Growth morphology of a glycine crystals in solutions an extended interface structure analysis 1

GROWTH MORPHOLOGY OF α-GLYCINE CRYSTALS IN SOLUTIONS: AN EXTENDED INTERFACE STRUCTURE... Then, EISA is applied to the interface molecules to calculate the concentration of effective grow

GROWTH MORPHOLOGY OF α-GLYCINE CRYSTALS IN

SOLUTIONS: AN EXTENDED INTERFACE STRUCTURE

ACKNOWLEDGEMENTS

The beauty vested in any research is driven by transformation and passion towards knowledge and experience triggered by moments of inspiration and support received with absolute gratitude

I am much indebted to Prof Raj Rajagopalan for the level of dedication and motivation demonstrated in every aspect of his supervision, technical guidance and relentless support during one of the memorable phases of my life as a researcher

I am greatly obliged to Dr Jiang Jianwen for his overwhelming enthusiasm and effort in shaping and instilling growth to my potential I thank Prof X.Y Liu (Physics, NUS) for the helpful technical discussions and suggestions

I must thank the National University of Singapore for the research scholarship Thanks to

Dr Soeren Enemark as a technical mentor I am thankful to Dr Li Jianguo, Dr Shaikh, Vigneshwar, Dhawal, Srivatsan and research colleagues for their kindness and for sharing

I will be missing the loving presence of my dear brother G Sathishkumar and my sister

G Kalaivani who would have taken pride in my achievements

Table of Contents

1.1  Importance of Crystal Morphology in Practice 1 

1.2  Role of Solvent in Defining the Morphology of Crystals 3 

1.3  Approaches to Predict the Morphology of Crystals 6 

1.4  Selection of Glycine as a Model to Study the Crystal Morphology 7 

1.5  Research Objectives 8 

1.6  Structure of the Thesis 13 

2  LITERATURE REVIEW 15  2.1  Historical Introduction 15 

2.2  Theories of Crystal Growth 16 

2.2.1  Two-Dimensional Growth Theories 17  2.2.2  Burton-Cabrera-Frank (BCF) Theory 19  2.3  Theoretical Models for Predicting the Morphology of Organic Crystals 20 

2.3.1  Models Based on Attachment Energy 21  2.3.2  Models Based on Step Energy 22  2.3.2  Models Based on Burton-Cabrera-Frank Theory 23  2.4  Principles Behind the Effect of Solvent on the Morphology of Organic Crystals 26 

2.4.1  Differences in the Morphology of Crystals Grown from Sublimation and in Solutions 28  2.4.2  Solvent as Solvates 29  2.4.3  A Relay Mechanism of Crystal Growth 30  2.4.4  Solvent-Induced Twinning of Crystal 32  2.5  Experimental Studies on Glycine Crystals Grown in Aqueous Solutions 33 

2.6  Theoretical Studies on Prediction of Morphology of Glycine

Crystals 35 

2.6.3  BCF Model Accounting for Solute-Solvent Interactions 38 

2.7  Experimental Studies on Glycine Crystals Grown in a Mixture of Solvents 39 

2.8  Summary 41 

3.1  Introduction: Crystal Growth in Solutions 42 

3.2  Theory for Growth Rates 46 

3.3  Interface Structure Analysis (ISA) 51 

3.4  Extended Interface Structure Analysis (EISA) 57 

3.5   Molecular Dynamics (MD) Simulations 59 

3.6   Summary 62 

4.1  Introduction: Importance of Force Field 63 

4.2  Models and Methodology 66 

5.3  Results and Discussion 99 

5.3.2   Relative Growth Rates 110 

5.4  Concluding Remarks 115 

6.1  Introduction: Importance of Solvent in Changing the Crystal Shape 117 

6.2  Models and Methodology 119 

SUMMARY

Understanding the molecular mechanisms of crystal growth is an essential step towards controlling crystal growth, morphology and shape, which are of prime interest and importance in chemical and pharmaceutical industries Since crystals interact with their surroundings predominantly through their surfaces, the shape of a crystal influences their behavior and chemical and physical properties Although the environment in which the crystals are grown has a strong influence on the crystal habits, the role played by solvent/crystal interface in crystal growth is not completely resolved This research seeks

to provide a systematic method for studying and incorporating the effects of solvents on crystal morphology, and to probe the effects of solvents as well as mixtures of solvents

on the morphology of organic crystals grown in solutions

We choose glycine for examination as it has a simple molecular structure, is a basic building block for proteins and has prochiral property and since glycine crystallization has been studied extensively experimentally The methodology we have chosen is an extended interface structure analysis (EISA) that includes the full orientational characterization of the interfacial molecules We use the so-called AMBER03 force field for glycine and water and have ascertained the consistency of the force field by using it in molecular dynamics simulations in both solution and crystal/solution environments of glycine/water mixtures and by comparing the resulting predictions of properties such as density, radial distribution functions, hydration numbers, diffusivity and enthalpy of sublimation against the known values in the literature

The morphologies of glycine crystals in aqueous solutions and in methanol/water mixture are then predicted using a three-stage procedure First, MD simulations are performed on the morphologically important surfaces (010) and (011) of glycine crystals using the validated force field to determine the orientational distributions of the interface molecules Then, EISA is applied to the interface molecules to calculate the concentration

of effective growth units, i.e., solute molecules which have the correct orientation for docking into the crystal surface Finally, the relative growth rate is calculated using previously proposed expressions in the literature, and the morphology is predicted using wulff constructions

 Our results demonstrate that the polar group present on the (011) face has

strong interactions with the solvent and reduces the growth rate – an observation which underscores the importance of the need to incorporate solvent effects in crystal growth analysis

 Our method is able to predict the growth morphology consistent with

experimental observations; e.g., a bipyramidical crystal shape with a less well-developed (010) surface is predicted and is supported by available experimental observations

 In addition, we observe that the growth rate of the (011) face is 2.88 times

greater than that of (010) face, a result that compares favorably with experimental observations (2.67), in contrast to the much higher relative growth rates (4 to 7) predicted by attachment energy calculations in the literature in the absence of solvent

 Finally, the method also captures the effect of mixtures of solvents We

show, from first principles, that the presence of methanol changes the crystal morphology significantly from that in pure aqueous solutions In particular,

we show that the crystals are plate-like in a 1:1 methanol/water (by volume), consistent with experimental observations in alcohol/water mixtures

In summary, the proposed method presents a sufficiently rigorous and systematic molecular approach to examine and predict the effects of solvent environments on crystal shape and morphology for the first time The approach presented thus paves the way for exploring the effects of other solvents and impurities on the kinetics and the morphology

of crystal growth

PBC Periodic Bond Chain analysis

ISA Interface Structure Analysis

SCF Self-Consistent Field

SAM Self-Assembled Monolayer

AFM Atomic Force Microscopy

SPM Scanning Probe Microscopy

SPC/E Extended Simple Point Charge model

BLYP Becke exchange plus Lee-Yang-Parr correlation functional DNP Double-Numerical plus d- and p-Polarization basis set

ESP Electrostatic Potential

RESP Restrained Electrostatic Potential

TIP Transferable Intermolecular Potential Functions

NPT Fixed pressure P, temperature T, and number of atoms N ensemble

NVT Fixed volume V, temperature T, and number of atoms N ensemble MSD Mean-Squared Displacement

DZP Double-Zeta plus Polarization

r radius of the two-dimensional nucleus

 molecular volume (m3/mol)

 chemical potential for S1 units

 fraction of effective growth units

K the force constant for bond

K the force constant for bond angle

b bond length (m)

eq

b equilibrium bond length (m)

 bond angle (degree)

eq

 equilibrium bond angle (degree)

n

V force constant

 dihedral angle (degree)

ij

A van der Waals term

List of Figures

Figure 1.1 Morphology of urea crystals in (a) an aqueous solution and (b) in methanol 3 

Figure 1.2 Photomicrographs of ibuprofen crystallized from (a) methanol,, (b) hexane

solution., and (c) 40% methanol/water mixture 5 

Figure 1.3 A Representation for a α-glycine unit cell 8 

Figure 1.4 A schematic diagram for morphology prediction of glycine crystals 10 

Figure 2 1 Surface structure of a growing crystal (Myerson 1993) 16 

Figure 2.2 A mode of crystal growth (a) migration towards desired location; (b) completed layer; (c) surface nucleation (Mullin 1993) 18 

Figure 2.3 Development of a growth spiral from a screw dislocation 19 

Figure 2.4 Representation of the attachment of host molecules into a slice d hkl releasing energy E sl and consequent attachment of the slice onto a growing surface of a crystal, releasing energy E att 22 

Figure 2.5 Important diffusional processes (volume and diffusion) affecting crystal growth (Myerson 1993) 27 

Figure 2.6 Free energy barriers to be overcome during crystal growth (Gkink – Energy barrier for the integration to kink sites, Gs – Energy barrier for surface diffusion and Gdesolv – Energy barrier for desolvation) (Myerson 1993) 27  Figure 2.7 Morphology of glycine: (a) theoretical, and (b) obtained from sublimation (c) Morphology obtained in aqueous solutions (Lahav and Leiserowitz 2001) 28 

Figure 2.8 (a) Packing arrangement of α-rhamnose monohydrate crystal viewed along the a-axis; (b) Morphology grown in aqueous solutions; and (c) Morphology grown in methanol:water solutions (Lahav and Leiserowitz 2001) 30 

Figure 2.9 Scheme for the relay mechanism (Lahav and Leiserowitz 2001) 31 

Figure 2.10 Packing arrangement of (R,S) analine by crystal faces (Lahav and Leiserowitz 2001) 31 

Figure 2.11 Schematic representations of the (001) face of (R,S) alanine during crystal growth: (a) solute alanine molecules are bound in the pockets, and (b) bond alanine molecule (Lahav and Leiserowitz 2001) 32 

Figure 2.12 Twin interface in saccharin (Davey et al 2002) 33 

Figure 2.13 Glycine crystals grown in aqueous solutions: (a) Berkovitch-Yellin 1985, (b) Boek et al 1991, and (c) Poornachary et al 2007 34 

Figure 2.14 BFDH model of glycine crystals predicted by (a) Berkovitch-Yellin (1985), and (b) Boek et al (1991) 36 

Figure 2.15 Glycine crystals with hydrogen bonding bilayers (Bisker-Leib and Doherty 2003) 37 

Figure 2.16 Predictions of glycine crystals by the attachment energy model 38 

(a) Shape reported by Berkovitch-Yellin (1985); 38 

(b) & (c) Shape reported by Boek et al (1991); 38 

(d) & (e) Shape using Scheraga and Dreiding force field (Bisker-Leib and Doherty 2003)

38 

Figure 2.17 BCF model for glycine crystals predicted by Bisker-Leib and Doherty

(2003): (a) Dimer as the growth unit; (b) Monomer as the growth unit 39 

Figure 2.18 Morphology of glycine crystals in 1: 9 ethanol/water mixture (Weissbuch et

al 2005) 40 

Figure 3.1 Schematic representation to show the experimental, theoretical and

computational methods available in the literature for investigating crystal growth in solutions The dotted ellipse indicates the methods used for the present work 43 

Figure 3.2 Schematic representations to show (a) spiral dislocations, (b) terminologies

used to represent the spiral dislocations, and (c) growing surface of a crystal 46 

Figure 3.3 A Schematic representation for different states of structural units at the

interface and equilibrium between different states 52 

Figure 3.4 A typical potential energy landscape for the structural units at the interface.54 

Figure 3.5 Schematic representation for the overall methodology for crystal morphology

prediction 59 

Figure 3.6 Schematic representation of various steps involved in crystal/fluid interface

simulations 60 

Figure 4.1 A zwitterionic glycine molecule Label: Red-Oxygen, Blue-Nitrogen,

Cyan-Carbon and White-Hydrogen 67 

Figure 4.2 A sample simulation box for solution environment The box consists of 27

glycine molecules and 1300 water molecules 72 

Figure 4.3 A typical snapshots of water molecules above the (010) surface of the

α-glycine crystal obtained from the simulations (a) Top view normal to the (010) plane (b) and (c) Side views normal to (100) and (001) planes Water molecules are indicated by red spheres (O atoms) connected by grey spheres (H atoms) 75 

Figure 4.4 Density comparison between simulated and experimental values

Experimental values are from Dalton and Schmidt (1933) 78 

Figure 4.5 Radial distribution functions between (a) OC (b) H (c) N of glycine and OW

of water in glycine solutions The arrows show the direction of increase in

xglycine 80 

Figure 4.6 Mean-squared displacements of glycine in a solution The arrow shows the

direction of increase in xglycine 84 

Figure 4.7 Comparison between experimental and simulated diffusion coefficients of

glycine in solutions Lines are to guide the eye 84 

Figure 4.8 Water density profile in the y-direction, normal to the (010) surface of the

-glycine crystal 88 

Figure 4.9 Mean-squared displacements of water in the x, y, and z directions and along

the xz plane in the vicinity of the (010) surface (in a layer of 0.3 nm in

thickness) 90 

Figure 5.1 Arrangement of the glycine molecules relative to the (010) and (011) surfaces

(a) (010) surface indicated by broken red line and the surface exposes molecule type 2 (b) (011) surface indicated by broken red line and the surface exposes molecule types 2 and 3 Note that the “transformed unitcell” for showing the (011) surface is generated by cleaving the (011) plane from the glycine unit cell by using Material Studio Label: Red-Oxygen, Blue-Nitrogen, Cyan-Carbon and White-Hydrogen 96 

Figure 5.2 Typical snapshots of the crystal/solution interface of an α-glycine crystal

from the simulations (a) (010) plane (b) (011) plane The projected view is

to show the proper orientation and also mis-orientation of adsorbed molecules on the surface Water molecules are indicated by red spheres (O atoms) connected by grey spheres (H atoms) 100 

Figure 5.3 Density profiles for crystalline glycine, glycine in solution and water

molecule as a function of distance from (a) (010) plane and (b) (011) plane 102 

Figure 5.4 Schematic representations to show the interfaces along with the density

profile (a) (010) surface with the adsorbed glycine molecules (next growing layer) on the interface shown in blue colour (b) (011) surface and the next growing layer molecules are shown in metallic blue 103 

Figure 5.5a Probability density distribution for the (010) surface as a function of θ CC and

CC at θ CN = 116˚ (corresponding to the growth unit; Type 3 molecule in

Figure 5.1 and Table 5.2, with θ CC = 99˚, CC = 110˚, and θ CN = 116˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth unit (Type 3 molecule) is represented by 106 

Figure 5.5b Probability density distribution for the (011) surface as a function of θ CN

and CC at θ CC = 156˚ (corresponding to the growth unit; Type 4 molecule in

Figure 5.1 and Table 5.2, with θ CC = 156˚, CC = 48˚, and θ CN = 92˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth units (Type 4 & 1 molecule) are represented by and 107 

Figure 5.6a Gibbs free energy distribution for the (010) surface as a function of θ CC and

CC at θ CN = 116˚ (corresponding to the growth unit; Type 3 molecule in

Figure 5.1 and Table 5.2, with θ CC = 99˚, CC = 110˚, and θ CN = 116˚) The

contour plot shown corresponds to the Gibbs free energy surface in the 3D plot The growth unit (Type 3 molecule) is represented by 108 

Figure 5.6b Gibbs free energy density distribution for the (011) surface as a function of

θ CN and CC at θ CC = 156˚ (corresponding to the growth unit; Type 4

molecule in Figure 5.1 and Table 5.2, with θ CC = 156˚, CC = 48˚, and θ CN = 92˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth units (Type 4 & 1 molecule) are represented by and 109 

Figure 5.7 A snapshot indicating the existence of hydrogen bonding between a molecule

of Type 2 on the (011) surface and with a molecule in the interfacial region

on the solution side This figure is the same as the expanded portion of Figure 5.2(b) Blue: Nitrogen; Metalic Aqua: Carbon; Red: Oxygen; Light Gray: Hydrogen All the other molecules (including the molecules in the background in this two-dimensional projection) are in shadow Water molecules are not shown 112 

Figure 5.8 Comparison between the experimental and the predicted morphology of

glycine in aqueous solutions (A) Morphology of glycine crystal in aqueous solution predicted from simulations (this work) (B) Experimentally observed morphology of glycine in aqueous solutions (Poornachary et al 2008) (C) Morphology predicted by attachment energy theory (Poornachary

Figure 6.3 Typical snapshots of the crystal/solution interface of an α-glycine crystal

from the simulations (a) (010) plane (b) (011) plane Glycine molecules in the solution and at the interface are shown balls and sticks in blue Water and methanol molecules are indicated by blue and green sticks, respectively 124 

Figure 6.4 Density profiles for crystalline glycine, glycine in solution and water

molecule as a function of distance from (a) (010) plane and (b) (011) plane 125 

Figure 6.5a Probability density distribution for the (010) surface as a function of θ CN and

CC at θ CC = 99˚ (corresponding to the growth unit; Type 3 molecule with

θ CC = 99˚, CC = 110˚, and θ CN = 116˚) The contour plot shown corresponds

to the probability surface in the 3D plot The growth unit (Type 3 molecule)

is represented by 128 

Figure 6.5b Probability density distribution for the (011) surface as a function of θ CN

and CC at θ CC = 156˚ (corresponding to the growth unit; Type 4 molecule

with θ CC = 156˚, CC = 48˚, and θ CN = 92˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth units (Type 4 & 1 molecule) are represented by and 129 

Figure 6.6a Gibbs free energy distribution for the (010) surface as a function of θ CN and

CC at θ CC = 99˚ (corresponding to the growth unit; Type 3 molecule with

θ CC = 99˚, CC = 110˚, and θ CN = 116˚) The contour plot shown corresponds

to the Gibbs free energy surface in the 3D plot The growth unit (Type 3 molecule) is represented by 130 

Figure 6.6b Gibbs free energy density distribution for the (011) surface as a function of

θ CN and CC at θ CC = 156˚ (corresponding to the growth unit; Type 4

molecule with θ CC = 156˚, CC = 48˚, and θ CN = 92˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth units (Type 4 & 1 molecule) are represented by and 131 

Figure 6.7 Comparison between the predicted morphologies in solutions: (A)

Morphology of glycine crystals in aqueous solutions predicted from simulations (Gnanasambandam and Rajagopalan 2010; Gnanasambandam and Rajagopalan 2010 (Accepted for publication)) and (B) Morphology of glycine crystals in methanol/water mixtures predicted from simulations 134 

Figure A.1 Probability density distribution for the (010) surface as a function of θ CC and

θ CN atCC = 110˚ (corresponding to the growth unit; Type 3 molecule in

Figure 5.1 and Table 5.2, with θ CC = 99˚, CC = 110˚, and θ CN = 116˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth unit (Type 3 molecule) is represented by 160 

Figure A.2 Probability density distribution for the (010) surface as a function of θ CN

andCC at θ CC = 99˚ (corresponding to the growth unit; Type 3 molecule in

Figure 5.1 and Table 5.2, with θ CC = 99˚, CC = 110˚, and θ CN = 116˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth unit (Type 3 molecule) is represented by 161 

Figure A.3 Probability density distribution for the (011) surface as a function of θ CN and

θ CC at CC = 48˚ (corresponding to the growth unit; Type 4 molecule in

Figure 5.1 and Table 5.2, with θ CC = 156˚, CC = 48˚, and θ CN = 92˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth units (Type 4 & 1 molecule) are represented by and 162 

Figure A.4 Probability density distribution for the (011) surface as a function of θ CC and

CC at θ CN = 92˚ (corresponding to the growth unit; Type 4 molecule in

Figure 5.1 and Table 5.2, with θ CC = 156˚, CC = 48˚, and θ CN = 92˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth units (Type 4 & 1 molecule) are represented by and 163 

Figure A.5 Gibbs free energy distribution for the (010) surface as a function of θ CC and

θ at  = 110˚ (corresponding to the growth unit; Type 3 molecule in

Figure 5.1 and Table 5.2, with θ CC = 99˚, CC = 110˚, and θ CN = 116˚) The contour plot shown corresponds to the Gibbs free energy surface in the 3D plot The growth unit (Type 3 molecule) is represented by 164 

Figure A.6 Gibbs free energy distribution for the (010) surface as a function of θ CN and

CC at θ CC = 99˚ (corresponding to the growth unit; Type 3 molecule in

Figure 5.1 and Table 5.2, with θ CC = 99˚, CC = 110˚, and θ CN = 116˚) The contour plot shown corresponds to the Gibbs free energy surface in the 3D plot The growth unit (Type 3 molecule) is represented by 165 

Figure A.7 Gibbs free energy density distribution for the (011) surface as a function of

θ CN and θ CC at CC = 48˚ (corresponding to the growth unit; Type 4 molecule

in Figure 5.1 and Table 5.2, with θ CC = 156˚, CC = 48˚, and θ CN = 92˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth units (Type 4 & 1 molecule) are represented by and 166 

Figure A.8 Gibbs free energy density distribution for the (011) surface as a function of

θ CC and CC at θ CN = 92˚ (corresponding to the growth unit; Type 4 molecule

in Figure 5.1 and Table 5.2, with θ CC = 156˚, CC = 48˚, and θ CN = 92˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth units (Type 4 & 1 m molecule) are represented by and 167 

List of Tables

Table 4.1 Mulliken atomic charges of zwitterionic glycine 69 

Table 4.2 Charge models tested for solubility and lattice energy calculations 71 

Table 4.3 Glycine/Water mixtures simulated in the solution environmenta 72 

Table 4.4 MD Parameters for the simulation of the solution environment 73 

Table 4.5 Comparison of densities from simulations (this work) and experiments

(Dalton and Schmidt (1933)) 77 

Table 4.6 Hydration numbers of carboxylic and amino groups of the glycine molecule 81 

Table 4.7 Self-diffusion coefficients of glycine and water from simulations (this work)

and experiments (Krynicki et al 1978; Ma et al 2005; Wu et al 2006) 83 

Table 4.8 Diffusion coefficients of water (105 cm2/s) in the x, y, and z -directions over

the (010) surface of -glycine crystal 89 

Table 5.1 Glycine/water mixtures for the crystal/bulk solution 97 

Table 5.2 The orientations of glycine molecules in a unit cell 101 

Table 5.3 Molecular level crystallographic properties for the relative growth rate on the

(010) and (011) planes of glycine crystal 111 

Table 5.4 Solvent-dependent properties and relative growth rate for the (010) and (011)

planes of glycine crystal 111 

Publications and Conferences

Journal Publication:

1 Gnanasambandam, S., Z Hu, Jianwen J and R Rajagopalan (2009) "ForceField for Molecular Dynamics Studies of Glycine/Water Mixtures in Crystal/Solution

Environments" J Phys Chem B 113(3): 752-758

2 Gnanasambandam, S and R Rajagopalan (2010) "Growth Morphology of α-Glycine Crystals in Solution Environments: An Extended Interface Structure Analysis"

CrystEngComm.12(6):1740-49

3 Gnanasambandam, S., Enemark, S and R Rajagopalan (2011) "First-Principle Prediction of Crystal Habit in Mixed Solvents: α-Glycine Crystals in Methanol/Water Mixture” CrystEngComm.DOI:10.1039/COCE00614A

4 Enemark, S., Gnanasambandam, S., and R Rajagopalan “The Number of Glycine Dimers Depends on Solution: Glycine in Water and in a Water-Methanol Mixture” (in

Symposium, National University of Singapore, Sep 6

2 Gnanasambandam, S and R Rajagopalan (2008) Selection of Force Field for Pharmaceutical Crystal Growth Studies, ISPE Singapore Conference, Student Poster

Competition, SUNTEC Singapore, June 2

3 Gnanasambandam, S., Jianwen, J and R Rajagopalan (2009) Effect of Solvent on the Morphology of Pharmaceutical Crystals, ISPE Singapore Conference, Student Poster

Competition, SUNTEC Singapore, June 1

4 Gnanasambandam, S., Jianwen, J and R Rajagopalan (2009) Growth Morphology of Alpha Glycine crystals in Aqueous Solutions: A Computational Study, ICMAT-IUMRS-ICA, SUNTEC Singapore, June 30

5 Gnanasambandam, S and R Rajagopalan (2009) Effect of Solvent on the Morphology

of α-Glycine Crystals: An Interface Structure Analysis, British Association for Crystal

Growth (BACG), Bristol, United Kingdom, Sep 6

6 Gnanasambandam, S and R Rajagopalan (2010) Prediction of Morphology of Glycine Crystals in Different Solvent Environments: A Computational Study, Annual

α-Graduate Student Symposium, National University of Singapore, Jan 28

1 Introduction

_

Organic crystals are ubiquitous in industry either as final products or as intermediates in

specialty chemicals, pharmaceutical and personal care industries The shape and

morphology of such crystals often determine the desired properties of products The

objective of the present work is to develop a computational method to predict crystal

morphology as a function of the solvent and impurities or cosolvents starting from

intermolecular forces and molecular architecture of the crystallizing solute The

importance of crystal morphology in industry, the role of the solvent in determining the

morphology of crystals, the current approaches used for morphology prediction, the

choice of the material chosen here for study and the research objectives are described

briefly in the following sections of this chapter The concluding part of the chapter

presents an outline of the overall organization of the thesis and serves as a preamble to

the rest of the thesis

1.1 Importance of Crystal Morphology in Practice

As noted above, industrial products are often crystalline; hence, in order to tailor the

shape and size of materials as a function of molecular architecture and solvent properties,

prediction and control of the crystal habit in terms of the above properties has been the

cornerstone of the crystallographic community Methods to manipulate and control

crystal growth often labeled as “crystal engineering”, a term introduced by Schmidt

(Schmidt 1971) for depicting the molecular packing arrangement in photodimerization,

have benefited from developments in physics and chemistry and have evolved towards the possibilities of designing organic (and inorganic) solids with the desired chemical and physical properties An understanding of crystal structure and shape allows the crystal designer to examine the crystal chemistry which ultimately governs the key industrial relevant properties such as particle flow, filtration rate, agglomeration, fragmentation, and attrition (Berkovitch-Yellin 1985) An off-shoot of crystal engineering is “surface engineering”, which has prospective applications in catalysis, where catalytic activities are controlled through different index faces (Snyder and Doherty 2007)

Considerable research and progress on drug formulation has been evident in pharmaceutical industries, in which crystalline products are developed through control and prediction of crystal shape About 90% of the drugs with the molecular mass typically in the range of 200 – 600 g/mol are isolated as crystalline products(Variankaval

et al 2008) In the formulation of drugs, crystallization offers many advantages, such as, easy isolation, better impurity rejection, improved handling characteristics, etc, and provides better chemical and physical stability to the drugs in both processing and post processing stages The morphology of a crystal is of very high importance in drug industries for another reason; the crystal morphology can have enormous impact on the properties of potential drugs (Coombes et al 2002) In the production stage, there can be considerable problems if the morphology of the crystal changes due to impurities or changes of solvent In storage, crystals that allow maximum packing and do not cause problems with caking will be most viable as potential drugs The crystal form, shape and size of the active pharmaceutical ingredient (API) have an impact on the performance of the drugs, and drug design is enhanced through effective control of solvents and

additives, which, in turn, paves the way for better pharmaceutical products For example, Tedesco et al (Tedesco et al 2002) demonstrated the effect of polar and non-polar solvents on the size of the crystallites in a recent drug for asthma treatment Another interesting problem in the pharmaceutical industry is the issue polymorphism (Lommerse

et al 2000) The different polymorphic forms of a given compound generally have significantly different physical properties such as solubility, bioavailability, crystal habit, crystal size, color, etc Hence, there is a need for predicting polymorphic forms so as to avoid those forms that impede the retention of the drug properties during the drug’s useful shelf-life

1.2 Role of Solvent in Defining the Morphology of Crystals

The effects of the environment on crystal shape have received considerable attention for centuries The ability of a compound to crystallize in various shapes with distinct internal crystal structure is determined by solid-state physics and chemistry and the nature of external conditions such as the type of solvent, the level of supersaturation, and the impurities (Bisker-Leib and Doherty 2001)

(a) (b)

Fig r 1.1.Morp olo y of ure crystals n (a) an aq eo s solut o an (b) n methan l

For example, urea crystals in an aqueous solution have a needle-like morphology whereas in methanol solutions they assume a plate-like structure (Piana et al 2005), as shown in Figure 1.1 This illustrates the effect of solvent on the shape and size of crystals

Modification of the crystal habit using a change of solvent or using a mixture of solvents is an effective method to change the dissolution behavior and improving the bioavailability of less soluble drugs (Lee and Myerson 2006) In such cases, using a mixture of solvents is more advantageous than using a pure solvent, since the use of a mixture of solvents enhances the degree of supersaturation and increases the crystal yield (Lee and Hung 2008)

Ibuprofen is a classical example that illustrates the importance of solvent in changing the crystal shape Ibuprofen is a well-known and effective anti-inflammatory compound Commercially, ibuprofen is crystallized in hexane or heptanes as rod-like or needle-shaped crystals as shown in Figure 1.2 The resulting shape (needle or rod) has a major impact on the characteristics of ibuprofen tablets The shape enhances the tendency of ibuprofen to stick to the faces of the tablet punches and dies (tablet compression machine parts) during compression and cap or laminate in the die during decompression Further, it reduces flowability during the process

When the same compound is crystallized in 40 % methanol/water mixture, the shape is equant (cube, sphere or grain) The aspect ratio is about 4:1 in methanol solutions whereas in heptane, it is 6:1 or greater The crystallized ibuprofen (equant shape) has excellent flow characteristics, larger particle size and low bulk volume

Further, it has a good dissolution rate, increased bulk density and reduced sublimation rate and hence promotes better compaction or bonding properties As a result, a more cost-effective manufacturing process can be developed by reducing the downtime of pharmaceutical production that may be caused by compressing problems (sticking and lamination) Further, equat shape of a crystal requires less formulation time, handling and eliminating energy cost required in the drying operations (Gordon and Amin 1984)

(a) (b)

(c)

Fig r 1.2.P otomicro rap s of b profen crystal z d f om (a) methan l (b) hexane solut o an (c)

The underlying fact is that the solvent has the potential to change the dimension of the evolving crystal The role of solvent in directing the morphological development of crystals remains elusive despite the advances in crystallization techniques Hence, the focus of the present research described in this thesis is to initiate a program on deciphering the nature of crystal growth from solutions and the effects of solvent on morphology

1.3 Approaches to Predict the Morphology of Crystals

Crystal growth is defined as a transition from a fluid to a solid phase Two conventional methodologies have been in practice to relate crystal lattices with crystal morphology One is based on thermodynamic considerations to establish the equilibrium form of a crystal, while the other relies on kinetics in defining the growth form of a crystal The equilibrium approach (Bennema and Gilmer 1973) is based on the surface free energy of the faces (Coombes et al.) However, calculating surface free energies of the crystallographic orientations is difficult due to a lack of sufficient knowledge of the solid/fluid interfaces.We focus here on calculating relative growth rates using molecular dynamics (MD) simulations in combination with certain thermodynamic formulations in order to obtain the crystal morphology

Crystal growth processes and subsequent morphology prediction are too complex for a completely analytical description, and it is therefore often necessary to resort to simulations In this respect, molecular dynamics (MD) is a versatile technique for exploring the possible processes of the crystal growth Therefore, we have chosen molecular dynamics simulations to identify and extract molecular level information of the crystal/fluid interface Since the crystal/fluid interface is the region between the growing

crystal phase and the solution environment, the structural details of the interface has a major impact on the growth kinetics The information obtained from simulations then forms the basis for subsequent analysis of the growth rate for a particular crystallographic face Note that the growth rate may differ for different crystallographic faces depending

on the surface-solvent interactions, and this impacts crystal morphology

1.4 Selection of Glycine as a Model to Study the Crystal Morphology

We have selected glycine (H2NCH2COOH) to investigate the effect of solvent on crystal shape and the resulting morphology because of glycine’s wide use as a therapeutic nutrient and excipient Other considerations in support of the choice of glycine are

 simple molecular structure,

 similarity of intermolecular hydrogen bonding with that of protein crystals and

As a simple amino acid, glycine crystallizes as α-polymorphic form in aqueous solutions (Fischer 1905; Bernal 1931; Albrecht and Corey 1939; Marsh 1958), β-form in

a mixture of alcohol and water (Weissbuch et al 2005) and γ-form with changes in the

solution pH (Iitaka 1961), in the presence of additives (Weissbuch et al 2003) and at

other conditions (Hughes et al 2007) in aqueous solutions Polymorphism of glycine crystals in solutions is well studied in the literature (Perlovich et al 2001; Boldyreva et

al 2003; Ferrari et al 2003; Yin et al 2005; Louhi-Kultanen et al 2006; Geo et al 2009) Glycine is zwitterionic (+H3NCH2CO2–) in solid and liquid phases (Takagi et al 1959) and neutral in gaseous phase (Bonaccorsi et al 1984; Raabe 1999) The lattice constants

of α-glycine (Jönsson and Kvick 1972) as shown in Figure 1.3 are well known (a = 5.1054 Ǻ, b = 11.9688 Ǻ, c = 5.4645 Ǻ, α = γ = 90˚ and β = 111.697˚; the unit cell

belongs to monoclinic space group P21/n)

Fig r 1.3.A Representat o for a α-glycine u i c l

Our primary objective is to predict the morphology of glycine crystals grown in solutions Previous theoretical studies on this topic include explorations of the morphology of glycine crystals grown from vapor (Berkovitch-Yellin 1985; Boek et al 1991; Bisker-Leib and Doherty 2003) or solutions (Bisker-Leib and Doherty 2003) In solution-grown crystals, the solvent-solute interactions are critical whereas they become trivial in vapor-

c

b

a

grown crystals The solvent-solute interactions have been taken into account in prior studies, but they are based on highly limiting approximations or assumptions For example, for predicting crystal morphology, assumptions concerning the details of growth units, i.e., the molecules that dock onto the surface (growth unit) of the crystal,

are important The prediction of the morphology is highly dependent on assumptions

concerning the structure or form of the growth units (e.g., whether they are single molecules or dimers or aggregates) (Bisker-Leib and Doherty 2003) An accurate prediction of morphology of the crystals requires a methodology that takes into account solvent-solute interactions, thereby making the assumptions on the growth unit redundant

The computational approach we adopt here overcomes the limitation, arising from

a priori assumptions concerning growth unitand involves two basic steps:

(1) Molecular Scale Characterization of the Interface: Here, we use molecular

dynamics simulations with atomic details and force fields to characterize the crystal/bulk interface

(2) Macroscale Analysis of Growth Rates and Morphology: The information

from the molecular scale calculations are then used for calculating relative growth rates by considering the crystal geometry and the solvent-dependent factors using thermodynamic formulations The interface structure analysis (ISA) developed by Liu and Bennama is implemented to capture the effect of solvent (Liu and Bennema 1994; Liu et al 1995; Liu and Bennema 1996) As ISA as presented by Liu and Bennama does not consider the molecular orientations of the growth units in full, we have

extended the analysis through refined definition of the growth units and have renamed the method as “Extended Interface Structure Analysis (EISA)” Finally, from the relative growth rates, the morphology of crystal

is predicted using Wulff plots1(Wulff 1901)

The above multi-scale approach is schematically illustrated in Figure 1.4 A full molecular scale approach is difficult because of computational demand

Fig r 1.4.A schemat c diagram for morp olo y predict o of glycine crystals.

We employ the above multi-scale approach in this work for exploring the role of solvents on the growth rate of different faces of glycine crystals.Our primary objectives are as follows

1 A Wulff plot is a construction that allows one to determine the equilibrium shape of a crystal In such a

plot, the crystal faces {hkl} are drawn from the center of a crystal at distances proportional to the growth

rates of the respective crystal faces, and the crystal morphology is obtained from the resulting polyhedron

Objective 1: Selection and Testing of Force Field for Glycine/Water Mixtures

Defining a force field for the theoretical predictions of the structure and growth of pharmaceutical crystals is complicated by the intermolecular bonding found in crystals Therefore, our first objective is the choice of force field Here, we test the AMBER ff03 force field (Duan et al 2003) for -glycine molecules using molecular dynamics We validate the force field in both solution and crystal/solution environments The needed atomic charge for glycine is determined using density-functional theory Water is represented through extended simple point charge (SPC/E) model (Berendsen et al 1987)

 In a pure solution environment, simulations have been carried out to determine

the physical and structural properties of glycine, such as solution density, diffusion coefficient, radial distribution functions and hydration number We then compare the simulated results with available experimental values to validate the chosen force field

 In the crystal/solution environment, we calculate the lattice energy and compare it

with available literature results The force field has also been tested to identify the hydrophilic nature of the (010) surface for glycine crystal by calculating the density profile and diffusivity of water layer above the interface

A good agreement between simulation results and experimental data will indicate the applicability of chosen force field for investigation of glycine crystal growth from solutions

Objective 2: Effect of Solvent on the Morphology of Glycine Crystals

As already noted, the solvent has a strong influence on the morphology of glycine crystals However, since currently available theoretical studies do not consider the effects

of solvent, it is not known whether the solvent-solute interactions at the interfaces enhance or inhibit crystal growth Favorable interactions between the solute and the solvent on specific crystal faces will reduce interfacial tension and enhance the crystal growth (Bourne and Davey 1976; Elwenspoek et al 1987; Bennema 1992) Preferential adsorption of solvent molecules on specific crystal faces may delay the removal of solvation layer, in turn delaying the deposition of the next layer and thus inhibiting crystal growth (Berkovitch-Yellin et al 1985; Lahav and Leiserowitz 2001) In order to shed light on these, we employ the multi-scale approach shown in Figure 1.3 to account the effect of solvents on the growth morphology of glycine crystals

 Morphology in Aqueous Solutions

Experimental observations for glycine crystals in aqueous solutions show a bipyramidical shape with (010), (011), (110) and (120) as morphologically important (MI)2 faces For simplicity, we consider the (010) and (011) faces for the growth rate calculations because these two faces are very important to define the overall shape of glycine crystals We first construct crystal/fluid interfaces created by the exposure of the faces to the bulk solution Molecular dynamics simulations are then performed by using the validated force field (see Objective 1) Theextended interface structure analysis is used subsequently to calculate the concentration of molecules about to crystallize on the surface The growth

2 A morphologically important crystal face is a face that occurs at relatively higher frequency compared to other faces during the formation of crystals (Berkovitch-Yellin 1985) It also has a larger area relative to those of others

rate is calculated by considering the crystal geometry and the solution variables Finally, the morphology is predicted and compared with the experimental observations for validation of the approach

 Morphology in a Methanol/Water Mixture

We also examine and predict the morphology of glycine crystals in a mixture of methanol/water solutions (50-50% (v/v)) Experimental observations on glycine crystals grown in a mixture of ethanol/water show a well developed (010) surface (Weissbuch et

al 2005).There is no theoretical or computational work available in the literature on this topic Our work is aimed at providing insights into the role of mixture of solvents in determining the shape and morphology of glycine crystals for the first time

Although crystallization accompanied by various crystal shape and morphology is

a complex phenomenon and the prediction of morphology is based on thermodynamic formulations used in this research is somewhat simplified, the results are expected to further our understanding of the mechanisms behind crystal growth in arbitrary solvents The methodology can be extended to situations where impurities are present, and such an extension is useful from the industrial point of view

1.6 Structure of the Thesis

The thesis is organized as follows A comprehensive literature review of the various crystal growth theories and theoretical models available for the crystal morphology prediction are presented in Chapter 2 This chapter also presents a brief overview of previous experimental and theoretical studies on glycine crystallization Chapters 3 through 6 present the computational methodology and results and a discussion of the

results More specifically, in Chapter 3, thermodynamic formalism behind the determination of the relative growth, interface structure analysis and molecular dynamics used for calculating the interfacial concentrations are elaborated In addition, the extension of the interface structure analysis is also described in this chapter The molecular models used for glycine and water and the simulation methodology for testing the force field in both solution and crystal interface environments are described in Chapter 4, which also includes a discussion of the validation of the force field In Chapter 5, the prediction of morphology of glycine crystals in aqueous solutions is explained, and a comparison with the experimental observations is presented Chapter 6 addresses the prediction methodology for glycine crystals in a methanol-water mixture (50-50% (v/v)) Finally, some of the major conclusions and some recommendations for future work on the effect of impurities are summarized in Chapter 7

2 Literature Review

_

At the turn of the 18th century, crystallization had been widely known as a technique for

separating solid from liquid phase, and the drive towards better understanding of the

fundamentals of crystal growth came into prominence in the 19th century Development

of the thermodynamic theories, largely contributed by the pioneering works of Gibbs,

Arrehenius and Van’t Haff, have been the foundations for the formulation of theories of

nucleation, crystal growth and transport phenomena behind these processes The rates of

nucleation and crystallization in glasses have been the basis for the development of the

nucleation theory The Kossel model advanced in 1927 plays a major role in

understanding the crystal growth mechanism Another effort was made in the same

direction by Stanshi and Kaishew in 1934, who proposed the concept of crystal growth as

units of repeatable steps Further, crystal growth theories gained momentum with the

understanding of the role of screw dislocations in the formation of growth hillocks by

Frank in 1949, the generalized crystal growth theory by Burton, Cabrera and Frank in

1951, density of bonds in the crystal structure by Hartman and Perdok (1955) and facet

formation as a function of enthalpy of fusion by Jackson in 1958 (Scheel 2003) The

following sections describe the crystal growth theories and associated models in detail

The fundamental theories on crystal growth have been dealt in detail in Section

2.2, which outlines crystal growth mechanisms and in Section 2.3, which focuses on