Growth morphology of a glycine crystals in solutions an extended interface structure analysis 2

Testing of Force Field for Glycine/Water Mixtures in Crystal/Solution Environments density and diffusivity and structural properties such as the radial distribution functions and hydration number in good agreement with data available in the literature In the crystal interface environment, the calculated lattice energy and proton transfer energy agree well with previously reported computational results The calculated sublimation enthalpy is also predicted within experimental errors Most importantly, the force field is able to elucidate the nature of the crystal surface (namely, that it is hydrophilic), based on the calculation of the solvent density profile relative to the crystal interface and the solvent diffusivity in the vicinity of the interface Hence, we conclude that the chosen force field is suitable to describe glycine molecules in the solution as well as in the crystalline environments In addition, the results lend confidence to the practical use of the force field in further study of glycine crystal growth from aqueous solutions and methanol/water mixture Using the validated force field from the present study, the growth of glycine crystals in solutions will be studied using the methodology (relative growth rate form EISA) proposed in Chapter The details follow in the next two chapters 91 Prediction of α-Glycine Crystals Morphology in Aqueous Solutions _ 5.1 Introduction As emphasized in Chapter 1, prediction of crystal morphology is essential in the drug development process to reduce cost and time involved A prior knowledge about the crystal shape in a particular solvent can enhance the solvent screening process for the drug manufacturing in a more effective manner This chapter provides a methodology for predicting the shape of glycine crystals in aqueous solutions Glycine crystals formed in an aqueous solution have a bipyramidical shape with (020), (110), (120) and (011) faces as morphologically important faces (Boek et al 1991; Li and Rodriguez-Hornedo 1992; Bisker-Leib and Doherty 2003; Poornachary et al 2008) The experimentally observed aspect ratio (c/b) is 2.62 ± 0.5 for the crystals grown in aqueous solutions (Poornachary et al 2008) The crystal structure of α-glycine comprises of a bilayer arrangement of molecules Each glycine molecule displays a strong N-HO hydrogen bonding interactions with the molecules in the same layer along the c-axis and also interacts with molecules in the neighboring layer of a bilayer through a centrosymmetric double-hydrogen bonded motif, and these dimers are stacked along the b-axis through C-HO interactions 92 Prediction of α-Glycine Crystals Morphology in Aqueous Solutions The crystal morphology of glycine has been studied using computational methods in the past as discussed in detail in Chapter Using a semi-empirical method, Berkovitch-Yellin (Berkovitch-Yellin 1985) predicted a morphology that resembled the shape obtained from vapor, but it showed a distinct difference from the shape grown in aqueous solutions Specifically, the major differences found between theoretically predicted and experimentally observed morphologies are (i) the presence of the (001) and (101) faces in the theoretical predictions (in contrast to their absence in experiments), and (ii) the areas of the (010) and (011) faces For example, crystals obtained in experiments have much larger areas for the (010) face compared to the theoretical predictions The opposite is found in the case of the (011) face To make further improvements in the prediction, Boek et al (Boek et al 1991) developed a relation between electron density distributions in glycine molecules and crystal morphology A systematic approach was followed to predict the morphology of the crystals with PBC analysis, Ising model and attachment energy models Boek et al (Boek et al 1991) explored the crystal morphology with three different charge models and emphasized the need for including proton transfer energy in the energy calculations In the case of glycine, the proton transfer energy is defined as the energy needed to transfer a proton from the –NH3+ group to the –COO group Interestingly and fortuitously, the theoretical morphology predicted by this method resembles that of crystals grown in an aqueous solution (although no solution environment is considered in the approach used), in contrast to the morphology expected from crystal growth through sublimation Recently, further improvements have been made by Bisker-Leib and Doherty (Bisker-Leib and Doherty 2003), who conducted an elaborate study on glycine crystal morphology using attachment energy calculations 93 Prediction of α-Glycine Crystals Morphology in Aqueous Solutions The resulting morphology had a shape similar to what was observed in experiments but the aspect ratio (b/c) was greater than seen in experiments The increase in the aspect ratio is due to the effect of solvent-solute interactions, which are not considered in the attachment energy calculations Bisker-Leib and Doherty (Bisker-Leib and Doherty 2003) also extended the work for including the effect of solvent in the energy calculations The model assumed the growth unit as a dimer or as a combination of a dimer and a monomer in predicting the morphology of the crystal The predicted shape was an elongated box with tilted edges and was very close to the experimental morphology The disadvantage of this method is that the model relies on the assumption that the growth unit is either a monomer or a dimer As noted in Chapter 3, the main objective of the present work is to predict morphology of glycine crystals in a systematic way by considering the effect of the solvent explicitly on the structure of the liquid/crystal interface (and hence on the crystal growth rates) and, in addition, without any a priori assumptions about what constitutes a growth unit We determine the relevant “internal factors” such as interplanar distance, coordination number and crystallographic orientation factor based on the crystal geometry and intermolecular interactions for the morphologically important faces (which are obtained using periodic bond chain analysis (Boek et al 1991)), and we determine “external factors” or “environmental factors” such as the density distributions of the solute in the vicinity of the interface, molecular orientations and corresponding free energies of the solutes that form growth units, concentrations of growth units at the interface, etc., using a combination of molecular dynamics and extended interface structure analysis for predicting the relative growth of the morphologically important 94 Prediction of α-Glycine Crystals Morphology in Aqueous Solutions faces Then, the relative growth rate is used to evaluate the morphology using Wulff plots (Wulff 1901) This chapter is organized as follows Section 5.2 outlines the molecular models for glycine and water and details about the simulation setup and protocols for MD simulations The results obtained from the simulations are discussed and compared with experimental morphology of glycine crystals in aqueous solutions in Section 5.3 Finally a summary of observations is presented in Section 5.4, along with relevant concluding remarks 5.2 In Silico Models for Glycine and Water The tested and validated force field and the partial charges as discussed in Chapter are used for glycine/water molecules (Gnanasambandam et al 2009) MD simulations have been performed using Gromacs package (Van der Spoel et al 2005), for the morphologically important (010) and (011) faces of the crystals 5.2.1 Simulation Protocol The simulation system, which consists of a crystal immersed in a saturated solution, is constructed in two steps, one for constructing a crystal slice with the chosen Miller plane exposed to the outside and another for creating the saturated solution These two are then incorporated into the simulation box First, in order to study a particular crystal surface [i.e., (010) and (011)], we take a unit cell and cut it to expose the surface of interest as shown in Figure 5.1 The molecules in the unit cell are numbered as per the pdb file obtained from the Cambridge Structural 95 Prediction of α-Glycine Crystals Morphology in Aqueous Solutions Database The exposed surface is then re-oriented so that it forms the x-z plane of the simulation box (with the y-direction being normal to the surface), and additional unit cells (full or spliced, as needed) are added to fill in the required portion of the simulation box, as described further below (a) b y a z c x (b) m z n l y x 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 (b) (011) surface indicated by broken red line and the surface exposes molecule types and 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, CyanCarbon and White-Hydrogen For the (011) surface, the modified unit cell has the dimension of l = 13.157 Å, m = 7.757 Å, n = 5.105 Å, α’= 90˚, β’ = 81.17˚ and γ’ = 90˚ The final dimensions of the 96 Prediction of α-Glycine Crystals Morphology in Aqueous Solutions crystal/fluid interfaces are given in Table 5.1 The (010) surface is constructed in such a way that the group exposed to the solvent is –CH2, as dictated by the experimental observation found in the literature (Gidalevitz et al 1997) The lower part of the box consists of the crystal, with a thickness of at least 3.5 times the cut-off distance taken for the intermolecular interactions The rest of the box is then filled with a saturated solution, constructed as follows Table 5.1 Glycine/water mixtures for the crystal/bulk solution Plane (010) (011) No of glycine molecules in the crystal No of glycine molecules in the solution No of water molecules Dimensions of the simulation box (Ǻ) 560 672 206 373 1931 x: 40.84 y: 85.90 z: 35.54 3544 x: 52.63 y: 102.08 z: 35.31 The saturated bulk solution is prepared by randomly adding glycine and water molecules in the simulation box, and the mole fraction of glycine in the bulk solution is set at a value of 0.096 MD simulations are carried out in the isothermal-isobaric (NPT) ensemble using Gromacs, with periodic boundary conditions applied in the three directions The solution is coupled to a Berendsen thermostat at 298 K and a Berendsen barostat at atm with a relaxation time of ps An anisotropic pressure coupling in the ydirection is applied to the system The time step for the simulation is fs The particlemesh Ewald (PME) method is used for treating the long-range electrostatic interactions with a cutoff radius of 0.9 nm For Lennard-Jones interactions, the cutoff is taken to be 97 Prediction of α-Glycine Crystals Morphology in Aqueous Solutions nm The bulk solution is initially subjected to energy minimization for 400 steps Thereafter, the velocities of all molecules including glycine and water are assigned according to the Boltzmann distribution at 100 K Then the system is heated up and equilibrated for ns, and an additional NPT simulation (anisotropic pressure coupling in the y-direction) of ns is performed The saturated bulk solution thus obtained is then added to the box with the crystal slice The numbers of crystalline and solute glycine molecules used in the simulations are listed in Table 5.1 The simulation parameters are same as that of bulk solution for simulation systems consisting of both solid and bulk glycine molecules The following steps are carried out for the systems with both crystalline glycine molecules and bulk glycine molecules during the course of the simulations First, an energy minimization is done by applying position restraint on glycine molecules for the initial adjustment of solvent molecules at the interface Then, anisotropic NPT equilibration is carried out at 100 K and bar by applying position restraint on glycine molecules for 500 ps This is followed by another anisotropic NPT equilibration for 500 ps but at room temperature (298 K) and bar The reason for employing pressure coupling in short simulations is to relax the molecules at the interface without perturbing the geometry of crystal (Boek et al 1994) Then, the simulation is continued by switching to the NVT ensemble at 298 K An equilibration simulation is carried out by positionally restraining the glycine molecules for 500 ps and followed by a 10 ns production run without position restraint on the glycine molecules The molecular trajectories from the production run are then recorded for further analysis to obtain the effective concentration of growth units 98 Prediction of α-Glycine Crystals Morphology in Aqueous Solutions 5.3 Results and Discussion We present the results of the above described calculations of crystal growth and discuss our results and predictions in the context of experimental results and an earlier theoretical prediction available in the literature As noted in Section 5.1, the effects of solvent are fully accounted for the first time for glycine, and MD simulations are used to identify the interfacial region and the growth units and to predict the growth of the morphologically important (010) and (011) faces The overall approach is as follows First, we calculate the solute (glycine) density profiles normal to the morphologically important faces to locate the boundaries of the interfacial region and then determine the orientations of interfacial solute molecules The effective concentrations of the growth units are determined using EISA, following which the growth rates of the faces are determined This information is then used in the Wulff construction to predict the morphology In addition, we also compare our results with predictions based on an alternative theoretical approach available in the literature (based on attachment energy calculations) and shows that the extended interface structure analysis presented here provides better predictions (i.e., close to what is observed experimentally) 5.3.1 Solution Structure at the Interface We begin with a visual examination of the crystal/solution interfaces Typical snapshots of the (010) and (011) faces at the end of a 10-ns MD simulation are shown in Figure 5.2 First, one notices that the molecules in the crystal are somewhat disordered in the vicinity of the interfaces due to thermal vibrations, as one would expect 99 Prediction of α-Glycine Crystals Morphology in Aqueous Solutions (a) Interfacial layer Bulk Crystal (b) 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 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VDI Berichte B-8: 325-329 158 Appendix A: 3D Plots for Morphology Prediction in Aqueous Solutions 159 p ×    0.0 0.1 0.2 0.3     Co s  CN                  CC  os C Figure A.1 Probability density distribution for the (010) surface as a function of θCC and θCN atCC = 110˚  (corresponding to the growth unit; Type molecule in Figure 5.1 and Table 5.2, with θCC = 99˚, CC = 110˚, and θCN = 116˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth unit (Type molecule) is represented by 160  p ×   0.0 0.4 0.8 1.2       CC   (de  g)               CN  os C Figure A.2 Probability density distribution for the (010) surface as a function of θCN andCC at θCC = 99˚  (corresponding to the growth unit; Type molecule in Figure 5.1 and Table 5.2, with θCC = 99˚, CC = 110˚, and θCN = 116˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth unit (Type molecule) is represented by 161 p ×    0.0 0.1 0.2 0.3     Co s  CN            C       CC os Figure A.3 Probability density distribution for the (011) surface as a function of θCN and θCC at CC = 48˚ (corresponding to the growth unit; Type molecule in Figure 5.1 and Table 5.2, with θCC = 156˚, CC = 48˚, and θCN = 92˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth units (Type & molecule) are represented by and 162  p ×     0.0 0.1 0.2 0.3    CC   (de   g)                  CC s Co Figure A.4 Probability density distribution for the (011) surface as a function of θCC and CC at θCN = 92˚ (corresponding to the growth unit; Type molecule in Figure 5.1 and Table 5.2, with θCC = 156˚, CC = 48˚, and θCN = 92˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth units (Type & molecule) are represented by and 163 G*/k BT       Co s    CN               CC  os C Figure A.5 Gibbs free energy distribution for the (010) surface as a function of θCC and θCN at CC = 110˚ (corresponding to the growth unit; Type molecule in Figure 5.1 and Table 5.2, with θCC = 99˚, CC = 110˚, and θCN = 116˚) The contour plot shown corresponds to the Gibbs free energy surface in the 3D plot The growth unit (Type molecule) is represented by 164  G*/k BT  10 11 12     CC   (de   g)          C       CN  os Figure A.6 Gibbs free energy distribution for the (010) surface as a function of θCN and CC at θCC = 99˚ (corresponding to the growth unit; Type molecule in Figure 5.1 and Table 5.2, with θCC = 99˚, CC = 110˚, and θCN = 116˚) The contour plot shown corresponds to the Gibbs free energy surface in the 3D plot The growth unit (Type molecule) is represented by 165 G*/k BT      Co s    CN          C      CC  os Figure A.7 Gibbs free energy density distribution for the (011) surface as a function of θCN and θCC at CC = 48˚ (corresponding to the growth unit; Type molecule in Figure 5.1 and Table 5.2, with θCC = 156˚, CC = 48˚, and θCN = 92˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth units (Type & molecule) are represented by and 166 G*/k BT   10 12 14    CC   (de   g)          C       CC  os Figure A.8 Gibbs free energy density distribution for the (011) surface as a function of θCC and CC at θCN = 92˚ (corresponding to the growth unit; Type molecule in Figure 5.1 and Table 5.2, with θCC = 156˚, CC = 48˚, and θCN = 92˚) The contour plot shown corresponds to the probability surface in the 3D plot The growth units (Type & m molecule) are represented by and 167 ... morphologies in solutions: (A) Morphology of glycine crystals in aqueous solutions predicted from simulations (Gnanasambandam and Rajagopalan 20 10; Gnanasambandam and Rajagopalan 20 10 (Accepted for... quantitative analysis of the solution structure at the interface is needed to establish the available growth units and the relative growth rates at each of the faces Such an analysis, based on... profiles for crystalline glycine, glycine in solution and water molecule as a function of distance from (a) (010) plane and (b) (011) plane 1 02 Prediction of α -Glycine Crystals Morphology in Aqueous