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 ANALYSIS SIVASHANGARI GNANASAMBANDAM (B. Eng. & M. Eng., Annamalai University) A THESIS SUBMITTED FOR THE DEGREE OF PhD DEPARTMENT OF CHEMICAL AND BIOMOLECULAR ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2010 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 a friendly atmosphere. I am gifted in many respects to have earnestly caring father R. Gnanasambandam, ever affectionate mother G. Rajakumari and lovable husband Dr. H. Hariharan. I am grateful to my sister Dr. G. Kalarani and her husband Dr. M. G. Mohan and friends for their ceaseless support and affection. i 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. ii Table of Contents ACKNOWLEDGEMENTS I  SUMMARY VI  NOMENCLATURE IX  LIST OF FIGURES XV  LIST OF TABLES XXII  PUBLICATIONS AND CONFERENCES 1  XXIII  INTRODUCTION 1  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  iii 2.6  Theoretical Studies on Prediction of Morphology of Glycine Crystals . 35  2.6.1  Donnay-Harker Model 35  2.6.2  Attachment Energy Model 36  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  METHODOLOGY FOR CRYSTAL MORPHOLOGY PREDICTION 42  3.1  Introduction: Crystal Growth in Solutions . 42  3.2  Theory for Growth Rates 46  3.3  Interface Structure Analysis (ISA) 51  3.3.1  Limitations of ISA 56  3.4  Extended Interface Structure Analysis (EISA) 57  3.5   Molecular Dynamics (MD) Simulations 59  3.6   Summary 62  4  TESTING OF FORCE FIELD FOR GLYCINE/WATER MIXTURES IN CRYSTAL/SOLUTION ENVIRONMENTS 63  4.1  Introduction: Importance of Force Field 63  4.2  Models and Methodology . 66  4.2.1  Models for Glycine and Water 66  4.2.2 Simulation Methodology 71  4.3  Results and Discussion . 76  4.3.1 Solution Environment 76  4.3.2  Crystal Interface Environment 85  4.4 Summary 90  5  PREDICTION OF Α-GLYCINE CRYSTALS MORPHOLOGY IN AQUEOUS SOLUTIONS 92  5.1  Introduction 92  5.2  In Silico Models for Glycine and Water 95  5.2.1 5.3  Simulation Protocol 95  Results and Discussion . 99  5.3.1   Solution Structure at the Interface iv 99  5.3.2   5.4  6  Relative Growth Rates 110  Concluding Remarks 115  PREDICTION OF Α-GLYCINE CRYSTALS MORPHOLOGY IN METHANOL/ WATER MIXTURES 117  6.1  Introduction: Importance of Solvent in Changing the Crystal Shape 117  6.2  Models and Methodology . 119  6.2.1  6.3  Simulation Protocol 120  Results & Discussions 123  6.3.1  Solution at Interface 123  6.3.2  Relative Growth Rates 132  6.4  7  Concluding Remarks 135  CONCLUDING REMARKS 7.1  137  Conclusions 138  7.1.1  Summary of the Computational Method 138  7.1.2  Conclusions on Force Field 139  7.1.3  Conclusions on Crystal Morphology 140  7.2   Recommendations 142  7.2.1  Improvements in EISA 143  7.2.2  Extending the Methodology to Predict Crystal Morphology in the Presence of Impurities 147  REFERENCES 1  APPENDIX A: 3D PLOTS FOR MORPHOLOGY PREDICTION IN AQUEOUS SOLUTIONS 159  v 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. vi 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. vii  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. viii NOMENCLATURE ABBREVIATIONS API Active Pharmaceutical Ingredient MD Molecular Dynamics MI Morphologically Important BFDH Bravais-Friedel-Donnay-Harker rule BCF Burton-Cabrera-Frank theory 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 ix Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments (a) (b) (c) 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). We followed the same simulation methodology as in the solution environment, but an anisotropic pressure coupling in the y direction was used in this case, because anisotropic coupling is more appropriate than isotropic coupling, for the study of both solid and liquid phases (Piana and Gale 2005). After the energy minimization, the glycine molecules were positionally restrained (Boek et al. 1992) during both the equilibrium and the production steps while we examined the behavior of water at the glycine/water interface at 300 K and atm. Applying positional restraint implies that the mobility of glycine in the crystal (including at the surface) is restrained, and this, in principle, could affect the calculated properties. Nevertheless, Boek et al. (Boek et al. 1994) have already shown, by examining the effect of positional restraint on a urea/water system, the positional restraint has very little influence on the density and diffusivity of water both in the vicinity of the interface and beyond. Therefore, we expect the positional restraint in our case to have a negligible impact on the results. 75 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments 4.3 Results and Discussion We report here the results of the molecular dynamics simulations in the above two environments at 300 K and bar. First, the force field is examined in the solution environment to study the structural details and molecular properties of glycine in solution. Then the force field is tested for the crystal interface environment to check its suitability in investigating crystal growth. 4.3.1 Solution Environment In the case of the solution environment, we compare the simulated density, glycine diffusivity, radial distribution functions and hydration number to experimental data as functions of glycine molar fraction as discussed in detail below. 4.3.1.1 Density The density of the glycine/water mixture as a function of glycine concentration at 300 K is reported in Table 4.5 and plotted in Figure 4.4. Some experimental data (Dalton and Schmidt 1933) available in the literature (at 298 K) for glycine/water mixture are included for comparison. For pure water, Wu et al. (Wu et al. 2006) report the density based on the SPC/E model from molecular dynamics simulations as 0.999 (± 0.017) g/cm3. 76 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments Table 4.5. Comparison of densities from simulations (this work) and experiments (Dalton and Schmidt (1933)) Density (g/cm3) xglycine 0.0020 0.0093 0.0203 0.0329 0.0485 a b simulationa 1.013 1.015 1.026 1.042 1.059 1.079 experimentb 0.998 1.000 1.013 1.031 1.051 1.084 Standard deviation in the simulation is less than 1%. Standard deviation in the experiment is less than 1.5%. The density for pure water from our simulation is 1.013 g/cm3, and differs from experimental value by 0.014 g/cm3, which is within the statistical error (0.017 g/cm3) reported by Wu et al. (2006). With increasing mole fraction xglycine, the density of the mixture increases slightly. It can be seen that the force field used in our simulations predicts the density of glycine-water mixtures well. The agreements between the simulated and experimental densities are good particularly at high xglycine when the contribution from glycine-glycine interaction plays an increasingly important role in the density calculation. The accuracy of the predicted density is sufficient for further use of the selected force field in crystallization studies. 77 Density (x) (g/ml) Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments  Simulations Experiments   LIQUID PHASE        xglycine Figure 4.4. Density comparison between simulated and experimental values. Experimental values are from Dalton and Schmidt (1933). 4.3.1.2 Radial Distribution Functions The radial distribution functions describe how the atoms are distributed radially around each other. Here, they are used to test the ability of the chosen force field to capture the structural features at the atomic level. Figure 4.5 shows the radial distribution functions between the atoms OC, H and N in glycine and the oxygen atom in water (OW). There are two OC atoms (OC1 and OC2) in glycine; therefore, the calculated radial distribution functions for OC were averaged over the two OC atoms. Similarly, for the H atom, the average was taken over the three H atoms H1, H2 and H3. The results show that the locations of the first peaks in the radial distribution functions, denoted here by rOC-OW, rHOW and rN-OW, are 2.71, 2.05 and 2.95 Å, respectively. Each of these represents the position of first hydration shell for the corresponding atom in glycine. These values of 78 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments rOC-OW, rH-OW and rN-OW are in good agreement with the average hydrogen bond distances rO…OW = 2.72 Å, r H…OW ≈ 2.0 Å and rN-H…OW = 2.89 Å reported for various organic crystals (Kuleshova and Zorkii 1981). One may note that, as shown in Figure 4.5, the heights of the peaks decrease slightly with increasing number of glycine molecules, since this increase perturbs the number of water molecules in the hydration shell.  (a) (r)  OC-OW xglycine  g            r (nm) 79   Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments (b)  g H-OW (r)  xglycine              r (nm)    (c) xglycine       g N-OW (r)          r (nm) 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 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments 4.3.1.4 Hydration Number The hydration number of a given molecule is defined as the number of water molecules around that molecule. Table 4.6 gives the hydration numbers of the amino and carboxylic and groups in glycine. At infinite dilution, the hydration numbers are 2.97 and 5.38, respectively, for the amino and carboxylic groups. On average, there are water molecules around the amino group and to 5.5 water molecules around the carboxylic group. This observation represents the more hydrophilic nature of the carboxylic group than the amino group in glycine. Further, the hydration number decreases with the increase in the concentration of glycine. This is attributed to the enhanced solute-solute interactions, which perturb the hydration shell to some extent. Table 4.6. Hydration numbers of carboxylic and amino groups of the glycine molecule xglycine 0.0020 0.0093 0.0203 0.0329 0.0485 COO 5.38 5.12 4.86 4.60 4.28 NH3+ 2.97 2.82 2.70 2.55 2.40 The calculated hydration numbers at infinite dilution agree well with the reported literature values. Kameda et al. (1994) reported water molecules around the amino group from a neutron diffraction measurement with H/D isotopic substitution method and also predicted the number of water molecules around the carboxylic molecule to be about to 4.5 as found in formate (Sasaki et al. 2003). In a Monte Carlo simulation study, Alagona et al. (1988) found 2.3 and 5.3 water molecules around the amino and carboxylic groups, respectively, using the charges obtained from the best fit to the electrostatic 81 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments potential produced by a 6-31G* basis set (Krishnan et al. 1980). Using ab initio molecular dynamics calculations and the BLYP (Becke 1988; Lee et al. 1988) correlation functional, Leung and Rempe (2005) obtained and 4.7 water molecules around the amino and the carboxylic groups, respectively. Campo (2006) found 2.8 and 5.4 water molecules around the amino and carboxylic groups from MD simulations, using the GROMOS96 force field (as noted previously). Thus, the predicted values of hydration numbers in our calculations are very close to the experimental values found in the literature and those computed by independent methods. Therefore, we conclude that the force field chosen here predicts the structural features around the glycine molecules in a solution very accurately. 4.3.1.4. Self-diffusivity of Glycine One of the key transport properties of glycine needed in crystallization studies is the selfdiffusivity. The self-diffusivity D(c) of glycine at a concentration c can be evaluated using the Einstein expression D (c )  lim t   r (t )  r (0)  6t (4.2) where r (t ) is the position of the molecule at time t. The ensemble averaged mean2 squared displacement (MSD) is represented by  r (t )  r (0)  . Figure 4.6 shows the MSDs of pure water and of glycine in mixtures as functions of time. We have determined the diffusivity from the slopes of the MSDs in the time range of 100 ps to 300 ps. These are reported in Table 4.7. 82 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments 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) xglycine 0 0.0020 0.0093 0.0203 0.0329 0.0485 D (105 cm2s1) simulationa experimentb 2.01 2.30 1.39 1.21 0.97 1.03 0.96 0.93 0.98 0.78 0.67  Diffusion coefficients given are those of water. Standard deviation for simulation is less than 1%. b Standard deviation for experiment is 1% (Ma et al. 2005). c Standard deviation for experiment is 5% (Krynicki et al. (1978). a The magnitudes of self-diffusion coefficient of pure water we obtain are in good agreement with the independent simulation result of Wu et al. (Wu et al. 2006), namely, (2.41 ± 0.08)  105 cm2/s, as well as with the experimental value reported by Krynicki et al. (1978), i.e., 2.3  105 cm2/s. For glycine in water, Figure 4.7 shows the comparison between simulated and experimental diffusivities (Ma et al. 2005) as a function of mole fraction of glycine. As seen, the diffusivity of glycine decreases with increasing concentration. In general, the agreement between simulation and experiment improves with the glycine concentration, which shows the accuracy of the force field in predicting the dynamic properties of glycine in solution. (Please note that the value at infinite dilution is difficult to predict precisely statistically as the number of glycine molecules is very small at very low concentrations.) 83 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments  xglycine     Water MSD(nm )          Time (ps) Figure 4.6. Mean-squared displacements of glycine in a solution. The arrow shows the direction of increase in xglycine. Experiments Simulations  5 D (10 cm /sec)   LIQUID PHASE        xglycine Figure 4.7. Comparison between experimental and simulated diffusion coefficients of glycine in solutions. Lines are to guide the eye. 84 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments 4.3.2 Crystal Interface Environment The lattice energy of a crystal is an important property to assess crystal/solution kinetics and equilibrium. We first estimate the lattice energy of -glycine crystal, and subsequently the sublimation enthalpy, which can then be compared with the available experimental values to validate the force field in crystalline environments. In addition to the sublimation enthalpy, we also examine the water density profile close to the crystal/liquid interface in order to provide more information about the nature of the surface for crystal growth studies. Moreover, calculations of diffusivity are also presented. 4.3.2.1 Lattice Energy and Sublimation Enthalpy The lattice energy Ecr is the configurational energy of a molecule in the crystal. An accurate estimation of the lattice energy is very important for crystal growth studies as it determines the transfer of a molecule from a crystal to the solution (dissolution of the crystal) or depositing on a crystal surface from the solution (crystal growth). As the lattice energy cannot be measured directly experimentally, the validity of the force field has to be tested by comparing the theoretical values of the sublimation enthalpy (obtained from the calculated lattice energy) with the experimental sublimation enthalpy (Docherty 1995). The relation between the lattice energy and the sublimation enthalpy is described below. First we note that our calculations for lattice energy lead to a value of 306 kJ/mol, obtained through energy minimization of glycine crystal structure. This value matches well with the simulated value reported by Boek et al. (Boek et al. 1991) (also 85 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments 306 kJ/mol), who used the same Mulliken population analysis for charges, as we do, but with a Double-Zeta plus Polarization (DZP) basis set and Buckingham potential for the nonbonded interactions. Our calculated value is also very close to the value reported by No et al. (No et al. 1994) ( 285 kJ/mol), who used the same Mulliken population analysis for charges but with different basis set (6-31G* basis set). We now compare sublimation enthalpies obtained theoretically with experimental values. The lattice energy and sublimation enthalpy are connected through the protonation of the glycine molecules, which exist in the zwitterionic state in crystals (Takagi et al. 1959) and in the non-zwitterionic in the gas phase (Bonaccorsi et al. 1984). Therefore, during crystallization from the gas phase or during sublimation, a proton is transferred from –NH3+ to –COO and the energy required for this process is called the proton transfer energy Upr, and this needs to be incorporated in the calculation of the enthalpy of sublimation Hsub, as shown in Equation (4.3) below: H sub   E cr  U pr  2RT (4.3) The term 2RT represents a correction for the difference between the vibrational contribution to the crystal enthalpy of 6RT (Hagler et al. 1974) and the gas phase enthalpy (pV + 3RT). Our calculations of Upr using the density functional theory with the BLYP functional and DNP basis set leads to a value of 138.22 kJ/mol and falls within the range of 133 to 178 kJ/mol reported by Voogd et al. (Voogd et al. 1981) for the aliphatic - amino acids. 86 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments Also, Voogd et al. (Voogd et al. 1981) report that the values for Upr of glycine may range from 136.8 kJ/mol to 167 kJ/mol depending on the basis set used for estimating the partial charges. Therefore, the force field we use here leads to a reasonable estimate for Upr. Using the calculated Upr and Ecr in Equation (4.3), we arrive at a sublimation enthalpy of 162.8 kJ/mol, which agrees with the experimental value, 136 kJ/mol reported in the literature (Svec and Clyde 1965) with an experimental error of about  kJ/mol. Slightly higher experimental values have been reported by others (e.g., 145 kJ/mol cited by Boek et al. (Boek et al. 1991) without attribution and 143 kJ/mol by Docherty (Docherty 1995)), but our calculated value does not differ significantly from the experimental values when one considers the experimental and theoretical uncertainties involved. The above observations support the applicability of the chosen force field in crystal growth studies since the calculated sublimation enthalpy is closer to the available experimental data. Moreover, some previous studies in glycine crystals ignored the significance of proton transfer energy in the sublimation enthalpy calculation (BiskerLeib and Doherty 2003), but our calculations emphasize the importance of including the proton transfer energy in calculating sublimation enthalpy of glycine, as also noted by No et al. (No et al. 1994) and Boek et al. (Boek et al. 1991). 4.3.2.2 Density Profile of Water Relative to the Crystal Surface We calculated the density distribution of the water normal to the (010) surface in order to examine the solvent structure relative to the surface. The simulation box is symmetric in the y direction due to periodic boundary conditions and crystal symmetry. Crystalline 87 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments glycine molecules are located in the range from to 3.5 nm in the y direction. The density was calculated by dividing the simulation box into thin slices, each with a thickness of 0.3 nm in the y direction and plotted against the distance as shown in Figure 4.8.  Density (y) g/cm      CRYSTAL-LIQUID PHASE     y (nm)   Figure 4.8. Water density profile in the y-direction, normal to the (010) surface of the -glycine crystal. The density profile obtained reveals a strong peak near the interface, and this peak is then followed by a small peak away from the surface. Further, the local density reaches the bulk density quickly as one move away from the interface. The heights and the positions of the density oscillations in the vicinity of the crystal interface are insensitive to the changes in the bulk density, and therefore the density peaks can be safely described as corresponding to the adsorption of water at the interface, thereby indicating that the (010) surface of the glycine crystal is hydrophilic. This result provides essential 88 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments information for carrying out crystal growth studies on the (010) surface, and such information can be useful for finding the effect of solvent on this surface. 4.3.2.3 Water Diffusivity Because of the interaction of a water molecule with the crystal surface, it is expected that the mobility of water would depend on the distance from the crystal surface. In order to examine the influence of the interface on the diffusivity of water, we divide the “water bath” over the crystal surface into four layers, as indicated in Figure 4.8. Layer is the closest to the (010) surface, followed by layers 2, and bulk. Figure 4.9 shows the meansquared displacements of the water molecules in layer 1. As seen, the displacement in the y direction reaches a plateau after approximately ps, indicating the relatively marginal mobility of water normal to the surface in the vicinity of the crystal surface. In contrast, the displacements in x and z directions, which are parallel to the surface, are far greater. 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 Layer Layer Layer Layer Bulk Dx 0.341 0.991 1.650 2.211 Dy 0.018 0.028 0.065 1.878 Dz 0.298 0.982 1.606 2.212 Dxz 0.320 0.989 1.629 2.211 Note: Dxz denotes the diffusion coefficient in xz plane. The diffusivities calculated from Figure 4.9 are listed in Table 4.8. As evident from Table 4.8 (or, equivalently, from Figure 4.9), we observe that in all the layers Dxz = D|| (parallel to the surface) is larger than Dy = D (perpendicular to the surface). The 89 Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments magnitude of diffusivity increases when going from layer to 3, and the difference is smaller in the parallel and normal directions.  MSD (nm )   MSDx MSDy MSDz MSDxz         Time (ps) 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). Finally, as one moves away from the interface, one recovers the diffusivity of bulk water. The diffusivity calculation again supports the hydrophilic nature of the (010) surface of glycine crystal as observed through the density profile of water. 4.4 Summary We have examined, using molecular dynamics simulations, the suitability of the AMBER ff03 force field and partial charges based on density-functional theory to investigate glycine/water mixtures in both the solution and crystal interface environments. In the solution environment, the chosen force field predicts the physical properties such as 90 [...]... morphologies in solutions: (A) Morphology of glycine crystals in aqueous solutions predicted from simulations (Gnanasambandam and Rajagopalan 2 010 ; Gnanasambandam and Rajagopalan 2 010 (Accepted for publication)) and (B) Morphology of glycine crystals in methanol/water mixtures predicted from simulations 13 4  Figure A. 1 Probability density distribution for the ( 010 ) surface as a function of θCC and θCN atCC... 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 11 3(3): 752-758 2 Gnanasambandam, S and R Rajagopalan (2 010 ) "Growth Morphology of α -Glycine Crystals in Solution Environments: An Extended Interface Structure Analysis" CrystEngComm .12 (6) :17 40-49 3 Gnanasambandam, S., Enemark,... 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,... 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 xxiii 6 Gnanasambandam, S and R Rajagopalan (2 010 ) Prediction of Morphology of Glycine Crystals in Different Solvent Environments: A Computational Study, Annual Graduate Student Symposium, National... S and R Rajagopalan (2 011 ) "First-Principle Prediction of Crystal Habit in Mixed Solvents: α -Glycine Crystals in Methanol/Water Mixture” CrystEngComm.DOI :10 .10 39/COCE00 61 4A 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 preparation) Conferences: Best Poster Runner Up and Fourth position in. .. the a- axis; (b) Morphology grown in aqueous solutions; and (c) Morphology grown in methanol:water solutions (Lahav and Leiserowitz 20 01) 30  Figure 2.9 Scheme for the relay mechanism (Lahav and Leiserowitz 20 01) 31 Figure 2 .10 Packing arrangement of (R,S) analine by crystal faces (Lahav and Leiserowitz 20 01) 31 Figure 2 .11 Schematic representations of the (0 01) 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 20 01) 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 19 85, (b) Boek et al 19 91, and (c) Poornachary et al 2007 34  Figure 2 .14 BFDH model of glycine crystals. .. (2008 & 2009) 1 Gnanasambandam, S., Hu, Z., Jianwen, J and R Rajagopalan (2007) A Computational Study on α -Glycine Zwitterion- Water Mixtures, Annual Graduate Student 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... Table 5.2 The orientations of glycine molecules in a unit cell 10 1  Table 5.3 Molecular level crystallographic properties for the relative growth rate on the ( 010 ) and ( 011 ) planes of glycine crystal 11 1  Table 5.4 Solvent-dependent properties and relative growth rate for the ( 010 ) and ( 011 ) planes of glycine crystal 11 1  xxii Publications and Conferences Journal Publication: 1. .. (Weissbuch et al 2005) 11 8  Figure 6.2 Representation for a methanol molecule Label: Red-Oxygen, Cyan-Carbon and White-Hydrogen 12 0  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 . GROWTH MORPHOLOGY OF α -GLYCINE CRYSTALS IN SOLUTIONS: AN EXTENDED INTERFACE STRUCTURE ANALYSIS SIVASHANGARI GNANASAMBANDAM (B. Eng. & M. Eng., Annamalai University) A. Comparison between the predicted morphologies in solutions: (A) Morphology of glycine crystals in aqueous solutions predicted from simulations (Gnanasambandam and Rajagopalan 2 010 ; Gnanasambandam. 31 Figure 2 .10 . Packing arrangement of (R,S) analine by crystal faces (Lahav and Leiserowitz 20 01) . 31 Figure 2 .11 . Schematic representations of the (0 01) face of (R,S) alanine during crystal growth: