The Pennsylvania State University

The Graduate School

Department of Chemistry

ARTIFICIAL INTELLIGENCE:

COLLECTIVE BEHAVIORS OF SYNTHETIC MICROMACHINES

A Dissertation in

Chemistry

by

Wentao Duan

2015 Wentao Duan

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

May 2015

The dissertation of Wentao Duan was reviewed and approved* by the following:

Ayusman Sen

Distinguished Professor of Chemistry

Dissertation Advisor

Chair of Committee

Thomas E. Mallouk

Evan Pugh Professor of Materials Chemistry and Physics

John Badding

Professor of Chemistry

Darrell Velegol

Distinguished Professor of Chemical Engineering

Kenneth S. Feldman

Professor of Chemistry

Graduate Program Chair of Department of Chemistry

*Signatures are on file in the Graduate School

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ABSTRACT

Synthetic nano- and micromotors function through the conversion of chemical free

energy or forms of energy into mechanical motion. Ever since the first reports, such motors have

been the subject of growing interest. In addition to motility in response to gradients, these motors

interact with each other, resulting in emergent collective behavior like schooling, exclusion, and

predator-prey. However, most of these systems only exhibit a single type of collective behavior in

response to a certain stimuli. The research projects in the disseratation aim at designing synthetic

micromotors that can exhibit transition between various collective behaviors in response to

different stimuli, as well as quantitative understanding on the pairwise interaction and propulsion

mechanism of such motors.

Chapter 1 offers an overview on development of synthetic micromachines. Interactions

and collective behaviors of micromotors are also summarized and included.

Chapter 2 presents a silver orthophosphate microparticle system that exhibits collective

behaviors. Transition between two collective patterns, clustering and dispersion, can be triggered

by shift in chemical equilibrium upon the addition or removal of ammonia, in response to UV

light, or under two orthogonal stimuli (UV and acoustic field) and powering mechanisms. The

transitions can be explained by the self-diffusiophoresis mechanism resulting from either ionic or

neutral solute gradients. Potential applications of the reported system in logic gates, microscale

pumping, and hierarchical assembly have been demonstrated.

Chapter 3 introduces a self-powered oscillatory micromotor system in which active col-

loids form clusters whose size changes periodically. The system consists of an aqueous

suspension of silver orthophosphate particles under UV radiation, in the presence of a mixture of

glucose and hydrogen peroxide. The colloid particles first attract with each other to form clusters.

After a lag time of around 5min, chemical oscillation initiates, and triggers periodic change of the

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associated self-diffusiophoretic effects as well as interactions between particles. As a result,

dispersion and clustering of particles take place alternatively, and sizes of colloidal clusters vary

periodically together with local colloid concentration, formulating a namely “colloidal clock”. In

the system, oscillation can propagate from individual clusters to nearby clusters, and there can

exist more than one oscillation frequencies in one system, possibly due to different local particle

concentrations or cluster size.

Chapter 4 quantitatively investigates the influence of pairwise interaction between motors

on their diffusional behaviors by analyzing motion of light-powered silver chloride particles.

Powered by UV light, nano/micrometer-sized silver chloride (AgCl) particles exhibit autonomous

movement and form “schools” in aqueous solution. Motion of these AgCl particles are tracked

and analyzed. AgCl particles exhibit ballistic motion at short time intervals that transition to

enhanced diffusive motion as the time interval is increased. The onset of this transition was found

to occur more quickly for particles with more neighbors. If the active particles became “trapped”

in a formed “school”, the diffusive behavior further changes to subdiffusion. The correlation

between these transitions and the number of neighboring particles was verified by simulation, and

confirms the influence of pairwise interaction between motors.

Chapter 5 aims at quantitative understanding on the self-diffusiophoresis propulsion

mechanism through numerical simulation with COMSOL Multiphysics. A self-powered

micropump based on ion-exchange is chosen as the experimental model system. Weakly acidic-

form ion-exchange resin can function as self-powered micropumps in aqueous solution,

manipulating fluid flow at vicinity and transporting inert tracer colloids. Pumping direction in the

system can be dynamically altered in response to pH change: lower pH leads to outward

pumping, and higer pH results in inward particle motion. A COMSOL Multiphysics model is

built with different boundary conditions and parameters, in accordance with the experimental

system. The reasonable agreement between experimental and simulation results confirms self-

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diffusiophoresis as the powering mechanism. By varing parameters, the model also suggests

possible routes to tune the performance of the micropump. COMSOL simulations on micropumps

that are based on density-driven mechanism are also included.

vi

TABLE OF CONTENTS

List of Figures ......................................................................................................................... viii

Acknowledgements .................................................................................................................. xv

Chapter 1 Introduction ............................................................................................................. 1

1.1 Development of synthetic autonomous nano- and micromachines ............................ 3 1.1.1 Development of nano- and micromotors ......................................................... 3 1.1.2 Development of micropumps .......................................................................... 4

1.2 Interaction and collective behaviors of synthetic nano- and micromotors ................. 6 1.2.1 Chemotaxis ...................................................................................................... 7 1.2.2 Diffusiophoretic interactions ........................................................................... 8 1.2.3 Collective behaviors of synthetic micromotors .............................................. 10

1.3 Research motivation and summary ............................................................................ 11 1.4 References .................................................................................................................. 13

Chapter 2 Transition between Collective Behaviors in Response to Different Stimuli ........... 19

2.1 Introduction ................................................................................................................ 19 2.2 Experimental section .................................................................................................. 21

2.2.1 Synthesis of Ag3PO4 microparticles ................................................................ 21 2.2.2 Observation ..................................................................................................... 21 2.2.3 Characterizations ............................................................................................. 22

2.3 Results and discussions .............................................................................................. 22 2.3.1 Reversible transition between two collective behaviors in response to

ammonia signals ............................................................................................... 22 2.3.2 Collective behavior in response to UV light signals ....................................... 33 2.3.3 Design of logic gates ....................................................................................... 34 2.3.4 Transition between assembly and dispersion in response to orthogonal

stimuli ............................................................................................................... 35 2.4 Conclusion ................................................................................................................. 38 2.5 Perspective ................................................................................................................. 38 2.6 References .................................................................................................................. 39

Chapter 3 Self-powered “Colloidal Clock” with Chemical Inputs .......................................... 42

3.1 Introduction ................................................................................................................ 42 3.2 Experimental section .................................................................................................. 44

3.2.1 Synthesis of Ag3PO4 particles. ........................................................................ 44 3.2.2 Observation. .................................................................................................... 44 3.2.3. Video analysis ................................................................................................ 45 3.2.4. Zeta potential measurement............................................................................ 45

3.3 Results and discussion ............................................................................................... 45 3.3.1 Phenomena ...................................................................................................... 45 3.3.2 Mechanism ...................................................................................................... 49

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3.3.3 Multiple Frequencies ....................................................................................... 51 3.3.4 Continuum model ............................................................................................ 53

3.4 Conclusion ................................................................................................................. 60 3.5 Perspective ................................................................................................................. 60 3.6 References .................................................................................................................. 61

Chapter 4 Motion Analysis on Silver Chloride Nanomotors ................................................... 62

4.1 Introduction ................................................................................................................ 62 4.2 Experimental section .................................................................................................. 65

4.2.1 Synthesis of AgCl particles ............................................................................. 65 4.2.2 Observation and tracking of particles .............................................................. 66 4.2.3 Netlogo model ................................................................................................. 67

4.3 Results and discussion ............................................................................................... 69 4.3.1 Isolated particles in the absence of UV light. .................................................. 70 4.3.2 Isolated particles in the presence of UV light. ................................................ 71 4.3.3 Coupled particles ............................................................................................. 75 4.3.4 Schooled particles ........................................................................................... 79 4.3.5 Simulation results ............................................................................................ 82

4.4 Conclusions ................................................................................................................ 84 4.5 Perspective ................................................................................................................. 84 4.6 References .................................................................................................................. 85

Chapter 5 Numerical Simulation on Micropumps with COMSOL Multiphysics .................... 87

5.1 Introduction ................................................................................................................ 87 5.2 Experimental section .................................................................................................. 88

5.2.1 Observation. .................................................................................................... 88 5.2.2. COMSOL Multiphysics Simulation ............................................................... 89

5.3 Results and Discussion ............................................................................................... 89 5.3.1 Phenomena ...................................................................................................... 89 5.3.2 Mechanism ...................................................................................................... 90 5.3.3 Numerical simulation on ionic diffusiophoretic micropumps ......................... 93 5.3.4 Numerical simulation on density-driven pumps.............................................. 98

5.4 Conclusion ................................................................................................................. 102 5.5 Perspective ................................................................................................................. 102 5.6 References .................................................................................................................. 102

viii

LIST OF FIGURES

Figure 1-1. Catalytic micromotors, rotors and pumps. Electrocatalytic reactions of fuels

in bi- and trimetallic structures of different designs can result in different kinds of

micromachines such as motors, rotors and pumps. .......................................................... 3

Figure 1-2. Synthetic micro- and nanomachines that are powered by different

mechanisms. a) Propulsion of bimetallic Pt-Au nanorods in H2O2 solution powered

by self-electrophoresis. The electrochemical reactions at the two ends of the rod

produce a gradient of protons pointing from the Pt to the Au end, and thus an electric

field in the same direction. The electric field then drives the motion of the rod itself.

b) .Diagram showing the active mechanism for the polymerization powered motor.

Fluid flows from low concentration to high concentration causing the motor to move

in the opposite direction. c) Propulsion of bimetallic nanorods in an acoustic field.

The acoustic field levitates the motors to a certain plane where they move around. d)

Fluid pumping by photoacid generators in response to UV light. Upon addition of

UV light, the chemical reaction produces gradients of ions near the pump, and the

difference in ion diffusivities leads to local electric fields that induce electroosmotic

flows near the charged surface of the substrate. e) Fluid pumping of a DNA

polymerase-modified Au pattern in response to dATP and magnesium ions. ................. 6

Figure 1-3. Ionic diffusiophoretic interactions between active colloids. a) When colloids

are producing faster cations, inward electric fields are induced, leading to

dominating inward osmotic flows, and colloids attract each other. b) When colloids

are producing faster anions, outward electric fields are induced, leading to

dominating outward osmotic flows, and colloids repel each other. ................................. 10

Figure 2-1. Transition between the “exclusion” behavior and “schooling” behavior based

on self-diffusiophoresis. With ammonia added, OH- produced by the reaction

diffuses away faster from the silver orthophosphate microparticles than the other

ions, resulting in an electric field pointed outward (orange arrow). This leads to

inward electrophoresis of the particles (red arrows) and outward electroosmotic flow

(blue arrows) along the glass substrate, with the latter dominating resulting in

“exclusion” behavior. With ammonia removed, the reaction is reversed and so are

the effects mentioned above, and “schooling” behavior is observed. .............................. 20

Figure 2-2. Transition between two emergent behaviors for silver orthophosphate

microparticles. Optical microscope images: a) particles show “exclusion” behavior

right after addition of 2 mM ammonia, (b-d) particles show “schooling” behavior

following elapsed time after addition of ammonia: b) 3 min c) 5 min d) 7 min. Scale

bar, 50μm. ........................................................................................................................ 22

Figure 2-3. Time-lapse optical microscope images demonstrating dynamic merging of

smaller “schools” to form larger ones. (a-e) Four small schools within the white

circle gradually merge with each other to form a large one. Scale bar, 20μm.. ............... 23

Figure 2-4. Zeta potentials of Ag3PO4 particles at different ammonia concentrations. ........... 26

ix

Figure 2-5. Time-lapse optical microscope images demonstrating collective behavior in

closed system. (a-b) Upon addition of ammonia, silver phosphate particles exhibit

“exclusion”. (b-d) Over time, no schooling behaviors are observed. Time stamps: 0,

10, 480 and 960s. Scale bar, 20μm. ................................................................................ 27

Figure 2-6. Time-lapse optical microscope images demonstrating collective behavior in

0.02 M ethylenediamine solution. (a-b) Upon addition of ethylenediamine, silver

phosphate particles exhibit “exclusion”. (b-d) Over time, no schooling behaviors are

observed. Time stamps: 0, 5, 300 and 600s. Scale bar, 20μm. ....................................... 28

Figure 2-7. Time-lapse optical microscope images demonstrating influence of ionic

strength on the transition of collective behaviors. (a-d) Compared with the two

cased with 0.5mM and 1mM NaNO3, the system with higher ionic strength (3mM

NaNO3) does not exhibit transition from “exclusion” to “schooling”. Time stamp: 0,

5, 120 and 240s. Scale bar, 20μm. ................................................................................... 29

Figure 2-8. Schemes for diffusiophoretic interaction between the central particle and

nearby particles with an inward electric field. a) When the nearby particles are

positively charged, the directions of electrophoresis and electroosmosis are both

inwards, the diffusiophoretic interactions are attractive, and the system shows a

“schooling” pattern. B) When the nearby particles are negatively charged and the

magnitude of 𝜁P is larger than that of 𝜁w, the outward electrophoresis dominates

over the inward electroosmosis, the diffusiophoretic interactions are thus repulsive,

and the system shows “exclusion” patterns with exclusion zones between them. C)

When the nearby particles are negatively charged and the magnitude of 𝜁P is smaller

than that of 𝜁w, the inward electroosmosis dominates the diffusiophoretic

interactions are attractive, and the system shows “schooling” patterns. However,

when the particles come close enough to the central one, a repulsive electrophoretic

force dominates again and small exclusion zones are formed between the central

particle and nearby particles............................................................................................. 30

Figure 2-9. Time-lapse optical microscope images showing silver orthophosphate

microscale pump system with 0.9 μm PS-carboxylate tracer particles in 2 mM

ammonia solution. With addition of ammonia solution, tracer particles are pumped

away from the large pump particles and “exclusion” zones (areas within the white

circles) are formed within seconds. The sizes of “exclusion” zones vary from pump

particles. Scale bar, 50μm. ............................................................................................... 32

Figure 2-10. Time-lapse optical microscope images showing hierarchical particle

assembly between Ag3PO4 microparticles and 2.34 μm silica tracers in 2 mM

ammonia solution. a) With removal of ammonia, Ag3PO4 microparticles forms

“schools” with silica tracers on the outer boundary; b) when the smaller “schools”

start to merge, silica tracers are “excluded” to the periphery of the newly formed

larger “schools”. c) Hierarchical particle assembly between Ag3PO4 microparticles

and silica tracers is achieved with Ag3PO4 microparticles “schools” as the core and

silica tracers on the periphery. Scale bar, 20μm. ............................................................ 33

x

Figure 2-11. Time-lapse optical microscope images demonstrating formation of exclusion

zones around silver phosphate particles upon UV exposure (a) before UV exposure

b) UV turned on, c) 15s after UV exposure. Scale bar, 20μm. ........................................ 34

Figure 2-12. NOR Gate with UV and ammonia as inputs, collective behaviors as outputs:

“schooling” and “exclusion” behaviors as 1 and 0, respectively. .................................... 35

Figure 2-13. Under acoustic fields, Ag3PO4 MPs form stripes (a,c) and disperse (b,d)

reversibly with UV light off and on, respectively. Scale bar: 50 m ............................... 36

Figure 2-14. With UV light off, stripes of particles form with dominating inward acoustic

forces (Facou). And with UV light on, stronger outward chemical forces (Fchem) are

induced, and stripes disassembled. Scale bar: 20 m ...................................................... 38

Figure 3-1. Oscillatory transition between dispersion and clustering of Ag3PO4 MPs

based on self-diffusiophoresis. With addition of glucose/UV light, silver

orthophosphate is reduced to silver metal, and OH- produced by the reaction diffuses

away faster from the microparticles than the other ions, resulting in an electric field

pointed outward (orange arrow). This leads to inward electrophoresis of the particles

(red arrows) and outward electroosmotic flow (blue arrows) along the glass

substrate. The latter dominates and results in repulsion and dispersion of particles,

and the clusters split into smaller ones or single particles (Trough). With peroxide

and UV light, silver is oxidized back to silver phosphate, the ion gradients are

reversed together with the effects mentioned above. Therefore particles or smaller

clusters attract each other to form larger clusters (Crest). The alternation of the two

reactions hence leads to oscillatory motion of the particles and periodic alternation

of cluster sizes. ................................................................................................................. 43

Figure 3-2. Microscope images demonstrating periodic oscillation of Ag3PO4 MPs in a

mixture of 50mM glucose and 0.25% hydrogen peroxide under UV. Over time,

clusters of Ag3PO4 MPs alternatively reassemble (a, c and e) and disassemble (b, d

and f), by extracting and releasing particles, respectively. Scale bar: 20m ................... 46

Figure 3-3. Bigger remainder clusters function as “nuclei” and pull in particles and

smaller clusters nearby. Scale bar: 10m ......................................................................... 46

Figure 3-4. Motion of an individual cluster through asymmetric particle extraction and

release. Scale bar: 20m .................................................................................................. 47

Figure 3-5. Merging of two oscillating clusters. Scale bar: 10m ........................................... 48

Figure 3-6. Propagation of particle oscillation. a-b) Oscillation first initiates at the upper

left corner, where clusters with in the circle are oscillating. c) Oscillation propagates

to a wider range on the left side d) Oscillation eventually propagates throughout the

whole screen. Scale bar: 50m ........................................................................................ 48

Figure 3-7. Design of a microscale pump with glucose and a bulky silver orthophosphate

particle. a-b) The bulky pump particle drives nearby particles to migrate away,

xi

forming an exclusion zone around itself. b)-c) The exclusion zone grows over time.

Scale bar: 20m ............................................................................................................... 50

Figure 3-8. Existence of two frequencies in one system. FFT analysis of the results in the

top graph reveals two frequencies as demonstrated in the bottom graph. Top: Video

analysis results. Bottom: FFT resutls. Note that the results are based on a 4x faster

video. ................................................................................................................................ 52

Figure 3-9. FFT results of the entire videos and cluster-based cropped ones. The resutls

demonstrate that the two clusters in the blue and green rectangles are governed by

different frequencies. ....................................................................................................... 53

Figure 3-10. Influence of hydrogen peroxide (increases as C2 grows) on the stability of

the basic state. (a): Neutral stability curves α*(K) for two values of C2 . (b):

variation of the critical values of αc with C2 ; for both panels the oscillatory regime

emerges above the curves. (c): variation of the critical wavenumber Kc (right axis,

dashed line) and frequency of perturbations ωc (left axis, dotted line) with C2 . The

other parameters, as they are defined in Eqs. (9) and (10), are A1 = 0.5, A2 = 0.1, B2

= 0.8, D2 = 1.3, D3 = 0.5. .................................................................................................. 59

Figure 4-1. A microscope image showing examples of isolated, coupled, and schooled

classifications of AgCl particles....................................................................................... 64

Figure 4-2. SEM images of AgCl particles, the radius of which are around 1μm. .................. 66

Figure 4-3. Interface for the Netlogo Model ............................................................................ 68

Figure 4-4. Example trajectories of four different AgCl particles selected from each of the

four particle classifications: AgCl in the absence of UV light, AgCl in the presence

of UV light, coupled AgCl particles, and schooled AgCl particles. ................................ 70

Figure 4-5. Mean squared displacement of AgCl particles in the absence of UV. Linear

relation indicates normal diffusive behavior as expected for Brownian motion. At

each time interval, thirty particles’ MSD values are calculated. Each data point in the

figure represents the average of these MSD values at the corresponding time

interval, and the corresponding error bar is calculated from the standard deviation of

the MSD values with a 95% confidence level.................................................................. 71

Figure 4-6. Time-lapse optical microscope images showing the movement and leading

end of an isolated particle (the one within the white circle): the particle moves along

its leading end ( a-b ), and then changes its moving direction due to rotational

diffusion ( c ), the particle then moves along this new direction with the same

leading end( c-e ) before changing the moving direction again. ( f ) Scale bar, 10μm.

Time stamp, 1s ................................................................................................................. 73

Figure 4-7. Mean squared displacement of isolated particles under UV light. At each time

interval, thirty particles’ MSD values are calculated. Each data point in the figure

represents the average of these MSD values at the corresponding time interval, and

the corresponding error bar is calculated from the standard deviation of the MSD

xii

values with a 95% confidence level. The red, black and blue lines represent fitting

results for short, all and long time intervals, respectively, indicating a transition from

ballistic motion to enhanced diffusion. The left and right inserts are mean squared

displacement of isolated particles at short and long time intervals, respectively. ............ 74

Figure 4-8. Scheme of interaction between AgCl particles based on self-diffusiophoresis.

For each AgCl particle, the chemical reaction taking place at its surface generates a

concentration gradient of protons and chloride ions, and this concentration gradient

leads to diffusiophoretic flows as shown in a):28 Because protons travel away from

the surface of AgCl much faster than the chloride ions (DH+ = 9.311x10-5 cm2s-1,

DCl- = 1.385x10-5 cm2s-1 ), an electrical field (E) will be generated pointing back

towards the AgCl particle. The electrical field acts phoretically on the nearby

negatively charged AgCl particles (𝜁 = -50 mV) by pushing them away from the

central one (VEp). The electrical field also acts osmotically on the adsorbed protons

in the double layer of the microscope slide wall (𝜁 = -62 mV) by pumping the fluid

along the slide’s surface towards the AgCl particles. (VEo) At long distances from

the central AgCl particle, osmotic flow dominates because the magnitude of the

particle zeta potential is less than that of the slide, and the electroosmotic flow pulls

the nearby particles to the central one leading to schooling, as shown in b). The

electroosmotic flow decays to zero very near to the AgCl particle due to fluid

continuity, and repulsive electrophoretic force starts to dominate resulting in a small

exclusion zone around each AgCl particle. In addition, for the formed “school” (area

circled in c)), the electroosmotic flow remains persistent due to the continued

generation of ions and this serves to prevent individual particles from escaping. For

a particle (the sphere with blue arrow in d) that interacts with a certain

“neighboring” particle (the red sphere in d), it will move towards the neighbor

without changing the orientation, and the net path is similar to a particle that

changes its orientation by rotational diffusion and then moves along the new

direction by ballistic motion, as shown in e). As a result, particles that interact with

neighboring particles appear to be rotating more frequently than isolated particles. ...... 76

Figure 4-9. Time-lapse optical microscope images showing that there is no preferential

orientation of particles with respect to their neighbors: the rod-like particle within

the white circle has different orientations with respect to the particle nearby in a)-d).

Scale bar, 5μm. Time stamp, 5s ....................................................................................... 78

Figure 4-10. Mean squared displacement of coupled particles. At each time interval,

thirty particles’ MSD values are calculated. Each data point in the figure represents

the average of these MSD values at the corresponding time interval, and the

corresponding error bar is calculated from the standard deviation of the MSD values

with a 95% confidence level. ........................................................................................... 78

Figure 4-11. Mean squared displacement of schooled particles. At each time interval,

thirty particles’ MSD values are calculated. Each data point in the figure represents

the average of these MSD values at the corresponding time interval, and the

corresponding error bar is calculated from the standard deviation of the MSD values

with a 95% confidence level. The red and black lines represent fitting results for

short and all time intervals, respectively, indicating a transition from powered

diffusion to sub-diffusive behavior. ................................................................................. 81

xiii

Figure 4-12. Mean squared displacement of schooled particles at short time intervals.

Schooled particles show normal diffusion behavior at short time interval, with an

effective diffusion constant Deff = 0.50 m2 s-1. ............................................................. 81

Figure 4-13. Time-lapse optical microscope images showing a particle (the green marked

particle within the white circle) stays “trapped” inside the formed “school” with

neighboring particles (green marked particles outside the white circle) around in a)-

d). Scale bar, 10μm. Time stamp, 5s ................................................................................ 82

Figure 4-14. Simulation results for mean squared displacements of “spectator” particles

with different number of neighboring particles: (a) no neighbors (b) one neighbor

(c) three neighbors (d) five neighbors (e) ten neighbors and (f) twenty neighbors.

Transitions from superdiffusion to normal diffusion and then subdiffusion can be

correlated with the increasing number of neighboring particles. ..................................... 83

Figure 5-1 Ion-exchange at different pH values: a) pH 4.7, b) pH 3 ....................................... 88

Figure 5-2 Pumping of silica tracers by Amberlite particles at pH ~ 4.7: a) Formation of

inward electric field due to ion-exchange. Inset demonstrates faster diffusion of

protons, which results in inward electrical fields and dominating inward

electroosmotic flows. b) Inward particle motion, as indicated by black arrows, due to

pumping towards Amberlite, trajectories of ten particles during a time interval of 4s

are shown in different colours. Scale bar 10 µm. ............................................................. 89

Figure 5-3 Pumping of silica tracers by Amberlite particles at pH ~ 3: a) Formation of

outward electric field due to ion-exchange. Inset demonstrates faster diffusion of

protons, which results in outward electrical fields and dominating outward

electroosmotic flows. b) Outward particle motion, as indicated by black arrows, due

to pumping towards Amberlite, trajectories of ten particles during a time interval of

4s are shown in different colours. Scale bar 10 µm. ........................................................ 90

Figure 5-4 pH change with Amberlite pump system: (a) ~100 amberlite particles in 5mL

1mM NaCl and (b) ~100 NaCl-processed amberlite particles in 5 mL 1mM HCl

solutions over a time period of 3 min. .............................................................................. 92

Figure 5-5 a) Concentration distribution of protons (CH), chloride ions (CCl) and HCl

(CHCl) molecules. b) Profile of CH-CCl.............................................................................. 94

Figure 5-6 a) Electrical field distribution at different heights above the bottom. b) Fluid

flow profile. ...................................................................................................................... 94

Figure 5-7 Simulation results with constant fluxes. Top: Inward flows based on exchange

from sodium ions to protons. Bottom: Outward flows based on exchange from

protons to sodium ions. .................................................................................................... 96

Figure 5-8 Simulation results with fluxes that are linear with local concentrations. Top:

Inward flows based on exchange from sodium ions to protons. Bottom: Outward

flows based on exchange from protons to sodium ions. .................................................. 97

xiv

Figure 5-9 COMSOL Multiphysics simulation results. a) Geometry of the model, red line

indicates the constant temperature boundary condition. b) Shear rate distribution for

~1µm/s fluid flow along the line as marked by red in the inset, which is 100µm

away from the pump boundary. c) Fluid velocity distribution at 10-4 W power input. .... 100

Figure 5-10 COMSOL Multiphysics simulation results. a) Geometry of the model, red

line indicates the constant temperature boundary condition. b) Fluid velocity

distribution at 1.64 * 10-5 W power input. c) Fluid velocity distribution of an

inversed pump at 1.64 * 10-5 W power input. d) Fluid velocity distribution at 3.77 *

10-5 W power input. .......................................................................................................... 101

xv

ACKNOWLEDGEMENTS

I would start by dedicating my most sincere gratitude to my advisor and “Boss man”, Dr.

Sen. It has always been a blessing to spend my five and a half years under his mentorship doing

research and enjoying life (although it may still take time to develop my taste for wine). Dr. Sen

always supports me to try on my own ideas and motivates me to learn new things. I am especially

thankful to his encouragement and optimism. And it is only under his guidance that I start to learn

state of the art in science, and evolve from a pure synthetic chemist to someone who can combine

experiments with models and theories. I would surely benefit from such experience during my

future reseach.

I also highly appreciate the guidance and support of my committee members, Dr.

Badding, Dr. Mallouk and Dr. Velegol, as well as Dr. Butler, Dr. Crespi and Dr. Huang, for

offering me tremendous help over my research projects. I am thankful towards all my

collaborators in and out of Penn State, Dr. Ran Liu, Dr. Hua Zhang, Dr. Samudra Sengupta,

María Antonieta Sánchez-Farrán, Feng Guo, Dr. Daniel Ahmed, Dr. Sergey Shklyaev, Steve

Schulz, Dr. Ubaldo M. Córdova-Figueroa, all the Sen group members and guest members: Dr.

Wei Wang, Suzanne Ahmed, Dr. Tso-Yi Chiang and Abhishek Kar. I also owe my gratitude to all

the staff members in Nanofab, Department of Chemistry and Penn State MRSEC for all the

support. It has been my pleasure and good fortune to work with and learn from these brilliant and

nice people. Special thanks to Dr. Michael Ibele, for leading me into this exciting research field

and teaching me all the fundamentals and Netlogo.

Life toward PhD is not easy. Fortunately, I have got my friends that have been fighting

together with me: Dr. Zheng Shen, Baiyang Ren, Dr. Yijia Gu, Dr. Jinling Liu, Baoming Tang,

Jun Zhao, Yannan Shen, Dr. Mengchu Huang, Yin Li, Peng Zhang, Dr. Weiran Yang, Meng Wu,

Peng Zhou, Shuyi Zhang and Mingda Zhou. All the best to everyone!

xvi

Last but certainly not least, I want to thank my family and family-to-be for their love. My

parents have always been supportive on my every single decision, and place their confidence in

my abilities and potentials. And for my lovely and beloved fiancée, it is really my blessing to get

to know her here at Penn State. She always encourages me and cheers me up, and I want to thank

her for accompanying me through all the highs and the lows. We would continue our happy

journey beyond and forever!

1

Chapter 1

Introduction

Machines are a fundamental part of civilization, catalyzing the evolution of human

society. People have long dreamed of shrinking these machines down to the micro- or nanoscale

to send them, for example, into human body and carry out delicate in vivo operations. However,

at this small scale it has been difficult to overcome the dominance of viscous and frictional

forces, fluctuation from Brownian motion, and scaling laws that restrict the speed and power of

microscale motors. It is only in the last decade that researchers have managed to design self-

powered synthetic nano- and micromachines1, 2 that convert chemical energy into mechanical

motion. The initial discoveries have sparked tremendous interest in this emerging field3-37, and a

wide repertoire of synthetic machines have been designed, which can be powered by chemical

fuels5, 12, 18, 38-47 or externally applied fields that deliver magnetic48-56, electrical14, 57, light58-61,

acoustic62-64, or thermal65-67 energy.

Like their macroscale counterparts, nano- and micromachines also work by converting

other forms of energy into mechanical motion. Interestingly, unlike their macroscale counterparts,

synthetic nano- and micromachines typically do not have moving parts and are constrained by the

time reversal symmetry that applies in the low Reynolds number regime: the scallop theorem 37, 68,

69. Also, for low Reynolds number regime, surface forces and interfacial effects70-73 dominate

over body forces like inertia. These limitations require the development of new energy

transduction mechanisms to propel small scale machines.

One common way to break time reversal symmetry and power nano- and micromachines

is to expose them to a field or gradient. Self-generated gradients allow autonomous machines to

2

move independently from each other. Alternatively, externally applied fields can cause non-

autonomous machines to move collectively in unison. Autonomous nano- and micromachines

driven by self-generated fields constitute a significant part of current motor research, and are the

focus of this dissertation.

Autonomous nano- and micromachines can be divided into three major categories:

motors that exhibit directional translational motion, rotors that follow circular trajectories, and

pumps that stand still but drive the movement of fluids and tracer particles (Fig. 1-1). These

three types of micromachines break symmetry in different ways to induce movement.

Micropumps break the symmetry of local concentrations of chemical species and fluid

flow. Motors and rotors require a gradient along their body to generate motion. They are

mostly rods or spheres with asymmetry in composition (e.g., one side composed of active

material and the other inert material) 18, activity (chemical reaction rate is higher at one

side than the other)1 or shape (two ends respond to the external field differently) 74. The

asymmetry is broken along one axis, which dictates the direction of motion. Nano- and

microscale motors can become rotors if asymmetry (composition, shape or activity) is

introduced perpendicular to the long axis of the particle instead of along the axis.

Interestingly physical boundaries can also induce rotation10.

3

Figure 1-1. Catalytic micromotors, rotors and pumps. Electrocatalytic reactions of fuels in bi- and

trimetallic structures of different designs can result in different kinds of micromachines such as

motors, rotors and pumps.

1.1 Development of synthetic autonomous nano- and micromachines

1.1.1 Development of nano- and micromotors

Nature uses chemistry to power a myriad of biological machines and motors 75, and

similar strategies have been utilized to power synthetic motors. Two independent early

discoveries established that bimetallic metal microrods moved autonomously in hydrogen

peroxide solutions (H2O2) 1, 2. As shown in Fig. 1-2(a), the mechanism by which these

motors are propelled was determined to be self-electrophoresis through a series of

experimental and simulation efforts42, 76-79. The essence of this mechanism is that motor

particles generate a concentration gradients of ions (protons, halide ions, etc.) through

bipolar electrochemical reactions at the two ends of the rods. The resulting electric field

induces motion of the motors themselves through electrophoresis. Other forms of motion

driven by self-generated gradients have more recently been demonstrated. For example,

4

motors driven by self-diffusiophoresis (Fig.1-2(b)) are propelled by self-generated

chemical concentration gradients,60, 80-82 and self-acoustophoretic motors (Fig.1-2(c)) are

propelled by asymmetric steady streaming of the fluid around them in an acoustic field 63,

74, 83, 84. Temperature gradients can also be used by microparticles to create motion, and

this mechanism is called self-thermophoresis65-67.

1.1.2 Development of micropumps

When anchored to a surface, motors transfer their mechanical energy to the surrounding

fluid, directionally transporting fluid and tracer particles. The first micropumps 76, 85-87 were

developed using the same principle as that of the rods that move through bipolar electrochemical

reactions and involved two metals in electrical contact. With the addition of fuel, redox reactions

occur at the surfaces of the metals, creating an ion gradient in solution over the metals. The

resultant electric field acts both phoretically on the charged tracer particles, and osmotically on

the electric double layer at the charged surface of the substrate. Tracer particles suspended in the

fluid move through electrophoresis, whereas the motion of those that are close to the surface is

determined by the interplay between phoresis and osmosis.

Synthetic micropumps based on self-diffusiophoresis (Fig.1-2(d)) were subsequently

developed 31, 88, 89. In response to external stimuli such as chemicals 31, 88 or light 89, reactions at

the surface of micropumps lead to concentration gradients of ions and molecules, and thus

generate fluid flows. Self-diffusiophoresis arises from two effects: electrophoresis and

chemiphoresis. In electrophoresis, the difference in diffusivities of the cations and anions leads to

a local electric field resulting in phoretic motion of tracer particles and osmotic fluid flows along

the surface of the substrate. In addition, concentration gradients result in different thicknesses of

5

double layers and thus a pressure difference along the surfaces of the particles and the pump. This

causes chemiphoretic fluid flow towards areas of higher chemical concentration. The

chemiphoretic effect is normally small compared to electrophoresis, and only governs fluid

pumping when the cations and anions have similar diffusivities, e.g. K+ and Cl-.

Unlike electrophoretic micropumps that require electro-conductive substrates,

diffusiophoretic pumps can operate on various substrates like glass and polystyrene 89, although

both systems perform poorly at high ionic strengths due to squeezed electrical double layers and

attenuated diffusiophoretic flow 60, 81.

Micropumps based on density gradients (Fig.1-2(e)) that are largely unaffected by high

electrolyte concentrations have also been designed 90, 91. Chemical reactions at pump surfaces

(64), are almost always coupled with heat generation or consumption 90. This heat flux leads to

temperature gradients and thus density differences across the solution. Due to the buoyancy

effect, lighter fluids move up, and denser ones settle down, which leads to convective fluid flows

91. For exothermic reactions, i.e. pumps that generate heat, fluids are pumped inwards near the

substrate, and for endothermic ones, outward fluid flows are generated. Density gradients can also

result from density differences between reactants and products 91. Unlike the phoretic pumps

discussed above, fluid velocities in density-driven pumps are influenced by the cell dimensions:

for example, a seven-fold increase of velocity was observed upon doubling the cell height 90. In

addition, the directions of fluid flows in density-driven systems can be reversed by inverting the

pumps.

Other examples of micropumps have also been reported, including ones based on host-

guest interactions 92 and bubble propulsion 93. The former generate fluid flow by uptake/release of

water molecules through host-guest complexation, and the latter function by a capillary effect.

6

Figure 1-2. Synthetic micro- and nanomachines that are powered by different mechanisms. a)

Propulsion of bimetallic Pt-Au nanorods in H2O2 solution powered by self-electrophoresis. The

electrochemical reactions at the two ends of the rod produce a gradient of protons pointing from

the Pt to the Au end, and thus an electric field in the same direction. The electric field then drives

the motion of the rod itself. b) .Diagram showing the active mechanism for the polymerization

powered motor. Fluid flows from low concentration to high concentration causing the motor to

move in the opposite direction. c) Propulsion of bimetallic nanorods in an acoustic field. The

acoustic field levitates the motors to a certain plane where they move around. d) Fluid pumping by

photoacid generators in response to UV light. Upon addition of UV light, the chemical reaction

produces gradients of ions near the pump, and the difference in ion diffusivities leads to local

electric fields that induce electroosmotic flows near the charged surface of the substrate. e) Fluid

pumping of a DNA polymerase-modified Au pattern in response to dATP and magnesium ions.

1.2 Interaction and collective behaviors of synthetic nano- and micromotors

The self-generated gradients by motors can not only power their own motion, but also

induce interactions between the motors. Through such interactions, motors can exhibit a good

wealth of collective behaviors, showing a high similarity with their biological counterparts.

7

As discussed above, most commonly the self-generated gradients are constituted by

chemicals “secreted” by the motor colloids.

1.2.1 Chemotaxis

Colloids can respond to chemical gradients, and migrate up or down along them, a

phenomenon known as chemotaxis. Chemotaxis has long been observed in biological active

systems like bacteria.94, 95 Recently such phenomena have been discovered in artificial

counterparts as well: bimetallic nanorods and Janus colloids can chemotaxi up externally-

imposed gradients of their fuels, and accumulate at regions with higher fuel concentrations.47, 96, 97

In a gradient of their substrates, enzyme molecules like catalase and urease also exhibit molecular

chemotaxis towards higher substrate concentration.98, 99 And this was utilized to separate enzymes

in a microfluidic device by placing the mixture of two enzymes in one channel, and the substrate

for one in the other.100 Although the exact mechanism is not clear, it has been suggested that

chemotactic behavior of artificial and enzyme molecular colloids originate from an enhanced

diffusion mechanism. Since these colloids exhibit higher diffusivities with higher fuel/substrate

concentrations,47, 101 the diffusion rate increases on moving up the gradient and decreases on

moving down the gradient at every point in space. A higher diffusion rate leads to a greater

spread of the colloids, and thus migration of the “center of gravity” of the colloid ensemble

towards the side of higher fuel/substrate concentration. The postulated mechanism does not

require temporal memory of the gradients as in biological chemotaxis,95 and is supported by a

finite element simulation of convection-diffusion equation.98

Besides external gradients, motor colloids can also respond to the chemical gradients

produced by others, and migrate towards or away from them, a localized chemotaxis. And in the

form of such relative drift, attraction or repulsion arises between motors. The observed

8

chemotactic behavior of single enzymes suggested that an enzyme that acts on the products of a

second, nearby enzymatic reaction might exhibit collective movement up the substrate gradient

towards this second enzyme, an example of collective behaviors at the molecular level. Indeed,

catalase can be attracted towards glucose oxidase in the presence of glucose, as the latter

catalyzes oxidation of glucose to produce substrate of the former (i.e. H2O2).98

1.2.2 Diffusiophoretic interactions

Another common scheme for the concentration gradient-driven interactions is

diffusiophoresis, which, unlike enhanced diffusion mechanism, describes directional motion and

interactions of individual colloids instead of statistical ensemble.102, 103 The mechanism can be

further classified as neutral or ionic diffusiophoresis, depending on whether the gradients are

composed of electrically neutral or charged solute species.34

When motors are producing neutral solutes, interaction can be attributed to pressure

gradients along the surfaces of colloids and substrates that originate from affinity between solutes

and surfaces.104-107 Self-assembly of self-propelled Pt-Silica dimers in hydrogen peroxide solution

might be based on such mechanism.108 In this system, active Pt parts catalyze the decomposition

of H2O2 into O2 and H2O. Such reaction depletes H2O2 and produces excess O2 in the vicinity of

particles, and establishes chemical gradients that not only powers linear motion and rotation of

particles,5, 9, 82, 109, 110 but may also lead to formation of tetramers, hexamers or even more

complexes structures. It is interesting to notice that the assembled structures are also moving

around but exhibiting different structure-dependent trajectories.108 Similar behaviors were

observed in Pt-polystyrene Janus doublet system in hydrogen peroxide solutions, where the

relative orientation of the two Janus particles in the doublets affects their trajectories.109

9

And what if motors are secreting ions instead of neutral species? In this case, different

diffusivities of cations and anions result in local electric fields, as shown in Fig. 1-3. The induced

electric fields can further lead to interaction between colloids through a combination of

electrophoretic and electroosmotic effects. The two effects describe, under a certain electric field,

motion of charged colloids and fluid flows along charged substrate surfaces, respectively, and

their magnitudes are determined by the zeta potentials (or surface charge densities) of the

corresponding surfaces. Here we focus on colloids that have lower surface charge density

compared to the substrates, and thus electroosmotic effects dominate and govern the interactions

between colloids. Therefore, for colloids like silver chloride (AgCl) that are producing faster

cations like protons (Fig. 1-3(a)), inward electric fields are induced, and the coupled dominating

inward electroosmotic flows bring the colloids together, resulting in diffusiophoretic attraction

between them. Similarly, when anions are the faster species (e.g. hydroxide ions compared with

Mg2+), as shown in Fig. 1-3(b), the electric fields are reversed together with electroosmotic flows,

and colloids diffusiophoretically repel each other as a result. Since concentration fields are

decaying slower over distance,102, 111 such interactions are dominant long-range forces compared

to others like hydrodynamic interactions in active colloid systems,112, 113 and can lead to collective

behaviors that will be discussed below.58, 60, 80, 81, 112-116

10

Figure 1-3. Ionic diffusiophoretic interactions between active colloids. a) When colloids are

producing faster cations, inward electric fields are induced, leading to dominating inward osmotic

flows, and colloids attract each other. b) When colloids are producing faster anions, outward

electric fields are induced, leading to dominating outward osmotic flows, and colloids repel each

other.

1.2.3 Collective behaviors of synthetic micromotors

Upon the above pairwise interactions between colloids, large-scale collective behaviors

can emerge with increased colloid concentrations.58, 60, 80, 81, 112-116 Although effects like

hydrodynamic interaction117 and capillary forces118 may also contribute, here we only focus on

collective behaviors that arise from chemical sensing and associated diffusiophoretic interactions.

Chemical sensing is a common strategy for biological systems like bacteria119 to conduct

intercellular communication, regulate different processes like gene expression, and coordinate

population-wide behaviors. In response to stimuli, bacteria produce and secret signaling

chemicals (a.k.a inducers) that others detect and respond to through receptors. Similarly, artificial

active colloids, depending on their composition, can respond to chemical stimuli80, 112 or light,58,

60, 116 and initiate reactions to synthesize and release chemical signals including neutral species

like oxygen molecules and ions like protons. The colloids also actively seek out signals sent out

by others, which then induce a certain mode of collective behaviors like microfireworks,58

dynamic clustering,112, 116 swarming and schooling60 through diffusiophoretic interactions. AgCl

colloids, for example, release protons and chloride ions through decomposition of AgCl under

UV light.60 Since positive protons are diffusing faster (DH+ = 9.311x10-5 cm2s-1, DCl- = 1.385x10-5

cm2s-1), as discussed in previous session, AgCl colloids diffusiophoretically attract each other to

form “schools” of colloids. These schools can grow over time by capturing nearby colloids, and

also attract each other to merge into larger ones. Inert colloids like silica, although not producing

any inducers, can also respond to the chemical signals from active colloids like AgCl, and

11

migrate towards them, a kind of predator-prey interactions. The propensity of such collective

behaviors increases with colloid number density and chemical reactivity, as supported by both

experiments112 and simulations.7 This is similar to the prediction on formation of bacteria clusters

through chemotactic collapse in Keller-Segel model (KS model).120, 121 KS model investigates the

role of chemical sensing in bacteria pattern formation by taking into account the diffusion and

chemical drift of bacteria as well as production and transportation of chemical signals. And the

model proposes that cluster formation of bacteria only occurs beyond a threshold population

density (“Chandrasekhar” number) that is proportional to the reciprocal of chemical production

rate (i.e. chemical reactivity). Although such threshold has not yet been quantitatively identified

in the above colloidal systems, the similarities between artificial and biological systems should

further our understanding of active matter, and may help the design of synthetic collective

systems that better mimic their natural counterparts.

1.3 Research motivation and summary

Natural systems like ants can transition between various modes of collective behaviors

(e.g. defensive and foraging) in response to different stimuli (e.g. enemies and food). To mimic

such complexity, we aim to design artificial systems with more than one collective behavior.

Specifically, we want synthetic micromotors that can respond to multiple stimuli and change their

collective behaviors correspondingly. One route is to match chemical reactions on motor surfaces

with the stimuli and consequently tune the diffusiophoretic interactions among the motors that

govern their collective behaviors. Recall that diffusiophoretic interactions are governed by two

factors regarding gradients of certain chemical signals: direction and magnitude. Therefore, we

can reverse the gradients or change the dominant chemical reaction, and in turn alternate the

interactions between the motors, as well as their collective behaviors.

12

This dissertation aims at coupling different chemical reactions and powering mechanisms

with artificial motor systems, so that motors can respond to multiple external stimuli, and exhibit

transition between collective behaviors. Chapter 2 and 3 will demonstrate such examples with

silver orthophosphate micromotor system. Quantitative understanding on interaction and

propulsion mechanism of the synthetic motors is the other focus of this dissertation. Chapter 4

and 5 aim at exploring such topic by combining experimental results with agent-oriented

modeling and numerical simulations.

Chapter 2 demonstrates transition of silver phosphate particles between two states,

assembly and dispersion, in response to different stimuli, including chemical fuels, UV light, and

acoustic field.

Chapter 3 describes oscillatory motion of silver phosphate particles in glucose and

hydrogen peroxide solution under UV light. Multiple oscillation frequencies can exist in one

single system, possibly due to different local particle concentrations or cluster size.

Chapter 4 quantitatively investigates the influence of pairwise interaction between motors

on their diffusional behaviors. It is identified that increasing particle concentration and pairwise

interaction would cause the diffusion of motor particles to transition from superdiffusion to

normal diffusion and finally subdiffusion. Such transition is also verified by agent-oriented

Netlogo models.

Chapter 5 presents a synthetic micropump system that is powered by ion-exchange and

associated ionic-diffusiophoresis mechanism. The direction of fluid pumping and silica tracer

motion can be altered by tuning pH of the system: lower pH leads to outward pumping, and

higher pH results in inward particle motion. The ionic-diffusiophoresis mechanism is verified by

numerical simulation with COMSOL Multiphysics. COMSOL simulations on density-driven

micropumps are also included.

13

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19

Chapter 2

Transition between Collective Behaviors in Response to Different Stimuli

2.1 Introduction

Despite numerous reports on synthetic micro- or nanomotors that are powered by

chemical catalysis,1-11 light,12, 13 acoustic wave,14, 15 and electric16-18 or magnetic field,19-22 only few

examples of synthetic motors showing collective emergent behaviors have been reported:12, 23, 24

Ibele et al.12, 24 discovered that silver chloride microparticles form “schools” when powered with

UV, and the motion characteristics these particles depend on the number of other particles

surrounding them.25 Kagan et al.23 found that gold microparticles in hydrogen peroxide solution

swarm upon addition of hydrazine. These collective emergent behaviors of synthetic

micro/nanomotors are based on the mechanism of self-diffusiophoresis: 26 In response to a

stimulus like light or chemicals, reactions are initiated on the particle surface, generating

concentration gradients of ions, which in turn power the motion of the particles themselves.

The above mentioned micro- and nanomotor systems, including those exhibiting

collective behavior, are typically based on “irreversible” reactions. As a result, motion of

motor particles is mostly controlled by the supply/drainage of chemical fuels or energy (light,

electric or magnetic field). Likewise, the observed collective behavior cannot be actively

reversed.

In this chapter, a new micro/nanomotor system that exhibits reversible collective

behaviors in response to several external stimuli is under discussion: Silver orthophosphate

microparticles (Ag3PO4 MPs) in aqueous medium show transition between “exclusion”

20

(repulsion-like dispersion) and “schooling” (attraction-like clustering), and the transition can be

triggered by shift in chemical equilibrium (by addition or removal of ammonia) or in response to

UV light. The collective behaviors are based on self-diffusiophoresis mechanism,12, 23, 24 as shown

in Fig. 2-1.

Figure 2-1. Transition between the “exclusion” behavior and “schooling” behavior based on self-

diffusiophoresis. With ammonia added, OH- produced by the reaction diffuses away faster from the

silver orthophosphate microparticles than the other ions, resulting in an electric field pointed

outward (orange arrow). This leads to inward electrophoresis of the particles (red arrows) and

outward electroosmotic flow (blue arrows) along the glass substrate, with the latter dominating

resulting in “exclusion” behavior. With ammonia removed, the reaction is reversed and so are the

effects mentioned above, and “schooling” behavior is observed.

The system can work as a NOR gate with ammonia and UV as inputs, function as a

microscale pump, and lead to hierarchical assembly of active (Ag3PO4 MPs) and inert particles

(0.9 μm PS-carboxylate and 2.34 μm silica tracers). It is also among the few reported examples of

synthetic micro/nanomotor systems46 that are based on a non-redox reaction, and demonstrates

new design principles for micro/nanomotors.

21

2.2 Experimental section

2.2.1 Synthesis of Ag3PO4 microparticles

Ag3PO4 particles were synthesized using the following procedure. 0.267 g

Na2HPO4·2H2O (Sigma-Aldrich) was dissolved in 10 mL deionized water, and the

solution was heated to 60°C. Under vigorous stirring, this solution was added to a second

10 mL solution which contained 0.750 g AgNO3 (99.9%, ACS grade, Stream Chemicals),

which was also at 60°C. Stirring was halted after 1 min. The resulting mixture was kept

at 60°C for 30 min. The supernatant was decanted from the resulting yellow Ag3PO4

particles, which were then immediately (while still hot) resuspended in room temperature

deionized water. The particles were centrifuged and washed with deionized water several

times. Large aggregates were removed by centrifuging the suspended Ag3PO4 particles at

2000 rpm for 2 min and collecting the supernatant.

2.2.2 Observation

20 μL of a solution of Ag3PO4 particles in deionized water was placed inside a circular

well (9 mm diameter, 0.12 mm deep, Secure Seal Spacer, Invitrogen) on a microscope slide and

imaged with a microscope (Zeiss, Axiovert 200 Mat), 20 μL of a solution of 4mM ammonium

hydroxide (diluted from 28-30% ammonium hydroxide, A.C.S reagent, Sigma-Aldrich) was then

added to the system. UV light (320–380 nm, 2.5 W cm−2, Chroma 31000v2) using a 100×

imaging objective. Videos were then taken under microscope with Roxio easy media creator

(Roxio).

22

2.2.3 Characterizations

Zeta potentials of the particles in aqueous solution with different concentrations of

ammonia were measured by ZetaPlus from Brookhaven instrument.

2.3 Results and discussions

2.3.1 Reversible transition between two collective behaviors in response to ammonia signals

2.3.1.1 Phenomena

With addition of 2 mM ammonia solution, Ag3PO4 MPs (approx. 2 μm) that sit above a

negatively charged glass slide show within seconds an “exclusion” behavior with exclusion zones

formed between particles as shown in Fig. 2-2(a). When the ammonia starts to evaporate (ca. 3

min), the particles begin to “school,” forming small clusters as shown in Fig. 2-2(b). These

clusters then serve as “nuclei” for larger schools, attracting other nearby particles, as shown in

Fig. 2-2(c), (d). Furthermore, the formed schools respond to the chemical trails secreted by other

schools, and swarm with them to form even larger sized schools (Fig.2-3).

Figure 2-2. Transition between two emergent behaviors for silver orthophosphate microparticles.

Optical microscope images: a) particles show “exclusion” behavior right after addition of 2 mM

23

ammonia, (b-d) particles show “schooling” behavior following elapsed time after addition of

ammonia: b) 3 min c) 5 min d) 7 min. Scale bar, 50μm.

Figure 2-3. Time-lapse optical microscope images demonstrating dynamic merging of smaller

“schools” to form larger ones. (a-e) Four small schools within the white circle gradually merge

with each other to form a large one. Scale bar, 20μm..

2.3.1.2 Mechanism

The observed phenomenon is consistent with a self-diffusiophoresis mechanism, in which

the motion of particles arises from the concentration gradient of electrolytes generated by

particles themselves or their neighbors. For self-diffusiophoresis near a wall (in this case, glass

slide), two effects contribute to the motion of the particles:12 Electrophoretic/electroosmotic effect

and chemophoretic effect. The former results from the different diffusivities of cations and anions

which contribute to the ion gradient in a given direction. The difference leads to a net electric

field, which acts both phoretically on the particles and osmotically on the protons adsorbed in the

double layer of the negatively charged glass slide. Also, the concentration gradient of the

electrolytes causes a gradient in the thickness of the electrical double layer, and thus a “pressure”

difference along the glass slide. As a result, the solution flows from the area of higher electrolyte

concentration to that of lower concentration, which is the chemophoretic effect. The

diffusiophoretic speed of particles near a wall in a monovalent salt gradient can be approximated

from Eqn. 2-1:12

24

(2-1)

where U is the diffusiophoretic speed of particles, dln(C)/dx is the electrolyte gradient,

DC and DA are the diffusivities of the cation and anion components of the gradient, kB is the

Boltzmann constant, T is the temperature, e is the elementary charge, 𝜀 is the solution

permittivity, η is the dynamic viscosity of the solution, 𝜁P is the zeta potential of particles, and 𝜁W

is the zeta potential of the wall (glass slide). Diffusiophoretic speed drops as electrolyte

concentration goes up, as shown in Eqn. 2-2,

(2-2)

For Ag3PO4 MPs with added ammonia, the following reactions in Eqn. 2-3, 2-4 and 2-5

take place at pH around 10.5:

Ag3PO4 + 6 NH3 + H2O ⇋ 3 Ag(NH3)2+ + HPO4

2- + OH- (2-3)

NH3+ H2O ⇋ NH4+ + OH- (2-4)

PO43-+ H2O ⇋ HPO4

2- + OH- (2-5)

The equilibrium constants of the reactions are 9.1 x 103, 1.8 x 10-5 and 2.5 x 10-2,

respectively. K2-3 can be calculated by combining Ksp of silver orthophosphate and Kf for the

silver ammonia complex, as shown in Eqn. 2-6:27

𝐾2−3 = 𝐾𝑏(𝑃𝑂43−) × (𝐾𝑓(𝐴𝑔(𝑁𝐻3))2+))3 × 𝐾𝑠𝑝(𝐴𝑔3𝑃𝑂4) = 9.1 e3 (2-6)

ln( ) 1d C dC dC

dx Cdx C dx

25

At a low concentration of ammonia (2 mM), the reaction does not proceed to completion,

with about 19% ammonia left unreacted as estimated below:

At pH 10.5, for reactions 2-4 and 2-5, NH3 and HPO42- dominate over NH4+ and

PO43-, respectively. In that case, we have the following relations between the concentrations of

species:

[OH-] = [ HPO42-]= 3.16 e-4 M

[Ag(NH3)2+] = 3 [OH-] = 9.48 e-4 M

By plugging these relations back into K2-3, we then estimate the concentrations of the

various species. The results are as follows: [NH3] = 4.6 e-4 M, [Ag(NH3)2+] = 9.48 e-4 M, and

[NH4+] = 5.4 e-5 M. With the original concentration of ammonia as 2.4 e-3 M, there will be around

19% of ammonia remaining as free NH3 in the system.

As ammonia is added to the system, the equilibrium (3) shifts to the right, generating an

ion gradient of Ag(NH3)2+, HPO4

2- (D = 0.759 x 10-5 cm2 s-1) and OH- (D = 5.273 x 10-5 cm2 s-1),

with the highest electrolyte concentration near the particle surfaces. For a given Ag3PO4 particle

(now considered as the central particle), OH- ion diffuses away from its surface much faster than

the rest because of its smaller size, and a net electric field is generated pointing away from the

particle.45 The electric field acts phoretically on the other negatively charged Ag3PO4 MPs by

pulling them towards the central one. The electric field also acts osmotically on the adsorbed

protons in the double layer of glass slide by pumping the fluid away from the central Ag3PO4

particle along the wall. Because the absolute value of zeta potential of the Ag3PO4 particle (𝜁p = -

55 mV) is smaller than that of the glass slide (𝜁w = -85mV28), electroosmosis dominates over

electrophoresis and the other particles are pumped away from the central particle. Although the

zeta potential of silver phosphate particles varies with ammonia concentration, it is still less

negative than that of the glass substrate (Fig.2-4). As for chemophoretic effect, the higher

electrolyte concentration near the particle’s surface will also drive the other particles away. These

26

effects together cause the Ag3PO4 MPs to move away from one another and the system shows an

“exclusion” pattern (Fig. 2-1, left).

Figure 2-4. Zeta potentials of Ag3PO4 particles at different ammonia concentrations.

When ammonia is removed from the system by evaporation, the equilibrium 2-3 shifts to

the left, as predicted from Le Chatelier’s principle. The existing Ag3PO4 MPs in the system work

as seed crystals with the ions Ag(NH3)2+, HPO4

2- and OH- migrating back, the lower electrolyte

concentration being near the particle surfaces. As a result, the electric field points towards the

particles and situation discussed above is reversed with particles being pumped towards one

another to form “schools” (Fig. 2-1 right).

2.3.1.3 Mechanism verification

To verify that it is the removal of ammonia that leads to the shift in equilibrium, an

experiment was conducted in a closed system and in this case only “exclusion” behavior was

observed (Fig.2-5). In addition, when a nonvolatile ligand, ethylenediamine, was employed

27

instead of ammonia, only “exclusion” behavior was observed (Fig.2-6). To further verify the self-

diffusiophoresis mechanism, we conducted experiments in presence of high salt concentrations,

since diffusiophoretic motion is sharply attenuated by increasing ionic conductivity of the fluid.

By using 0.5, 1, and 3 mM NaNO3 solutions, we found that “schooling” propensity decreased

with higher electrolyte concentration (Fig.2-7), as predicted from Eqn.2-2 and the simulation

results of Sen et al.29

Figure 2-5. Time-lapse optical microscope images demonstrating collective behavior in closed

system. (a-b) Upon addition of ammonia, silver phosphate particles exhibit “exclusion”. (b-d) Over

time, no schooling behaviors are observed. Time stamps: 0, 10, 480 and 960s. Scale bar, 20μm.

28

Figure 2-6. Time-lapse optical microscope images demonstrating collective behavior in 0.02 M

ethylenediamine solution. (a-b) Upon addition of ethylenediamine, silver phosphate particles

exhibit “exclusion”. (b-d) Over time, no schooling behaviors are observed. Time stamps: 0, 5, 300

and 600s. Scale bar, 20μm.

29

Figure 2-7. Time-lapse optical microscope images demonstrating influence of ionic strength on the

transition of collective behaviors. (a-d) Compared with the two cased with 0.5mM and 1mM

NaNO3, the system with higher ionic strength (3mM NaNO3) does not exhibit transition from

“exclusion” to “schooling”. Time stamp: 0, 5, 120 and 240s. Scale bar, 20μm.

2.3.1.4 Interaction with inert tracers and applications

So far we merely focus on interactions between active colloids and associated collective

behaviors, and in this section we will investigate interactions between active and inert tracer

particles. In this case, we consider the active colloid as the central particle, and study its

interaction with nearby particles through the self-diffusiophoresis mechanism.

According to classical DLVO theory30, 31, interactions between colloidal particles is a

combination of van der Waals forces (generally attractive) and electrostatic interaction between

double layers. However, for an active particle that generates a concentration gradient of ions, it

will have additional interactions with the other nearby particles (be they active or inert) based on

electrolyte diffusiophoresis. Whether these diffusiophoretic interactions are attractive or repulsive

depend on several factors, including the zeta potentials of particles and the wall (in many cases,

negatively charged glass slides), the mobility of ions, and distances between particles.

If the active particles are “secreting” cations which diffuse faster than the anions, the

different diffusion rates will result in a net electric field pointing back towards the particles.. Fig.

2-8 summarizes possible interactions between the central active particle and nearby particles

under such inward electric fields. And when anions exhibit higher diffusivities, the electric fields

are inversed (i.e. outward electric fields) together with all the interactions.

30

Figure 2-8. Schemes for diffusiophoretic interaction between the central particle and nearby

particles with an inward electric field. a) When the nearby particles are positively charged, the

directions of electrophoresis and electroosmosis are both inwards, the diffusiophoretic interactions

are attractive, and the system shows a “schooling” pattern. B) When the nearby particles are

negatively charged and the magnitude of 𝜁P is larger than that of 𝜁w, the outward electrophoresis

dominates over the inward electroosmosis, the diffusiophoretic interactions are thus repulsive, and

the system shows “exclusion” patterns with exclusion zones between them. C) When the nearby

particles are negatively charged and the magnitude of 𝜁P is smaller than that of 𝜁w, the inward

electroosmosis dominates the diffusiophoretic interactions are attractive, and the system shows

“schooling” patterns. However, when the particles come close enough to the central one, a repulsive

electrophoretic force dominates again and small exclusion zones are formed between the central

particle and nearby particles.

. For nearby positively charged particles, the inward electric field acts phoretically on

them pulling them towards the central particle. The electric field also acts osmotically on the

adsorbed cations in the double layer of the negatively charged glass wall pumping the fluid along

the wall’s surface together with the nearby particles towards the central particle. In this case, the

electric field effect, which is the combination of electrophoresis and electroosmosis, leads to a

diffusiophoretic attraction between the central particle and nearby positive particles. (Fig.2-8a)

The chemophoretic effect counteracts this slightly, and attempts to pump the fluid along with

nearby particles away from the central particle, where the double layer is thinner at the glass

surface.

In general, an inward electric field leads to diffusiophoretic attraction between central

particles and nearby positive particles, and this attraction results in the formation of “schools”,

i.e. regions in which the number density of particles is significantly higher than the global

average. If the direction of the electric field is reversed when the active particles are releasing

faster anions and slower cations, the diffusiophoretic interaction will become repulsive because of

the reversed electric field, and the system shows “exclusion” patterns with exclusion zones

formed between one another, i.e. regions in which particles are absent. The size of exclusion

zones depends on the strength of the diffusiophoretic repulsion.

31

So what if the nearby particles are negatively charged? Again, for the inward electric

field, the electroosmotic flow along the glass slide carries them towards the central particle, and

the relatively negligible chemophoretic flow directs them outwards. However, in this case, the

electrophoretic interaction turns repulsive, and the net direction of movement depends on the

difference in zeta potential between the particles and the wall (Eqn. 2-1).

If the magnitude of the particle zeta potential (𝜁p) is larger than that of the wall (𝜁w), then

electrophoresis dominates, diffusiophoretic interaction will be repulsive, and the negative

particles will be pumped away from the central one. (Fig.2-8b) On the other hand, if the

magnitude of the wall’s zeta potential is larger, electroosmotic flow dominates and is sufficient to

overcome the outward electrophoretic and chemophoretic effects. In this case, the

diffusiophoretic interaction will be attractive. The dominance of electroosmosis is valid as long as

the particles are on the same plane along the wall. However, fluid continuity dictates that the

inward electroosmotic flow along the wall will approach zero very near to the central particle as

the fluid is forced upwards and away from the wall. Therefore, repulsive electrophoretic

interaction dominates very near to the central particle. Thus the diffusiophoretic interaction will

be attractive over long distances but repulsive at close range, and the nearby negative particles

will be pumped towards the central one, but with a small exclusion zone left between them.

(Fig.2-8(c)). Finally, if the electric field is reversed with faster anions and slower cations, the

diffusiophoretic interaction will be reversed as well, i.e. from attraction to repulsion.

In the current Ag3PO4 MP system, interactions with inert negatively charged particles in

response to ammonia stimuli can also be extended to applications like design of micropump and

hierarchical particle assembly.

When ammonia was added to the system, equilibrium (2-3) shifts to the right, and the

resulting ions secreted from the active Ag3PO4 particles generate diffusiophoretic flows that cause

“exclusion” zones to form not only between active particles, but also between the active and inert

32

ones (in this case, 0.9 μm PS-carboxylate tracer particles). As a result, the PS-carboxylate tracers

are pumped away from large Ag3PO4 particles that sit on the glass slide. Also, probably due to the

difference in reactivity, the size of exclusion zones formed increase with increasing size of the

Ag3PO4 “pump” particles (Fig. 2-9)

Figure 2-9. Time-lapse optical microscope images showing silver orthophosphate microscale pump

system with 0.9 μm PS-carboxylate tracer particles in 2 mM ammonia solution. With addition of

ammonia solution, tracer particles are pumped away from the large pump particles and “exclusion”

zones (areas within the white circles) are formed within seconds. The sizes of “exclusion” zones

vary from pump particles. Scale bar, 50μm.

On the other hand, with ammonia removed from the system, the ion concentration

gradient and the directions of diffusiophoretic flow are reversed. As a result, the active silver

phosphate particles attract each other as well as the silica tracers, and form “schools”. It is

interesting to note that the inert silica tracers mainly sit on the outer boundary of the formed

“schools”, and when the smaller “schools” start to fuse, the silica tracers that are at the merging

boundaries are “excluded” to the periphery of the newly formed larger “school”. Thus, with

smaller schools merging altogether, hierarchical particle assembly of active Ag3PO4 particles and

inert silica tracers is achieved. (Fig. 2-10)

33

Figure 2-10. Time-lapse optical microscope images showing hierarchical particle assembly

between Ag3PO4 microparticles and 2.34 μm silica tracers in 2 mM ammonia solution. a) With

removal of ammonia, Ag3PO4 microparticles forms “schools” with silica tracers on the outer

boundary; b) when the smaller “schools” start to merge, silica tracers are “excluded” to the

periphery of the newly formed larger “schools”. c) Hierarchical particle assembly between Ag3PO4

microparticles and silica tracers is achieved with Ag3PO4 microparticles “schools” as the core and

silica tracers on the periphery. Scale bar, 20μm.

2.3.2 Collective behavior in response to UV light signals

Silver phosphate particles also respond to UV light, with the following reaction taking

place:

(4x+4y) Ag3PO4 + (4y-2x) H2O = 12x Ag + 12y Ag+ + 3x O2 + (4y-8x) OH- + (4x+4y)

HPO42- (2-7)

Upon UV exposure, ions are generated through reaction (2-7) and the faster diffusivity of

OH- leads to an outward electric field. Similar to the cases described in sections 2.3.1.2 and

2.3.1.4, outward electric field leads to repulsion between silver phosphate particles and nearby

silica tracers, and exclusion zones form around the silver phosphates, as shown in Fig. 2-11.

34

Figure 2-11. Time-lapse optical microscope images demonstrating formation of exclusion zones

around silver phosphate particles upon UV exposure (a) before UV exposure b) UV turned on, c)

15s after UV exposure. Scale bar, 20μm.

2.3.3 Design of logic gates

Now that we have two stimuli for the Ag3PO4 microparticles /ammonia system, we will

investigate the influence of their combination on transition between collective behaviors.

For an already “schooled” system through removal of ammonia (Fig. 2-12a), addition of

UV to results in transition from “schooling” to “exclusion” behavior with “schools” disassembled

and exclusion zones formed between particles (Fig. 2-12 a and b). In addition, continued UV

exposure prevents “schooling” behavior in Ag3PO4 MPs/ammonia system: UV light causes the

exclusion zones to last longer, and Ag3PO4 MPs will only relax to normal state slowly, with no

“schools” formed (Fig. 2-12 c and d). This relaxation also suggests negligible contribution from

thermophoresis. Thermophoresis is also ruled out by the failure of inert silica particles to exhibit

collective behavior in the presence of UV light. The transitions can be explained by dominating

repulsion between active Ag3PO4 particles in response to UV light.

With the above discussed transitions, a NOR gate can be designed with UV and ammonia

as inputs, while “schooling” and “exclusion” behaviors as output 1 and 0, respectively (Figure 2-

12): After the formation of “schools” in the Ag3PO4 MPs/ammonia system, without inputs of UV

or ammonia, the “schooling” behavior results with ammonia removal and “1” as the output, while

any input, either UV or ammonia, causes a shift to “exclusion” behavior and output of “0”. The

NOR gate design, as shown by Pierce, can be used to reproduce the functions of all the other

logic gates,32 and therefore perform any logical operation required.

35

Figure 2-12. NOR Gate with UV and ammonia as inputs, collective behaviors as outputs:

“schooling” and “exclusion” behaviors as 1 and 0, respectively.

2.3.4 Transition between assembly and dispersion in response to orthogonal stimuli

The above discussed system only takes advantage of chemically-powered interactions. It

is also possible to govern the transition between assembly and dispersion through a combination

of acoustic forces and chemically-powered interactions. Moreover, it is possible to actively

control such transition by employing photocatalytic chemical reactions and turning on/off light

inputs. For silver orthophosphate microparticles (Ag3PO4 MPs) in H2O2 solution under acoustic

field (1 MHz), their self-assembly leads to formation of microstructures like stripes near the

substrate surface. And upon UV exposure, Ag3PO4 MPs repel each other and dispersed, with

stripes disassembled. Such assembly/disassembly process can be reversibly triggered with UV

light off/on, respectively, as shown in Fig. 2-13. And the phenomena can be explained through a

combination of acoustically and chemically induced forces as follows.

36

Figure 2-13. Under acoustic fields, Ag3PO4 MPs form stripes (a,c) and disperse (b,d) reversibly

with UV light off and on, respectively. Scale bar: 50 m

Without UV light, since the employed frequency (1 MHz) is lower than the resonant

frequency (~ 3.7 MHz), Ag3PO4 MPs settle down to the substrate surface, instead of being

levitated. Under such acoustic fields, as shown in Fig. X, solid particles are subject to acoustic

forces (Facou), including both primary and secondary radiation forces, as well as Stokes drag

forces from the induced acoustic streaming flows (note that this does not include drag forces

caused by relative motion between particle and streaming fluid). Radiation forces usually

dominate for particles larger than 5 m in diameter, and as particle sizes shrink down, viscous

effects become significant, and streaming-induced drag force also starts to contribute.33, 34 Such

scaling effect can also lead to cross-over from radiation-domination to streaming-domination, as

previously reported.35 Numerical studies predict that the critical particle size for such transition is

around 1-2m,34, 36 which is about the size of Ag3PO4 MPs. Therefore, in the current system, both

radiation and streaming-induced drag forces might play important roles. And particles are pushed

together by these acoustic forces, assembling into stripes.

And upon addition of UV light, Ag3PO4, known for its photocatalytic properties,

catalyzes decomposition of H2O2 into H2O and O2. Such light-triggered reaction leads to

37

concentration gradients of H2O2 and O2 around Ag3PO4 particles that can be sensed by other

nearby particles. Particles can respond to non-electrolyte solute gradients, and migrate up/down

along them. Such phenomena are known as neutral diffusiophoresis,37, 38 and have been suggested

as the governing mechanism for the propulsion and assembly in several synthetic motor

systems.39-46 In neutral diffusiophoresis, due to affinity between the solute and substrate, the

solute gradients lead to unbalanced osmotic pressure within the diffuse layer of the substrate, and

induces fluid flow that carry particles with them.47-49 Direction of the diffusiophoretic flow

depends on materials of the particles and substrates, and can be tuned by external parameters like

pH of the solution.50 In the current system, gradients of H2O2 and O2 induce outward flows along

the substrate surface that push the particles away from each other. In the form of such relative

drift, chemically-powered diffusiophoretic repulsion (Fchem) arises between Ag3PO4 particles. As

shown in Fig. X, since the outward UV-induced chemical forces outpower inward acoustic forces,

particles are pumped out, and stripes disassembled.

38

Figure 2-14. With UV light off, stripes of particles form with dominating inward acoustic forces

(Facou). And with UV light on, stronger outward chemical forces (Fchem) are induced, and stripes

disassembled. Scale bar: 20 m

2.4 Conclusion

In conclusion, we have demonstrated a new reaction-induced self-diffusiophoresis

system, in which two different collective behaviors, “exclusion” and “schooling”, can be attained

using either a chemical or light stimulus. This system is also the first example of micromotors

based on a non-redox chemical equilibrium shift, and demonstrates new principles for

micromotor design. The system has potential applications in the fields of microscale pumping and

hierarchical particle assembly. In addition, micromotors with different stimuli may be employed

as logic gates.

2.5 Perspective

To get a better understanding of the system, influence of UV intensity, cluster size and

particle concentration on the oscillation frequency should be investigated. And based on these, a

more detailed coarse-grain simulation could be built to better explain the system.

The application of frequency tuning in computation should also be tested. It is also

possible to encapsulate the silver phosphate particles inside microstructures like capsules,

emulsions and droplets,51 and see how the oscillation of particles would affect motion of the

microstructures.

39

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42

Chapter 3

Self-powered “Colloidal Clock” with Chemical Inputs

3.1 Introduction

Oscillation can originate from systems that are far from equilibrium, e.g. ones exhibiting

nonlinear chemical dynamics.1-3 The best known chemical oscillator is the prototypical Belousov-

Zhabotinsky (BZ) reaction.4 In typical BZ reactions, metal ion (e.g. Ce4+/ Ce3+) or complex (e.g.

ferroin(II)/ferriin(III)) redox couples catalyze oxidation of organic substrates like malonic acid by

bromate ions in a solution of sulfuric or nitric acid. Such catalytic reactions are composed of

several steps,4 and competition between the steps leads to periodic change in concentrations of

chemicals, namely a “chemical clock”. BZ oscillation has also been extended to heterogeneous

systems, namely “structured media”,2, 3 like BZ gels,5, 6 ion-exchange beads7, 8 and

microemulsions.9 Chemical oscillation in such systems can lead to local color or temperature

alternation, and hence pattern formation10 or self-motility.11, 12

In this chapter, I will demonstrate another example of coupling chemical complexity with

collective behaviors of micromotors, and introduce a new oscillatory system based on self-

powered micromotors: silver orthophosphate microparticles (Ag3PO4 MPs) in a glucose-hydrogen

peroxide aqueous solution under UV. In such system, Ag3PO4 MPs act as photocatalyst for the

oxidation of glucose by hydrogen peroxide or decomposition of hydrogen peroxide. The reactions

can be divided into two competing steps, reduction of silver ion to silver by glucose or UV, and

oxidation of silver back to silver ion by hydrogen peroxide under UV. The two steps comprise a

negative feedback loop which triggers chemical oscillation. As shown in Fig. 3-1, with such

“chemical clock”, Ag3PO4 MPs periodically transition between two collective patterns under a

43

self-diffusiophoresis mechanism, with particles inside preformed clusters attracting and repelling

each other alternatively over time. The oscillatory transition between particle-particle interactions

leads to periodic change of cluster size and local colloid concentration, formulating a “colloidal

clock”. There might exist more than one frequencies in one single system, possibly due to

difference in local chemical and particle concentrations, or sizes of the clusters. The coupling of

nonlinear chemical systems with collective behaviors should lead to better understanding of

dynamics and interaction of active matter, be it biological or synthetic.

Figure 3-1. Oscillatory transition between dispersion and clustering of Ag3PO4 MPs based on self-

diffusiophoresis. With addition of glucose/UV light, silver orthophosphate is reduced to silver

metal, and OH- produced by the reaction diffuses away faster from the microparticles than the other

ions, resulting in an electric field pointed outward (orange arrow). This leads to inward

electrophoresis of the particles (red arrows) and outward electroosmotic flow (blue arrows) along

the glass substrate. The latter dominates and results in repulsion and dispersion of particles, and the

clusters split into smaller ones or single particles (Trough). With peroxide and UV light, silver is

oxidized back to silver phosphate, the ion gradients are reversed together with the effects mentioned

above. Therefore particles or smaller clusters attract each other to form larger clusters (Crest). The

alternation of the two reactions hence leads to oscillatory motion of the particles and periodic

alternation of cluster sizes.

44

3.2 Experimental section

3.2.1 Synthesis of Ag3PO4 particles.

Ag3PO4 particles were synthesized using the same procedure as our previous report:13

0.267 g Na2HPO4·2H2O (Sigma-Aldrich) was dissolved in 10 mL deionized water, and

the solution was heated to 60°C. Under vigorous stirring, this solution was added to a second 10

mL solution which contained 0.750 g AgNO3 (99.9%, ACS grade, Stream Chemicals), which was

also at 60°C. Stirring was halted after 1 min. The resulting mixture was kept at 60°C for 30 min.

The supernatant was decanted from the resulting yellow Ag3PO4 particles, which were then

immediately (while still hot) resuspended in room temperature deionized water. The particles

were centrifuged and washed with deionized water several times. Large aggregates were removed

by centrifuging the suspended Ag3PO4 particles at 2000 rpm for 2 min and collecting the

supernatant.

3.2.2 Observation.

50 μL of a mixture solution of Ag3PO4 particles, 2~5mM glucose and 0.1-0.25%

hydrogen peroxide was placed inside a circular well (9 mm diameter, 0.12 mm deep, Secure Seal

Spacer, Invitrogen) on a microscope slide and imaged with a microscope (Zeiss, Axiovert 200

Mat). Motion of particles under UV light (320–380 nm, 2.5 W cm−2, Chroma 31000v2) were

observed through a 100× imaging objective. Videos were then taken under microscope with

Roxio easy media creator (Roxio).

45

3.2.3. Video analysis

Quantitative characterization of cluster dynamics was done by identifying silver

phosphate particles based on the contrast existing between the background solution and the

particles. We defined an RGB interval that accurately captures the cluster features, and

implemented an algorithm in MATLAB to identify individual clusters as well as their size

(number of pixels) for each video snapshot.

3.2.4. Zeta potential measurement

Zeta potential of the silver orthophosphate particles was measured by ZetaPlus from

Brookhaven instrument.

3.3 Results and discussion

3.3.1 Phenomena

With addition of 50mM glucose and 0.25% hydrogen peroxide, Ag3PO4 MPs that sit on

negatively charged glass first “school” with ambient particles to form clusters. Inside the formed

clusters, colloids initiate oscillatory motion after a certain time delay. This time delay

demonstrates that the oscillatory regime emerges as a result of instability, and the time is needed

to reach the terminal (oscillatory) state from the initial uniform distribution of the reac-tants. As

shown in Fig.3-2, particles attract and repel each other alternatively over time. With repulsion

between particles, the preformed clusters release particles and split into smaller clusters, which

lowers average cluster size. And with attraction between particles, bigger remainder clusters

46

function as “nuclei” and pull in particles and smaller clusters near-by (Fig. 3-3), which increases

average cluster size. Therefore, the oscillatory motion of active colloids leads to oscillation of

average cluster size, as shown by video analysis results in Fig.3-1.

Figure 3-2. Microscope images demonstrating periodic oscillation of Ag3PO4 MPs in a mixture of

50mM glucose and 0.25% hydrogen peroxide under UV. Over time, clusters of Ag3PO4 MPs

alternatively reassemble (a, c and e) and disassemble (b, d and f), by extracting and releasing

particles, respectively. Scale bar: 20m

Figure 3-3. Bigger remainder clusters function as “nuclei” and pull in particles and smaller clusters

nearby. Scale bar: 10m

47

Such oscillation can only take place above certain concentration threshold: when

hydrogen peroxide concentration is low, say 0.01%, particles exhibit “exclusion” behavior13 with

exclusion zones formed between them. It is interesting to notice that sometimes the extraction and

release of particles only take place on one side of the clusters, perhaps due to non-uniform

distribution of particles outside clusters or difference in reactivity inside clusters. Such

asymmetry may drive motion of the clusters, especially smaller ones, as shown in Fig. 3-4. The

existence of a nearby cluster can also trigger asymmetrical disassembly, and may lead to the

merging of two clusters when particles start to attract each other. (Fig. 3-5)

Figure 3-4. Motion of an individual cluster through asymmetric particle extraction and release.

Scale bar: 20m

48

Figure 3-5. Merging of two oscillating clusters. Scale bar: 10m

Besides merging, clusters can also synchronize with other clusters through transportation

of chemical signals, which results in the propagation of oscillation. As shown in Fig.3-6, after an

oscillation initiates, it propagates gradually to clusters nearby (oscillating clusters are within the

white circles), and eventually all the clusters under scope start oscillating.

Figure 3-6. Propagation of particle oscillation. a-b) Oscillation first initiates at the upper left corner,

where clusters with in the circle are oscillating. c) Oscillation propagates to a wider range on the

left side d) Oscillation eventually propagates throughout the whole screen. Scale bar: 50m

49

3.3.2 Mechanism

The oscillatory change of interaction between active colloids can be explained with an

electrolyte self-diffusiophoresis mechanism. Around neutral pH, Ag3PO4 MPs, in an aqueous

solution of glucose and hydrogen peroxide, the two following reactions mentioned above might

take place at particle surfaces: CH2OH(CHOH)4COH + H2O2 = CH2OH(CHOH)4COOH + H2O,

2 H2O2 = O2 + 2 H2O. For both reactions, they can be divided into two steps: reduction from silver

phosphate to silver metal and oxidation of silver metal to silver phosphate. For the first part,

glucose might be the reducing agent, as shown in reaction (3-1) below, although UV can also be

contributing through the following reaction: 4 Ag3PO4 + 6 H2O = 4 Ag + 8 Ag+ + O2+ 4 H2PO4-+

4OH-, and further studies are needed to clarify the contributions from the two factors. (Ksp of

Ag2O and Ag3PO4 are 1.52·10−8 and 8.9·10−17, respectively, and therefore at pH around neutral,

silver ions could accumulate before initiating precipitation in the system):

2 Ag3PO4 + CH2OH(CHOH)4COH + 2 H2O = 2 Ag + 4 Ag+ + CH2OH(CHOH)4COO- + 2

H2PO4-+ OH- (3-1)

2 Ag + 4 Ag+ + 2 H2PO4- + H2O2 + 2 OH- = 2 Ag3PO4 + 4 H2O (3-2)

OH- has higher diffusivities among the products at ambient temperature. (DOH- = 5.273 x

10-5 cm2 s-1, DAg+= 1.648 x 10-5 cm2 s-1, DH2PO4−= 0.959 x 10-5 cm2 s-1, DGlucose = 5.7x 10-6 cm2 s-

1, , DH2O2= 1.71 x 10-5 cm2 s-1)14 As shown in the left bottom figure in Scheme 1, for a central

particle, outward local electric fields (orange arrows) are formed along the gradients of ionic

products. In response to such electric fields, nearby particles migrate under the combination of

electrophoretic and electroosmotic effects. The latter dominates, as the absolute value of zeta

potential of the Ag3PO4 particle (𝜁p = -45 mV) is smaller than that of the glass slide (𝜁w = -

65mV15), and hence particles repel each other and clusters disassemble.

50

Based on reaction (3-1), a self-powered microscale pump can be designed. As shown in

Fig. 3-7 in Supporting Information, with addition of 50mM glucose, the bulky Ag3PO4 MP starts

to pump other smaller particles away, creating an exclusion zone (as identified by the blue

circles) near itself. Such exclusion zone grows over time, as smaller particles are pumped further

away.

Figure 3-7. Design of a microscale pump with glucose and a bulky silver orthophosphate particle.

a-b) The bulky pump particle drives nearby particles to migrate away, forming an exclusion zone

around itself. b)-c) The exclusion zone grows over time. Scale bar: 20m

The second reaction is initiated by UV light, and the silver metal that was formed from

reduction is oxidized back into silver phosphate by hydrogen peroxide. This reaction consumes

the ionic products produced in reaction (3-1), and reverses the gradient of ionic products, as well

as all the associated electrokinetic effects. As a result, particles attract each other to reassemble

clusters again. Such process and mechanism are verified by the following control experiment:

Ag3PO4 MPs in DI water are first subject to UV light, and as discussed in our previous report,13

partially decomposed into silver metal. The sequential addition of hydrogen peroxide then leads

to schooling of the particles.

The self-diffusiophoresis mechanism proposed above is verified by a control experiment

under higher ionic strength: with 50mM glucose, 0.25% hydrogen peroxide and 3mM KNO3,

Ag3PO4 MPs only exhibit Brownian motion, with no collective behavior observed. Such

phenomena could be explained by the fact that diffusiophoretic flows are suppressed by the high

ionic strength, and particles can no longer sense the chemical gradients generated by others.13, 16

51

3.3.3 Multiple Frequencies

The two competing reactions compose a “chemical clock” similar to the BZ reactions.

Such nonlinear chemical system governs the collective behaviors of active Ag3PO4 colloids

through self-diffusiophoresis. It is interesting to notice that there may exist more than one

oscillation frequencies in the system, i.e. different clusters may exhibit different oscillation

frequencies.

As shown in the FFT results in Fig. 3-8, there exist two frequencies inside a single

system. A further analysis, as shown in Fig. 3-9, reveals that the two frequencies originate from

two individual clusters. The two different frequencies might be a result from different local

chemical or particle concentrations, as qualitatively predicted by the continuum model below.

52

Figure 3-8. Existence of two frequencies in one system. FFT analysis of the results in the top graph

reveals two frequencies as demonstrated in the bottom graph. Top: Video analysis results. Bottom:

FFT resutls. Note that the results are based on a 4x faster video.

53

Figure 3-9. FFT results of the entire videos and cluster-based cropped ones. The resutls demonstrate

that the two clusters in the blue and green rectangles are governed by different frequencies.

3.3.4 Continuum model

Ag3PO4 microparticles, in an aqueous solution of glucose (with concentration C1) and

hydrogen peroxide (with concentration C2), produce ionic products in reaction (3-1) that are

54

mostly reactants in reaction (3-2). For simplicity, we assume that they compose a group of

chemicals with concentration C3 and mainly identify this component with OH-, as it diffuses

faster in comparison with other ionic products, and hence decides the direction of local electric

fields as well as that of self-diffusiophoretic flows.

Particles are modeled as a continuum with the concentration n . This assumption is

obviously an oversimplification, but it allows finding several phenomena inherent to the system.

As mentioned above, particles are primarily resting on the glass slide surface, therefore a two-

dimensional concentration field can characterize their distribution. For the sake of simplicity, we

also assume the concentrations of chemical agents C1,2,3 are two-dimensional, thus only deal with

the layer of the solution adjacent to the bottom boundary. Due to this assumption, the vertical

distribution of reagents is unimportant, but the presence of the ‘bulk’ with a prescribed

concentration of both peroxide and glucose is important.

Based on experimental observation, the effects on particles and chemical species taken

into account are as follows:

For particles migration, it is mainly caused by the electrolyte diffusiophoresis originating

from gradients of ionic products (C3): since OH- have higher diffusivities among the products

(DOH- = 5.273 x 10-5 cm2 s-1, DAg+ = 1.648 x 10-5 cm2 s-1, DH2PO4- = 0.959 x 10-5 cm2 s-1, DGlucose =

5.7x 10-6 cm2 s-1, DPeroxide = 1.71 x 10-5 cm2 s-1,).14 One can adopt a simple model for chemotaxis

of bacteria to emulate fundamental observations of the experiments.17 The propulsion velocity of

the particles is given by the chemosensitivity function 3 times the concentration gradient of ionic

products,∇C3. In the context of hydrodynamics, 3 represents a mobility function that depends on

the interaction between the ionic products and the particle. Convective and self-diffusion effects

are neglected.

55

As for chemical species, their concentration changes are governed by a combination of

chemical reaction, exchange with the upper layer (bulk) and diffusion, with diffusivities given by

jd ( 1,2,3j ). For the exchange, there are fluxes of both solutes (glucose and peroxide) from

the upper layers of the fluid to the proximity of the substrate, where the modeling is performed.

Those fluxes are given by 1,2 1,2 1,2b C С , where the constants 1,2C correspond to equilibrium

values of both species in the absence of the particles. Although these coefficients are not identical

with the bulk concentrations of the glucose and hydrogen peroxide (which are three-dimensional

concentrations), there exists a positive correltion between them. The coefficients b1,2 show the

magnitude of fluxes from the bulk of the glucose and peroxide, respectively. Physically, b1,2-1 are

the characteristic times to reach the equilibrium values 1,2C for glucose and peroxide,

respectively.

Correspondingly, the governing equations are as follows:

3 3

nn C

t

, (3-3)

211 1 1 1 1 1 1

Cb C С a nC d C

t

, (3-4)

222 2 2 2 2 3 2 2

Cb C C a nC C d C

t

, (3-5)

231 1 2 2 3 3 3

Ca nC a nC C d C

t

. (3-6)

All the coefficients are positive; 1,2a are the reactions rates for reactions (3-1) and (3-2),

respectively.

The basic state for this system corresponds to the uniform distributions of all three

reagents and particles with the concentrations 0

1,2,3C and 0n . The equilibrium concentrations are

56

00 0 0 01 01 1 1 11 2 2 1 3 0

1 1 0 2 2 2

, ,a nb C a C

С C C C Cb a n b a C

; (3-7)

This basic state allows two interpretations: first, it can be considered as a uniform

distribution of MPs and solutes over the whole domain (Case I); secondly, one can apply the

same theory to a single cluster with almost uniform distribution of MPs there (Case II). Of course,

for Case II the theory can be used for qualitative estimations only. Usually in experiments first

clusters of MPs are formed, whereas the rest space is almost free of MPs, and those clusters start

to oscillate, therefore, Case II takes place. However, under certain conditions the oscillations

emerge with a nonzero background concentration of MPs. This situation can be treated as Case I,

the oscillatory regime that sets in as the uniform state becomes unstable.

Now we analyze the stability of the basic state, introducing small perturbations and

the corresponding equilibrium concentrations. Substituting the perturbed fields and

into Eqn. 3-3- Eqn. 3-6 and linearizing the equations with respect to small

perturbations, one arrives at

,

.

.

.

The solution of this linear set of equation is proportional to exp t ikx , where and

k are the growth rate and wavenumber of perturbation, respectively. The real part of the growth

57

rate shows whether the basic (uniform) state is stable ( 0 r ) or not ( 0 r ), and the imaginary

part ( i ) represents the frequency of oscillations. The wavenumber can be treated as an inverse

lengthscale of the resulting pattern. More precisely, 2 k is the wavelength of perfectly periodic

solution, but 1k can be used as an estimate for the typical lengthscale of emerging pattern even in

the absence of periodicity. For Case I the spectrum of the wavenumber is continuous and limited

from below only by the problem geometry:

1kL (3-8)

where L is minimum characteristic lengthscale (either a horizontal cavity length or a

decay length for UV). For Case II the spectrum is discrete and Eqn. 3-8 is again valid with L

being approximately the cluster size.

In general case the complex-valued dispersion relation k should be studied

numerically, but in a number of limiting cases theoretical progress is possible. Most interesting

case corresponds to large 0

3 1 1С d , which is the dimensionless measure of the

chemotactical (diffusiophoretic) coefficient 3 with respect to diffusion of ionic products in

reaction (3-1). In this case one can readily show that the primary branches of the growth rate

solve the cubic equation:

3 22 2 0

1

1 0, ;C

C Q CC

. (3-9)

where Q is unimportant positive constant. The parameter 2C is the ratio of

equilibrium peroxide concentration 2C to the glucose concentration in the basic state

0

1C . In

fact, in view of Eqn. 3-7, 2C is proportional to the ratio 2 1C C , therefore an increase in this

58

parameter corresponds to either growth of peroxide equilibrium concentration or to diminish of

glucose equilibrium concentration. For 2 1C , one of the root of Eqn. 3-9 is negative and two

others form a complex-conjugate pair with 0 r :

32

1 31

2

iC Q

,

and therefore the oscillatory instability takes place. This solution provides a guess, where

the oscillatory regimes can be found numerically.

In computations we use non-dimensionalized variables introducing the following

parameters (in addition to the above-mentioned and 2C )

02,31 0 2 0 1 2

1 2 2 2,3

1 1 0 1 1 0 1 1 0 1

, , ,da n a n C b

A A B Db a n b a n b a n d

; (3-10)

the nondimensionalized wavenumber 1 1 1 0K k d b a n and growth rate

1 1 0b a n are also used below.

We obtain numerically the neutral stability curve a*K( ) such that at * K the

basic state becomes unstable; 0r along this curve. If additionally 0i K at

* K , an oscillatory regime sets in as a result of the bifurcation with being the

frequency of oscillation. Typical neutral stability curves are shown in Fig. 3-10(a); the uniform

state is stable below the lines, whereas oscillatory regime emerges above the lines. For Case I the

system can be interpreted as an infinite layer and any value of the wavenumber is possible.

Therefore, the instability first starts at the critical value с corresponding to the minimum of

the neutral stability curve. Variation of с with dimensionless peroxide concentration 2C is

59

depicted in Fig. 3-10(b). The corresponding values of the wavenumber and the imaginary part of

the growth rate are referred to as critical wavenumber сK and frequency с , respectively. They

determine a typical length of the oscillatory pattern and its frequency near the stability threshold.

The variation of the critical values with 2C is shown in Fig. 2(c). It is clear that for higher

peroxide concentration the critical frequency grows; the typical lengthscale of the pattern

decreases.

Figure 3-10. Influence of hydrogen peroxide (increases as C2 grows) on the stability of the basic

state. (a): Neutral stability curves α*(K) for two values of C2 . (b): variation of the critical values

of αc with C2 ; for both panels the oscillatory regime emerges above the curves. (c): variation of

the critical wavenumber Kc (right axis, dashed line) and frequency of perturbations ωc (left axis,

dotted line) with C2 . The other parameters, as they are defined in Eqs. (9) and (10), are A1 = 0.5,

A2 = 0.1, B2 = 0.8, D2 = 1.3, D3 = 0.5.

For Case II there is no need in minimization; K can be fixed corresponding to a cluster

size. According to the results shown in Fig. 3-10(a) at higher concentration of hydrogen peroxide,

smaller clusters start oscillating; the frequency of the oscillation grows.

Now let us discuss the influence of glucose concentration on the stability of the basic

state. To that end, we have to vary 2C excluding 0

1C from the other parameters; for example,

dealing with 2C and 2 2A C , which do not depend on 0

1C anymore. The similar computations

are performed for this case and the results are quite similar. However, since an increase in 2C

60

leads to decrease in the glucose concentration, the interpretation of the results is the opposite: the

growth of the glucose concentration results in the diminution of the eigen-frequency.

We have to note that the analysis presented here is valid for small perturbations to the

uniform basic state, whereas in the most of experiments the oscillations are not of small

amplitude. To describe fully nonlinear (finite-amplitude) patterns, more complicated modeling

should be developed.

3.4 Conclusion

In conclusion, a new reaction-induced oscillatory active colloid system is introduced in

this chapter. The colloidal particles can synchronize with each other to form oscillating clusters,

and the synchronization of clusters leads to propagation of oscillation. There can exist multiple

frequencies in one system, perhaps due to different local chemical and particle frequency or

cluster size, which agrees qualitatively with the preliminary continuum model.

3.5 Perspective

To get a better understanding of the system, influence of UV intensity, cluster size and

particle concentration on the oscillation should be investigated. And based on these, a more

detailed coarse-grain simulation could be built to better explain the system.

It is also possible to encapsulate the silver phosphate particles inside microstructures like

capsules, emulsions and droplets,18 and see how the oscillation of particles would affect motion of

the microstructures.

61

3.6 References

1. Mikhailov, A. S.; Showalter, K. Introduction to Focus Issue: Design and Control of Self-

Organization in Distributed Active Systems. Chaos 2008, 18, -.

2. Epstein, I. R. Coupled chemical oscillators and emergent system properties. Chem.

Commun. 2014, 50, 10758-10767.

3. Epstein, I. R.; Vanag, V. K.; Balazs, A. C.; Kuksenok, O.; Dayal, P.; Bhattacharya, A.

Chemical Oscillators in Structured Media. Acc. Chem. Res. 2011, 45, 2160-2168.

4. Field, R. J.; Koros, E.; Noyes, R. M. Oscillations in chemical systems. II. Thorough

analysis of temporal oscillation in the bromate-cerium-malonic acid system. J. Am.

Chem. Soc. 1972, 94, 8649-8664.

5. Yoshida, R.; Takahashi, T.; Yamaguchi, T.; Ichijo, H. Self-Oscillating Gel. J. Am. Chem.

Soc. 1996, 118, 5134-5135.

6. Kuksenok, O.; Dayal, P.; Bhattacharya, A.; Yashin, V. V.; Deb, D.; Chen, I. C.; Van

Vliet, K. J.; Balazs, A. C. Chemo-responsive, self-oscillating gels that undergo

biomimetic communication. Chem. Soc. Rev. 2013, 42, 7257-7277.

7. Taylor, A. F.; Tinsley, M. R.; Wang, F.; Huang, Z.; Showalter, K. Dynamical Quorum

Sensing and Synchronization in Large Populations of Chemical Oscillators. Science

2009, 323, 614-617.

8. Tinsley, M. R.; Taylor, A. F.; Huang, Z.; Wang, F.; Showalter, K. Dynamical quorum

sensing and synchronization in collections of excitable and oscillatory catalytic particles.

Phys. D 2010, 239, 785-790.

9. Vanag, V. K.; Epstein, I. R. Inwardly Rotating Spiral Waves in a Reaction-Diffusion

System. Science 2001, 294, 835-837.

10. Vanag, V. K.; Epstein, I. R. Segmented spiral waves in a reaction-diffusion system. Proc.

Natl. Acad. Sci. U.S.A. 2003, 100, 14635-14638.

11. Dayal, P.; Kuksenok, O.; Balazs, A. C. Using Light to Guide the Self-Sustained Motion

of Active Gels. Langmuir 2009, 25, 4298-4301.

12. Shinohara, S.-i.; Seki, T.; Sakai, T.; Yoshida, R.; Takeoka, Y. Photoregulated Wormlike

Motion of a Gel. Angew. Chem. Int. Ed. 2008, 47, 9039-9043.

13. Duan, W.; Liu, R.; Sen, A. Transition between Collective Behaviors of Micromotors in

Response to Different Stimuli. J. Am. Chem. Soc. 2013, 135, 1280-1283.

14. Speight, J. G. Lange's handbook of chemistry. 16th ed.

15. Gu, Y.; Li, D. The ζ-Potential of Glass Surface in Contact with Aqueous Solutions. J.

Colloid Interface Sci. 2000, 226, 328-339.

16. Ibele, M.; Mallouk, T. E.; Sen, A. Schooling Behavior of Light-Powered Autonomous

Micromotors in Water. Angew. Chem. Int. Ed. 2009, 48, 3308-3312.

17. Shklyaev, S.; Straube, A. V. The impact of bubble diffusivity on confined oscillated

bubbly liquid. Physics of Fluids (1994-present) 2009, 21, -.

18. Dewey, D. C.; Strulson, C. A.; Cacace, D. N.; Bevilacqua, P. C.; Keating, C. D.

Bioreactor droplets from liposome-stabilized all-aqueous emulsions. Nat Commun 2014,

5.

62

Chapter 4

Motion Analysis on Silver Chloride Nanomotors

4.1 Introduction

In addition to purely phenomenological experimental studies and theoretical mechanistic

descriptions on motor systems, 1-7 several groups have recently begun to statistically analyze and

characterize the motion patterns of these nanomotors.8-14 These studies reveal the correlation

between the external conditions (e.g., viscosity at interface,8 and fuel concentrations9, 10) and the

diffusive behavior of the motor particle.

In Chapter 2 and 3, two motor systems exhibiting collective behaviors were introduced.

Through motor-motor interaction, motors in these systems are able to form various collective

patterns. However, a quantitative understanding of the individual motion of motor particles in

such systems is still lacking: for example, how does motor-motor interaction affect the motor

movement? In this chapter, the question is answered by analyzing the motion of microscale silver

chloride (AgCl) particles under UV light in deionized water.

Often, when examining the statistics of particle motion the question is: how far do these

particles travel in a given time interval, τ; or in a more mathematical sense, what is the objects’

root-mean-squared-displacement (RMSD) over that time interval? For convenience, this value is

typically squared, and the mean-squared-displacement (MSD) of the collection of particles is

examined. For several idealized types of motions, the MSD has been shown to increase as a

function of τ raised to some power, α (Eqn. 4-115). In the case of a particle undergoing a ballistic,

constant velocity motion, α is simply 2. For particles undergoing a purely diffusive, random,

Brownian walk, Einstein16 proved that the MSD increases linearly with τ (i.e., α = 1). Another

63

kind of motion observed in a variety of living and non-living systems is the Levy-walk17, where

during most of the identically-sized time intervals, the displacements encountered would be

relatively small, but occasionally a much longer displacement would be seen. Accordingly, a

Levy-walk type motion is characterized by an α value which is between 1 and 2. Since ordinary

Brownian diffusion is by far the most commonly observed motion, systems in which α does not

equal 1 are often deemed as having “anomalous” diffusive behavior, with values greater than 1

corresponding to “superdiffusive” systems18-21 and values less than 1 corresponding to

“subdiffusive” systems22-26.

The three idealized scenarios mentioned above are similar in that they are all

essentially fractal in nature. That is, no matter how small the value of τ, Eqn. 4-1 still holds,

where Kα is some constant specific to the system at hand (e.g. diffusion constant).

MSD = Kατα (4-1)

In real world systems, however, the fractal nature of the system often breaks down at

some level. For instance, for the Brownian motion of an inert colloid suspended in a solvent, the

MSD of the particle during a given time interval, τ, does indeed go as τ except when that time

interval is very small, e.g., time interval between collisions. At these very small timescales, the

particle may appear to be undergoing a ballistic, constant velocity, motion as it traverses its

mean-free-path between solvent collisions27. In light of these potential subtleties, it is often

advantageous to plot the MSD vs. the size of the time interval, τ, studied. In such a plot, the time

intervals at which α changes signify the important timescales governing the system in question.

In the current system, AgCl particles (d ~ 2 m) can move autonomously when exposed

to UV light in deionized water because they slowly and asymmetrically decompose into ions.28

64

Over the course of a few minutes, the ion trails of neighboring colloids begin to overlap, and the

particles respond by diffusiophoretically29 collecting themselves into particulate “schools,” i.e.

regions in which the number density of particles is significantly higher than the global average.

To study the influence of motor-motor interaction, we analyzed the motion of four

distinct classes of particles in this system, three examples of which can be seen in Fig. 4-1: (1)

Isolated AgCl particles in the absence of UV light. (2) Isolated AgCl particles in the presence of

UV light. (3) “Coupled” AgCl particles in the presence of UV light. Coupled particles are

defined here as those particles which only have 1-3 neighboring particles within a radius of five

body lengths. (~ 10 m). The neighboring particles around a specific “coupled” particle may

change over time, and their number may continue to vary from 1 to 3. Also, the actual distance

between the “coupled” particle and its neighbors may change while remaining within five particle

body lengths. (4) “Schooled” AgCl particles in the presence of UV light. Here, a “schooled”

particle is a particle which is surrounded by more than 3 other particles within a radius of five

body lengths and whose nearest neighbors are roughly symmetrically distributed in space (i.e.,

the “schooled” particles were selected from near the center of the particle schools, not the edges.)

Figure 4-1. A microscope image showing examples of isolated, coupled, and schooled

classifications of AgCl particles

65

Besides experimental observation and data analysis, an agent-oriented model with

Netlogo was built to simulate and analyze motion of an individual motor particle with different

particle populations. A similar trend to that in experimental results was found, as particles

transition from “superdiffusion” to normal diffusion and finally “subdiffusion” with increasing

particle population. Such trend and agreement between experimental and simulation results

confirm the influence of motor-motor interaction on diffusion of motor particles.

4.2 Experimental section

4.2.1 Synthesis of AgCl particles

AgCl particles were synthesized according to the reported procedure28: 0.075 g sodium

tripolyphosphate (85%, Aldrich) was added to a 50 mL solution of 1.491 g KCl (ACS grade,

EMD Chemicals) in deionized water, and the solution was heated to 70°C. Under vigorous

stirring, this solution was added to a second 25 mL solution of which contained 3.400 g AgNO3

(99.9%, ACS grade, Stream Chemicals), which was also at 70°C. The reaction flask was covered

with aluminum foil, and stirring was halted after 1 min. The resulting mixture was kept at 70°C

for 3 hr followed by 100°C for 1 hr. The supernatant was decanted from the resulting white AgCl

particles, which were then immediately (while still hot) resuspended in room temperature

deionized water. The particles were centrifuged and washed with deionized water several times.

Large aggregates of AgCl were removed by centrifuging the suspended AgCl particles at 2000

rpm for 2 min and collecting the supernatant. Size and morphology of the particles were

characterized by SEM, and result is as shown in Fig. 4-2.

66

Figure 4-2. SEM images of AgCl particles, the radius of which are around 1μm.

4.2.2 Observation and tracking of particles

30 μL of a solution of AgCl particles in deionized water was placed inside a circular well

(9 mm diameter, 0.12 mm deep, Secure Seal Spacer, Invitrogen) on a microscope slide and

imaged with a microscope (Zeiss, Axiovert 200 Mat). UV light (320–380 nm, 2.5 W cm−2,

Chroma 31000v2) using a 100× imaging objective. Videos were then taken under microscope

with Roxio easy media creator (Roxio), and then compressed with Virtual Dub (Virtual Dub.org).

Motions of isolated, coupled and schooled particles were tracked manually using Physvis

(Kenyon College). For each group of AgCl, 30 particles were tracked, and each particle was

tracked every three frame numbers (0.1 s) for a total of 2010 frame numbers. We also tracked the

movement of AgCl particles when UV was turned off. Data was processed with OriginPro 8

(OriginLab).

67

4.2.3 Netlogo model

NetLogo is a multi-agent programmable modeling environment written mostly in Java. It

is particularly suited for modeling complex systems developing over time. Modelers can give

instructions to hundreds of “agents” all operating independently, which makes it possible to

explore the connection between the micro-level behavior of individuals and the macro-level

patterns that emerge from the interaction of many individuals. The software could be downloaded

free of charge from http://ccl.northwestern.edu/netlogo/index.shtml.

In the simulation, as shown in Fig. 4-3, we have a test particle (red), the movement of

which we analyze and several “neighboring” particles (green). The number of “neighboring”

particles is varied by the “school-population” slider, and originally distributed within a certain

distance of the test particle. The distance is given by multiplying the values of “particle-size” and

“radius-ratio” sliders. (radius-ratio is the ratio between radius of the school and that of the

particles)

68

Figure 4-3. Interface for the Netlogo Model

Motion of the particles is the summation of four effectively independent behaviors: (1) A

translational diffusive motion, in which particles advance with a speed controlled by the

“translational-diffusion-speed” slider, but at a randomly chosen direction. (2) A rotational

diffusive motion, in which particles change their orientation by a certain angle, and the angle is

normally distributed with mean value 0 and standard deviation given by the “rotational-value”

slider. (3) A ballistic motion, in which particles are propelled with a given speed along the

directions of their own orientations, and the speed is given by multiplying the values of

“translational-diffusion-speed” and “b-t-speed-ratio” (speed ratio between ballistic motion and

translational diffusion) sliders. (4) The interaction of the particle with its neighbors, in which

particles, without changing their orientations, attract and repel others according to the distances

between them. Each particle has an attraction zone (blue area) and a repulsion zone (white area),

but we only display the zones of the test particle here. If a particle comes into the attraction zone

of a certain neighbor, it moves without changing its orientation, towards the neighbor with an

adjusted speed based on the values of “translational-diffusion-speed” and “n-t-speed-ratio” (speed

ratio between particle attraction and translational diffusion) sliders, distance between the neighbor

and itself, and the total number of particles in the system. If a particle comes into the repulsion

zone of a certain neighbor, it moves without changing its orientation, away from the neighbor

with an adjusted speed based on the values of “translational-diffusion-speed” and “repulsion-

constant” sliders, as well as distance between the neighbor and itself. Also, the speeds of

particles’ ballistic motion and particle interaction were adjusted according to the number of

particles in the system, based on the assumption that more particles would generate more ions and

a higher solution conductivity, and particles powered by diffusiophoresis will have lower speeds

69

in solutions with higher conductivity. By turning on/off the “set-up-patches” switch, we can

choose whether to display the attraction and repulsion zones.

To run the simulation, first click on the “setup” button on the left side, and then click on

the “go” button. The simulation will automatically stop after 5000 ticks. Then click on the “do the

calculation and plot MSD” button to plot mean squared displacements of the test particle over

different time intervals. The time intervals are chosen according to the values from “max-time-

steps” and “time-step-increment” sliders.

Simulations were run with 6 different particle populations: 1, 2 4, 6, 11 and 21.

4.3 Results and discussion

When a dilute suspension of AgCl particles in water was placed on a microscope slide,

the unstablized AgCl particles, being more dense (5.56 g/cm3) than water, settled to within a few

microns of the underlying slide’s surface. Electrostatic repulsion between the negatively charged

glass slide and the negatively charged AgCl surface kept the particles from contacting the slide

directly.

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Figure 4-4. Example trajectories of four different AgCl particles selected from each of the four

particle classifications: AgCl in the absence of UV light, AgCl in the presence of UV light, coupled

AgCl particles, and schooled AgCl particles.

Over the course of a given experiment, the positions of individual particles were

recorded. Because the particles are not uniform (Fig. 4-2), only the movements of particles with

size around 2 m (1.6-2.4 m) were recorded and analyzed. Example trajectories can be seen in

Fig. 4-4. For each particle, several squared-displacement values over consecutive time intervals

of a given length, τ, were recorded. These displacements were averaged (arithmetic mean)

together to generate the MSD for that τ value. This process was then repeated on the same

particles for various other τ values ranging from 0.1 s to 15 s. Then, for each of the 30 particles in

each group (coupled, schooled, etc), MSD values at the same τ were collected and averaged to get

a MSD value representing the whole group for that time interval. These MSD values were plotted

versus τ to analyze the motion of particles in each group. Although it was relatively common to

observe particles whose designations changed as the experiment progressed (e.g. beginning the

experiment as an isolated particle, then becoming a coupled particle, and finally migrating into a

school), data were only taken for particles whose designations remained unchanged throughout

the entire experiment.

4.3.1 Isolated particles in the absence of UV light.

In the absence of UV light, the AgCl particles translate two-dimensionally in the plane

just above the slide’s surface, as they are buffeted about by Brownian forces. As expected,

analysis of these particles generated an α value of 1, consistent with Brownian motion (Fig. 4-5).

Using this α value and understanding that for a system undergoing two dimensional diffusion, Kα

corresponds to 4D, where D is the diffusion constant of the particle, an average particle diffusion

71

constant of 0.35 μm2 s-1 ± 0.05 was calculated. This is in reasonable agreement with the

theoretical diffusion constant for an inert, spherical 1 m radius particle (approx. size of AgCl

particles, see Fig. 4-2) at 25°C, which is 0.22 m2 s-1. The difference can be attributed to two

reasons: a) The movements of particles may perhaps be powered by the trace amount of UV in

daylight and may not be strictly Brownian. b) The AgCl particles mostly have elongated shapes

(as shown in Fig.4-2), which results in a deviation from the theoretical value that is based on

spherical particles.

Figure 4-5. Mean squared displacement of AgCl particles in the absence of UV. Linear relation

indicates normal diffusive behavior as expected for Brownian motion. At each time interval, thirty

particles’ MSD values are calculated. Each data point in the figure represents the average of these

MSD values at the corresponding time interval, and the corresponding error bar is calculated from

the standard deviation of the MSD values with a 95% confidence level.

4.3.2 Isolated particles in the presence of UV light.

For the previous examples of Janus motor systems, their propulsion mechanism relies on

the compositional asymmetry across the surface, i.e. one side composed of active catalyst and the

other inert material. The AgCl motor system, however, is uniform in composition and thus needs

other ways to break symmetry for particle propulsion. For AgCl particles, it is the surface

72

heterogeneity that contributes to the particle propulsion. The particles as synthesized have

unsymmetrical shapes (Fig 4-2). Further, different morphology (e.g., surface roughness and

surface area) across the surface of the particles will also lead to asymmetry in reactivity, i.e. the

side with higher roughness is likely to be more reactive. In the presence of UV light, AgCl

particles begin to slowly decompose in water to release H+ and Cl- ions. Due to asymmetry in

reactivity across the particle surface, the resultant asymmetric ion gradient diffusiophoretically

propels the particles forward. As the particles move, however, they are still subject to Brownian

reorientations as they collide with solvent molecules. Thus, the particles move through solution

in a manner similar to that of a wayward rocket: typically moving with the same end forward

(Fig. 4-6), but in a direction that is constantly changing. There is, therefore, in this system two

important inherent timescales: (1) The time it takes for a particle’s trajectory to randomize, τR

(which is equal to the inverse of the particle’s rotational diffusion constant, DR), and (2) the time

it takes for a particle to travel ballistically an arbitrary distance. At short time intervals (τ << τR),

the particle’s ballistic displacement is likely to be high compared to its rotational reorientation

and the the particle will appear to be travelling in essentially a straight path (i.e., α = 2).

Whereas, at very long time intervals (τ >> τR), the particle will have ample time to randomize its

ballistic trajectories and its overall motion path will look like a random diffusive walk (i.e., α =

1). However, for this random walk, because of the ballistic force imparted to the particle, the

apparent translational diffusion constant will be enhanced compared to the diffusion constant of a

comparably sized inert particle (Deff > D). Indeed, when the MSD of isolated AgCl particles

exposed to UV light were plotted against τ (Fig. 4-7), a shift from α >1 to α ≈ 1 was seen as the

time interval was increased to values above τcrit ≈ 1.6 s. For comparison, the rotational diffusion

time τR of an ideal 2 m particle in water at 25°C is 6 s. This difference between the

experimental τcrit and the theoretical τR is due to the additional torque on the particle from the

73

reaction occurring on its surface, which causes it to rotate faster than an inert particle in an

idealized system.

Particles exhibiting this type of enhanced diffusive motion have been analyzed

previously,8, 9 and it was shown that for any arbitrary sampling time interval, τ, the MSD is given

by Eqn. 4-2,9

(4-2)

where V is the axial velocity of the motor. This equation has two limiting forms: (a) If τ

<< τR, the MSD is given by 4Dτ + V2τ2, and (b) if τ >> τR the MSD is equal to τ(4D +V2τR).

Figure 4-6. Time-lapse optical microscope images showing the movement and leading end of an

isolated particle (the one within the white circle): the particle moves along its leading end ( a-b ),

and then changes its moving direction due to rotational diffusion ( c ), the particle then moves along

this new direction with the same leading end( c-e ) before changing the moving direction again. ( f )

Scale bar, 10μm. Time stamp, 1s

2 2

2 /2=4 + [ 1]

2

R R

R

VMSD D e

74

Fitting the experimental MSD data for UV-powered isolated AgCl particles (Fig. 4-7) to

Eqn. 4-2, yields an estimate for the purely ballistic speed of the particles (V = 3.3 m s-1), and an

estimate of their unpowered diffusion constant (D = 0.28 m2 s-1). This extrapolated unpowered

diffusion constant is quite close to the measured diffusion constant of unpowered particles (0.35

μm2 s-1, see section A). It is also possible using the limiting form, τ >> τR, of Eqn. 4-2 to define

an effective diffusion constant of the particles (Deff). This value is given by Eqn. 4-3, and for the

particles in our system is 4.5 m2 s-1, which is highly enhanced compared to that for isolated

particles in the absence of UV light (0.35 m2 s-1 ).

2

4

Reff

VD D

(4-3)

Figure 4-7. Mean squared displacement of isolated particles under UV light. At each time interval,

thirty particles’ MSD values are calculated. Each data point in the figure represents the average of

these MSD values at the corresponding time interval, and the corresponding error bar is calculated

from the standard deviation of the MSD values with a 95% confidence level. The red, black and

75

blue lines represent fitting results for short, all and long time intervals, respectively, indicating a

transition from ballistic motion to enhanced diffusion. The left and right inserts are mean squared

displacement of isolated particles at short and long time intervals, respectively.

4.3.3 Coupled particles

For isolated particles that propel themselves when illuminated with UV, the motion of the

particles can be considered as the summation of three effectively independent behaviors: (1) A

translational diffusive motion, (2) a rotational diffusive motion, and (3) a ballistic motion due to

the chemical reaction occurring on the particle surface. In the case of coupled particles, there is a

fourth interaction to consider, namely, the interaction of the particle with its neighbors. The AgCl

particles illuminated with UV light interact with one another along a surface by attracting other

AgCl particles from long distances (on the order of 10-20 m), while maintaining a thin

exclusion zone (1-2 m) bereft of other particles.28

These interactions are powered by the response of the particles to the gradient of

electrolyte produced in solution (Fig. 4-8). Let us take for example, a couplet comprised of only

two particles, and consider how the particle-particle interaction affects a member’s rotational

diffusive, translational diffusive, and ballistic motions. Because the particle-particle interactions

are mediated by surface chemistry, it is conceivable that, for a coupled particle, a force may exist

which would cause the particle to line up preferentially with respect to its neighbor. Although the

surfaces of these UV-exposed AgCl particles have been shown to be somewhat heterogeneous,

preferential orientation of particles with respect to their neighbors was not observed (Fig. 4-9).

The next question is whether two identical particles that are coupled by some potential well

would be expected to diffuse faster or slower than similar particles that are free. This question

has been addressed in a somewhat related system, which is the diffusion of ion pairs in solution.

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When ion pairs diffuse, the constituent ions are coupled, and the diffusion constant of the pair as

a whole is equal to the harmonic average of the diffusion constants of the constituent ions. Thus,

if the two ions, or in our case the two particles, are identical, the diffusion constant of the couple

may be considered to be the average of the diffusion constants of the individual constituents.

Figure 4-8. Scheme of interaction between AgCl particles based on self-diffusiophoresis. For each

AgCl particle, the chemical reaction taking place at its surface generates a concentration gradient

of protons and chloride ions, and this concentration gradient leads to diffusiophoretic flows as

shown in a):28 Because protons travel away from the surface of AgCl much faster than the chloride

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ions (DH+ = 9.311x10-5 cm2s-1, DCl- = 1.385x10-5 cm2s-1 ), an electrical field (E) will be generated

pointing back towards the AgCl particle. The electrical field acts phoretically on the nearby

negatively charged AgCl particles (𝜁 = -50 mV) by pushing them away from the central one (VEp).

The electrical field also acts osmotically on the adsorbed protons in the double layer of the

microscope slide wall (𝜁 = -62 mV) by pumping the fluid along the slide’s surface towards the

AgCl particles. (VEo) At long distances from the central AgCl particle, osmotic flow dominates

because the magnitude of the particle zeta potential is less than that of the slide, and the

electroosmotic flow pulls the nearby particles to the central one leading to schooling, as shown in

b). The electroosmotic flow decays to zero very near to the AgCl particle due to fluid continuity,

and repulsive electrophoretic force starts to dominate resulting in a small exclusion zone around

each AgCl particle. In addition, for the formed “school” (area circled in c)), the electroosmotic flow

remains persistent due to the continued generation of ions and this serves to prevent individual

particles from escaping. For a particle (the sphere with blue arrow in d) that interacts with a certain

“neighboring” particle (the red sphere in d), it will move towards the neighbor without changing

the orientation, and the net path is similar to a particle that changes its orientation by rotational

diffusion and then moves along the new direction by ballistic motion, as shown in e). As a result,

particles that interact with neighboring particles appear to be rotating more frequently than isolated

particles.

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Figure 4-9. Time-lapse optical microscope images showing that there is no preferential orientation

of particles with respect to their neighbors: the rod-like particle within the white circle has different

orientations with respect to the particle nearby in a)-d). Scale bar, 5μm. Time stamp, 5s

The final factor that needs to be considered is the impact that particle-particle interactions

have on the ballistic motion of the constituent particles. In nearly all cases, excepting those in

which the particle is ballistically moving directly towards or away from its neighbor, the inter-

particle interaction will deflect the trajectory of the otherwise linearly travelling particle.

Although the exact orientation of the particle may not be altered (the force is minimal, as noted

above), the net path of the particle will be the same as that of a hypothetical particle which has

undergone rotation, as shown in Fig.4-8 (d) and (e). For this reason, it is expected that coupled

particles will appear to be rotating faster than isolated particles, (i.e. their effective rotational

diffusion time, τReff, will be smaller than their actual rotational time, τR).

Figure 4-10. Mean squared displacement of coupled particles. At each time interval, thirty particles’

MSD values are calculated. Each data point in the figure represents the average of these MSD

values at the corresponding time interval, and the corresponding error bar is calculated from the

standard deviation of the MSD values with a 95% confidence level.

When the MSD data for the coupled particles were analyzed (Fig. 4-10), the data showed

a remarkable fit to Equation 1 with an α value of 1 at all time intervals measured. At first glance,

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with increasing number of neighboring particles, the local concentration of ions around each

particle will increase and, according to Equation 4, with increased electrolyte concentration (C)

diffusiophoretic flow will be reduced. While suppressing diffusiophoresis may lead to normal

diffusive behavior, the coupled particles do not exhibit simple Brownian diffusion, since the

diffusion constant of coupled particles are significantly higher (1.53 m2 s-1) than that of

unpowered particles without UV (0.35 m2 s-1), suggesting that other factors may be responsible

for the transition from superdiffusion to normal diffusion, such as particle-particle interaction.

We propose that the particle-particle interaction decreases the τR of the particles to such a degree

that the τReff became smaller than the smallest timescale measured. That is, the transition from

ballistic-dominated motion to diffusion-dominated motion occurs at timescales smaller than that

observable under our experimental conditions. At the longer available timescales, the effective

diffusion constant of these coupled particles (Deff) was found to be 1.53 m2 s-1.

4.3.4 Schooled particles

Similar to the data from coupled particles, the MSD data for schooled particles for the

timescales measured (Fig. 4-11) showed no region in which the particles primarily exhibited

ballistic motion (α >1). Like the coupled particles, the schooled particles appear to be undergoing

an enhanced diffusive walk, with an effective diffusion coefficient Deff of 0.50 m2 s-1 (Fig. 4-12)

which is significantly smaller in comparison to the cases of isolated and coupled particles. But

unlike the coupled particles, at the longer timescales measured, a surprising transition occurred

from (enhanced) diffusive motion (α ≈ 1) to a subdiffusive behavior (α ≈ 0.8). This subdiffusive

behavior is not predicted by the general interaction rules outlined above. The sub-diffusive

behavior indicates that either the ballistic motion of the particles is decelerating over time (and

80

more pronouncedly than for isolated or coupled particles) or the particles are undergoing a

confined random walk16 due to the confinement in the “school” (Fig.4-13). Both explanations are

plausible. Because the ballistic motion of particles is powered by diffusiophoresis, the ballistic

speed is inversely proportional to the electrolyte concentration in solution as shown in Eqn. 4-4,28

(4-4)

where U is the diffusiophoresis speed of particles, C is the electrolyte concentration, DC

and DA are the diffusivities of the cation and anion components of the gradient, kB is the

Boltzmann constant, T is the temperature, e is the elementary charge, 𝜀 is the solution

permittivity, η is the dynamic viscosity of the solution, 𝜁P is the zeta potential of the particles, and

𝜁W is the zeta potential of the wall (glass slide). Over time, the electrolyte concentration of the

solution within a particulate school is expected to increase, as the local concentration of ionic

decomposition products build up. As a result, the ballistic motion of the particles will steadily

decay over time. This buildup of background electrolyte concentration centered on the school

effectively creates a macroscopic electrolyte gradient in solution. The resultant persistent

electroosmotic flow provides an additional force which keeps particles from exiting the school

and keeps the school itself from transnationally diffusing as quickly as might be expected (Fig. 4-

8).

81

Figure 4-11. Mean squared displacement of schooled particles. At each time interval, thirty

particles’ MSD values are calculated. Each data point in the figure represents the average of these

MSD values at the corresponding time interval, and the corresponding error bar is calculated from

the standard deviation of the MSD values with a 95% confidence level. The red and black lines

represent fitting results for short and all time intervals, respectively, indicating a transition from

powered diffusion to sub-diffusive behavior.

Figure 4-12. Mean squared displacement of schooled particles at short time intervals. Schooled

particles show normal diffusion behavior at short time interval, with an effective diffusion constant

Deff = 0.50 m2 s-1.

82

Figure 4-13. Time-lapse optical microscope images showing a particle (the green marked particle

within the white circle) stays “trapped” inside the formed “school” with neighboring particles

(green marked particles outside the white circle) around in a)-d). Scale bar, 10μm. Time stamp, 5s

4.3.5 Simulation results

With the Netlogo model, we simulated the different diffusive behavior of the particles in

which the motion of the particles was the summation of four effectively independent behaviors:

(1) A translational diffusive motion, in which particles advance with a given speed, but at a

randomly chosen direction. (2) A rotational diffusive motion, in which particles change their

orientation. (3) A ballistic motion, in which particles are propelled with a given speed along the

directions of their own orientations. (4) The interaction of the particle with its neighbors, in which

particles, without changing their orientations, attract and repel others according to the distances

83

between them. By changing number of particles in the system, diffusion of the test particle was

observed to transition from superdiffusion to normal diffusion and finally subdiffusion. As shown

in Fig. 4-14, without neighboring particles, the test particle shows superdiffusion with a

combination of ballistic motion at short time intervals and enhanced diffusion at long time

intervals (when rotational diffusion dominates). As the number of neighboring particles is

increased, the transition to enhanced diffusion occurs at successively shorter time intervals due to

particle-particle interactions. If the number of neighboring particles is further increased, the test

particle becomes “trapped” inside the formed “school” and starts to show subdiffusive behavior.

Such results are in good agreement with the experimental results, and thus confirms the influence

of motor-motor interaction on diffusion of individual particles.

Figure 4-14. Simulation results for mean squared displacements of “spectator” particles with

different number of neighboring particles: (a) no neighbors (b) one neighbor (c) three neighbors

(d) five neighbors (e) ten neighbors and (f) twenty neighbors. Transitions from superdiffusion to

normal diffusion and then subdiffusion can be correlated with the increasing number of neighboring

particles.

84

4.4 Conclusions

In conclusion, we have observed different diffusive behaviors for the four classes of

silver chloride particles studied: inert isolated, active isolated, active coupled, and active

schooled. We find that active particles exhibit ballistic motion at short time intervals that

transition to enhanced diffusive motion as the time interval is increased. The onset of this

transition was found to occur more quickly for particles with more neighbors. If the active

particles became “trapped” in a formed “school”, the diffusive behavior further changes to

subdiffusion. The correlation between these transitions and the number of neighboring particles

was verified by simulation. This is the first time three different diffusive behaviors were observed

in a single motor system, and transitions between them occur by changing the number of

neighboring particles. Such transition confirms the effect of motor-motor interaction on the

diffusional behaviors of individual motors, which enriches quantitative understanding of pairwise

interaction between motors.

4.5 Perspective

Although the influence of motor-motor interaction on diffusional behaviors of individual

motors has been confirmed, the following questions are still to be solved: 1. How would the

strength of pair-wise interaction affect the diffusion pattern of motors? 2. What is governing the

size of schools with a given particle concentration, and how would school size affect the diffusion

pattern of motors within? 3. Is it possible to tune the ratio between self-propulsion force and

interaction force?

The first question might be answered by changing the parameters that are related to

diffusiophoretic strength: e.g. reaction rate (ion gradients) and bulk ionic strength. In the current

85

system, it might be of interest to repeat the experiments and analysis under different UV

intensities and bulk electrolyte concentrations.

Besides motor-motor interaction, school sizes with a given particle population are also

governed by lag time, as schools would grow over time. Therefore, to answer this question, a

time-dependent or time-series model has to be introduces, both for data analysis and simulation.

As for the relative strength between two forces, it is hard to achieve such delicate tuning

with the existing schooling systems, in which propulsion and interaction are based on the same

mechanism (aka electrolyte self-diffusiophoresis). A hybrid motor system that combines two

different mechanisms would be desirable, e.g. a segmented Pt/Au/AgCl nanomotor system.

4.6 References

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Nanomotors and Nanorotors. Small 2010, 6, 159-167.

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Powered Nanomotors Out-Swim Nature’s Flagellated Bacteria. ACS Nano 2010, 4, 1782-

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3. Hong, Y.; Velegol, D.; Chaturvedi, N.; Sen, A. Biomimetic behavior of synthetic

particles: from microscopic randomness to macroscopic control. Phys. Chem. Chem.

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4. Ebbens, S. J.; Howse, J. R. In pursuit of propulsion at the nanoscale. Soft Matter 2010, 6,

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5. Wang, J. Can Man-Made Nanomachines Compete with Nature Biomotors? ACS Nano

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6. Sánchez, S.; Pumera, M. Nanorobots: The Ultimate Wireless Self-Propelled Sensing and

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8. Dhar, P.; Fischer, T. M.; Wang, Y.; Mallouk, T. E.; Paxton, W. F.; Sen, A.

Autonomously Moving Nanorods at a Viscous Interface. Nano Lett. 2005, 6, 66-72.

9. Howse, J. R.; Jones, R. A. L.; Ryan, A. J.; Gough, T.; Vafabakhsh, R.; Golestanian, R.

Self-Motile Colloidal Particles: From Directed Propulsion to Random Walk. Phys. Rev.

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10. Ke, H.; Ye, S.; Carroll, R. L.; Showalter, K. Motion Analysis of Self-Propelled Pt−Silica

Particles in Hydrogen Peroxide Solutions. J. Phys. Chem. A 2010, 114, 5462-5467.

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12. Miño, G.; Mallouk, T. E.; Darnige, T.; Hoyos, M.; Dauchet, J.; Dunstan, J.; Soto, R.;

Wang, Y.; Rousselet, A.; Clement, E. Enhanced Diffusion due to Active Swimmers at a

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13. Golestanian, R. Anomalous Diffusion of Symmetric and Asymmetric Active Colloids.

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14. Ebbens, S. J.; Howse, J. R. Direct Observation of the Direction of Motion for Spherical

Catalytic Swimmers. Langmuir 2011, 27, 12293-12296.

15. Metzler, R.; Klafter, J. The random walk's guide to anomalous diffusion: a fractional

dynamics approach. Phys. Rep. 2000, 339, 1-77.

16. Einstein, A. Does the Inertia of a Body Depend on its Energy Content? Ann. Phys. 1905,

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17. de Jager, M.; Weissing, F. J.; Herman, P. M. J.; Nolet, B. A.; van de Koppel, J. Levy

Walks Evolve Through Interaction Between Movement and Environmental Complexity.

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18. Matthaus, F.; Jagodic, M.; Dobnikar, J. E. coli Superdiffusion and Chemotaxis-Search

Strategy, Precision, and Motility. Biophys. J. 2009, 97, 946-957.

19. Ott, T.; Bonitz, M.; Donko, Z.; Hartmann, P. Superdiffusion in quasi-two-dimensional

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21. Chechkin, A. V.; Gonchar, V. Y.; Szydlowski, M. Fractional kinetics for relaxation and

superdiffusion in a magnetic field. Physics of Plasmas 2002, 9, 78-88.

22. Neusius, T.; Sokolov, I. M.; Smith, J. C. Subdiffusion in time-averaged, confined random

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Chapter 5

Numerical Simulation on Micropumps with COMSOL Multiphysics

5.1 Introduction

To better understand the interaction and propulsion mechanisms, a quantitative analysis

on the synthetic machine systems is needed. To achieve such goal, numerial simulations with

COMSOL Multiphysics are employed to investigate the self-diffusiophoresis mechanism, and a

self-powered micropump based on ion-exchange is chosen as the experimental model system.

The ability to manipulate fluid is essential to deliver cargos on demand in fields like

microfluidics and drug delivery. The main challenge for achieving such goal is to overcome the

viscous force that dominates at low Reynolds number, which requires constant propulsion for

objects to move.1 One method to introduce such propulsion force and generate fluid flows is to

convert chemical energy into mechanical motion. In response to external stimuli like chemicals or

light,2-9 chemical reactions at the surface of micropumps induce effects like phoresis10, 11 (e.g.

diffusiophoresis2-4, electrophoresis7-9) or density-driven fluid flows,12, 13 which then leads to

directional migration of inert tracer particles. Unlike biological counterparts, most of these

synthetic micropumps can only be turned “on/off” with supply/drainage of fuels (chemical) or

energy (external fields), and only few of them exhibit the ability to actively adjust the pumping

direction of particles in response to stimuli.14

Herein we report a self-powered microscale pump system based on ion-exchange, in

which pumping direction of silica tracer particles can be tuned by pH of the system. Weakly

acidic Amberlite (ion exchange resin, IRC 76) particles can generate convective fluid flows in

1mM NaCl aqueous through reversible ion-exchange between protons and sodium ions, as shown

88

in Fig. 5-1. At higher pH (~4.7), 2.34 µm silica tracer particles move towards the Amberlite pump

at a speed of 0.7±0.1 µm/s; and when pH is lowered to ~3.0 by addition of 1mM HCl, silica

tracers are pumped away at a speed of 1.2±0.1 µm/s. Such fluid pumping is powered by an ionic

diffusiophoresis mechanism, as verified by numerical simulation results with COMSOL

Multiphysics. A COMSOL simulation model on density-driven micropumps is also included.

Figure 5-1 Ion-exchange at different pH values: a) pH 4.7, b) pH 3

5.2 Experimental section

5.2.1 Observation.

40 μL of a mixture solution of 1 mM NaCl and 2.34 µm silica tracer particles was placed

inside a circular well (9 mm diameter, 0.12 mm deep, Secure Seal Spacer, Invitrogen) with

Amberlite particles (~0.6 mm diamter) on a microscope slide and imaged with a microscope

(Zeiss, Axiovert 200 Mat). Motion of particles were observed through a 20X or 50X imaging

objective. Videos were then taken under microscope with Roxio easy media creator (Roxio).

89

5.2.2. COMSOL Multiphysics Simulation

Finite element simulations were developed with COMSOL Multiphysics (v4.3) coupling

the physics of laminar flow, diffusion of dilute species and electrostatics for the ionic

diffusiophoretic pump, and the physics of laminar flow and heat transfer in fluids for the density-

driven one. Following the geometry of the experimental setup, the simulation contour was

defined in 2-D as a rectangular region of dimension 600 m 300 m positioned within a larger

region of dimension 4000 m 2000 m for the former, and as a rectangular region of dimension

6000 m 0.1 m positioned within a larger region of dimension 20000 m 1300 m for the

latter.

5.3 Results and Discussion

5.3.1 Phenomena

When mixed with 2.34 µm silica tracer particles, Amberlite particles that sit above a

negatively charged glass lead to fluid flows, and negatively charged silica tracer particles migrate

towards them near the glass surface with a speed of 0.7±0.1 µm/s (Fig. 5-2).

Figure 5-2 Pumping of silica tracers by Amberlite particles at pH ~ 4.7: a) Formation of inward

electric field due to ion-exchange. Inset demonstrates faster diffusion of protons, which results in

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inward electrical fields and dominating inward electroosmotic flows. b) Inward particle motion, as

indicated by black arrows, due to pumping towards Amberlite, trajectories of ten particles during a

time interval of 4s are shown in different colours. Scale bar 10 µm.

And pumping direction reversion occurs when Amberlite pumps function in much lower

pH. In 1mM HCl solution, Amberlite pumps start to pump fluids away, and silica tracers move

away from them with a speed of 1.2±0.1 µm/s (Fig. 5-3)

Figure 5-3 Pumping of silica tracers by Amberlite particles at pH ~ 3: a) Formation of outward

electric field due to ion-exchange. Inset demonstrates faster diffusion of protons, which results in

outward electrical fields and dominating outward electroosmotic flows. b) Outward particle motion,

as indicated by black arrows, due to pumping towards Amberlite, trajectories of ten particles during

a time interval of 4s are shown in different colours. Scale bar 10 µm.

5.3.2 Mechanism

The above observed phenomena can be explained with an ionic diffusiophoresis

mechanism, in which motion of particles are induced by electrolyte concentration gradients.15-19

The electrolyte concentration gradient ∇C contributes to motion of charged particles at a speed U

by a combination of two effects, as shown in Eqn.5-1:

91

𝑈 =∇c

𝑐0[(𝐷+−𝐷−

𝐷++𝐷−)(𝑘𝐵𝑇

𝑒)(𝜀(𝜁𝑝−𝜁𝑤))

𝜂]

⏟ 𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝐹𝑖𝑒𝑙𝑑 𝑇𝑒𝑟𝑚

+∇c

𝑐0[(2𝜀𝑘𝐵

2T2

𝜂𝑒2) {ln(1 − γ𝑤

2 ) − ln(1 − γ𝑝2)}]

⏟ 𝐶ℎ𝑒𝑚𝑜𝑝ℎ𝑜𝑟𝑒𝑡𝑖𝑐 𝑇𝑒𝑟𝑚

(5-1)

where DC and DA are the diffusivities of the cation and anion components of the gradient,

kB is the Boltzmann constant, T is the temperature, e is the elementary charge, 𝜀 is the solution

permittivity, η is the dynamic viscosity of the solution, 𝜁P is the zeta potential of particles, and 𝜁W

is the zeta potential of the wall (glass slide). In electrical field effect, the different diffusivities of

cations and anions leads to a net electrical field, which acts both phoretically on the particles and

osmotically on the protons adsorbed in the double layer of the negatively charged glass slide. In

chemophoretic effect, the concentration gradient of the electrolytes causes a gradient in the

thickness of the electrical double layer, and thus a “pressure” difference along the glass slide. As

a result, the solution flows from the area of higher electrolyte concentration to that of lower

concentration. In most cases, electrical field effect dominates, and the moving direction of

particles can be predicted from where electric fields are pointing.20

A − COOH + Na+ ⇋ A − COO−Na+ + H+ (5-2)

For Amberlite particles, there exists an equilibrium as shown in eqn. 5-2.21 At higher pH

(around 4.7), as shown in Fig..5-1 a, protons on acidic form Amberlite particles exchange with

cations (i.e. sodium ions), and migrate into the solution, leading to lower pH, as shown Fig. 5-4 a.

Since protons diffuse faster compared to sodium ions ions (DH+ =9.311 x 10-5 cm2 s-1 and DNa

+

=1.344 x 10-5 cm2 s-1), positive ions accumulate at regions away from the pump, leading to inward

electric fields. inward electric fields are formed, which lead to outward electrophoresis of the

negatively charged silica tracer particles and inward electroosmotic flows along the negatively

charged glass slide surface. (Fig. 5-1a) Because the magnitude of zeta potential of silica particles

(𝜁p ~ -30 mV)22 is smaller than that of the glass (𝜁w ~ -60mV)23 in 1mM NaCl at pH 4.7, inward

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electroosmotic flows dominate, and silica particles are pumped towards the Amberlite particle.

(Fig. 5-1b)

And with addition of acid, pH lowers to ~3, which pushes the equilibria from right to left,

and reverses the ion-exchange reaction (and hence pH gradually increases over time, as shown in

Fig. 5-4 b)) together with ion gradients and all the associated phoretic effects (Fig. 5-2 a). At such

condition (pH ~3), since the magnitude of zeta potential of the glass substrate is still larger (-45

mV) compared with that of silica particles (-10 mV), outward electroosmosis dominates, and

particles are pumped away from amberlite, as shown in Fig. 5-2 b. Increase in NaCl concentration

leads to suppression of pumping, as tracer particles are only exhibiting Brownian motion in 10

mM NaCl solution. Such decay in motion verifies ionic diffusiophoresis as the main powering

mechanism, and rules out other mechanisms like swelling and osmophoresis.

Figure 5-4 pH change with Amberlite pump system: (a) ~100 amberlite particles in 5mL 1mM

NaCl and (b) ~100 NaCl-processed amberlite particles in 5 mL 1mM HCl solutions over a time

period of 3 min.

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5.3.3 Numerical simulation on ionic diffusiophoretic micropumps

To further verify and quantitatively understand the powering mechanism, numerical

simulations with COMSOL Multiphysics are conducted as follows.

5.3.3.1 Simulation on HCl-releasing gel

A simple model on diffusiophoresis is first built on a HCl-releasing gel. The 600 m x

600 m gel is releasing positive protons, negative chloride ions, as well as “neutral” HCl with a

flux of 1x10-6 mol/m2 inside a 20000 m x 10000 m chamber. Diffusion coefficients of protons

and chloride ions are DH =9.311 x 10-5 cm2 s-1 and DCl = 2.032 x 10-5 cm2 s-1,respectively, and that

of HCl is calculated as 2*DH*DCl/(DH+DCl). The aqueous phase is set as electrical neutral with

initial concentrations of the three species as 0.01 mM, and boundary conditions are as follows:

for the chamber, the bottom is set as zero-charge, non-flux and electroosmotic wall (which

follows the electroosmotic equation with a zeta potential of -50 mV), and the other three

boundaries are set as zero-Volt, constant concentration (the same as the initial concentrations,

0.01 mM), and open-boundary condition. As shown in Fig. 5-5(a), concentration distributions of

protons and chloride ions are similar to that of HCl. In addition, protons are leading chloride ions

during diffusion process (Fig. 5-5 (b)), and hence generating inward electrical fields as well as

inward fluid flow, as shown in Fig. 5-6 Such results verify that the model agrees well with

diffusiophoresis mechanism. Note that simulation results reflect the situation at steady states.

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Figure 5-5 a) Concentration distribution of protons (CH), chloride ions (CCl) and HCl (CHCl)

molecules. b) Profile of CH-CCl

Figure 5-6 a) Electrical field distribution at different heights above the bottom. b) Fluid flow profile.

5.3.3.2 Simulation on ion-exchange micropumps with constant fluxes

After verification of the model, the above ion-exchange pumps are simulated with the

same boundary conditions except that the initial conditions are changed to 1 mM NaCl or HCl.

For the system in 1mM NaCl, at pump surfaces, there are 1x10-6 mol/m2 inward flux of sodium

ions, and outward flux of protons with the same magnitue. The surface flux magnitudes are

estimated from the pH measurement experiments, and agree well with numerical estimation for a

time span around 100s in eqn. 5-3:24

95

J = D ∗C

√𝐷𝑡 (5-3)

Size of the pump is set the same as experimental setup (~ 0.6 mm), and size of the

chamber is set as 3 mm by estimation from L = √𝐷𝑡. Zeta potential of the bottom wall is set at -

30 mV, as the zeta potential difference between the silica tracers and the glass substrate.

Under such setup, an inward flow with speed around 0.22 m/s is produced, as shown in

Fig. 5-7 top figure. And similarly, for the ion-exchange pump in 1mM HCl solution, flux is set as

1x10-5 mol/m2 inward flux of protons, and outward flux of sodium ions with the same magnitue,

as estimated from both pH measurements and numerical calculation. And in this case, an outward

flow of 1.1 m/s is produced, as shown in Fig.5-7 bottom figure.

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Figure 5-7 Simulation results with constant fluxes. Top: Inward flows based on exchange from

sodium ions to protons. Bottom: Outward flows based on exchange from protons to sodium ions.

5.3.3.3 Simulation on ion-exchange micropumps with concentration-dependent fluxes

This seesion employs fluxes that would change with local ion concentration, and assume

linear relationship between the flux and local ion concentration. And the flow speeds associated

with the two processes change from 0.22 m/s to 0.19 m/s, and from 1.1 m/s to 0.7 m/s,

respectively, as shown in Fig. 5-8.

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Figure 5-8 Simulation results with fluxes that are linear with local concentrations. Top: Inward

flows based on exchange from sodium ions to protons. Bottom: Outward flows based on exchange

from protons to sodium ions.

The model in the previous session assumes a constant flux. However, as the reaction flux

leads to variation of local chemical/ion concentration, a concentration-dependent flux may better

describe the experimental system. In addition, the simulation results are in reasonable agreement

with the experimental ones, and verify the self-diffusiophoresis mechanism proposed above.

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5.3.4 Numerical simulation on density-driven pumps

Another commonly employed mechanism for microscale fluid pumping is density-driven

convective flows.12, 13, 25, 26 In such systems, chemical reactions at pump surfaces result in local

density change either due to local temperature change or density difference between the reactants

and products. Since the latter is hard to measure or estimate, this part focues on simulation about

the contribution of reaction heat in establishing convection.

5.3.4.1 Simulation on DNA polymerase pump

The first example is about DNA polymerase pump with ~1µm/s inward flow.12 when

molecules of DNA polymerase are immobilized over a surface, finite element simulations were

developed with COMSOL Multiphysics (v4.3) coupling the physics of laminar flow and heat

transfer in fluids. Following the geometry of the experimental setup, the simulation contour was

defined in 2-D as a rectangular region of dimension 6000 m 0.1 m positioned within a

larger region of dimension 20000 m 1300 m , as shown in Fig. 5-9(a).

Physics of heat transfer in fluids is governed by eqn. 5-4

pC T = k T Q u (5-4)

where is temperature-dependent density of fluid, pC heat capacity of water at constant

pressure, u fluid velocity, T temperature of fluid, k thermal conductivity of water, and Q heat flux

caused by power input from chemical reaction.

As for the boundary conditions: top boundary of the chamber (highlighted in Fig. (a)) is

defined at a constant temperature 273.15K, surface of the pump produces heat flux Q, and all the

other boundaries are thermal insulating.

99

For the physics of laminar flow, the governing equations are as shown in eqn. 5-5 and 5-

6:

2

μ μ F3

Tp + u u u u u (5-5)

ρ 0 u (5-6)

where p is pressure, µ dynamic viscosity of solution, and F a volume force. In the current

simulation, the volume force F is a buoyancy force, as temperature gradients caused by heat flux

lead to difference in fluid density. All the boundaries are subject to non-slip boundary conditions.

With the model, the shear rate distribution for a ~1µm/s fluid flow at 100µm away from

the pump boundary is as demonstrated in Fig. 5-9(b). Finally as shown in Fig. 5-9(c), a power

input of ~10-4 W is required for the ~1µm/s fluid flow, this is much higer than the calculated

energy input from DNA polymerization reactions (8x10-9 W), and hence verifies that contribution

from thermal effect of the reaction is minimal.

100

Figure 5-9 COMSOL Multiphysics simulation results. a) Geometry of the model, red line indicates

the constant temperature boundary condition. b) Shear rate distribution for ~1µm/s fluid flow along

the line as marked by red in the inset, which is 100µm away from the pump boundary. c) Fluid

velocity distribution at 10-4 W power input.

5.3.4.2 Simulation on Glucose-powered micropumps

The other example is about glucose powered micropump with ~0.1µm/s inward flow in 10 mM

glucose solution. Energy input in the current system is estimated to be 1.64 * 10-5 W. To verify the

101

contribution of reaction heat in establishing convection, a finite element model was developed with

COMSOL Multiphysics (v4.3) coupling the physics of laminar flow and heat transfer in fluids,

imilarFollowing the geometry of the experimental setup, the simulation contour was defined in 2-D as a

square region of dimension 1000 m x 1000 m positioned within a larger region of dimension 20000 mm

x 1300 mm, as shown in Fig. 5-10(a). As shown in Fig. 5-10 (b)-(d), a power input of ~1.64 * 10-5 W

results in 0.1 µm/s inward fluid flow along the glass substrate, flipping the pump leads to fluid pumping in

the opposite direction, and increase in power input causes faster pumping, which agree well with

experimental observations.25

Figure 5-10 COMSOL Multiphysics simulation results. a) Geometry of the model, red line indicates

the constant temperature boundary condition. b) Fluid velocity distribution at 1.64 * 10-5 W power

102

input. c) Fluid velocity distribution of an inversed pump at 1.64 * 10-5 W power input. d) Fluid

velocity distribution at 3.77 * 10-5 W power input.

As demonstrated by the simulation results in the sessions of thermal effect on density-

drive micropumps, it can be seen that fluid flows are mainly governed by the magnitude of heat

flux, as well as the geometric parameters, especially height of the chamber.

5.4 Conclusion

In conclusion, this chapter describes a micropump system based on ion-exchange.

Pumping direction in the system can be changed by tuning pH of the system. Fluid pumping is

based on a self-diffusiophoresis mechanism, as verified by numerical simulation results from

COMSOL Multiphysics. COMSOL models on density-driven micropumps are also included.

5.5 Perspective

Future work would focus on tuning the micropump systems with different parameters,

and use the numerical simulations to predict and verify the influence of these parameter change.

Another possiblity is to compare different powering mechansims through numerical

simulations, and study energy effieciencies in each system.

5.6 References

1. Purcell, E. M. Life at low Reynolds number. Am. J. Phys. 1977, 45, 9.

2. Zhang, H.; Yeung, K.; Robbins, J. S.; Pavlick, R. A.; Wu, M.; Liu, R.; Sen, A.; Phillips,

S. T. Angew. Chem., Int. Ed. 2012, 51, 2400.

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3. Yadav, V.; Zhang, H.; Pavlick, R.; Sen, A. Triggered “On/Off” Micropumps and

Colloidal Photodiode. J. Am. Chem. Soc. 2012, 134, 15688-15691.

4. Reinmuller, A.; Oguz, E. C.; Messina, R.; Lowen, H.; Schope, H. J.; Palberg, T. Colloidal

crystallization in the quasi-two-dimensional induced by electrolyte gradients. J. Chem.

Phys. 2012, 136, 164505-10.

5. Smith, E. J.; Xi, W.; Makarov, D.; Monch, I.; Harazim, S.; Quinones, V. A. B.; Schmidt,

C. K.; Mei, Y.; Sanchez, S.; Schmidt, O. G. Lab Chip 2012, 12, 1917.

6. Solovev, A. A.; Sanchez, S.; Mei, Y.; Schmidt, O. G. Phys. Chem. Chem. Phys. 2011, 13,

10131.

7. Jun, I. K.; Hess, H. Adv. Mater. 2010, 22, 4823.

8. Ibele, M. E.; Wang, Y.; Kline, T. R.; Mallouk, T. E.; Sen, A. J. Am. Chem. Soc. 2007,

129, 7762.

9. Kline, T. R.; Paxton, W. F.; Wang, Y.; Velegol, D.; Mallouk, T. E.; Sen, A. J. Am. Chem.

Soc. 2005, 127, 17150.

10. Golestanian, R.; Liverpool, T. B.; Ajdari, A. Designing phoretic micro- and nano-

swimmers. New J. Phys. 2007, 9.

11. Anderson, J. L. Transport Mechanisms of Biological Colloidsa. Ann. N.Y. Acad. Sci.

1986, 469, 166-177.

12. Sengupta, S.; Spiering, M. M.; Dey, K. K.; Duan, W.; Patra, D.; Butler, P. J.; Astumian,

R. D.; Benkovic, S. J.; Sen, A. DNA Polymerase as a Molecular Motor and Pump. ACS

Nano 2014, 8, 2410-2418.

13. Sengupta, S.; Patra, D.; Rivera, I. O.; Agrawal, A.; Dey, K. K.; Shklyaev, S.; Mallouk, T.

E.; Sen, A. Self-powered enzyme micropumps. Nat. Chem. 2014, 6, 415-422.

14. Kline, T. R.; Sen, A. Reversible Pattern Formation through Photolysis. Langmuir 2006,

22, 7124-7127.

15. Anderson, J. L. Colloid Transport by Interfacial Forces. Annu. Rev. Fluid. Mech. 1989,

21, 61-99.

16. Ibele, M.; Mallouk, T. E.; Sen, A. Schooling Behavior of Light-Powered Autonomous

Micromotors in Water. Angew. Chem. Int. Ed. 2009, 48, 3308-3312.

17. Duan, W.; Liu, R.; Sen, A. Transition between Collective Behaviors of Micromotors in

Response to Different Stimuli. J. Am. Chem. Soc. 2013, 135, 1280-1283.

18. McDermott, J. J.; Kar, A.; Daher, M.; Klara, S.; Wang, G.; Sen, A.; Velegol, D. Self-

Generated Diffusioosmotic Flows from Calcium Carbonate Micropumps. Langmuir

2012, 28, 15491-15497.

19. Kagan, D.; Balasubramanian, S.; Wang, J. Chemically Triggered Swarming of Gold

Microparticles. Angew. Chem. Int. Ed. 2011, 50, 503-506.

20. Duan, W.; Pavlick, R.; Sen, A. Biology of nanobots. In Engineering of Chemical

Complexity, Mikhailov, A.; Ertl, G., Eds. World Scientific Publishing Company:

Singapore, 2013; Vol. 6, pp 125-144.

21. Höll, W.; Sontheimer, H. Ion exchange kinetics of the protonation of weak acid ion

exchange resins. Chem. Eng. Sci. 1977, 32, 755-762.

22. Franks, G. V. Zeta Potentials and Yield Stresses of Silica Suspensions in Concentrated

Monovalent Electrolytes: Isoelectric Point Shift and Additional Attraction. J. Colloid

Interface Sci. 2002, 249, 44-51.

23. Scales, P. J.; Grieser, F.; Healy, T. W.; White, L. R.; Chan, D. Y. C. Electrokinetics of

the silica-solution interface: a flat plate streaming potential study. Langmuir 1992, 8,

965-974.

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24. Lagzi, I.; Soh, S.; Wesson, P. J.; Browne, K. P.; Grzybowski, B. A. Maze Solving by

Chemotactic Droplets. J. Am. Chem. Soc. 2010, 132, 1198-1199.

25. Zhang, H.; Duan, W.; Lu, M.; Zhao, X.; Shklyaev, S.; Liu, L.; Huang, T. J.; Sen, A. Self-

Powered Glucose-Responsive Micropumps. ACS Nano 2014, 8, 8537-8542.

26. Zhang, H.; Yeung, K.; Robbins, J. S.; Pavlick, R. A.; Wu, M.; Liu, R.; Sen, A.; Phillips,

S. T. Self-Powered Microscale Pumps Based on Analyte-Initiated Depolymerization

Reactions. Angew. Chem. Int. Ed. 2012, 51, 2400-2404.

VITA

Wentao Duan

Education

Ph.D. in Chemistry Pennsylvania State University, University Park, PA

Advisor: Dr. Ayusman Sen May, 2015 (GPA 3.96/4.0)

B.S. in Chemistry Peking University, Beijing, China

Advisor: Dr. Chunhua Yan Aug, 2009 (GPA 3.51/4.0)

Research Interest

Design of self-powered synthetic micromachines

Investigation on collective behaviors of micromotors

Statistical analysis on motion of micromotors

Numerical simulation on fluid dynamics of the micromachine systems with COMSOL

Multiphysics

Agent-oriented modelling on micromotor systems with Netlogo and Python

Selected Publications (Google Scholar Profile)

Duan, W.; Wang, W.; Das, S.; Yadav, V.; Sen, A., Synthetic Nano and Micromachines for

Analytical Chemistry, submitted.

Duan, W.; Liu, R.; Sen, A., Transition between Collective Behaviors of Micromotors in

Response to Different Stimuli. J. Am. Chem. Soc. 2013, 135 (4), 1280.

Duan, W.; Ibele, M.; Liu, R.; Sen, A., Motion analysis of light-powered autonomous silver

chloride nanomotors. Eur. Phys. J. E 2012, 35 (8), 77.

Duan, W.; Pavlick, R.A.; Sen, A. Biology of Nanobots, Engineering of Chemical

Complexity ,Chapter 6, pg 125

Zhang, H.; Duan, W.; Lu, M. ;Zhao, X.; Shklyaev, S.; Liu, L.; Dewey, D.; Huang, T.; Sen, A.,

Self-powered glucose responsive drug delivery micropump based on boronate chemistry, ACS

Nano 2014, 8, 8537

Wang, W.; Duan, W.; Sen, A.; Mallouk, T. E., Catalytically powered dynamic assembly of

rod-shaped nanomotors and passive tracer particles. Proc. Natl. Acad. Sci. U.S.A. 2013, 110

(44), 17744.

Zhang, H.; Duan, W.; Liu, L.; Sen, A., Depolymerization-Powered Autonomous Motors Using

Biocompatible Fuel. J. Am. Chem. Soc. 2013, 135 (42), 15734.

Sengupata, S.; Spiering, M. M.; Dey, K. K.; Duan,W.; Patra, D.; Butler, P. J.; Astumian R. D.;

Benkovic, S. J.; Sen, A., DNA polymerase as a molecular motor and pump, ACS Nano, 2014,

8, 2410.