influence of expansins on forming new cellulose contacts. Therefore,

expansins may influence the adhesion between contacts as they are forming but not after they

are already formed. Additionally, as part of the preparation of substrates for the dip-and-drag

technique, the cellulose network is air-dried before gluing to the glass substrate. The moisture

level in the network after air drying is unknown. Depending on the level of drying, the

structure of the normally hydrated paracrystalline surface layer of cellulose fibres may be

affected, consequently reducing the ability of expansins to bind to the fibres. Expansin

activity has been measured on filter paper substrates which are dried during processing,

although the cellulose material is also subjected to other chemical and mechanical processes

that are likely to change the nature of cellulose fibre contacts. This filter paper result suggests


163

that the paracrystalline surface layer may not be crucial for the binding of expansins to

cellulose fibres. Thus it is unclear why there is no observable effect of YOAJ on the pull-off

force between cellulose fibres measured using the dip-and-drag technique.

Figure 7.9. The pull-off force is calculated from the Jarzynski’s average of the population of

experimentally measured peak heights in the force-distance curves from the dip-and-drag

technique. The pull-off force in the presence of YOAJ is normalised against the value in the

absence of YOAJ for cellulose (C), CAX, and CXG networks.

7.5 Discussion

The WWY mutant does not bind to cellulose2 and has no significant effect on the interfacial

yield stress in Figure 7.8. Figure 7.8 indicates that D82 has the highest activity followed by

YOAJ and RKKQ, and all of these expansins reduce the interfacial yield stress such that it is

statistically different from the control. This is an unexpected result as YOAJ and RKKQ are

putatively effective and D82 is a putatively ineffective expansin, yet this does not appear as a

clear trend in these experimental outcomes. Due to the low concentration of expansins

required for the observed activity, it is improbable that there would be sufficient surface

coverage of expansins bound to cellulose to directly prevent fibre contact. Silveira et al.3

suggest that D2 allows the expansin protein to slide along cellulose fibres as D1 introduces a

structural defect in one of the glucan chains on the surface. D82 has a mutation on D1.

However, the functioning D2 may permit the expansin to rapidly move along the cellulose

fibres and reduce the probability that the fibres form contacts at the interface, thus reducing

the interfacial yield stress. When both D1 and D2 are functioning, as for YOAJ and RKKQ,

C CAX CXG

Rela

tive p

ull-

off forc

e

0.0

0.2

0.4

0.6

0.8

1.0

1.2


164

the surface glucan chain that has undergone a conformational change is expected to behave

similarly to a XG chain mediating a cellulose fibre contact. In Chapter 6: Section 6.3.3, XG

is shown to reduce the adhesion between cellulose fibres by reducing the contact strength and

increasing the separation between the cellulose fibres in contact. By inducing a 90-degree

twist in a surface glucan chain3, I propose that expansins increase the separation distance

between cellulose fibres in contact, compared to when the surface chain is in planar

conformation.


The activity of native expansin (YOAJ) and protein variants (WWY, RKKQ, D82) on

bacterial cellulose hydrogels is measured using two mechanical assays: the tribo-rheological

technique in Chapter 4, and the dip-and-drag technique in Chapter 6. The WWY variant

shows no activity for either assays, which is attributed to a mutation of the binding site that

prevents binding to cellulose. YOAJ, RKKQ, and D82 reduce the surface interaction between

cellulose hydrogels measured using the tribo-rheological technique.

Previous mechanical assays of these expansin’s activity include creep tests and tensile tests2.

Based on these tests the expansins are described as having ‘loosening’ or ‘weakening’

activities, however the exact mechanistic detail is unclear. The advantage of the tribo-

rheological test as an assay is that, through the computation model in Chapter 4: Section

4.2.3, the measured results can be interpreted in terms of what is physically occurring at the

interface. The results from the tribo-rheological test lead to two clear hypotheses for the

activity of expansins.

(1) Prevent the formation of new contact between cellulose fibres.

(2) Reduce the adhesion between fibres that come into contact.

There are two mechanisms of action that could explain these 2 hypotheses. The first is that,

through D2, the expansins attach to cellulose fibres and move rapidly along the length of the

fibres such that there is a high probability that the expansin will get in the way of

approaching cellulose fibres. The second is that expansins attach to cellulose fibres and,

through D1, cause a structural defect in one of the surface glucan molecules. The

conformational change in the surface glucan is proposed to reduce the adhesion between

fibres by reducing the contact modulus and increasing the separation distance between

cellulose fibres. The results are largely consistent with the recent model of expansin action,


165

whereby expansins bind to cellulose and introduce a conformational change in a single

surface glucan chain along the fibre2-4. Structural similarity between plant and bacterial

sources of cellulose and expansins means that key learnings from this study provide insights

into the mechanism of action of plant expansins on cell walls during plant growth.


166


1. P. Marowa, A. M. Ding and Y. Z. Kong, Plant Cell Reports, 2016, 35, 949-965.

2. N. Georgelis, A. Tabuchi, N. Nikolaidis and D. J. Cosgrove, Journal of Biological

Chemistry, 2011, 286, 16814-16823.

3. R. L. Silveira and M. S. Skaf, Physical Chemistry Chemical Physics, 2016, 18, 3510-

3521.

4. A. Lipchinsky, Acta Physiologiae Plantarum, 2013, 35, 3277-3284.

167

Chapter 8

Concluding Remarks and Future

Work


The primary objective of this thesis is to investigate the individual contributions of plant cell

wall components and their assembly on the lubrication of moving surfaces at multiple length

scales during plant growth. Based on an extensive review of the literature on plant cell wall

architecture, mechanics, and growth processes, key tribological contacts that are considered

to be important for elongation growth are identified. The tribological contacts comprise of the

sliding interface between adjacent elongating cell walls that are typically mediated by a

pectin rich middle lamella layer, and the contact between cellulose fibres and other matrix

polymers that move relative to each other as cell walls extend. Using bacterial cellulose

hydrogels as cell wall analogues, two techniques are developed to probe these tribological

contacts.

A tribo-rheological technique is developed in a rotational rheometer and is used to measure

the in situ mechanical properties and friction behaviour at the interface between cellulose

hydrogels, which is akin to the contact between adjacent cell walls. Pairs of hydrogels are

brought into compressive contact in a solvated environment and then sheared. Due to the

poroelasticity of cellulose hydrogels, a pressure gradient develops along the interface upon

compression and leads to a region of fluid in the centre surrounded by an annulus of surface

contact. Thus, the shear forces measured at the interface are due to a combination of the

viscous forces of the solvent and the adhesion between the hydrogel surfaces that are in

CHAPTER 8. CONCLUSIONS Grace Dolan, PhD Thesis

168

contact. A computational simulation of the experiment is performed in order to predict the

thickness of the solvent film and the contact area at the interface. The contact area is sensitive

to the axial modulus of the hydrogels and the viscosity of the solvent. The interfacial yield

stress (or static friction) at the true contact area is shown to linearly scale with the

concentration of cellulose fibres at the interface. Thus the interfacial yield stress is a measure

of the interactive forces between cellulose fibres. The cellulose-XG composite shows a

reduced interfacial yield stress for the same cellulose concentration compared to the cellulose

and cellulose-AX composite hydrogels. This result indicates that XG reduces the adhesion

between cellulose fibres.

The potential lubricating role of pectin at the interface between sliding surfaces is

investigated using the tribo-rheological technique by compressing a viscous pectin film

between cellulose hydrogel pairs prior to shearing the surfaces. Increasing the pectin

concentration, and thus the solvent viscosity, is shown to reduce the interfacial yield stress by

directly reducing the contact area between the hydrogel surfaces. Pectin has a complex

concentration gradient and distribution of structures within the plant cell wall. A pectin rich

layer is typically observed at the interface between adjacent plant cell walls and the range of

structures is such that pectin can exist in solution or in a cross-linked gel with calcium. From

the results presented in this thesis it is inferred that pectin in solution decreases the contact

area and thus the shear forces between adjacent elongating cell walls. Enzymes that

modulated pectin structure in the middle lamella layer control the viscosity and can therefore

modulate the interfacial separation between neighbouring cell walls.

A dip-and-drag technique is developed using the AFM to directly measure the adhesive

interactions between individual cellulose nano-fibres in a network. The technique is

successfully validated using model electrospun polymer fibres by comparing experimental

adhesive forces to theoretical predictions based on DLVO interactions (Chapter 5: Section

5.3.3). The dip-and-drag method applied to bacterial cellulose and composite networks

reveals a reduced adhesive force at cellulose fibre contacts that are mediated by XG, whereas

AX has no effect. This is in agreement with the results from the tribo-rheological technique.

Fibre detachment simulations in silico show that XG reduces the contact strength, which

decreases the measured adhesion force. Furthermore, for a cellulose fibre contact mediated by

XG, the computational model predicts a separation distance between the fibres that matches

the length of the repeating unit in a XG molecule.


169

XG and AX interact differently at cellulose fibre contacts. Both polymers adsorb to cellulose

fibre surfaces, and it is expected that there is some competitive binding. XG reduces the

adhesion at fibre contacts, particularly under dynamic conditions when the cellulose fibres

are in relative motion as the cell wall extends. On the other hand, AX does not change the

adhesion between cellulose fibres but prevents XG from adsorbing to the fibre surface. The

relative synthesis of XG and AX and their incorporation into the cell wall structure can thus

modulate the overall mechanics of the plant cell wall.

Both the tribo-rheological and dip-and-drag techniques are used as mechanical assays for

assessing the activity of bacterial expansins on bacterial cellulose. Expansins have no

measurable effect on the adhesive interactions between cellulose fibres using the dip-and drag

technique. However, expansins reduce the interaction between cellulose fibres at the interface

between hydrogels. The implication of these findings is that expansins effect the formation of

new fibre contacts, but don’t act on pre-formed fibre contacts. However, the results from the

dip-and-drag technique are limited by the fact that the cellulose network is partially dried

during substrate preparation. Drying potentially changes the structure of cellulose fibre

contacts, making them inaccessible for expansin action. The results from the tribo-rheological

technique are consistent with the most recently proposed mechanism of action of expansins.

Expansins are purported to change the conformation of a single glucan chain on the surface

of a cellulose fibre. This surface chain appears to act similarly to a XG molecule mediating a

cellulose fibre contact based on the results from the tribo-rheological technique.

8.2 Recommendations for Future Work

In this thesis, the role of individual cell wall components on the interaction between cellulose

fibres has been investigated. The next step is to consider the influence of cell wall

components in combination. The relative concentrations of AX and XG in bacterial cellulose

model systems should be systematically varied to capture the complexity of the plant cell

wall composition and structure. Finally, the influence of gelled (calcium cross-linked) pectin

on the poroelastic mechanics of the cell wall and the interaction between cellulose fibres

should be investigated.

The dip-and-drag and tribo-rheological techniques developed in this thesis are shown to be

promising assays for the activity of bacterial expansins on bacterial cellulose substrates. This

is the key recommended area for future work, where a more comprehensive use of these


170

techniques may be revealing in terms of the exact mechanistic detail of expansin action.

Firstly, the dip-and-drag technique should be applied to never-dried cellulose networks. This

will involve refining the method of gluing the cellulose networks to the glass substrate. One

idea would be to grow networks in a shape that will allow sections of the network to be dried

and glued, whilst the rest of the network is kept hydrated. An example of this is illustrated in

Figure 8.1. Furthermore, advanced statistical analysis of the peak heights in the force-

distance curves collected in the absence and presence of expansins may be able to pick up

more subtle differences that are not detected with the Jarzynski’s equality averaging. Finally,

the dip-and-drag technique should be applied to bacterial cellulose networks that are grown in

the presence of expansins. This will provide further evidence for determining whether

expansins prevent cellulose fibre contacts or reduce the adhesion between cellulose fibre

contacts. The tribo-rheological technique gives a qualitative indication of the formation of

new fibre contacts within a hydrogel after compression (Chapter 4: Section 4.3.1). Thus if

sufficient volumes of expansins are available to add to uncompressed hydrogels, the effect of

expansins on the formation of new cellulose fibre contacts during compression can be

investigated.

Figure 8.1. Design for shape of cellulose networks grown in PDMS mould (of the same

shape). The circles on the ends can be dried and glued whilst the length of the rectangular

section in the middle is long enough to add a water droplet and keep hydrated. The size of the

circle should be large enough to manually glue to the glass substrate.

Key findings from this thesis and the results from the recommended future work should be

used to build a multiscale 3-D model of plant cell wall mechanics and growth. The


171

descriptive model should have the capability of predicting the mechanical response to

deformation, and the effect of changes in the wall composition and assembly. This would

include the activation of expansins, or enzymes that modulate pectic polysaccharide structure.

The direct visualisation of plant tissue during plant growth and other deformations may be

useful for model validation. For example, monitoring the thickness of the middle lamella

layer as the pectin structure is modified through enzyme action would be informative for

confirming the relationship between solvent viscosity and surface contact between adjacent

cell walls.

172

Appendices

Appendix A: Producing bacterial cellulose from

Gluconacetobacter xylinus

DAY 0

50% D-Glucose solution preparation

1. Dissolve 25 g D-Glucose into 50 mL Milli-Q water (adding the glucose little by little while it

is stirring, leave the solution stirring until totally dissolved)

In laminar flow, sterilize the 50% D-glucose solution by using 0.2 μm filter. Keep the sterilized 50%

D-glucose solution in the fridge.

Bacteria Revival

For 100mL of HS medium:

- Peptone = 0.5g

- Yeast Extract = 0.5g

- Na2HPO4.2H2O = 0.338g

- Citric acid = 0.115g

- Glucose (50%) = 4mL

- dH2O = 96mL

1. Prepare 100mL HS medium, add 1.5g agar, then autoclave.

2. After autoclaving, when the temperature is about 700C, add in 4 mL 50% D-glucose solution

into each HS-agar medium.

3. Pour a certain amount of liquid HS-agar medium into 90 mm petri dish and leave them on the

bench to make solid. 100 mL is good for 6 or 7 plates.

4. It will form a solid plate in around 30 min to 1 hr. Use 2 plates for revival and keep the rest 5

plates for subculture.

5. Prepare some ice in a small plastic beaker (from level 3). Take a whole tube of beads (where

we store the ATCC53524) from -80 °C freezer and place the tube into ice immediately.

6. In the laminar flow, use a needle to bring one bead out and put into the agar plate. Use loop to

spread the bead on one corner of the agar plate.

7. Change the side of the loop or change to a new loop every time when change corner (see

figure below).

APPENDICES Grace Dolan, PhD Thesis

173

8. Put the plate upside down and cultivate into 30 °C incubator for 48-72 hr.

***Make sure that the incubator fan is turned off.

***Revival plates last a month, only 2 subcultures from a revival plate is recommended or

you could subculture once from the first subculture (i.e. maximum of 2 passages).

Subculture (48 or 72hours after revival)

1. 9 am bring all the plate out from the fridge to warm up (either put them on the bench of the

laminar flow or in the incubator)

2. 10am take one loop of bacteria from the revival plate and spread it onto a new plate to finish

subculture. Repeat the same movement as revival.

DAY 1

Preparing HS Medium

For 300mL of medium:

- Peptone = 1.5g

- Yeast Extract = 1.5g

- Na2HPO4.2H2O = 1.014g

- Citric acid = 0.345g

- Glucose (50%) = 12mL

- dH2O = 288mL

**make 2x concentrated for composites

1. Weigh dry materials directly into a 500mL glass beaker on the open balance in the following

order: Na2HPO4.2H2O, citric acid, YE, peptone (make sure you replace the parafilm on the

containers of the last two materials). Note: you should wipe spatula with paper towel between

measuring different materials and you need to change spatula if the dry powder does not wipe

off completely.

2. Turn MilliQ water on and let it run until it reads 18.2. Using a measuring cylinder add

approximately 200 mL (or some volume that is less than the total volume needed) of milliQ

water to beaker containing the dry powders and a magnetic stirring bar. Turn the stirrer on as

the first bit of water is added. Mix until dissolved.

3. Calibrate pH meter if required. Wash pH probe with distilled water (make sure you do not get

water above the black line on the probe) and dry with kimwipes. Place probe in the medium

(should generally get a reading around the 6.2 mark). Add drops of 1M HCl to bring the pH

reading down to 5.


174

4. Add contents of the beaker to the measuring cylinder (can use another magnetic stirrer bar in

order to hold the stirrer inside the beaker to the bottom making it easier to pour out the

medium) and then add additional milliQ water to get the volume up to 300 mL. Pour the

contents of the measuring cylinder back into the beaker and put back on stirrer. Adjust the pH

so it’s 5 again (this should require no more than a few drops).

5. Pour the medium into a schott bottle and leave the lid so that it is not tight. Cover the lid with

alfoil, put a strip of autoclave tape on the bottle and label.

6. Place in autoclave.

Preparing AX solution

(AX solution is used to prepare a cellulose-AX composite network, the procedure is the same for XG

to prepare a cellulose-XG composite)

7. Prepare a bottle of water for autoclaving to be later used for dissolving AX. Rinse 500mL

Schott bottle and fill to the 400mL mark. Autoclave for 15min.

8. Need a 500mL Schott bottle autoclaved the day before (or a few days before). Take out the

autoclaved 500mL Schott bottle and allow to stand at room temperature so that it is not hot

when you are weighting the AX powder.

Labelling primary and scale up containers

9. Whilst autoclave is running start labelling containers required for primary inoculum and

scale-up. Label primary with: HS, 10, date of primary inoculum, initials, 1

0 on the lids. Label

scale ups with: HS, #no., date of scale up, initials, #no. on the lids.

Primary Inoculum

BC BC composite

4 x 70mL containers

filled with 10mL HS

medium

4 x 70mL containers filled

with 20mL HS medium

Scale up

o Cellulose hydrogel

70mL container (φ=41mm)

Primary Inoculum 1mL

HS medium 9mL

o Composite hydrogel (with AX or XG)

70mL container (φ=41mm)

Primary Inoculum 2mL

HS medium 18mL

Preparing AX solution continued.

10. For dissolving AX set up hot plate and stirrer with mineral oil in a beaker in the laminar flow

cabinet. Have the Bunsen burner on and wipe hands with ethanol to prevent contamination.

11. Temporarily move the balance in the cabinet.

12. Using an autoclaved spatula (wrapped in foil) measure of 3g AX (for 300mL) into a 500mL

Schott bottle.


175

13. Add autoclaved magnetic stirrer bar (wrapped in foil).

14. Set the hot plate to 850C with the temperature probe in the oil (in order to get solution to

800C).

15. Set the stirrer to 240rpm.

16. Add 300mL of the autoclaved water (autoclaved earlier this day so the water is still hot which

will help with the dissolving) in 10mL lots using a pipette. Add the first 3 lots and mix around

well by swirling the bottle (the powder will go gluggy). Increase the rpm and continue to

slowing add the water.

17. Leave the AX solution to dissolve overnight.

DAY 2

Aliquot medium

Cellulose hydrogel

1. Wipe outside of schott bottle containing medium with ethanol.

2. Add 12mL (2x6mL) glucose to HS medium.

3. Pipette 10mL of medium into primary containers.

4. Change pipette to 9mL with tip still on and pipette 9mL into all 70mL scale up containers.

5. Pipette 1000µL to all 5mL scale up containers followed by another 350µL (1.35mL total

volume).

Cellulose composite (with AX or XG)

1. Take AX solution off hotplate after it has dissolved overnight. Let cool after taking off the

hotplate (to speed up this process put the bottle in some water). Need to be able to touch the

AX solution to the skin on the inside of your arm comfortably.

2. Make sure you have autoclaved pipette tips – put tips in the dry oven after autoclaving to

remove any condensation.

3. Light Bunsen burner.

4. Pipette 12mL (2x6mL) glucose into each batch of HS medium (2x concentrated), swirl bottle

to mix around.

5. Split AX solution evenly between the 2 bottles of HS medium. Make sure you record how

much total volume you’ve added (will be greater than 150mL as the AX powder increases the

volume). Swirl around to mix.

6. Pipette/aliquot medium into primary and scale up containers that have been labelled.

7. **With pipette tip on you can only adjust the volume DOWN.

Put all scale up containers in the fridge.

Primary inoculum

1. With plastic loop take a loopful of bacteria off the subculture plate and stir into the medium

which has been aliquotted into the primary containers.

2. With the lids ajar place in the incubator.

DAY 5

**Take primary containers out of the incubator and scale up containers out of the fridge to get to

room temperature.


176

For cellulose micro-gels

Cleaning Microarrays

Place microarrays that have been bonded to petri dishes in the plasma cleaner and turn the vacuum on

for 15minutes.

1. Plasma clean for 1.5minutes on high.

2. Turn off for 1 minute (to let cool)

3. Plasma clean for another 1.5minutes on high.

4. Cover the surface of the microarrays with water to maintain hydrophilicity

5. With petri dish lids on and in a large 14cm petri dish with the lid on, transport to the

microbiology lab.

Scale up

1. Place the primary inoculum containers onto the shaker and shake for 5minutes on 350rpm.

2. Combine all the primary inoculum into 1 container to homogenise.

3. Pipette 200µL of primary inoculum onto the surface of the microarrays. Leave for 10 minutes

for the bacteria to sediment.

4. Pipette 150µL of primary inoculum into all 5mL scale up containers.

5. Pipette 1mL of primary inoculum into all 70mL scale up containers.

6. Put all containers in the incubator with lids ajar and record the time (they will need to

incubate for 72hours).

Blotting

1. For the microarrays, with a 50µL pipette remove excess liquid.

2. Fold up and Olympus lens cleaning tissue, hold briefly near the flame, then rub lightly on the

surface of the microarray.

3. Place 5mL milli-Q water in the bottom of 70mL sterile container (to create 100% RH).

4. Place the lids back on the petri dishes and drop into the containers.

5. Put all containers in the incubator with lids ajar and record the time (they will need to

incubate for 72hours).

DAY 8

Harvesting

1. Take containers out of the incubator and place them on the shaker (350rpm, 5mins).

2. Pour pellicles in 5mL containers into tea strainer over a glass beaker.

3. Invert tea strainer over a 1L beaker and pour 500mL of cold water over the pellicle so that

they fall into the beaker.

4. With fine tip tweezer slide the individual 41mm pellicles over the edge of the cups to remove

excess strands of cellulose etc. and place in a 1L beaker. Pour 500mL of cold water over the

pellicles.

5. Place the beaker on the shaker for 3x30min and 3x10min at 100rpm replacing the water each

time.

6. After all washes, drain off the water and place in batches in 70mL sterile containers then

cover with 0.2% sodium azide solution.

For the cellulose microgels


177

7. Wash the microarray 4 times by pipetting cold water on the surface, swirling around, and the

removing the water with the pipette. After the final washing step, cover the surface of the

microarray with 0.2% sodium azide solution.


178

Appendix B: Chromium Mask Fabrication

This standard operating procedure is provided by the Australian National Fabrication Facility,

Queensland (ANFF-Q).

EQUIPMENT Heidelberg uPG 101 laser direct writer

4 containers (large enough to hold 5” mask)

AZ 726 MIF Developer

Milli-Q water

Chrome etchant

Acetone

Isopropanol

Design file (format: GDSII, Gerber or DXF)

NOTE: This protocol uses a GDSII file as an example

Always use Writemode III – for other writemodes contact ANFF staff

LOADING MASK AND EXPOSING DESIGN 1. Make booking online (Raspberry).

2. Fill in EXPERIMENT IN PROGRESS sheet.

3. Copy design file into the following location on the Heidelberg computer and in the folder name

that corresponds to the file type (e.g. GDSII file in GDSII folder) :

C:\Himt\ExposureWizard\Designs\GDSII

4. Double click on file to open it in LayoutEditor software. Check the design for any error.

5. Start the uPG 101 Exposure Wizard using the link icon on the desktop:

6. WELCOME screen opens. Check that it reads “Writemode III – 20mm”. If not, immediately

contact ANFF staff. If it is Writemode III then wait for initialisation to complete then click Next.


179

7. Click Load Design and select design file.


180

8. GDSII OPTIONS screen opens. Magnification Factor is for scaling purposes – if no scaling is

required enter the value ‘1’. Select GDSII structure containing the layers (e.g. MainSymbol) and

tick the specific layer to expose. Click Create to load design file.


181

9. Once design file is loaded click Next. “Exp Time” is the approximate time take to expose the

design.


182

10. CHECK OPTIONS screen opens.

a. Expose Options:


183

Parameters are selected based on the substrate type and brand that is used. Currently, the values

to use are 9mW laser output power, 53% pixel pulse duration, and Energy Mode 1x1.

b. Design Options:

INVERTED - By default, the structures that were defined in the design are exposed on the

substrate (positive photoresist process). If the checkbox option Inverted is selected, all areas with

no structure defined are exposed instead. The limits of the exposure file are defined by the

outmost structures. If a larger area should be exposed around the structures, a frame had to be

defined by entering the required distance from the structures to the edge of the exposed area into

the text box. Maximum value for the frame is 10mm.


184

AUTOMATIC CENTERING – If Automatic Centering option is not selected, the design will be

positioned so that the origin of the mask drawing is exposed on the center of the substrate. If

Automatic Centering is selected, the wizard automatically shifts any design so that the

geometrical center is exposed on the center of the substrate, regardless of where the origin is

located. The option of automatic centering greys out when the origin of the design is the

geometrical center.

To keep things simple, we recommend including a border of 120mmx120mm around your design

and always select Automatic Centering. c. Once design options are selected, click on Show Control Panel.

11. CONTROLS screen opens. Press To Un/Load (1) - the stage moves to the loading position at

the front of the machine. Once the Loading Status window opens, immediately press Close (2) on

the CONTROLS screen.

WARNING: DO NOT press ANY other buttons on the CONTROLS screen as this may

accidentally causes the write head to come crashing down on the stage. Such damages will

be extremely costly and may take months to fix.


185

12. LOAD the substrate:

a. Wait until all movement has finished. Open the cover lid. Mount the substrate against the

alignment pins on the stage – make sure the resist coated side of the substrate is turned up. Do

NOT load the mask if the stage is not in this position.

b. Switch ON the vacuum with the vacuum knob. Check whether the plate is really held tight by

trying to move it slightly sideways. If plate is not held, switch off the vacuum and clean the plate

backside and chuck before trying again.


186

13. Return to OPTIONS screen and press Next.

14. MANUAL ALIGNMENT screen opens. Press Find Plate Center.


187

15. FIND PLATE CENTER screen opens. Tick fast mode and press Start.


188

16. Once FIND PLATE CENTRE finishes scanning the edges, press ACCEPT.


189

17. Return to MANUAL ALIGNMENT screen and press Next.


190

18. EXPOSE DESIGN screen opens. Tick Auto Unload after Exposure and press Expose.


191

DEVELOPING MASK Summary Table

* Note: Time may vary slightly depending on the chrome

etchant solution

A. Prepare 4 large containers. Separately pour the following solutions into the containers:

1. 200mL AZ 726 MIF Developer

2. 400mL Milli-Q water

3. 400mL Chrome etchant

4. 200mL Acetone


192

B. Place the mask in the container with AZ 726 MIF Developer for 45sec.

C. Immediately transfer the mask into the container with Milli-Q water and rinse for about 10secs. Remove the mask from the container and spray down with fresh Milli-Q water.

D. Dry the mask with a gentle stream of nitrogen.

E. Place the mask in the container with chrome etchant for 1min 15secs or until area to be

etched appears clear.

F. Immediately transfer the mask into the container with Milli-Q water and rinse for about

20secs. Remove the mask from the container and spray down with fresh Milli-Q water.

G. Dry the mask with a gentle stream of nitrogen and inspect the mask under the microscope to

check etching is complete. If not, return the mask into the container with chrome etchant for further etching – take care with time as over etching may occur.

H. Place the mask in the container with acetone for about 2mins with sonication to remove the

resist layer. If required, while the mask is in acetone, use a soft wipe to wipe the surface of the mask to assist with removal of resist debris – be gentle as scratching may occur.

I. The mask is rinsed with isopropanol and spray dried with a gentle stream of nitrogen.

J. Chrome etchant may be reused – pour it back into its bottle for storage.

K. Discard all other solutions in the corresponding waste containers provided.


193

Appendix C: SU-8 Master Fabrication

This standard operating procedure is provided by the Australian National Fabrication Facility,

Queensland (ANFF-Q).

MATERIALS AND EQUIPMENT Photo-mask

Silicon wafer

Acetone

Isopropanol (IPA)

Propylene glycol monomethyl ether acetate (PGMEA)

UV Light source

Hot plates

SU-8 Photo-resist (select type for desired feature height)

PROCEDURE 1. CLEAN the silicon wafer with acetone then IPA and dry with a stream of nitrogen.

2. DEHYDRATE the wafer on a hot-plate at 180 °C for 20 min.

3. Ti PRIMER TREATMENT (Optional)

a. Spin-coat Ti Primer on wafer (about 1mL per 4 inch wafer)

Step 1) 500 rpm 100 rpm/s 10s

Step 2) 3000 rpm 300 rpm/s 30s

b. Bake at 200 °C for 1 min and allow to cool down to room temperature.

4. Pour photo-resist onto the wafer (1 mL per inch of wafer diameter) and SPIN-COAT at the

appropriate speed for the required thickness:

* Recommended speed values are shown in the following table.

SPIN-COATING SPEED (RPM) FOR COMMON THICKNESSES


194

5. SOFT BAKE the wafer on a hot-plate through a series of step change in temperature (from 65

°C → 95 °C → 65 °C, see Summary Table). Always allow the wafer to cool down to room temperature before next step.

6. Place photo-mask onto the wafer and UV EXPOSE for applicable exposure dose (see

Summary Table). Make sure the printed side (i.e. for chrome mask, “bronze” side and not “silver”

side) of the mask is in direct contact with the photo-resist layer, and check UV intensity with radiometer before exposure.

7. POST BAKE the wafer on a hot-plate through a series of step change in temperature (from 65

°C → 95 °C → 65 °C, see Summary Table) to selectively cross-link the exposed portions.

Always allow the wafer to cool down to room temperature before next step. Extra baking step for

mask before development at 95 degrees for 2 mins

8. DEVELOPE the silicon wafer with PGMEA to remove any uncross-linked photo-resist – i.e.

until features are revealed. Strong agitation is recommended when developing high aspect ratio and thick film structures.

9. RINSE the PGMEA with IPA to stop the developing process. If streaks of milky white appear then re-rinse with PGMEA then IPA.

10. DRY the silicon wafer with a stream of nitrogen.

11. HARD BAKE the silicon wafer on a hot-plate at 120 °C for 20 min. This step is required for

DRIE (Deep Reactive Ion Etching) process.


195

SUMMARY TABLE (for Steps 5, 6 and 7)

CLEANING AND WASTE DISPOSAL 1. WIPE and CLEAN the spin-coater with acetone. Place all used wipes in the designated

container in the fumehood.

2. EMPTY WASTE SOLUTIONS into the appropriate waste containers:

BEFORE LEAVING CLEANROOM TURN-OFF hot-plates, spin-coater and UV light source. Leave UV light source on if you know

someone else will be using it in the same day.


196

Appendix D: PDMS Microarray Fabrication

Preparing PDMS

Using SYLGARD 184 Silicone Elastomer Kit prepare PDMS with base:binder ratio of 10:1

1. Tare weight of plastic cup.

2. Weigh 10g of base (record exact weight).

3. Tare balance again.

4. Weigh 1g of binder (record exact weight).

5. Mix well using a wooden stick.

6. Place PDMS under vacuum for 15minutes in order to degas (remove bubbles). Note: you can

spray dry with nitrogen to remove any extra bubbles remaining after 15minutes in the vacuum

desiccator.

Following this procedure will make enough PDMS to produce enough to fill the mould twice (i.e.

make 6 microarrays which can be cut into halves to fit the petri dishes, therefore 12 sets of microwells

in total)

Curing the PDMS in the mould

1. Using a plastic pipette/dropper, with a portion of the narrow end cut off, evenly spread the

PDMS into the mould.

2. Degas in the vacuum dessicator and spray dry with N2 to remove extra bubbles if required (or

you can use put in the plasma cleaner with the vacuum pump on to remove excess bubbles).

3. Place mould on the hotplate (whilst cold) and turn on to 800C. Leave for 20minutes to begin

curing.

4. Cut out of mould and repeat from step 1. With the remaining PDMS or put mould directly

into the 650C oven overnight.

Removing PDMS microarrays from the mould and binding to petri dishes

1. Cut through the PDMS around the individual silicon wafer moulds leaving a border of

approximately 3mm.

2. Trace around the edge inserting the tweezers to ensure the PDMS is cut all the way through.

3. Peel the PDMS off the mould and place onto 14cm petri dish with wells facing up.

4. Using tweezers push gently on the border of the PDMS so that it sticks to the petri dish

making it easier to cut.

5. With the scalpel, cut off the majority of the border (and cut the corners off if you need it to fit

in the circle area of the glass bottom petri dish).

6. Place the cut out microarrays on tape with the patterned side facing down onto the sticky side

of the tape.

7. Put the tape with the bottom of the microarrays facing up and the small petri dishes (without

lid) in the plasma cleaner.

8. Pump down for 15minutes (i.e. with the vacuum pump on before the oxygen is introduced).

9. Treat for 38second on high.

10. After treatment put the PDMS microarrays on the small petri dishes and press down to

remove air bubbles. Pull off tape and leave to bond overnight.


197

Appendix E: MATLAB code for poroelastic mechanical model

Linear_orthotropicF.m

close all clear all fclose('all'); global e0 t0 v31 E3 fdifer k_r2 ikest icomp Pinf2 ifast

A=importdata('C3000.txt','\t',1); %C3000.txt is the text file of the raw

data during the compression-relaxation steps for cellulose hydrogels

compressed to 3000microns B=A.data; t=B(:,1); %t=time in s tc=B(:,2); %tc=time in s for a certain step: compression or relaxation h=B(:,3); %h=gap between the rheometer plates P=B(:,4); %P=normal stress in Pa n=length(t); cycindex=zeros(30,2); paramcyc=zeros(30,7); tcyc=zeros(30,2); test=zeros(30,2); Pfit=0*P; tfit=0*t; extr=1; %1=Extrapolate relaxtation part through an exponential

decay (if relaxation is not complete) %0=Do not extrapolate ikest=1; %1=fit permeability %0=find permeability from intercept icomp=1; %1=fit compressive modulus %0=find compressive modulus from slope ifast=0; %1=fast compression

deltat=0.0; %Time between consecutive cycles

%Initial Model Parameters ramprate=33.333; %ramp rate um/s (positive for compression) h0=1996; %Initial sample thickness um r0=20e3; %Initial radius um v31=0.0; %Poisson ratio zr (=-err/ezz) v21=0.5; %Poisson ratio zphi (=-ephi/err) E1=1e5; %Young modulus rr, Pa tgf=0.1; %tramp/tporo nn=1;

if ifast==1 ikest=1; icomp=1; end

%Define lower and upper limits for fitting parameters lb(1)=1; ub(1)=1e7; %E1 lb(2)=0.1; ub(2)=0.99; %v21 ik=3; if icomp==1 ik=4; lb(3)=1; ub(3)=1e7; %E3


198

end

if ikest==1 lb(ik)=0.001/r0^2; ub(ik)=1e7/r0^2; %k_r2 end if ifast==1 fdifer0=-100; lb(5)=-1e8; ub(5)=0.0; %fdifer end

h00=h0; i1=1; tlast=0; cycle=0; while i1<n k=i1; nslope=0.4; %number of poins for determination of slope while k<n k=k+1; if tc(k)<1e-6 break end end cycle=cycle+1; disp(cycle) if cycle==13 disp(cycle) end

i2=k-1+floor(k/n); tdata=tc(i1:i2); Pdata=P(i1:i2)-P(i1); tcyc(cycle,1)=deltat+tlast; if cycle==1 tcyc(cycle,1)=0; end cycindex(cycle,1)=i1; cycindex(cycle,2)=i2; e0=ramprate/h00;

% Correct time data if ifast==0 count=1; for i=i1+1:i2 if tc(i)>tc(i-1) count=count+1; continue else ir=i; tcor=tc(i-1); t0=tcor; tcyc(cycle,2)=t0+deltat+tlast; if cycle==1 tcyc(cycle,2)=t0; end break end end tdata(count+1:end)=tc(ir:i2)+tcor; else


199

[fmax,count]=max(Pdata); t0=tdata(count); if Pdata(count+1)>0.95*Pdata(count) t0=(tdata(count)+tdata(count+1))/2; count=count+1; end tdata(count+1:end)=tdata(count+1:end)+deltat; ir=count+i1-1; end

% Determine the slope during compression nslope=round(nslope*count); tlin=tdata(count-nslope:count); Plin=Pdata(count-nslope:count); Pend=Plin(end); p = polyfit(tlin,Plin,1); E3=p(1)/e0; Pinf1=p(1)*t0; deltaP1=p(2);

% Extrapolate exponential decay if extr==1 Pdec=Pdata(count+1:end); tdec=tdata(count+1:end); ydecay=@(b,tt) b(1)+b(2)*exp(-b(3)*tt); b0=[Pdec(1)/2,Pdec(1)/2,0.01];

problem=createOptimProblem('lsqcurvefit','objective',ydecay,'xdata',tdec,..

. 'ydata',Pdec,'x0',b0,'lb',1e-6*b0,'ub',1e6*b0); ms=MultiStart; bdecay=run(ms,problem,12); ydecfit=ydecay(bdecay,tdec); plot(tdec,Pdec,'o',tdec,ydecfit,'r') Pinf2=bdecay(1); close else Pinf2=1/3*(Pdata(end)+Pdata(end-1)+Pdata(end-2)); end fdifer=Pinf2-Pinf1;

% Estimate the permeability k_r2=e0/8/deltaP1;

% Initial values beta0(1)=1.1*E1; beta0(2)=v21; ik=4; if ikest==1 beta0(ik)=k_r2; if k_r2<0 beta0(ik)=0.01*ub(ik); end end

if ifast==1 beta0(5)=fdifer0; end


200

if icomp==1 beta0(3)=1.1*E3; end

nsolver=nn*ik; if cycle==1

problem=createOptimProblem('lsqcurvefit','objective',@orthoF,'xdata',tdata,

... 'ydata',Pdata,'x0',beta0,'lb',lb,'ub',ub); ms=MultiStart; [beta,fval,exitflag]=run(ms,problem,nsolver); else

problem=createOptimProblem('lsqcurvefit','objective',@orthoF,'xdata',tdata,

... 'ydata',Pdata,'x0',beta0,'lb',lb,'ub',ub); ms=MultiStart; [beta,fval,exitflag]=run(ms,problem,nsolver);

%[beta,resnorm]=lsqcurvefit(@orthoF,beta0,tdata,Pdata,lb,ub); %[beta,fval,exitflag]=run(ms,problem,1); end if ikest==1 k_r2=beta(ik); end

if ifast==1 fdifer=beta(5); end if icomp==1 E3=beta(3); end yfit=orthoF(beta,tdata); Pfit(i1:i2)=yfit+P(i1)-P(1); tfit(i1:i2)=tdata+deltat+tlast; if cycle==1 tfit(i1:i2)=tdata; end

E1=beta(1); v21=beta(2); E1final=Pinf2/(e0*t0); paramcyc(cycle,2:4)=[E1,E3,v21];

delta1=1-v21-2*v31^2*E1/E3; C11=E1*(1-v31^2*E1/E3)/((1+v21)*delta1); k=1e-12*r0^2*k_r2; tg=1/C11/k_r2; paramcyc(cycle,5)=k; paramcyc(cycle,6)=-fdifer; paramcyc(cycle,7)=Pend; paramcyc(cycle,8)=E1final;

lb(1)=E1; ub(1)=1e9; %E1 ik=3; if icomp==1 ik=4; lb(3)=E3; ub(3)=1e9; %E3 end


201

tlast=tlast+tdata(end);

h00=h00-ramprate*t0; paramcyc(cycle,1)=(h0-h00)/h0; i1=i2+1; end

variab={'strain';'Er';'Ez';'v21';'k';'Aggreg. Force'}; nv=length(variab);

for i=1:nv BB{1,i}=variab{i,1}; end for i=2:cycle+1 for j=1:6 BB{i,j}=paramcyc(i-1,j); end end xlswrite('Fitting results',BB,1)

plot(tfit,Pfit,'LineWidth',3); xlabel('time(s)'); ylabel('P(Pa)'); hold on plot(tfit,P-P(1),'or','MarkerSize',3);

orthoF.m

function y=orthoF(beta,t)

global v31 t0 nt e0 fdifer icomp ikest E3 k_r2 ifast

y=0*t; nt=100; E33=E3; k_r22=k_r2; E1=beta(1); v21=beta(2); ik=3; if icomp==1 E33=beta(3); ik=4; end if ikest==1 k_r22=beta(ik); end if ifast==1 fdifer=beta(5); end

E3=E33; k_r2=k_r22; v312=v31^2; alpha = trascend(E1/E3,v312,v21); alpha=alpha.^2; delta1=1-v21-2*v312*E1/E3; delta2=(1-v312*E1/E3)/(1+v21); delta3=(1-2*v312)*delta2/delta1;


202

delta22=delta2^2; C11=delta2/delta1*E1; den=delta1/(1+v21); tg=1/(C11*k_r2);

[tm,ind]=min(abs(t-t0)); if tm>t0 ind=ind-1; end maxt=length(t); c1=E3*e0*t0; c2=E1*e0*tg*delta3;

for i=1:ind s=0; ti=t(i); for j=2:nt s=exp(-alpha(j)*ti/tg)/(alpha(j)*(delta22*alpha(j)-den))+s; end y(i)=c1*ti/t0+c2*(0.125-s); end k=0; ta=tg/alpha(2); for i=ind+1:maxt s=0; k=k+1; ti=t(i); ff=fdifer*(1-exp(-(ti-t0)/ta)); for j=2:nt s1=exp(-alpha(j)*ti/tg); s2=exp(-alpha(j)*(ti-t0)/tg); s=s+(s1-s2)/(alpha(j)*(delta22*alpha(j)-den)); end y(i)=c1-c2*s+ff; end

end

trascend.m

function alpha = trascend(E1_E3,v312,v21)

global nt

alpha=zeros(nt,1); alpha(1)=0; f=(1-v312*E1_E3)/(1-v21-2*v312*E1_E3);

fun=@(x)besselj(1,x)-x*besselj(0,x)*f;

a1=1e-5; a2=a1; s=1; for i=2:nt s1=fun(a1); while s>0 a2=a2+0.2; s2=fun(a2); s=s1*s2;


203

end x0=[a1,a2]; alpha0=fzero(fun,x0); a1=alpha0+1e-5; alpha(i)=alpha0; a2=a1; s=1; end

end


204

Appendix F: Text file of raw data for input into MATLAB code

for the poroelastic mechanical model

The raw data during the compression-relaxation steps is extracted from the Rheowin Data

Manager software.

- t in s, is the time throughout the compression and relaxation step.

- t_seg in s, which is labelled tc in the MATLAB code, is the time during a certain step

(i.e. compression or relaxation).

- h in mm, is the gap between the emry covered rheometer plates.

- P_in_ Pa, is the normal stress.


205

This data is copied into an text file and labelled C3000.txt for cellulose hydrogel compressed


206

Appendix G: Raw data from the compression-relaxation steps for

hydrogels (cellulose, CAX, CXG) at all CRs

Figure G.1. Normal stress during compression-relaxation steps for cellulose hydrogels at CR

0.4.


0.5.

Time (s)

0 20 40 60 80 100

Norm

al S

tress (

kP

a)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Time (s)

0 20 40 60 80 100

Norm

al S

tress (

kP

a)

0.0

0.5

1.0

1.5

2.0

2.5

3.0


207


0.6.


0.7.

Time (s)

0 20 40 60 80 100

Norm

al S

tress (

kP

a)

0

1

2

3

4

5

Time (s)

0 20 40 60 80 100

Norm

al S

tress (

kP

a)

0

2

4

6

8


208

Figure G.5. Normal stress during compression-relaxation steps for CAX hydrogels at CR

0.4.


0.5.

Time (s)

0 20 40 60 80 100

Norm

al S

tress (

kP

a)

0

1

2

3

4

Time (s)

0 20 40 60 80 100

Norm

al S

tress (

Pa)

0

2

4

6

8


209


0.6.


0.7.

Time (s)

0 20 40 60 80 100

Norm

al S

tre

ss (

kP

a)

0

2

4

6

8

10

12

14

16

Time (s)

0 20 40 60 80 100

Norm

al S

tre

ss (

kP

a)

0

5

10

15

20

25

30


210

Figure G.9. Normal stress during compression-relaxation steps for CXG hydrogels at CR

0.4.


0.5.

Time (s)

0 20 40 60 80 100

Norm

al S

tress (

kP

a)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Time (s)

0 20 40 60 80 100

Norm

al S

tress (

kP

a)

0

2

4

6

8


211


0.6.


0.7.

Time (s)

0 20 40 60 80 100

Norm

al S

tre

ss (

kP

a)

0

2

4

6

8

10

12

14

16

Time (s)

0 20 40 60 80 100

Norm

al S

tress (

kP

a)

0

5

10

15

20

25

30


212

Appendix H: Raw data from the tribo-rheological test for all

hydrogels and solvents

Friction curves for Cellulose, CAX and CXG at all CR values in water.

Figure H.1. Friction curves for Cellulose hydrogel pairs in water at all compression ratios.

Figure H.2. Friction curves for CAX hydrogel pairs in water at all compression ratios.

Shear Strain (-)

0.001 0.01 0.1 1 10

Shear

Str

ess (

kP

a)

0.01

0.1

1

10

CR = 0.7

CR = 0.4

Shear Strain (-)

0.001 0.01 0.1 1 10

Shear

Str

ess (

kP

a)

0.01

0.1

1

10

CR = 0.7

CR = 0.4


213

Figure H.3. Friction curves for CXG hydrogel pairs in water at all compression ratios.

Friction curves for Cellulose hydrogel in all pectin solutions at all CR values.

Figure H.4. Friction curves for a pair of cellulose hydrogels in 0.5 wt% pectin solution at all

values of CR.

Shear Strain (-)

0.001 0.01 0.1 1 10

Shear

Str

ess (

kP

a)

0.01

0.1

1

10

CR = 0.7

CR = 0.4

Shear Strain (-)

0.001 0.01 0.1 1 10

Shear

Str

ess (

kP

a)

0.01

0.1

1

10

CR = 0.7

CR = 0.4


214

Figure H.5. Friction curves for a pair of cellulose hydrogels in 1 wt% pectin solution at all

values of CR.


values of CR.

Shear Strain (-)

0.001 0.01 0.1 1 10

Shear

Str

ess (

kP

a)

0.01

0.1

1

10

CR = 0.7

CR = 0.4

Shear Strain (-)

0.001 0.01 0.1 1 10

Shear

Str

ess (

kP

a)

0.01

0.1

1

10

CR = 0.7

CR = 0.4


215


values of CR.

Shear Strain (-)

0.001 0.01 0.1 1 10

Shear

Str

ess (

kP

a)

0.01

0.1

1

10

CR = 0.7

CR = 0.4


216

Appendix I: Cellulose concentration based on the G’ of the

hydrogels for cellulose, CAX, and CXG.

Cellulose CAX CXG

G' Cellulose concentration G' Cellulose concentration G' Cellulose concentration

Pa % Pa % Pa %

101.9 0.71221 159 0.68698 112.7016 1.24404

159 0.73679 387 0.72277 203.6787 1.3418

237 0.7634 723 0.7625 335.9278 1.45624

331.4 0.79171 1160 0.80686 485.7625 1.59203

435.5 0.82221 1580 0.85669 716.3231 1.75574

607 0.85514 2010 0.91309 882.8999 1.95697

761.8 0.89083 2530 0.97743 999.65 2.21031

974.8 0.92962 3120 1.05153 1260.495 2.53899

1098 0.97195 3770 1.13778 1713.081 2.98251

1246 1.01831 4410 1.23945 2645.768 3.61376

1455 1.06932 5100 1.36107 5130.178 4.58396

1787 1.12512 6050 1.50916

2244 1.18772 7500 1.6934

2669 1.2577 9680 1.92889

2960 1.33643 14800 2.24045

3600 1.42569

4409 1.52772

5246 1.64675

5905 1.7844

6733 1.94894

8173 2.14475

10370 2.3843

13150 2.68409

19030 3.06571

24860 3.57981

31250 4.30108

33720 5.38633

30450 7.20408


217

Appendix J: Friction curves with angular velocity for hydrogel

pairs (cellulose, CAX, CXG) at all CRs

Figure J.1. Shear stress and angular velocity measured over time during the constant rotation

rate step for cellulose hydrogels in water at CR 0.4.



Time (s)

0 5 10 15 20

Sh

ea

r S

tre

ss (

, kP

a)

0.00

0.05

0.10

0.15

0.20

An

gu

lar

ve

locity (

, ra

d/s

)

0.0001

0.001

0.01

0.1

1

Time (s)

0 5 10 15 20

Sh

ea

r S

tre

ss (

, kP

a)

0.00

0.05

0.10

0.15

0.20

0.25

0.30A

ng

ula

r ve

locity (

, ra

d/s

)

0.0001

0.001

0.01

0.1

1


218





Time (s)

0 10 20 30 40

Shear

Str

ess (

, kP

a)

0.0

0.1

0.2

0.3

0.4

0.5

Angula

r velo

city (

, ra

d/s

)

0.0001

0.001

0.01

0.1

1

Time (s)

0 20 40 60 80 100 120

Shear

Str

ess (

, kP

a)

0.0

0.5

1.0

1.5

Angula

r velo

city (

, ra

d/s

)

0.0001

0.001

0.01

0.1

1


219


rate step for CAX hydrogels in water at CR 0.4.



Time (s)

0 2 4 6 8 10

Sh

ea

r S

tre

ss (

, kP

a)

0.000

0.015

0.030

0.045

0.060

An

gu

lar

ve

locity (

, ra

d/s

)

0.001

0.01

0.1

1

Time (s)

0 5 10 15 20

Shear

Str

ess (

, kP

a)

0.00

0.02

0.04

0.06

0.08

0.10

Angula

r velo

city (

, ra

d/s

)

0.001

0.01

0.1

1


220





Time (s)

0 5 10 15 20

Sh

ea

r S

tre

ss (

, kP

a)

0.00

0.05

0.10

0.15

An

gu

lar

ve

locity (

, ra

d/s

)

0.0001

0.001

0.01

0.1

1

Time (s)

0 10 20 30 40

Sh

ea

r S

tre

ss (

, kP

a)

0.00

0.05

0.10

0.15

0.20

0.25

An

gu

lar

ve

locity (

, ra

d/s

)

0.0001

0.001

0.01

0.1

1


221


rate step for CXG hydrogels in water at CR 0.4.

Figure J.10. Shear stress and angular velocity measured over time during the constant

rotation rate step for CXG hydrogels in water at CR 0.5.

Time (s)

0 5 10 15 20

Shear

Str

ess (

, kP

a)

0.00

0.01

0.02

0.03

Angula

r velo

city (

, ra

d/s

)

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Time (s)

0 5 10 15 20

Sh

ea

r S

tre

ss (

, kP

a)

0.00

0.01

0.02

0.03

0.04

An

gu

lar

ve

locity (

, ra

d/s

)

0.00

0.01

0.02

0.03

0.04


222





Time (s)

0 5 10 15 20

Shear

Str

ess (

, kP

a)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

Angula

r velo

city (

, ra

d/s

)

0.00

0.01

0.02

0.03

0.04

Time (s)

0 10 20 30 40

Shear

Str

ess (

, kP

a)

0.00

0.05

0.10

0.15

Angula

r velo

city (

, ra

d/s

)

0.00

0.01

0.02

0.03

0.04

0.05


223

Appendix K: Force-distance data for SPEEK fibres mats.

Figure K.1. Lateral force-distance curve of SPEEK sample A.

Figure K.2. Lateral force-distance curve of SPEEK sample B.

Lateral Distance ( m)

0 2 4 6 8 10 12 14

Late

ral F

orc

e (

N)

0

10

20

30

40


0 2 4 6 8 10 12 14

Late

ral F

orc

e (

N)

0

10

20

30

40


224

Figure K.3. Lateral force-distance curve of SPEEK sample C.

Figure K.4. Lateral force-distance curve of SPEEK sample D.


0 2 4 6 8 10 12 14

Late

ral F

orc

e (

N)

0

10

20

30

40

50

60


0 2 4 6 8 10 12 14

Late

ral F

orc

e (

N)

0

20

40

60

80

100


225

Figure K.5. Lateral force-distance curve of SPEEK sample E.


0 2 4 6 8 10 12 14 16

Late

ral F

orc

e (

N)

0

20

40

60

80


226

Appendix L: MATLAB code for finding the peaks in lateral

force-distance curves from the dip-and-drag technique

dist = load('NFC_air_distance_b.txt'); %this is for a single trace in a

curve i.e. the cantilever doesn't lift off during this data LatF = load ('NFC_air_Lateral Force_b.txt'); %this is for a single trace

in a curve i.e. the cantilever doesn't lift off during this data

%First step of peak identification. hold off %start new figure Peaks = zeros(size(LatF)); % Make another array to fill up with peaks in

Lateral Force data. for aa = 11:(numel(LatF)-11) % May need to change this range depending

on how many points you % specify on either side of the conditions

below. if ((LatF(aa-10) < LatF(aa)) && (LatF(aa+10) < LatF(aa))) % Identifies a

peak based on the average of % lateral forces a

certain number of points % either side being

less than the point of interest. % You can change

the number of points either side that % is in the

condition based on visual inspection. Peaks(aa) = LatF(aa); % Enter values that satify the conditions of being

a peak. else Peaks(aa) = 0; % Enters a zero if not a peak. %plot (dist,LatF) % Plot raw data. %hold on %scatter (dist,Peaks) % Plots peaks, points that aren't peaks fall on the

origin end end

% (dist,LatF) of local maximums. hold off % Start new graph. [row,col] = find (Peaks); % Find the location of nonzero values of

matrix. r=row; Peaks2 = zeros(numel(r),1); % Start a new matrix for nonzero values of

Peaks matrix. for bb = 1:numel(r); Peaks2(bb,1) = dist(r(bb)); % Distance corresponding to nonzero values of

Peaks matrix. Peaks2(bb,2) = Peaks(r(bb)); % Lateral force corresponding to nonzero

value of Peaks matrix. %plot (dist,LatF) % Plot raw data. %hold on %scatter (Peaks2(:,1),Peaks2(:,2)) % Plot (dist,LatF) of nonzero values

from Peaks matrix. end Peaksdist=(Peaks2(:,1)); % x-values of nonzero values from Peaks matrix. PeakLatF=(Peaks2(:,2)); % y-values of nonzero values from Peaks matrix.


227

GrpStartPts = zeros(numel(Peaksdist),1); % Make another array to fill up

with the end points of %groupings of peaks where only the %local maximum is an actual peak. for cc = 2:numel(Peaksdist) if Peaksdist(cc)-Peaksdist(cc-1)>0.03 %Conditions to make the end

point of a cluster of % data for which only the local % maximum is relavent. i.e. if % the separation between the % group end point and the next % group start point is at least % 0.1um GrpStartPts(cc) = Peaksdist(cc); % Enter points that satisfy the condition

above. else GrpStartPts(cc) = 0; % Enter zero for points that don't

satisfy the condition above. end end [row2,col2] = find (GrpStartPts); % Find nonzero values of GrpStartPts. r2 = row2; % Rows of nonzero values of

GrpStartPts. GrpStartPtsVal = zeros(numel(r2),1); % Start a new matrix for location

of GrpStartPts in Peaksdist matrix. for dd = 1:numel(r2) GrpStartPtsVal(dd)=GrpStartPts(r2(dd)); end

LocGrpStartPts = zeros(numel(GrpStartPtsVal),1); % Start a new matrix

for location of GrpStartPts in Peaksdist matrix. for ee = 1:numel(GrpStartPtsVal) LocGrpStartPts(ee)=find(Peaksdist==GrpStartPtsVal(ee)); end

LocalMaxLatF = zeros((numel(LocGrpStartPts)+1),1); %Start a new matrix for

local max within groups of peaks identified % by GrpStartPts. for ff=2:(numel(LocGrpStartPts)) LocalMaxLatF(1)= max(PeakLatF(1:(LocGrpStartPts(1)-1))); % First

group of peaks start from first row in matrix to the first % end point

which is the point before that specified in the % first row

of the GrpStartPts matrix. LocalMaxLatF(ff) = max(PeakLatF((LocGrpStartPts(ff-

1)):(LocGrpStartPts(ff)-1))); % range of the matrix of peaks

% bound by the GrpStartPts LocalMaxLatF(numel(LocGrpStartPts)+1)=

max(PeakLatF((LocGrpStartPts(numel(LocGrpStartPts))):numel(PeakLatF))); end

LocalMaxLoc2 = zeros(numel(LocalMaxLatF),2); % Start a new matrix for the

location of local maximums. for gg = 2:(numel(LocalMaxLatF)-1) LocalMaxLoc2(1,:)=find((PeakLatF(1:(LocGrpStartPts(1)-

1)))==LocalMaxLatF(1)); LocalMaxLoc2(gg,:)=((LocGrpStartPts(gg-1)-

1)+find(PeakLatF((LocGrpStartPts(gg-1)):(LocGrpStartPts(gg)-

1))==LocalMaxLatF(gg)));


228

LocalMaxLoc2(numel(LocalMaxLatF),:)=

(LocGrpStartPts(numel(LocGrpStartPts))-

1)+find(PeakLatF(LocGrpStartPts(numel(LocGrpStartPts)):numel(PeakLatF))==Lo

calMaxLatF(numel(LocalMaxLatF))); % need the first term on the RHS of the equation above because the location

given is the row from the selected region of % the matrix not the whole matrix so you need to correct for that. end

LocalMaxLoc= LocalMaxLoc2(:,1);

LocalMaxdist = zeros(numel(LocalMaxLoc),1); % Start a new matrix for the

distance corresponding to the local maximums. for hh=1:(numel(LocalMaxLoc)) LocalMaxdist(hh)= Peaksdist(LocalMaxLoc(hh)); end

%scatter(LocalMaxdist,LocalMaxLatF) % Plot the local maximums.

%First step of valley identification. hold off %start new figure Valleys = zeros(size(LatF)); % Make another array to fill up with valleys

in Lateral Force data. for kk = 11:(numel(LatF)-11) % May need to change this range depending

on how many points you % specify on either side of the conditions

below. if (LatF(kk-10) > LatF(kk)) && (LatF(kk+10) > LatF(kk)) % Identifies

valleys based on the value of % lateral force a

certain number of points % either side being

greater than the point of interest. % You can change

the number of points either side that % is in the

condition based on visual inspection. Valleys(kk) = LatF(kk); % Enter values that satify the conditions of

being a valley. else Valleys(kk) = 0; % Enters a zero if not a peak. %plot (dist,LatF) % Plot raw data. %hold on %scatter (dist,Valleys) % Plots peaks, points that aren't peaks fall on

the origin end end

% (dist,LatF) of local minimums. %hold off % Start new graph. [row3,col3] = find (Valleys); % Find the location of nonzero values of

matrix. r3=row3; Valleys2 = zeros(numel(r3),1); % Start a new matrix for nonzero values of

Valleys matrix. for ll = 1:numel(r3); Valleys2(ll,1) = dist(r3(ll)); % Distance corresponding to nonzero values

of Valleys matrix.


229

Valleys2(ll,2) = Valleys(r3(ll)); % Lateral force corresponding to

nonzero value of Valleys matrix. %plot (dist,LatF) % Plot raw data. %hold on %scatter (Valleys2(:,1),Valleys2(:,2)) % Plot (dist,LatF) of nonzero

values from Valleys matrix. end Valleysdist=(Valleys2(:,1)); % x-values of nonzero values from Valleys

matrix. ValleysLatF=(Valleys2(:,2)); % y-values of nonzero values from Valleys

matrix. GrpStartPts2 = zeros(numel(Valleysdist),1); % Make another array to fill up

with the end points of %groupings of valleys where only the %local minimum is an actual valley. GrpStartPts2(1) = Valleysdist(1); for mm = 2:numel(Valleysdist) if Valleysdist(mm)-Valleysdist(mm-1)>0.03 %Conditions to make the

start point of a cluster of % data for which only the local % minimum is relavent. i.e. if % the separation between the % group end point and the next % group start point is at least % 0.1um GrpStartPts2(mm) = Valleysdist(mm); % Enter points that satisfy the

condition above. else GrpStartPts2(mm) = 0; % Enter zero for points that don't

satisfy the condition above. end end [row4,col4] = find (GrpStartPts2); % Find nonzero values of GrpStartPts2. r4 = row4; % Rows of nonzero values of

GrpStartPts. GrpStartPtsVal2 = zeros(numel(r4),1); % Start a new matrix for location

of GrpStartPts2 in Valleysdist matrix. for nn = 1:numel(r4) GrpStartPtsVal2(nn)=GrpStartPts2(r4(nn)); end

LocGrpStartPts2 = zeros(numel(GrpStartPtsVal2),1); % Start a new matrix

for location of GrpStartPts in Valleysdist matrix. for oo = 1:numel(GrpStartPtsVal2) LocGrpStartPts2(oo)=find(Valleysdist==GrpStartPtsVal2(oo)); end

LocalMinLatF = zeros((numel(LocGrpStartPts2)),1); %Start a new matrix for

local min within groups of valleys identified % by GrpStartPts2. for pp=1:numel(LocGrpStartPts2)-1

LocalMinLatF(pp) =

min(ValleysLatF((LocGrpStartPts2(pp)):(LocGrpStartPts2(pp+1)-1))); % range

of the matrix of peaks

% bound by the GrpStartPts2. % Last grouping doesn't doesn't have an end point. make it bound by the % last point in the ValleysLatF matrix. LocalMinLatF(numel(LocGrpStartPts2))=

min(ValleysLatF((LocGrpStartPts2(numel(LocGrpStartPts2))):numel(ValleysLatF

)));


230

end

LocalMinLoc2 = zeros(numel(LocalMinLatF),2); % Start a new matrix for the

location of local minimums. for qq = 1:numel(LocalMinLatF)-1 LocalMinLoc2(qq,:)=(LocGrpStartPts2(qq)-

1)+find((ValleysLatF((LocGrpStartPts2(qq)):(LocGrpStartPts2(qq+1)-

1))==LocalMinLatF(qq))); % Need the first term on the RHS of the equation above because the

location given is the row from the selected region of % the matrix not the whole matrix so you need to correct for that. %LocalMinLoc2(numel(LocalMinLatF),:)=

LocGrpStartPts2(numel(LocGrpStartPts2)); % This last line is required because the number of minimums is 1 more % than the number of grouping start points. LocalMinLoc2(numel(LocalMinLatF),:)=

(LocGrpStartPts2(numel(LocGrpStartPts2))-

1)+find(ValleysLatF(LocGrpStartPts2(numel(LocGrpStartPts2)):numel(ValleysLa

tF))==LocalMinLatF(numel(LocalMinLatF))); end

LocalMinLoc= LocalMinLoc2(:,1);

LocalMindist = zeros(numel(LocalMinLoc),1); % Start a new matrix for the

distance corresponding to the local minimums. for rr=1:(numel(LocalMinLoc)) LocalMindist(rr)= Valleysdist(LocalMinLoc(rr)); end

%scatter(LocalMindist,LocalMinLatF) % Plot the local minimums.


231

Appendix M: MATLAB code for measure the slope before the

peaks in the lateral force-distance curves from the dip-and-drag

technique

% Slope before local maximums LocMaxdist = zeros(numel(LocalMaxdistreal),1); % Start a new matrix for

location of local maximum in raw data. for ii = 1:numel(LocalMaxdistreal); LocMaxdist(ii) = find(dist==LocalMaxdistreal(ii)); end linregbeforeMax = zeros(numel(LocalMaxdistreal),2); % Start a new matrix

for linear regression of the curve before local maximum. for jj = 1:numel(LocalMaxdistreal); linregbeforeMax(jj,:)=polyfit(dist((LocMaxdist(jj)-

30):LocMaxdist(jj)),LatF((LocMaxdist(jj)-30):(LocMaxdist(jj))),1); end Slopebeforemax=linregbeforeMax(:,1) LatFfit2 = zeros(31,numel(LocalMaxdistreal)); for jjj=1:numel(LocalMaxdistreal); LatFfit2(:,jjj) =

polyval(linregbeforeMax(jjj,:),(dist((LocMaxdist(jjj)-

30):(LocMaxdist(jjj))))); end


232

Appendix N: Solving 3 non-linear simultaneous equations in

MATLAB

function F = root3d(x) F(1)=exp(436.51-0.017*(x(2)).^0.5.*log(x(2))+1.05*log(x(2))-

130.2*1.45+24.86*1.45*log(1.45)-434.64*exp(-

1.45/11.67)+25.95*(1.45)^0.5.*log(1.45)+87.97*(1.45).^0.5)-0.15; F(2)=10*exp(-5.21-0.088./x(3)-2.67*exp(-x(3))-6*10^-4*x(2)+6*10^-

3*(x(2)).^0.5+log(x(2)))-1.79; F(3)=0.5*((x(2)*(3*10^-3)*(x(3))^2))-x(1);

fun = @root3d;

x0=[0.002,16,0.3];

x=fsolve(fun,x0)


233

Appendix O: Interfacial yield stress and G’ for triplicate hydrogel

pairs for each treatment (control, YOAJ, WWY, RKKQ, D82)

Figure O.1. Interfacial yield stress against G’ for 2 different (with different symbols)

hydrogel pairs that are untreated (from the same batch of cellulose hydrogels as those treated

with YOAJ in Figure O.2).

Figure O.2. Interfacial yield stress against G’ for triplicate (with different symbols) hydrogel

pairs that are treated with YOAJ.

G' (kPa)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Inte

rfa

cia

l Y

ield

Str

ess (

Pa)

20

40

60

80

100

120

140

G' (kPa)

0.2 0.4 0.6 0.8 1.0 1.2 1.4

Inte

rfa

cia

l Y

ield

Str

ess (

Pa)

0

20

40

60

80

100


234


pairs that are untreated (from the same batch of cellulose hydrogels as those treated with

WWY, RKKQ, D82 in Figure O.4 – O.6).


pairs that are treated with WWY.

G' (kPa)

0.0 0.4 0.8 1.2 1.6 2.0

Inte

rfa

cia

l Y

ield

Str

ess (

Pa)

0

20

40

60

80

100

120

140

G' (kPa)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Inte

rfa

cia

l Y

ield

Str

ess (

Pa)

0

20

40

60

80

100

120

140

160

180


235


pairs that are treated with RKKQ.


pairs that are treated with D82.

G' (kPa)

0 1 2 3 4

Inte

rfa

cia

l Y

ield

Str

ess (

Pa)

0

50

100

150

200

250

G' (kPa)

0.0 0.5 1.0 1.5 2.0 2.5

Inte

rfa

cia

l Y

ield

Str

ess (

Pa)

0

20

40

60

80

100


236

Appendix P: Raw data from dip-and-drag experiments on

Cellulose, CAX, and CXG networks with and without expansins

Figure P.1. Lateral deflection-distance curve for Cellulose network in 20 mM Hepes buffer

(pH 7.5).

Figure P.2. Lateral deflection-distance curve for Cellulose network in 20 mM Hepes buffer

(pH 7.5) with 200 g/mL of YOAJ expansin.

Distance ( m)

0 2 4 6 8 10

Late

ral D

eflection (

V)

0.0

0.2

0.4

0.6

0.8

1.0

Distance ( m)

0 2 4 6 8

La

tera

l D

efle

ctio

n (

V)

0.0

0.2

0.4

0.6

0.8

1.0


237

Figure P.3. Lateral deflection-distance curve for CAX network in 20 mM Hepes buffer (pH

7.5).

Figure P.4. Lateral deflection-distance curve for CAX network in 20 mM Hepes buffer (pH

7.5) with 200 g/mL of YOAJ expansin.

Distance ( m)

0 2 4 6 8 10 12

La

tera

l D

efle

ctio

n (

V)

0.0

0.5

1.0

1.5

2.0

Distance ( m)

0 2 4 6 8 10 12

Late

ral D

eflection (

V)

0

1

2

3

4


238

Figure P.5. Lateral deflection-distance curve for CXG network in 20 mM Hepes buffer (pH

7.5).

Figure P.6. Lateral deflection-distance curve for CXG network in 20 mM Hepes buffer (pH

7.5) with 200 g/mL of YOAJ expansin.

Distance ( m)

0 5 10 15 20

La

tera

l D

efle

ctio

n (

V)

0.0

0.5

1.0

1.5

2.0

2.5

Distance ( m)

0 5 10 15 20

La

tera

l D

efle

ctio

n (

V)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4


239

Appendix Q: Histogram of peak heights for Cellulose, CAX, and

CXG networks with and without expansins

Figure Q.1. Histogram of peaks heights (n = 166) from lateral deflection-distance curves for

Cellulose networks in 20 mM Hepes buffer (pH 7.5).


Cellulose networks in 20 mM Hepes buffer (pH 7.5) with 200 g/mL of YOAJ expansin.

Peak Height (V)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Cou

nt

0

20

40

60

80

100

Peak Height (V)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Cou

nt

0

20

40

60

80

100


240


CAX networks in 20 mM Hepes buffer (pH 7.5).


CAX networks in 20 mM Hepes buffer (pH 7.5) with 200 g/mL of YOAJ expansin.

Peak Height (V)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Cou

nt

0

10

20

30

40

50

60

Peak Height (V)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Count

0

10

20

30

40

50

60


241


CXG networks in 20 mM Hepes buffer (pH 7.5).


CXG networks in 20 mM Hepes buffer (pH 7.5) with 200 g/mL of YOAJ expansin.

Peak Height (V)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Cou

nt

0

10

20

30

40

50

Peak Height (V)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Count

0

10

20

30

40

50

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