Investigation of Amorphous Solid Dispersions of Poorly Water-soluble Drugs in Poly(2-Hydroxyethyl Methacrylate) Hydrogels for Enhanced Solubility and Controlled Release

by

Dajun Sun

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Pharmaceutical Sciences University of Toronto

© Copyright by Dajun Sun (2014)

ii

Amorphous Solid Dispersions of Poorly Water-soluble Drugs in Poly(2-Hydroxyethyl Methacrylate) Hydrogels for Enhanced Solubility and

Controlled Release

Dajun Sun

Doctor of Philosophy

Pharmaceutical Sciences

University of Toronto

2014

Abstract

The purpose of this study was to investigate the potential of applying amorphous solid dispersions

(ASD) in crosslinked PHEMA hydrogels to enhance the dissolution behavior of poorly water-

soluble drugs. The first part of the study identifies physicochemical properties affecting the solid

state and physical stability of ASD of the model drug indomethacin (IND) in PHEMA hydrogels.

The results of the second part show that ASD based on water-insoluble crosslinked PHEMA can

maintain a high level of supersaturation over a prolonged duration via a diffusion-controlled

feedback mechanism, thus avoiding the initial surge of supersaturation followed by a sharp decline

in drug concentration, which is typically encountered with ASD based on water-soluble polymers

(e.g., PVP, HPMCAS) under nonsink dissolution conditions. A subsequent study examines the

effect of supersaturation generation rate on the resulting kinetic solubility profiles of amorphous

pharmaceuticals and delineates the interplay between dissolution and precipitation processes from

iii

a mechanistic viewpoint. In the absence of any dissolved polymer to inhibit drug precipitation

from the supersaturated state, both our experimental and predicted results confirm that the faster

rise of the kinetic solubility profile of an amorphous drug will inevitably lead to an earlier but

higher maximum kinetic solubility and a sharper decline in the de-supersaturation phase, and vice

versa. The relationship between the achievable maximum supersaturation and the rate of

supersaturation generation in the observed kinetic solubility profiles has been described for the

first time by our comprehensive mechanistic model taking into account the role of supersaturation

in both the nucleation and crystallization processes as well as the associated competitive particle

growth and ripening effects. Finally, this theoretical framework was further employed to semi-

quantitatively predict the evolution of supersaturation of amorphous pharmaceuticals generated

from nonlinear dissolution profiles. The effects of initial degree of supersaturation, dissolution of

amorphous drug and that from the IND-PHEMA ASD under nonsink dissolution conditions were

subsequently examined in detail. The comparison of dissolution behaviors between amorphous

IND and IND-PHEMA ASD demonstrates the advantage of the diffusion-controlled feedback

mechanism that makes crosslinked PHEMA a unique and desirable carrier for amorphous drug

delivery systems.

iv

Acknowledgements

For those who studied in the disciplines of science and engineering, the term “problem set” should

sound familiar. The journey of my Ph.D. study feels like a very long problem set in which an

answer to a question indefinitely leads to and expands to more, larger and harder questions. This

daunting task would not have been achievable without a great amount of guidance, support and

assistance from many wonderful individuals. First and foremost, I would like to express my

greatest gratitude to my Ph.D. supervisor Professor Ping Lee for his endless advice, support and

supervision throughout my research project. His scientific insights and comprehensive expertise

in pharmaceutical science has not only provided immense leadership to this project but also shaped

me as an independent researcher. I have learnt many great personal characteristics from him,

especially diligence and professionalism. I will always remain thankful to his generous education.

Also, I am greatly thankful to my advisory committee members, Professors Edgar Acosta,

Christine Allen and Shirley Wu, for providing me with valuable guidance and direction to my

research as well as precious career advice. My thanks to Professor Carolyn Cummins for

completing my experience as a graduate student by giving me a teaching opportunity. I am grateful

to Dr. Rob Ju from Abbvie for a delightful experience of academia-industry collaboration. Special

thanks are due to the helpful staff and students in the Department of Geology, the Department of

Chemistry, University Health Network pre-formulation lab and Professor Allen’s lab for kindly

assisting me to use their laboratory equipment.

This research work was supported by research funding from Abbvie and Natural Sciences and

Engineering Research Council of Canada (NSERC), and I was also supported by a University of

Toronto Fellowship Award.

v

I would like to thank the past and present colleagues in the PIL research group, Dr. Beibei Qu, Dr.

Hui Zhao, Dr. Yan Li, Dr. Hongliang Jiang, Dr. Yanhong Luo, Sammi Liu, Arthur Li, Giovanna

Medeiros and many others, for their continuous assistance and advice. Working together with them

is always a nice and memorable experience. Lastly, I would like to thanks my family and friends,

especially my parents, my brother Peter and Che-chien Wang for their unreserved faith in me. I

could not have reached my goals without their unconditional love and support.

vi

Publications

- Dajun D. Sun and Ping I. Lee “Crosslinked hydrogel – a promising class of insoluble solid

molecular dispersion carriers for enhancing the delivery of poorly soluble drugs” Acta

Pharmaceutica Sinica B, Volume 4, Issue 1, pp 26-36 (2014). [Invited Review and Cover Story]

- Dajun D. Sun and Ping Lee, “Evolution of supersaturation of amorphous pharmaceuticals: the

effect of rate of supersaturation generation” Molecular Pharmaceutics, Volume 10, Issue 11, pp.

4330-4346 (2013).

- Dajun D. Sun, Tzu-chi Rob Ju, Ping I. Lee, “Enhanced kinetic solubility profiles of indomethacin

amorphous solid dispersions in poly(2-hydroxyethyl methacrylate) hydrogels” European Journal

of Pharmaceutics and Biopharmaceutics, Volume 81, Issue 1, pp. 149-158 (2012).

vii

Table of Contents

Abstract ii

Acknowledgments iv

Publications vi

Table of contents vii

List of tables xii

List of figures xiv

List of appendices xxi

List of symbols xxiii

List of abbreviations xxv

Chapter 1: Introduction

1.1 Solubility enhancement of poorly water-soluble drugs for oral drug delivery 1

1.2 Pharmaceutical significance of amorphous solid dispersions in polymeric carriers 3

1.2.1 Water-soluble carriers 7

1.2.2 Water-insoluble carriers 14

1.3 Crosslinked PHEMA hydrogels for amorphous solid dispersions carriers 16

1.4 Crystallization of amorphous pharmaceuticals in the solid state 19

1.4.1 Solubility advantage of amorphous solids 19

1.4.2 Classical nucleation theory (solid state) 21

1.4.3 Crystal growth (solid state) 23

1.4.4 Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory 24

1.5 Crystallization of supersaturated drug solutions 25

1.5.1 Classical nucleation theory (solution state) 25

1.5.2 Crystal growth (solution state) 26

viii

1.6 Overview of the Ph.D. research 27

1.6.1 Hypothesis 27

1.6.2 Research objectives 27

Chapter 2: Indomethacin amorphous solid dispersions in PHEMA

2.1 Introduction 29

2.2 Materials and methods 31

2.2.1 Materials 31

2.2.2 Synthesis of PHEMA hydrogel beads 31

2.2.3 Preparation of amorphous solid dispersion systems 34

2.2.4 Scanning electron microscopy (SEM) 36

2.2.5 X-ray diffraction (XRD) 36

2.2.6 Differential scanning calorimetry (DSC) 37

2.2.7 Fourier-transformed infrared (FTIR) spectroscopy 37

2.2.8 Solubility parameter estimation 37

2.3 Results and discussion 40

2.3.1 PHEMA hydrogel beads synthesis 40

2.3.2 Physical properties of ASD IND in PHEMA, PVP and HPMCAS 44

2.3.3 IND-polymer interactions 55

2.3.4 Solubility parameters 57

2.4 Conclusion 59

Chapter 3: Physical stability of amorphous indomethacin in PHEMA

3.1 Introduction 60

3.2 Materials and methods 62

3.2.1 Materials 62

3.2.2 Preparation of amorphous solid dispersion systems 63

3.2.3 Stability study 63

3.2.4 Preparation of physical mixtures of amorphous, crystalline - and -indomethacin

in polymeric carriers 63

3.2.5 Raman spectroscopy 64

3.2.6 Multivariate data analysis 65

ix

3.2.7 Isothermal crystallization kinetics 65

3.2.8 Water sorption isotherm 66

3.3 Results and discussion 66

3.3.1 Storage stability study 66

3.3.2 Quantification of ternary mixtures of different solid-state forms of indomethacin in

polymeric carriers 68

3.3.3 Crystallization kinetics of amorphous indomethacin in polymeric carriers 74

3.3.4 Estimation of drug solubility in polymers 78

3.3.5 Intermolecular forces between amorphous indomethacin and polymers 80

3.3.6 Analysis of isothermal water vapor absorption 82

3.4 Conclusion 86

Chapter 4: Enhanced kinetic solubility profiles of amorphous indomethacin in PHEMA

4.1 Introduction 87

4.2 Materials and methods 88

4.2.1 Materials 88

4.2.2 Dissolution testing of amorphous solid dispersion systems under nonsink

dissolution conditions 88

4.3 Results and discussion 90

4.3.1 Comparing solubility advantages of amorphous IND in PHEMA with that in water-

soluble polymers 90

4.3.2 Diffusion-controlled release of amorphous IND from PHEMA hydrogels 96

4.4 Conclusion 101

Chapter 5: Effect of rate of supersaturation generation on the kinetic solubility profiles

5.1 Introduction 103

5.2 Theory 106

5.3 Materials and methods 111

5.3.1 Materials 111

5.3.2 Measurement of kinetic solubility profiles 111

5.3.3 X-ray diffraction (XRD) 113

5.3.4 Differential scanning calorimetry (DSC) 114

x

5.3.5 Scanning electron microscopy (SEM) 114

5.3.6 Particle size distribution 114

5.3.7 Simulation of modeling equations 115

5.4 Results and discussion 115

5.4.1 Effect of rate of supersaturation generation on the kinetic solubility profiles 115

5.4.2 Amorphous solid dispersions in polymeric carriers 127

5.4.3 Kinetic solubility advantage of amorphous solids 129

5.4.4 Crystallization kinetics and particle size distribution 132

5.4.5 Evolution of concentration-time profiles due to dissolution and recrystallization

processes 140

5.5 Conclusion 142

Chapter 6: Semi-quantitative prediction of the kinetic solubility profiles of amorphous

indomethacin

6.1 Introduction 144

6.2 Theory 146

6.2.1 Effect of linear rate of supersaturation generation 146

6.2.2 Effect of initial degree of supersaturation 146

6.2.3 Effect of first-order supersaturation generation 147

6.2.4 Supersaturation generation with diffusion-controlled feedback mechanism –

Dissolution of amorphous solid dispersions from PHEMA hydrogel beads 148

6.3 Materials and methods 152

6.3.1 Materials 152

6.3.2 Preparation of amorphous indomethacin 152

6.3.3 Dissolution testing of amorphous IND and ASD IND-PHEMA under nonsink

dissolution conditions 152

6.3.4 Dissolution testing of solid-state amorphous IND under sink dissolution

conditions 153

6.4 Results and discussion 154

6.4.1 Effect of initial degree of supersaturation 154

6.4.2 Dissolution of amorphous IND from the solid state 158

6.4.3 Dissolution of amorphous IND from PHEMA hydrogels 163

xi

6.5 Conclusion 170

Chapter 7: Summary and future research directions

7.1 Summary 172

7.2 Future research directions 175

Appendices 177

References 202

xii

List of Tables

Chapter 1

Table 1.1: Selected studies of water-soluble carriers for amorphous drugs... 11

Table 1.2: Selected examples of insoluble carriers for amorphous drugs …. 13

Chapter 2

Table 2.1: Chemical structures of IND, PVP and HPMCAS and their

potential hydrogen bonding sites ………………………………. 36

Table 2.2: Solubility parameters of component group contribution from

van Krevenlen/Hoftyzer and Hoy’s methods ………………….. 40

Table 2.3: Measured and calculated solubility parameters of IND, PVP,

HPMCAS, PHEMA and PHEMA copolymers ………………… 58

Chapter 3

Table 3.1: Comparison of existing technology of quantification of drug

crystallinity in ASD ……………………………………………. 62

Table 3.2 Physical mixtures of crystalline -, - and amorphous IND …… 64

Table 3.3 Stability study of IND solid dispersions in PHEMA beads …..... 67

xiii

Table 3.4 Raman molecular assignment for the C=O stretching group …... 70

Table 3.5 KJMA isothermal crystallization parameters for amorphous

IND ……………………………………………………………... 77

Table 3.6 IND solubility in PHEMA, PVP and HPMCAS ……………….. 80

Table 3.7 Characteristics of the model drug and polymers relevant for

hydrogen bonding ……………………………………………… 81

Chapter 5

Table 5.1: Physicochemical properties of model poorly water-soluble IND,

NAP and PIR …………………………………………………… 112

Table 5.2 Summary of relevant physical constants for the numerical

simulation of IND crystallization kinetics …………………… 120

Chapter 6

Table 6.1: Dissolution rate constants of amorphous IND of various particle

size ranges ……………………………………………………… 161

xiv

List of Figures

Chapter 1

Figure 1.1: Biopharmaceutics Classification System (BCS) of drugs ………………. 2

Figure 1.2: Thermodynamic description of different solid states …………………… 4

Figure 1.3: Gibb’s free energy levels of the amorphous state (metastable), crystalline

(stable) and unstable state …..………………..………………………….. 5

Figure 1.4: Schematics of substitutional, interstitial and polymeric solid solution ….. 6

Figure 1.5: Classification of solid dispersion/solution of drug molecules in

polymeric carrier matrix …………………………………………………. 7

Figure 1.6: Dissolution performance of ASD containing a model poorly water-

soluble compound ………………………………………………………. 9

Figure 1.7 “Spring” and “parachute” dissolution behaviors ………………………… 10

Figure 1.8: Free energy diagram for nucleation process ……………………………. 22

Chapter 2

Figure 2.1: Experimental apparatus for PHEMA hydrogel beads synthesis ……….... 33

Figure 2.2: Microscopic images of PHEMA hydrogel beads ……………………….. 34

xv

Figure 2.3: Quantification of IND by UV-spectrometer …………………………….. 35

Figure 2.4: Particle size distributions of PHEMA hydrogel beads .………………….. 42

Figure 2.5: Images of failed batches of crosslinked PHEMA hydrogels…………….. 43

Figure 2.6: Equilibrium solvent content of PHEMA and IND solubility in

DMSO/ethanol mixtures for IND loading process ……………………… 45

Figure 2.7: IND loading levels in PHEMA hydrogel beads as a function of loading

solution concentration ………………………….. ……………………… 46

Figure 2.8: Residual solvent content in crosslinked PHMEA hydrogel after

equilibrium sorption …………………………………………………….. 47

Figure 2.9: Microscopic images of IND-loaded PHEMA hydrogel beads ………….. 48

Figure 2.10: Microscopic images of IND-loaded PHEMA-co-MMA, -co-EMA and -

co-BMA hydrogel beads ………………………………………………… 49

Figure 2.11: Microscopic images of IND-loaded PVP and HPMCAS cast films ……. 50

Figure 2.12: SEM images of surface morphology of IND-loaded PHEMA hydrogel

beads …………………............................................................................... 51

Figure 2.13: SEM images of cross-section of IND-loaded PHEMA hydrogel beads … 51

Figure 2.14: XRD spectra of IND-loaded PHEMA, PVP and HPMCAS …………….. 52

Figure 2.15: DSC thermograms of IND-loaded PHEMA, PVP and HPMCAS ………. 54

Figure 2.16: Carbonyl stretch region of FTIR spectra of ASD and physical mixture

IND-loaded PHEMA, PVP and HPMCAS ……………………………… 56

Figure 2.17: Determination of solubility parameters of PHEMA hydrogels by Gee’s

method of equilibrium swelling …………………………………………. 58

xvi

Chapter 3

Figure 3.1: Evolution of physical appearance of IND-PHEMA discs ………………. 67

Figure 3.2: XRD spectra of IND-PHEMA ASD after 8-month stability study ……… 68

Figure 3.3: XRD spectra of IND of different solid state forms and polymer carriers .. 69

Figure 3.4: Raman spectra of IND of different solid state forms and polymer carriers 70

Figure 3.5: Raman spectra and their statistical peak fittings of physical mixtures of

crystalline -. - and amorphous IND in PHEMA, PVP and HPMCAS in

the carbonyl stretching region ………………………………………….. 71

Figure 3.6: Raman spectra and their statistical peak fittings of physical mixtures of

different amount of -IND and amorphous IND in PHEMA …………… 72

Figure 3.7: Calibration standard curves of intensity ratio between IND polymorphs

and polymers …………………………………………………………….. 73

Figure 3.8: Effect of relative humidity on crystallization kinetics of IND in PHEMA

hydrogel (0-54% RH) ……………………………………………………. 75

Figure 3.9: Effect of relative humidity on crystallization kinetics of IND in PHEMA

hydrogel discs (76 and 95% RH) ……………………………………….. 75

Figure 3.10: Effect of temperature on crystallization kinetics of IND in PHEMA …… 76

Figure 3.11: Effect of the polymer type on crystallization kinetics of IND ………….. 78

Figure 3.12: Water sorption isotherms of -form crystalline and amorphous IND,

PHEMA, PVP and HPMCAS …………………………………………… 83

Figure 3.13: Water sorption isotherm of ASD of IND (25% drug loading) in polymers 84

Figure 3.14: DSC endotherms of polymers in various RH storage conditions ……….. 85

xvii

Chapter 4

Figure 4.1: Effect of drug loading on kinetic solubility profiles of ASD IND in

PHEMA, PVP and HPMCAS …………………………………………… 91

Figure 4.2: Effect of polymer type on kinetic solubility profiles of ASD IND in

PHEMA, PVP and HPMCAS …………………………………………… 94

Figure 4.3: Effect of particle size on kinetic solubility profiles of ASD IND-

PHEMA …………………………………………………………………. 95

Figure 4.4: Distribution of IND in the hydrogel and dissolution medium after 24 h of

dissolution from IND-PHEMA ASD …………………………………… 97

Figure 4.5: Effect of crosslinked PHEMA hydrogels in the dissolution medium on

the equilibrium solubility of crystalline IND.…………………………… 98

Figure 4.6: Amorphous drug release mechanism: crosslinked hydrogels vs. water-

soluble polymers ………………………………………………………… 100

Chapter 5

Figure 5.1: Schematic depiction of the nucleation and crystallization events due to

supersaturation generation by the infusion experiment …………………. 106

Figure 5.2: Representative UV absorbance spectra and second derivative spectra for

IND, NAP and PIR ………………………………………………………. 116

Figure 5.3 Calibration curve of drug concentration and the second-derivative UV

spectra for model drugs ………………………………………………….. 117

Figure 5.4: Elimination of spectral interference by second-derivate UV technique ….. 118

Figure 5.5: Experimental kinetic solubility profiles of IND, NAP and PIR as a

function of supersaturation rate generated with infusion rates ………….. 119

xviii

Figure 5.6: Comparison of experimental data and simulation results of kinetic

solubility profiles of IND as a function of supersaturation rate …………. 123

Figure 5.7: Predicted kinetic solubility profiles of IND as a function of

supersaturation rate ……………………………………………………… 124

Figure 5.8: Effect of rate of supersaturation generation on Cmax and AUC of kinetic

solubility profiles …………………………….………………………….. 125

Figure 5.9: Effect of rate schedule of supersaturation on kinetic solubility profiles.... 127

Figure 5.10: Effect of rate schedule of solid addition on kinetic solubility profiles of

IND-PVP ASD …………………………………………………………... 129

Figure 5.11: Cmax measured during the infusion experiment as a function of the

inverse of infusion rate raised to an exponent α …………………………. 130

Figure 5.12: Crystallization kinetics of IND, NAP and PIR as a function of

supersaturation rate generated with various drug solution infusion rates .. 133

Figure 5.13: XRD spectra of precipitated IND from the infusion experiment ..………. 135

Figure 5.14: DSC thermograms of precipitated IND from the infusion experiment ..… 136

Figure 5.15: SEM images of precipitated IND from the infusion experiment ..………. 137

Figure 5.16: Particle size distributions of precipitated IND from the infusion

experiment ……………………………………………………………….. 139

Figure 5.17: Simulated time-dependent growth of IND particle size under various

rates of supersaturation generation ………………………………………. 139

Figure 5.18: Conceptual concentration-time profile during dissolution and

precipitation of amorphous sparingly soluble drugs …………………….. 141

xix

Chapter 6

Figure 6.1: Schematics of diffusion-controlled release of amorphous drug from a

PHEMA hydrogel bead into a finite volume of dissolution medium ……. 149

Figure 6.2: Kinetic solubility profiles of IND at various initial degrees of

concentration …………………………………………………………….. 154

Figure 6.3: COMSOL simulation of kinetic solubility profiles of various initial

degrees of supersaturation ……………………………………………….. 156

Figure 6.4: Cmax and AUC of in vitro dissolution data and simulation results of the

kinetic solubility profiles of various initial degrees of supersaturation ….. 158

Figure 6.5: Kinetic solubility profiles of amorphous IND of different particle size

ranges under nonsink dissolution conditions…………………………….. 159

Figure 6.6: Dissolution of amorphous IND with various particle size ranges under a

sink dissolution condition ……………………………………………….. 160

Figure 6.7: COMSOL simulation of kinetic solubility profiles of amorphous IND

with various particle size ranges under nonsink dissolution conditions ... 162

Figure 6.8: Comparison of IND dissolution profiles from purely amorphous IND

versus that of IND-PHEMA ASD (10 wt % IND loading) ……………… 164

Figure 6.9: Dissolution profiles over an extended time period from IND-PHEMA

ASD (10 wt% drug loading) and crystalline IND ………..……………… 165

Figure 6.10: Determination of the partition coefficient p between PHEMA hydrogel

and external dissolution medium ………………………………………... 166

Figure 6.11: Illustration of one-dimensional lengths for one hydrogel bead and the

external dissolution medium in COMSOL simulation …………….….. 166

Figure 6.12: Diffusion coefficient of IND in PHEMA hydrogels …….………………. 168

xx

Figure 6.13: Comparison of COMSOL simulation results of kinetic solubility profiles

between amorphous IND solids and IND-PHEMA ASD system ……….. 170

xxi

List of Appendices

Chapter 2

Figure A2.1 XRD spectra of physical mixtures of IND and PHEMA with

various IND weight percentage ………………………………. 177

Figure A2.2 DSC thermograms of physical mixtures of IND and PHEMA

with various IND weight percentage …………………………. 178

Chapter 5

Table A5.1 Parameter input in COMSOL 3.5a (Figures 5.6 and 5.7) ….…. 180

Chapter 6

Table A6.1 Parameter input in COMSOL 3.5a (Figure 6.3) ……………… 184

Table A6.2 Parameter input in COMSOL 3.5a (Figure 6.7) ……………… 188

Table A6.3 Parameter input in COMSOL 3.5a (Figure 6.13) …………….. 192

Figure A6.1 COMSOL simulation results of time-dependent concentration

profiles of IND inside PHEMA hydrogel beads under various

sink conditions ……………………………………………….. 196

xxii

Figure A6.2 IND release profiles in the external dissolution medium from

Figure A6.2 …………………………………………………… 199

xxiii

List of Symbols

C concentration

Cb bulk concentration

Ceq concentration in equilibrium with a precipitate particle of radius r

Cmax maximum concentration

CS equilibrium solubility

Ct concentration assuming all drugs have dissolved

D diffusion coefficient

d molecular size (twice the molecular diameter)

Dose dose required

f molar concentration of precipitate

Fi molar attraction constant

G crystallization kinetics coefficient

J nucleation rate

Jc nucleation rate constant

k rate constant

kB Boltzmann’s constant

mo repeating monomer’s MW

MW molecular weight

N average particle number density

No Avogadro’s number

p partition coefficient

Q equilibrium swelling ratio

r particle size

xxiv

R rate of drug input

rn critical particle size

s supersaturation

s’ measured supersaturation at time t”

T temperature

t time

t’ time in which addition of dissolved drugs in solvent stops

t” time in which dissolution stops

u precipitation rate

V (molar) volume

wd dry weight of hydrogels

ws swollen weight of hydrogels

δ solubility parameter

ε thickness of Gibbs surface

ρ density

σ interfacial tension

Σ average surface of the precipitate particles per unit volume

υ molar volume of precipitate

Φ average radius of the particles per unit volume

ϕ volumetric fraction

Ψ radius dependence of the surface tension

ω capillary length

xxv

List of Abbreviations

AIBN Azobisisobutyronitrile [2,2′-Azobis(2-methylpropionitrile), 2-(azo(1-cyano-1-

methylethyl))-2-methylpropane nitrile]

API Active pharmaceutical ingredient

ASD Amorphous solid dispersion

AUC Area under the curve

BCS Biopharmaceutics classification system

BMA Butyl methacrylate

CAP Cellulose acetate phthalate

CNT Classical nucleation theory

DSC Differential scanning calorimetry

DMSO Dimethyl sulfoxide

ESC Equilibrium solvent content

EMA Ethyl methacrylate

EDGMA Ethylene glycol dimethylacrylate [2-(2-Methyl-acryloyloxy)ethyl 2-methyl-

acrylate]

FDA Food and Drug Administration

FTIR Fourier-transform infrared

GFA Glass forming ability

GI Gastrointestinal

GS Glass stability

ICH International conference on harmonization

Tg Glass transition temperature

HEMA Hydroxyethyl methacrylate [2-Hydroxyethyl 2-methylprop-2-enoate]

xxvi

HPMC Hydroxypropyl methylcellulose

HPMCAS Hydroxypropyl methylcellulose acetate succinate

HPMCP Hydroxypropylmethyl cellulose phthalate

IND Indomethacin [2-{1-[(4-chlorophenyl)carbonyl]-5-methoxy-2-methyl-1H-indol-3-

yl}acetic acid]

IR Infrared

MMA Methyl methacrylate

MW Molecular weight

NAP Naproxen [(+)-(S)-2-(6-methoxynaphthalen-2-yl) propanoic acid]

NMR Nuclear magnetic resonance

ODE Ordinary differential equation

PDE Partial differential equation

PHEMA Poly(2-hydroxyethyl methacrylate)

PIR Piroxicam [(8E)-8-[hydroxy-(pyridin-2-ylamino)methylidene]-9-methyl-10,10-

dioxo-10λ6-thia-9-azabicyclo[4.4.0]deca-1,3,5-trien-7-one]

PLS Partial least square

PVP Polyvinylpyrrolidone

RH Relative humidity

SEM Scanning electron microscopy

SI Sink index

SNV Standard normal variate

ss Solid state

UV Ultraviolet

XRD X-ray diffraction

1

Chapter 1

Introduction

1.1 Solubility enhancement of poorly water-soluble drugs for oral drug

delivery

Recent advances in combinatorial chemistry, automated synthesis and high-throughput screening

have significantly improved effectiveness of the drug discovery process (White, 2000). Although

many of these new chemical entities exhibit promising therapeutic potential, one major dilemma

in developing these candidate compounds into oral dosage forms, the most popular route of

administration, is their poor aqueous solubility and/or permeability across the intestinal villi in the

gastrointestinal (GI) tract. According to the Biopharmaceutics Classification System (BCS), drug

substances are classified into four categories according to their solubility and permeability

properties, as shown in Figure 1.1. Absorption of orally administered medications involves

solubilization of drug molecules in the GI fluid and transport across membranes of the epithelial

cells in the GI tract. Therefore, poorly water-soluble and/or poorly permeable drugs with

suboptimal bioavailability require enabling formulation approaches to develop oral dosage forms

with an enhanced solubility and/or permeability to reach systemic circulation. Improving drug

permeability often requires chemical modifications of the drug, which may fundamentally alter its

toxicity profile and therapeutic potential. On the other hand, various techniques are available for

the enhancement of the aqueous solubility of poorly water-soluble drugs without chemically

altering the molecular structure of the drug. It is estimated that approximately 60-70% of newly

discovered therapeutic compounds are classified in BCS II (high permeability, low solubility)

during the drug discovery process (Douroumis and Fahr, 2012; Lipinski et al., 1997). Hence, a

2

significant amount of current research focuses on enhancing the aqueous solubility of these BCS

II, small molecular weight (MW less than 1000 Da) active pharmaceutical ingredients (API).

Figure 1.1: The Biopharmaceutics Classification System (BCS) of drugs is based on the solubility

threshold above which the highest required dose is soluble in less than 250-mL aqueous media

over the pH 1.0 to 7.5 and the permeability threshold above which the extent of absorption in

humans is determined to be more than 90% of the dose administered by i.v.

(http://www.fda.gov/AboutFDA/CentersOffices/OfficeofMedicalProductsandTobacco/CDER/uc

m128219.htm).

In previous attempts to address this issue, methods commonly used to increase drug solubility have

practical limitations and may not always accomplish the desired enhancement in drug solubility

and bioavailability (Fahr and Liu, 2007; Pouton, 2006). For example, particle size reduction (or

increase in surface area) often has a threshold of achievable size reduction; creating stable salt

forms or pro-drug of therapeutic agents is not always feasible; introducing surfactants or co-

solvents may lead to liquid formulations that are usually poor in patient acceptability and

undesirable for commercialization (Serajuddin, 1999). Among various known approaches,

incorporating a poorly water-soluble compound in a suitable polymeric carrier to form an

amorphous solid dispersion (ASD) has become an increasingly important strategy in the solubility

and bioavailability enhancement for oral delivery of poorly water-soluble compounds. Various

approaches for the preparation, characterization and stabilization of ASDs for oral drug delivery

http://www.fda.gov/AboutFDA/CentersOffices/OfficeofMedicalProductsandTobacco/CDER/ucm128219.htmhttp://www.fda.gov/AboutFDA/CentersOffices/OfficeofMedicalProductsandTobacco/CDER/ucm128219.htm

3

have been reviewed comprehensively (Chiou and Riegelman, 1971; Craig, 2002; Kawakami, 2009;

Leuner and Dressman, 2000; Serajuddin, 1999; Yu, 2000). Poorly water-soluble drugs in their

stabilized amorphous form can generate a transient but highly supersaturated solution

concentration (i.e., kinetic solubility) significantly greater than the equilibrium saturation

concentration of their crystalline counterparts. Since drug supersaturation increases the driving

force for oral absorption, maintaining an elevated and sustained level of drug supersaturation is

critical to improving the bioavailability of poorly water-soluble drugs. The causality between

increased kinetic solubility from ASDs and improved oral bioavailability has been demonstrated

in many in vivo studies (Kohri et al., 1999; Law et al., 2004; Newa et al., 2007; Six et al., 2005;

Verreck et al., 2004; Yüksel et al., 2003).

1.2 Pharmaceutical significance of amorphous solid dispersions in polymeric

carriers

Solids in the amorphous state (also referred to as “unstable form”, “high-energy state”) are

structurally defined as the lack of a long-range order of molecular packing or the lack of a

crystalline state. The amorphous state has a higher internal energy and specific volume compared

to the crystalline state (Figure 1.2). Due to “loose” molecular packing, the amorphous state has a

high level of free energy, which leads to various physicochemical characteristics such as an

elevated aqueous solubility, higher vapor pressure, greater molecular mobility and higher chemical

reactivity than their crystalline counterpart (Figure 1.3). In contrast to the equilibrium solubility,

which is an intrinsic thermodynamic property of the crystalline drug, the dissolution of amorphous

pharmaceuticals achieves a transient supersaturation (i.e., a kinetic drug solubility that is higher

than the equilibrium solubility), as a result of the lack of crystalline lattice energy of the solids.

High-energy formulations based on amorphous pharmaceuticals can therefore improve oral

bioavailability of poorly water-soluble drugs by generating supersaturated drug solutions in the GI

tract. However, the metastable amorphous structure will be eventually converted to the equilibrium

crystalline state, provided that there is a thermodynamic driving force sufficient to overcome the

Gibb’s free energy barrier. The threshold drug loading level in ASD systems in different polymeric

matrices above which an amorphous-to-crystalline transition tends to occur has typically been

identified empirically. Stressed conditions including high relative humidity, elevated temperature

and aging are known to accelerate the kinetics of transformation from metastable amorphous drugs

4

into the crystalline state (Konno and Taylor, 2008). Unfortunately, questions on their solid-state

structure, mechanisms of dissolution enhancement, and criteria of solid dispersion stability upon

storage have remained mostly unanswered (Craig, 2002). Recurrence of crystallization in many of

these systems still represents the primary factor affecting product stability. The poor predictability

of ASD stability is due to the lack of a more fundamental understanding of their physical properties

and parameters which govern the stability of amorphous structures in retarding the initiation of

nucleation and the propagation of drug crystallization. The formation of stabilized ASD in an inert

carrier has been shown to be very effective in delaying nucleation and crystallization of amorphous

drugs to achieve a reasonable shelf life of pharmaceutical products.

Figure 1.2: Thermodynamic description of different solid states (crystalline, amorphous and

supercooled liquid).

5

Figure 1.3: Gibb’s free energy levels of the amorphous state (metastable), crystalline state (stable)

and unstable state.

From a list of pharmaceutically acceptable excipients that are FDA-approved in human oral

delivery, ideal carrier matrix systems have to demonstrate the ability to maintain amorphous drug

in solid dispersions, enhancing drug dissolutions and subsequent bioavailability, and a potential of

programmable release rates through the GI tract. Earlier investigations of incorporating poorly

water-soluble drugs in solubilizing agents were mostly concerned with identifying rapidly

dissolving small MW carriers (e.g., sulfathiazole-urea (Sekiguchi and Obi, 1961)) and polymeric

carriers (e.g., sulfathiazole-polyvinylpyrrolidone PVP (Simonelli et al., 1969)) to improve the drug

dissolution rate, the degree of supersaturation and the oral bioavailability. The solute molecules

(amorphous drug) can either be substituted for solvent molecules or be fitted into the interstices

between the solvent molecules in a eutectic mixture (Figure 1.4 A&B) (Leuner and Dressman,

2000). Recent research interests have gradually been shifting to relevant physicochemical

properties of drug-carrier composites that can enhance the stabilization of metastable amorphous

drugs, particularly in the form of solid solutions in polymeric carriers because of their ability to

inhibit nucleation and crystal growth in the solid state (Figure 1.4 C) (Bhugra and Pikal, 2008;

Khougaz and Clas, 2000b; Konno and Taylor, 2007). This generally involves the preparation of

solid solutions in polymers that have a glass transition temperature (Tg) higher than room

temperature as the low molecular mobility of which contributes to a slow crystallization rate at

ambient conditions. A variety of these carrier matrices can be categorized as hydrophilic,

6

hydrophobic, enteric and an association polymer system. In some cases, a ternary (polymer A-

polymer B-drug) system might be necessary to achieve both stabilization of an amorphous solid

state and controlled release. More recently, refinement of the solid dispersion approach has been

pursued to include surfactants, plasticizer, alkalizer, copolymer and disintegratants to form the

desired carrier matrices (Broman et al, 2001; Ghebremeskel et al, 2006; Tran et al, 2009).

Figure 1.4: Schematics of (A) substitutional (B) interstitial and (C) polymeric solid solution. Figure

adapted from Leuner and Dressman (Leuner and Dressman, 2000) (reproduced with permission

from the European Journal of Pharmaceutics and Biopharmaceutics, Copyright Elsevier 2000).

Entrapped drug molecules in polymeric carrier matrices can be classified as crystalline solid

dispersion (2-phase system), amorphous solid dispersion (2-phase system) and solid solution (1-

phase system) as illustrated in Figure 1.5. Compared to the 1-phase solid solution in which drug

molecules are molecularly dispersed in the carrier, 2-phase solid dispersion systems contain a

separate phase of either crystalline (long-range molecular order) or amorphous drugs (short-range

molecular order). Pharmaceutical solid dispersion systems are rarely in a completely amorphous

state. In most cases, pharmaceutical solids are in a state between crystalline and amorphous solids

(i.e., a mixture or hybrid of both the 2-phase and 1-phase systems). The magnitude of crystallinity

can be measured by x-ray diffraction (XRD) analysis, spectroscopic analysis (e.g., IR and Raman)

and thermal analysis (e.g., differential scanning calorimetry DSC and thermally stimulated current

TSC).

(A) (B) (C)

7

Figure 1.5: Classification of solid dispersion/solution of drug molecules in polymeric carrier

matrix. Figure adapted from Sun and Lee (Sun and Lee, 2014) (reproduced with permission from

Acta Pharmaceutica Sinica B, Copyright Elsevier 2014).

1.2.1 Water-soluble carriers

It is a common practice to employ water-soluble polymers as carriers in conventional ASDs to

enhance solubility and dissolution rate. The conventional design of oral dosage forms based on

amorphous solid dispersions for poorly water-soluble drugs typically focuses on increasing the

dissolution rates, elevating the degree of supersaturation and extending its duration following the

dissolution of various ASD systems. Table 1.1 summarizes recent studies of water-soluble ASD

carriers such as hydrophilic polymers and enteric polymers utilized to convert poorly water-soluble

model drugs into amorphous formulations. In this case, hydrophilic or hydrocolloid matrices form

solid dispersion systems from which water-soluble polymers and entrapped amorphous drugs can

dissolve in an aqueous medium. Available references commonly show enhanced dissolution rates

of poorly soluble drugs from hydrophilic polymers including PVP and derivatives of cellulose

such as hydroxypropyl methyl cellulose (HPMC or hypromellose), methylcellulose (MC),

carboxymethyl cellulose sodium, and hydroxyethyl cellulose (HEC). In addition, enteric polymers

are preferentially soluble in a pH environment above pH 5.5 to pH 6 of the intestine relative to the

acidic gastric fluid. For instance, rapid disintegration of enteric polymers like hydroxypropyl

8

methylcellulose phthalate (HPMCP) and hydroxypropyl methylcellulose acetate succinate

(HPMCAS) can be achieved in an elevated pH environment. Moreover, it is worth noting that the

frequently employed solid dispersion carrier polyethylene glycol (PEG) has a low glass transition

temperature (Tg) and is therefore more “rubbery” at ambient temperature. This unfortunately does

not offer much retardation in the rates of drug diffusion and crystallization. In fact, most PEG-

based solid dispersions are truly dispersions of micro-crystalline drug particles. A typical example

of this micro-crystalline drug dispersion is a product called Gris-PEG®, a solid crystalline

dispersion of griseofulvin in PEG. Ideal candidates of polymeric carriers should prevent

amorphous pharmaceutical solids from nucleating and becoming crystalline in order to achieve the

desired stability during shelf life.

Over the past decade, numerous in vitro and in vivo studies have displayed a variety of

combinations of carrier polymers and solid dispersion systems of poorly water-soluble drugs to

demonstrate the effectiveness of amorphous pharmaceuticals in solubility and bioavailability

enhancement. Regrettably, almost none of the research results drew any proper mechanistic

conclusions. Many of the literature reports investigated methods of preparation and evaluated

concomitant pharmacokinetic improvement of the drug-polymer amorphous solid dispersions by

means of in vivo studies. Well-characterized water-insoluble drugs such as indomethacin,

nifedipine, felodipine, and itraconazole were frequently investigated for their enhanced dissolution

rates in various polymer carriers. The common methods can generally be classified as solvent-

based (e.g., dissolution in co-solvent followed by solvent evaporation, spray-drying,

electrospinning), temperature-based (e.g., hot-stage melting, hot-melt extrusion), and physically

mixing (e.g., granulation, milling) in order to achieve a homogenous binary, ternary (Janssens et

al., 2008) or multi-component solid dispersion system (Yoo et al., 2009).

9

Figure 1.6: Dissolution performance of ASD containing a model poorly water-soluble compound

in various polymers at 10% drug loading. Dissolution was carried out using the microcentrifuge

tube under nonsink dissolution conditions in PBS at 37oC with 200 g/mL total drug concentration

(dissolved plus undissolved drug). Figure adapted from Curatolo et al. (Curatolo et al., 2009)

(reproduced with permission from Pharmaceutical Research, Copyright Springer 2009).

Typically, the dissolution of ASDs based on water-soluble polymers under nonsink dissolution

conditions is very rapid, resulting in an initial surge of drug concentration in the dissolution

medium followed by a decline in drug concentration due to the nucleation and crystallization

events triggered by the rapid buildup of drug supersaturation. Depending on the ability of the

dissolved polymer to inhibit drug precipitation from the supersaturated state, such a decline in drug

concentration can be retarded to different degrees. In general, the more gradual the decline in drug

concentration, the greater its effectiveness in inhibiting drug precipitation and in maintaining drug

supersaturation (Alonzo et al., 2011; Alonzo et al., 2010). In this regard, amphiphilic HPMCAS

has been identified as the most effective in achieving and maintaining drug supersaturation among

several available water-soluble polymers commonly employed in ASD-based oral drug products

(Figure 1.6) (Curatolo et al., 2009; Friesen et al., 2008). Typical dissolution profiles of ASDs

showing a rapid initial buildup of drug supersaturation and subsequent retardation of precipitation

have been qualitatively characterized as the “spring and parachute” approach (Figure 1.7)

(Brouwers et al., 2009; Guzman et al, 2007; Warren et al., 2010). This combination of a rapidly

dissolving and supersaturating “spring” with a precipitation-retarding “parachute” has been

pursued as an effective formulation strategy to enhance the rate and extent of oral absorption.

10

Although such “spring and parachute” dissolution data have been fitted to empirical rate equations

to estimate the time constants for the “spring” and “parachute” portions of the dissolution profiles

(Kawakami, 2012), the interplay between these two rate processes in achieving and maintaining

supersaturation remains inadequately understood.

Figure 1.7: Illustration of the time evolution of kinetic solubility profiles of a crystalline drug,

amorphous drug and ASD in water-soluble carriers under nonsink dissolution conditions. Profile

2 represents the dissolution of a higher energy “spring” form of the drug in absence of any

crystallization inhibitor; Profile 3 displays the combination of the rapidly supersaturating “spring”

form and precipitation-inhibiting “parachute” form. Cs indicates the equilibrium solubility. Figure

adapted from Brouwers et al. (Brouwers et al., 2009) (reproduced with permission from the

Journal of Pharmaceutical Sciences, Copyright John Wiley and Sons, 2009).

11

Model Drug Carrier* Additives (copolymer,

surfactant, plasticizers) Preparation method**

Ref

Felodipine PVP None C/SE (Marsac et al., 2010)

Tacrolimus HPMC

PEG6000, PEG4000, Poloxamer 188, Poloxamer 407, SDS SD (Park et al., 2009)

Indomethacin PVP None C/SE (Telang et al., 2009)

AMG 517 (VR1 antagonist) HPMCAS, HPMC None SD

(Kennedy et al., 2008)

Compound C35H35N5O3 PVP poloxamer 188 C/SE, HE

(Lakshman et al., 2008)

Itraconazole mannitol/lecithin None FD (URF), PM (Yang et al., 2008)

Itraconazole PEG / HPMC None SD (Janssens et al., 2008)

UC 781 (anti-HIV) PVP/VA, HPMC

TPGS (d-alpha-tocopheryl polyethylene glycol 1000 succinate) C/SE

(Goddeeris et al., 2008)

Felodipine PVP, HPMCAS, HPMC None C/SE

(Konno et al., 2008)

Nifedipine PVP, HPMC, PHPA None SD (Aso et al., 2007)

Ibuprofen

PVP (Kollidon 25, Kollidon 30, Kollidon VA64, Kollidon CL) None SD (Xu et al., 2007)

Itraconazole HPMC, HPMCP

Polysorbate 80, anhydrous silicic acid, croscarmellose sodium, magnesium stearate C/SE, HE

(Oshima et al., 2007)

Itraconazole PEG, HPMC None SD, HE (Janssens et al., 2007)

Itraconazole HPMCP, Eudragit (L100) None FD (URF)

(Overhoff et al., 2007)

Piroxicam

Polyoxyethylene 40 Stearate, Eudragit (E100) Mannitol, dextrin C/SE

(Valizadeh et al., 2007)

Compound (MW400)

PVP, Plasdone (S630), HPMC

Tween-80 and Docusate sodium HE

(Ghebremeskel et al., 2007)

Meloxicam PEG None C/SE, PM (Kumar and Mishra, 2006)

KRN633 (VEGF tyrosine kinase inhibitor) PVP None C/SE

(Matsunaga et al., 2006)

Nifedipine / Felodipine PVP None C/SE

(Marsac et al., 2006)

Acetaminophen HPMCP, chitosan None SD (Chen et al., 2006)

Bicalutamide PVP None C/SE, PM (Ren et al., 2006)

Felodipine PVP, HPMC Poloxamer 127 C/SE, PM (Kim et al., 2006)

Felodipine PVP, PEG sodium docusate C/SE (Karavas et al., 2005)

Nitrendipine HPMCP None HE (Wang et al., 2005)

12

Model Drug Carrier* Additives (copolymer,

surfactant, plasticizers) Preparation method** Ref

Felodipine HPMC

Poloxamer 188, Poloxamer 407, HCO-60 C/SE (Won et al., 2005)

Nifedipine HPMCAS, HPMCP, MAEA, PVP None C/SE (Tanno et al., 2004)

Nifedipine / Phenobarbital PVP None C/SE (Aso et al., 2004)

Ketoprofen PEO CrosPVP, SDS PM, ME (Schachter et al., 2004)

Ritonavir PEG None C/SE (Law et al., 2004)

Indomethacin PVP None PM (Watanabe et al., 2003)

Itraconazole HPMC None PM, HE (Verreck et al. 2003a,b,c)

Indomethacin Na-indomethacin / PVP None PM, C/SE

(Tong and Zografi, 2001)

Probucol PVP, PAA, PEO Tween 80 C/SE, ME (Broman et al., 2001b)

Furosemide PVP calcium alginate Floating multi-unit system

(Iannuccelli et al., 2000)

Itraconazole lactose Disintegrants: Primogel, Kollidon CL, and Ac-Di-Sol PM

(Chowdary and Rao, 2000)

*Carrier: HPMC hydroxypropyl methyl cellulose; HPMCAS hydroxypropyl methyl cellulose acetate succinate; HPMCP hydroxypropyl methyl

cellulose phthalate; MAEA methacrylic acid ethyl acrylate; PAA poly(acrylic acid); PEG polyethylene glycol; PEO polyethylene oxide; PHPA

poly(N-5-hydroxypentyl) aspartamide; PVP polyvinyl pyrrolidone; PVP/VA polyvinyl pyrrolidone/vinyl acetate; SDS sodium dodecyl sulfate.

**Preparation method: C/SE cosolvent/solvent evaporation; SD spray-drying; FD freeze-drying; URF ultra-rapid freezing; ME melting; HE hot-

melt extrusion; PM physical mixing

Table 1.1: Selected studies of water-soluble carriers for amorphous drugs.

13

Category Examples Carrier* Model Drug Preparation

method** Release mode***

Ref

a. Crosslinked hydrogel

cr-PHEMA hydrogel

diclofenac sodium, naproxen, piroxicam, indomethacin

S/SE IR/CR (Sun et al., 2012; Zahedi and Lee, 2007)

cr-PEO hydrogel

progesterone S/SE CR (Carelli et al., 1993)

Carbopol® phenacetin S/SE CR (Ozeki et al, 2000)

I. Non-porous

b. Water-insoluble polymer

Ethylcellulose indomethacin C/SE CR (Ohara et al, 2005)

Eudragit® RS, RL

indomethacin, dipyridamole

C/SE CR (Beten et al, 1994; Oth et al, 1989)

c. Lipid

Labrasol and Gelucire 44/14

piroxicam HM IR (Yüksel et al, 2003)

Gelucire 44/14 and Gelucire 50/13

gilbenclamide C/SE IR (Chauhan et al, 2005)

“popcorn” cr-PVP

griseofulvin, indomethacin I/SE, HG IR

(Fujii et al, 2005; Shibata et al, 2007; Carli et al, 1986)

II. Porous

silica

fenofibrate, carbamazepine, cinnarizine, danazol, ibuprofen diazepam, griseofulvin, indomethacin, ketoconazole, nifedipine, phenylbutazone

I/SE, SD IR

(Van Speybroeck et al, 2009; Van Speybroeck et al, 2010; Shen et al, 2010)

starch foam lovastatin I/SE IR (Wu et al, 2011)

carbon celecoxib I/SE IR (Zhao et al, 2012)

*Carrier: cr-PHEMA poly(2-hydroxyethyl methacrylate) crosslinked with ethylene glycol dimethacrylate; Carbopol® (910, 971P, 934P, 974P,

940) polyacrylic acid (lightly crosslinked with allyl sucrose or allyl pentacrythritol); cr-PEO poly(ethylene oxide) crosslinked with hexamethylene

diisocyanate (HMDIC) or tolylene-2,4-diisocyanate (TDIC); cr-PVP crosslinked polyvinylpyrrolidone; Gelucire 44/14, 50/13 polyethylene glycol

glycerides; Labrasol caprylocaproyl macrogolglycerides.

**Preparation method: S/SE swelling/solvent evaporation; C/SE cosolvent/solvent evaporation; I/SE immersion/solvent evaporation, HM hot melt;

HG heated granulation (

14

1.2.2 Water-insoluble carriers

In contrast to studies of water-soluble ASD carriers, previous efforts in applying water-insoluble

polymers as ASD carriers have primarily aimed to achieved controlled release (Tran et al. 2011;

Zhu et al. 2006). Table 1.2 summarizes available water-insoluble carriers utilized to convert poorly

water-soluble model drugs into amorphous formulations categorized by their physicochemical

characteristics such as porosity, location of amorphous drug and carrier chemical composition. In

the case of nonporous ASD carriers where amorphous drug molecules are completely dissolved

(i.e., one-phase solid solution), carriers with extremely low drug diffusivity such as “glassy

polymers” (i.e., Tg much higher than ambient temperature) will exhibit better ASD stability due

to hindered drug diffusion and inhibition of drug precipitation in the glassy matrix. The presence

of specific drug-carrier intermolecular interactions due to hydrogen bonding, dipole-dipole

attraction and van der Waals forces further stabilizes the entrapped amorphous drug, preventing it

from nucleating and becoming crystallite. By contrast, in porous carriers where the incorporated

amorphous drug is localized in interstitial pore space (i.e., not molecularly dispersed), the

nucleation and crystallization of this aggregated amorphous drug can give rise to stability issues.

However, the drug nucleation and crystallization rates can be reduced if the size of the pore is

sufficiently small compared to that of the critical nuclei, rendering it energetically unfavorable for

nuclei to grow (Rengarajan et al., 2008; Van Speybroeck et al., 2009; Van Speybroeck et al., 2010).

For inorganic mesoporous materials such as silica and silicon (Xu et al., 2012), their large surface

area and pore volume can accommodate a large amount of drug payload. Drug nucleation and

crystal growth in the porous channels will be energetically unfavorable if the size of the critical

nucleus is larger than that of the pore (Jackson and McKenna, 1996; Wang et al., 2006). In other

words, the spatial constraint of a capillary imposed on the amorphous drug below the critical

nucleus size has a stabilizing effect. In addition, a strong interaction with the pore walls (e.g.,

through hydrogen bonding) further stabilizes the confined drug molecules in the amorphous state

and this typically occurs in nano-sized pores with a pore diameter smaller than approximately 10

nm (Rengarajan et al., 2008). The drug loading process in such mesoporous materials commonly

involves immersing the carriers in a concentrated drug solution to fill the pores followed by the

evaporative removal of solvents. One study claims to have successfully accomplished solid

dispersion by means of a melt-mixing method, during which a physical mixture of nitrendipine

and mesoporous silica particles is heated above the melting point of the drug (Wang et al., 2006).

15

Nonetheless, in this case the high viscosity of the melted drug can interfere with the capillary

action within the pores, potentially causing an incomplete drug loading. Similar constraints also

apply to macroporous polymeric carriers such as crosslinked polyvinylpyrrolidone (crospovidone)

which exhibits a “popcorn” structure, containing many macroscopic cavities, as clearly shown

under the SEM (Carli et al., 1986; Fujii et al., 2005; Shibata et al., 2007). In this case, in addition

to the conventional loading method of sorption from a concentrated drug solution, an alternative

method of drug loading based on blending or milling of the drug and porous crospovidone particles

without solvent under high mechanical shear for an extended period of time has been proposed

(Fujii et al., 2005; Shibata et al., 2007). However, the “amorphous” material produced in this could

be a result of the well-known shear-induced phase transformation at the shear-fractured surfaces

on drug crystals (Greco and Bogner, 2010; Koike et al., 1990). As such, the long-term stability of

such mechanically generated amorphous systems is questionable since without any mechanism for

crystallization inhibition this exposed surface amorphous content can easily be converted to the

crystalline phase under accelerated temperature and/or in higher humidity.

Alternatively, in a nonporous insoluble carrier system, amorphous drugs can exist as surface

adsorbed or molecularly dissolved/dispersed in the matrix depending on the drug loading process.

For example, solvent or melt granulation of a crystalline drug with a nonporous insoluble carrier

typically results in an amorphous drug either adsorbed on the carrier surface or unevenly

distributed throughout the carrier-drug granule (i.e., a two-phase amorphous solid dispersion).

Such pure amorphous drug, either surface adsorbed or unevenly distributed lacks the benefit of

crystallization inhibition conferred by dissolving or molecularly dispersing the drug in a protective

carrier matrix and, therefore, is prone to undesirable nucleation and crystallization in the solid

state. Nonetheless, the creation of uniformly dissolved or molecularly dispersed drug in ASD

polymeric carriers (i.e., one-phase solid solution) through either drug sorption (e.g., from a good

swelling solvent) or co-precipitating from a common organic solvent (e.g., via spray drying or

freeze drying) is understandably more advantageous than producing dispersed two-phase ASD

systems in terms of its effectiveness in crystallization inhibition and its effect in enhancing the

physical stability. Therefore, applicable nonporous water-insoluble carriers include crosslinked

polymers (e.g., PHEMA), cellulose derivatives (e.g., ethylcellulose), and lipids (e.g., PEG-

glycerides). The common methods of preparation of ASD based on water-insoluble carriers can

be generally classified as supercooling of the melt (e.g., hot-stage melting, hot-melt extrusion), co-

16

precipitating from a common organic solvent (e.g., spray-drying, freeze-drying), and equilibrium

sorption (e.g., from a concentrated drug solution prepared in a good swelling solvent) to produce

a homogenous binary one-phase system. In this case, the carrier plays an essential role in

preserving the entrapped drug molecules in the amorphous state despite the fact that the exact

mechanisms of crystallization inhibition in solid molecular dispersions are still not completely

understood. Various factors such as molecular mobility, thermodynamic properties, and drug-

polymer interactions have been identified as responsible for inhibiting drug crystallization from

the amorphous state (Bhugra and Pikal, 2008; Hancock and Zografi, 1997; Khougaz and Clas,

2000). Stressed conditions involving high relative humidity and high temperature in combination

with ageing may accelerate the transformation of metastable amorphous drugs in an ASD into a

more thermodynamically stable crystalline state (Hancock and Zografi, 1997; Konno and Taylor,

2008).

1.3 Crosslinked PHEMA hydrogels for amorphous solid dispersions carriers

Poly (2-hydroxyethyl methacrylate) (PHEMA) has been widely utilized in controlled drug delivery

systems particularly for water-soluble drugs and in biomedical application such as contact lenses,

wound dressing and tissue engineering. Crosslinked PHEMA is probably the most extensively

studied gel-forming water-insoluble polymer among several other synthetic hydrogels based on

nonionic hydrophilic monomers (e.g., hydroxyalkyl acrylate, N-substituted methacrylamides and

N-vinyl-2-pyrrolidone) commonly used in swelling-controlled oral drug delivery (Gehrke, 2000).

The drug release kinetics and release rate modulation from such a spherical monolithic diffusion-

controlled system have previously been characterized in detail (Lee and Kim, 1991; Lee and

Peppas, 1987). Chemically, PHEMA has hydrophilic side groups which can promote the sorption

of a significant amount of polar solvent, thereby providing desired conditions to create solid

dispersions with high drug loading. PHEMA can also be easily copolymerized with other

hydrophobic monomers, such as methyl methacrylate (MMA) or its homologs, to improve the

compatibility of the hydrogel matrix with hydrophobic drugs. Furthermore, the crosslinker chain

length and crosslinking density can be adjusted to affect the network mesh size which provides

further control of the diffusional drug release (Hoare and Kohane, 2008). Thus, PHEMA is a good

candidate drug carrier because of the ease in regulating drug release by controlling particle size,

17

crosslinking density, chemical composition (e.g., copolymers) and water sorption rate to achieve

different drug loading levels and release profiles suitable for oral drug delivery.

Orally administered excipients must be stable, non-toxic, biocompatible in the GI tract and

compatible to API and other excipients in the formulation in order to satisfy regulatory

requirements. Full in vivo studies such as biodistribution, immune response, clearance, and chronic

toxicology studies for different durations are generally required to demonstrate the excipient’s

safety for use in human drug products. The approval process to introduce a new pharmaceutical

excipient onto the market requires expensive toxicological investigations and typically takes a

similar period of time as that of a new API (Katdare and Chaubal, 2006). Due to the complexity

and high cost of long-term toxicological and clinical testing, PHEMA has not yet been used as an

oral excipient in the FDA approved drug products (note: PHEMA is a FDA-approved inactive

ingredient for only topical and dressing application as on September 16, 2013). Nevertheless,

PHEMA hydrogel has a long history of human use as biomedical implants and for controlled drug

release from medical devices. A number of in vivo tests using PHEMA hydrogel delivery systems

have produced favorable results in blood and tissue compatibility (Imai and Masuhara, 1982).

Moreover, no toxic abnormalities were reported when crosslinked PHEMA hydrogels loaded with

diclofenac sodium and theophylline were administered orally and rectally, respectively, to human

subjects in clinical pharmacokinetic studies (De Leede et al., 1986; Thakker et al., 1992). Since

crosslinked hydrogels for the purpose of oral delivery are generally of micron sizes and insoluble

in the GI fluid, cellular internalization or absorption through the mucosal membrane of the GI tract

is very unlikely. Therefore, the above mentioned lines of evidence suggest that crosslinked

PHEMA hydrogel beads would be an attractive candidate excipient for oral drug delivery. To

promote the practical application of PHEMA hydrogels as an excipient for oral dosage forms,

long-term oral toxicity studies should be further investigated and established.

In selecting an appropriate polymer matrix for an ASD system, the carrier polymer must provide

sufficient stabilization effect in the solid state to prevent the entrapped amorphous drug from

crystallizing, thereby achieving a reasonable shelf life. From a mechanistic point of view,

nucleation and subsequent crystallization of an amorphous drug in a polymer matrix deplete the

local drug concentration around the crystallite and thus triggering drug diffusion from the

surrounding amorphous drug region to the crystallite surface to sustain crystal growth. The reduced

segmental mobility of polymer chains in glassy PHEMA hydrogels at ambient temperature well

18

below its Tg of 115 oC (Roorda et al., 1988) should lengthen the polymer molecular relaxation

time and retard the diffusional mobility as well as reduce the nucleation and crystallization rates

of the entrapped molecularly dispersed drug, thus resulting in enhanced stability of such hydrogel-

based solid dispersion systems. An additional advantage is that PHEMA hydrogels exist as

optically clear glassy solids at ambient temperature, which is suitable for direct microscopic

examination for any phase transformation and for the determination of the drug loading threshold

in the hydrogel matrix above in which amorphous-to-crystalline transition may occur.

In addition to the physical stability of ASDs, the extent of solubility and dissolution enhancement

is another key criterion to consider in selecting an appropriate ASD carrier. For a long while, the

kinetics of drug release from crosslinked water-insoluble hydrogels was characterized only in the

context of achieving controlled drug release under perfect sink dissolution conditions (Lee, 1985).

The swelling kinetics and diffusional drug release kinetics are important physical characteristics

of hydrogel-based drug delivery. The swelling kinetics of crosslinked hydrogels is important not

only to reach an adequate drug loading but also to regulate the rate of drug release. During drug

release, the time evolution of the solvent-penetrating front and normalized dimensional changes

of drug-loaded PHEMA hydrogel beads is a function of crosslinking density, drug solubility and

initial drug loading. For example, two moving boundaries (swelling front and drug dissolution

front) were generally observed for poorly water-soluble diclofenac sodium in PHEMA hydrogels

at a high drug loading range of 25-30% w/w as the aqueous medium penetrates into the matrix,

whereas a single fast-moving swelling front was observed below this range of drug loading (Lee

and Kim, 1991). In terms of dimensional transformation, the swelling PHEMA beads generally

first expand to a maximum in radius followed by a gradual decrease to an equilibrium dimension

during the drug release (Lee, 1983; Lee and Kim, 1991). Moreover, the dissolution of incorporated

drug from crosslinked PHEMA hydrogels is regulated by diffusion where the hydrogel matrix is

insoluble and the dissolved or dispersed drug slowly diffuses out of the hydrogel network.

Although the application of PHEMA hydrogel as a carrier for ASDs of model poorly water-soluble

drugs such as diclofenac sodium, naproxen and piroxicam have been proposed recently (Zahedi

and Lee, 2007), the effect of the hydrogel matrix on the maintenance of supersaturation was

virtually unknown. Crosslinked hydrogels with a unique diffusion-controlled mechanism of drug

release will hopefully provide an adequate alternative to the rapidly dissolving ASD carriers in

enhancing the solubility and dissolution rate of poorly water-soluble drugs.

19

1.4 Crystallization of amorphous pharmaceuticals in the solid state

1.4.1 Solubility advantage of amorphous solids

Several theoretical models present amorphous solids as having “excess” (Yu, 2000)

thermodynamic properties including higher volume, enthalpy, entropy and free energy, as

compared to its crystalline state. The change in free energy levels between amorphous and

crystalline states accounts for their significant differences in physiochemical properties such as the

apparent solubility (or the kinetic solubility) in water. Parks et al (Parks et al, 1934) for the first

time theoretically estimated the difference in kinetic solubility between amorphous and crystalline

glucose based on thermodynamic analysis, and experimentally confirmed their theoretical

predictions. The free energy difference between the amorphous and crystalline phases is expressed

by:

∆𝐺𝑎,𝑐 = −𝑅𝑇𝑙𝑛 (𝑎𝑎

𝑎𝑐) = −𝑅𝑇𝑙𝑛 (

𝛾𝑎𝐶𝑆𝑎

𝛾𝑐𝐶𝑆𝑐 ) Equation 1.1

where a is activity of the solute in the saturated solution (superscript: a for amorphous and c for

crystalline), R the gas constant, T the temperature, 𝛾 the activity coefficient (close to unity when

the system is in a diluted form) and Cs the concentration at saturation (i.e., solubility). One

important assumption of this equation is that an equilibrium solubility exits in both crystalline and

amorphous states. For crystalline materials, the equilibrium solubility refers to the physical state

when the molecules in the solid state are in chemical equilibrium with those in the solution state

in a close system. In other words, the rates of dissolution and precipitation of individual molecules

between the solid and solution phases are equal to each other. However, amorphous solids are in

a non-equilibrium state (i.e., metastable) at which the disordered molecular structure does not

require the breaking of crystal lattice upon dissolution. The apparent solubility of amorphous solids

generated by time-dependent rates of dissolution and precipitation is in fact a kinetic property.

Nevertheless, Parks et al (Parks et al, 1934) treated amorphous drug as either an equilibrium

supercooled liquid or a pseudo-equilibrium glass and estimated the ratio of solubility enhancement

between the amorphous and crystalline states by calculating the difference in Gibbs free energy

expressed in enthalpy (H) and entropy (S):

20

∆𝐺𝑎,𝑐 = ∆𝐻𝑎,𝑐 − 𝑇∆𝑆𝑎,𝑐 Equation 1.2

According to Kirchhoff’s law, ∆𝐻𝑎,𝑐and ∆𝑆𝑎,𝑐 can be calculated by:

∆𝐻𝑎,𝑐 = ∆𝐻𝑓𝑐 + ∫ ∆𝐶𝑝

𝑇

𝑇𝑚𝑑𝑇 = ∆𝐻𝑓

𝑐 − (𝐶𝑝𝑎 − 𝐶𝑝

𝑐) × (𝑇𝑚 − 𝑇) Equation 1.3

∆𝑆𝑎,𝑐 = ∆𝑆𝑓𝑐 + ∫

∆𝐶𝑝

𝑇

𝑇

𝑇𝑚𝑑𝑇 = ∆𝑆𝑓

𝑐 − (𝐶𝑝𝑎 − 𝐶𝑝

𝑐) × 𝑙𝑛 (𝑇𝑚

𝑇) Equation 1.4

where ∆𝐻𝑓𝑐 is the entropy of fusion, Cp the isobaric heat capacity, Tm melting temperature and

∆𝑆𝑓𝑐 entropy of fusion (calculated by ∆𝐻𝑓

𝑐/𝑇𝑚). The difference in isobaric heat capacity (∆𝐶𝑝)

has been estimated to be (1) zero (i.e., ∆𝐶𝑝 ≈ 0), (2) the heat capacity gained upon going through

the glass transition (i.e., ∆𝐶𝑝 ≈ ∆𝐶𝑝,𝑇𝑔), (3) the entropy of fusion (i.e., ∆𝐶𝑝 ≈ ∆𝑆𝑓), and (4) a non-

zero constant in which the difference in enthalpy between the two states vanishes at a temperature

T∞, slightly below Tg (i.e., ∆𝐶𝑝 ≈∆𝐻𝑓

𝑇𝑚−𝑇∞). The last approach can be further utilized to derive a

simple mathematical express of the Gibb’s free energy difference, also known as the Hoffman

equation:

∆𝐺𝑎,𝑐 =∆𝐻𝑓(𝑇𝑚−𝑇) 𝑇

𝑇𝑚2 Equation 1.5

This theoretical consideration has been the basis for many attempts on the thermodynamic

prediction of solubility enhancement ratios between the amorphous and crystalline forms of poorly

water-soluble drugs (Hancock and Parks, 2000; Alonzo et al, 2010; Alonzo et al, 2011). Additional

rigorous modifications including the consideration of configurational heat capacity, water sorption

during dissolution and different degrees of drug ionization in amorphous and crystalline forms

have provided further improvements in producing a closer agreement with the measured data

(Aceves‐Hernandez et al., 2009; Hoffman, 1958; Matteucci et al., 2008; Murdande et al., 2010a,

b, 2011a, b; Ogino et al., 1990). Nevertheless, both the theoretical prediction of the solubility

enhancement using thermodynamic analysis and the accurate experimental measurements of the

solubility of the amorphous state has proven to be very challenging.

21

1.4.2 Classical nucleation theory (solid state)

Due to the non-equilibrium nature of the amorphous solids, the amorphous state is less

thermodynamically stable than any crystalline form, leading to an inevitable tendency for the

amorphous materials to transform to a crystalline phase. The higher free energy level of the

amorphous form relative to the crystalline state provides the thermodynamic driving force for

nucleation and crystallization, causing physical instability (i.e., recrystallization) in the dosage

forms. Nonetheless, acceptable drug stability can still be achieved in amorphous formulations for

oral dosage forms during pharmaceutical development if the kinetics of amorphous-to-crystalline

phase transformation can be delayed to an adequate extent. The physical process of

recrystallization from a high-energy amorphous form in the solid state is a complex phenomenon

from a mechanistic viewpoint based on both nucleation and crystal growth. The Classical

Nucleation Theory (CNT) first describes the kinetics of the homogenous nucleation process by

considering the difference in the free energies of the crystalline and liquid phases (note: amorphous

materials which lack crystalline lattice energy have a molecular structure similar to that of a liquid).

The overall difference of Gibb’s free energy between the crystalline and amorphous phases is equal

to the sum of two surface excess energies, Gs (the difference between the surface and the bulk of

the crystalline phase) and GV (the difference between a very large crystalline particle (r = ∞) and

the amorphous phase). Considering the growth of a spherical crystalline particle, the overall excess

free energy is given:

∆𝐺 = ∆𝐺𝑆 + ∆𝐺𝑉 = 4𝜋𝑟2𝛾 +

4

3𝑟3∆𝐺𝜈 Equation 1.6

where r is the radius of the crystalline particle, γ the interfacial tension and ∆𝐺𝜈 the free energy

change of the transformation per unit volume. The overall ∆𝐺 as a sum of positive Gs and

negative GV has a local maximum corresponding to the critical nucleus, rc, as illustrated in Figure

1.8. This local maximum can be obtained by taking the first-derivative of Equation 1.6:

𝑑∆𝐺

𝑑𝑟= 8𝜋𝑟𝛾 + 4𝜋𝑟2∆𝐺𝜈 = 0 Equation 1.7

Therefore, the critical radius of a nucleus, rc, and the free energy difference for such a nucleus,

∆𝐺𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙, are given by:

22

𝑟𝑐 =−2𝛾

∆𝐺𝜈 Equation 1.8

∆𝐺𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 =16𝜋𝛾3

3(∆𝐺𝜈)2=

4𝜋𝛾𝑟𝑐2

3 Equation 1.9

Figure 1.8: Free energy diagram for nucleation process. Figure adapted from Crystallization 3rd

edition (Mullin, 2001) (reproduced with permission from the Crystallization 3rd edition, Copyright

Butterworth-Heinemann, 1993).

The nucleation rate J (i.e., the number of nuclei formed per unit volume per unit time) is expressed

in the form of an Arrhenius equation, commonly used for the rate process of a thermally activated

reaction:

𝐽 = 𝐴𝑒(−∆𝐺

𝑘𝑇) Equation 1.10

where A is the pre-exponential frequency factor, k the Boltzmann constant and R the gas constant.

For homogenous nucleation from the melt (i.e., liquid phase), the free energy change is estimated

by:

∆𝐺𝜈 = Δ𝐻𝑓(𝑇𝑚−𝑇)

𝑇𝑚 Equation 1.11

23

where Δ𝐻𝑓 is the latent heat of fusion and Tm the melting temperature (solid-liquid equilibrium

temperature). Therefore, the critical radius of a nucleus and the critical free energy difference are

given as:

𝑟𝑐 =−2𝛾𝑇𝑚

Δ𝐻𝑓(𝑇𝑚−𝑇) Equation 1.12

∆𝐺𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 =16𝜋𝛾3

3(∆𝐺𝜈)2=

16𝜋𝛾3𝑇𝑚2

3Δ𝐻𝑓2(𝑇𝑚−𝑇)2

Equation 1.13

and the nucleation rate for the amorphous-to-crystalline transformation in the solid state may be

expressed by substituting Equation 1.13 into Equation 1.10:

𝐽 = 𝐴𝑒(

−16𝜋𝛾3

3𝑘𝑇Δ𝐻𝑓2(𝑇/𝑇𝑚)(1−𝑇/𝑇𝑚)

2 )

Equation 1.14

The analytical solution describing the nucleation kinetics in the amorphous materials is a function

of heat of fusion, melting temperature and interfacial tension. It is worth noting that the

determination of specific interfacial tension between the developing crystalline surface and the

amorphous bulk is not easily measured experimentally.

1.4.3 Crystal growth (solid state)

After the barrier to nucleation has been overcome, a number of newly formed stable nuclei will

continue to grow into crystals of microscopic size. The process of crystal growth is generally

described by models of (1) normal or continuous growth, (2) two-dimensional growth and (3)

growth mediated by screw dislocation (Gutzow and Schmelzer, 2013). The crystal growth rate can

be described by the following equation in a general form:

𝑈 =𝐶𝑇𝜔

𝜂(1 − 𝑒(

−Δ𝐺𝑉𝑘𝑇

)) Equation 1.15

where C is a constant, ω the constant which depends on the mechanism of growth, η the viscosity

of the system and Δ𝐺𝑉 the free energy difference between the amorphous and crystalline phases.

The combination of equations calculating the nucleation rate (Equation 1.14) and the crystal

24

growth rate (Equation 1.15) can assess the overall crystallization kinetics of amorphous-to-

crystalline phase transformation. However, it is worth highlighting that many of the parameters

listed in the above mentioned equations are not easily accessible experimentally.

1.4.4 Kolmogorov-Johnson-Mehl-Avrami (KJMA) Theory

The kinetics of overall crystallization taking into account nucleation, crystallization and the lag

time in both of these events can be described by the Kolmogorov-Johnson-Mehl-Avrami (KJMA)

theory which reduces the complicated mechanism into a simple mathematical correlation

describing the process of overall crystallization as a function of time (Avrami, 1939; Avrami 1940),

which is convenient to use for the physical stability study of amorphous pharmaceuticals (Andronis

and Zografi, 2000; Miyazaki 2004, Bhugar and Pikal, 2000; Gutzow Schmelzer 2013). The

empirical equation is presented by an exponential term:

𝑥(𝑡) = 1 − exp [−𝑘𝑡𝑛] Equation 1.16

where x is the percentage of the crystalline phase, t the time, and k and n Avrami crystallization

constants. One limitation of the KJMA theory is that time-dependent crystallization kinetics is

only an approximation in which the constants of k or n may not have any physical significance.

Despite the fact that the KJMA theory provides limited mechanistic information on crystallization

kinetics, comparing the crystallization rate to the Avrami equation is very convenient. Therefore,

the use of the KJMA theory offers an easy tool of direct comparison of crystallization rates between

two systems.

25

1.5 Crystallization of supersaturated drug solutions

1.5.1 Classical nucleation theory (solution state)

Amorphous pharmaceuticals can generate a supersaturated concentration in aqueous solution

significantly higher than the equilibrium saturation concentration of their crystalline counterparts.

In a solute-solvent binary system (e.g., drug-water), solute concentration above the equilibrium

solubility (i.e., supersaturation) provides the thermodynamic driving force for nucleation and

crystallization. In a supersaturated drug solution, the free energy is higher in the solution phase

than any newly formed crystalline phase. Classical nucleation theory based on the free energy

difference can also be applied on the precipitation process of solute from a supersaturated solution.

Equations 1.6 to 1.10 describe the nucleation rate for homogenous nucleation of the solute from a

supersaturated solution. The free energy change ∆𝐺𝜈 in Equation 1.10 becomes

∆𝐺𝜈 =−2𝛾

𝑟𝑐=

−kTln(S)

𝜐 Equation 1.17

where υ is the molecular volume and s the supersaturation. This equation is derived from the basic

Gibbs-Thomson relationship for a non-electrolyte:

ln(𝑠) =2𝛾𝜐

𝑘𝑇𝑟 Equation 1.18

The substitution of Equation 1.17 into Equations 1.9 and 1.10 gives:

∆𝐺𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 =16𝜋𝛾3

3(∆𝐺𝜈)2=

16𝜋𝛾3𝜈2

3(𝑘𝑇𝑙𝑛𝑆)2 Equation 1.19

𝐽 = 𝐴𝑒(

−16𝜋𝛾3𝜈2

3𝑘3𝑇3(𝑙𝑛𝑆)2 )

Equation 1.20

where described here is the interfacial tension between the evolving crystalline surface and

aqueous solution (note: different from described in Equations 1.12 to 1.14). Equations 1.19 and

1.20 are for nucleation from a supersaturated solution which significantly depends on the degree

of supersaturation are analogous to Equations 1.13 and 1.14 for nucleation from the melt.

26

1.5.2 Crystal growth (solution state)

Once stable nuclei have formed (i.e., r > rc) in a supersaturated solution, these particles start to

grow into crystals of visible size. Crystallization in a supersaturated solution is the reverse process

of dissolution, and both phenomena are governed by diffusion in which the concentration gradient

between the solid surface and the bulk of solution provide the driving force. During the

precipitation process from a supersaturated solution, crystal growth requires both long-range

transport of solute to the growing particles (i.e., diffusion) and local atomic rearrangement as the

solutes near the particle surface (i.e., interface) are integrated into the crystal lattice. Depending

on the rate-limiting step, crystal growth kinetics can be either diffusion-controlled or interface-

controlled. In a diffusion-controlled crystallization process, the growth rate of a crystal can be

predicted by the molecular flux which is related to the concentration gradient between the bulk