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

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

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 3 The details follow in the next two chapters

5 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

The crystal morphology of glycine has been studied using computational methods

in the past as discussed in detail in Chapter 2 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 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

(101)

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

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 4 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

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

Fig r 5.1.Ar an ement of he glycine mole ules relat ve o he (0 0) an (0 1) sur a es (a) (0 0) sur a e

in ic ted b bro en red ine an he sur a e ex oses mole ule y e 2 (b) (0 1) sur a e

in ic ted b bro en red ine an he sur a e ex oses mole ule y es 2 an 3 Note hat the

“transformed u i c l ” for sh win he (0 1) sur a e s generated b cle vin he (0 1) plane

f om he glycine u i c l b usin Material Stu io Label Red-Ox gen, Blue-Ni ro en, Carb n an Whi e-Hy ro en.

Cyan-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

2 3

4 1

b

y x z

(a)

(b)

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

Ta le 5.1 Glycine/water mixtures for he crystal b lk solut o

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 1 atm with a relaxation time of 1 ps An anisotropic pressure coupling in the

y-direction is applied to the system The time step for the simulation is 2 fs The

particle-mesh 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 1

Dimensions of the simulation

box (Ǻ)

x: 40.84 y: 85.90 z: 35.54

x: 52.63 y: 102.08 z: 35.31

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 1 ns, and an additional NPT simulation (anisotropic pressure coupling in

the y-direction) of 5 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 1 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 1 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

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

Fig r 5.2.Ty ic l snapsh ts of he crystal solut o nter a e of an α-glycine crystal f om he simulat o s

(a) (0 0) plane (b) (0 1) plane The proje ted view s o sh w he pro er orientat o an also mis-orientat o of adsorbed mole ules o he sur a e Water mole ules are n ic ted b red

sp eres (O atoms) co ne ted b grey sp eres (H atoms).

In addition, Figure 5.2 indicates, as one would expect, a larger concentration and a certain amount of orientational “ordering” of the glycine molecules (with the latter harder

to perceive without a full quantitative analysis) near the interfaces relative to the bulk In general, an examination of a large number of such snapshots reveals that on the average there are more glycine molecules in the solution near the (011) face than near the (010) face, thereby suggesting that the (011) face is likely to grow faster than the (010) face While these snapshots provide an inkling of what can be expected, a more 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 solute density profiles and solute orientational distribution functions obtained by configurational-averaging the generated coordinates, is discussed below.

(a)

Interfacial layer

Bulk Crystal

(b)

Figure 5.3 shows the density profiles of glycine molecules in the crystal and in the solution and the density profiles of water molecules, respectively, all normal to the (010) and (011) faces, with the centers-of-mass as locator points The prominent peaks in the glycine density profiles at both the (010) and (011) surfaces indicate the accumulation of the molecules at each surface, with the larger magnitude of the peak at the (011) surface (ρ = 1099 kg/m3) suggesting that it is likely to grow faster than the (010) surface (ρ = 745 kg/m3)

Ta le 5.2.The orientat o s of glycine mole ules n a u i c l

Plane Molecules

(Labels 1 through 4 are marked in Figure 5.1)

θ Cα→C = θ CC

(Angle between

C α →C bond

and y-axis)

Cα→C = CC

(Angle between

C α →C bond

and xz plane)

θ Cα→N = θ CN

(Angle between

Note: The y-axis is normal to the crystal surface The x- and z- axes are parallel to the surface

For additional visual illustration and examination of the interfacial regions, we present the density profiles along with typical snapshots of the crystal/solution interfaces side by side in Figure 5.4

Fig r 5.3.Densi y profi es for crystal ne glycine, glycine n solut o an water mole ule as a fu ct o of

distanc f om (a) (0 0) plane an (b) (0 1) plane.

(011) Plane Crystalline glycine Solvent (water)

Solute glycine

Fig r 5.4. Schemat c representat o s o sh w he nter a es alo g wi h he densi y profi e (a) (0 0)

sur a e wi h he adsorbed glycine mole ules (next growin ayer o he nter a e sh wn n blue colo r (b) (0 1) sur a e an he next growin ayer mole ules are sh wn n metal c blue.

Figure 5.4a indicates the exposure of one of the C–H bonds in the –CH2 group of the solution in the case of the (010) surface (as we had required earlier; see also Figure 5.1) The growth units for this face then are those molecules with orientations closer to a molecule of Type 3 in the crystal, with a Cα→C dipole vector orientation θ CC = 99˚,

Crystal

Bulk solution Interface

Crystal

(b)

azimuthal angle CC = 110˚ and Cα→N dipole vector orientation θ CN = 116˚ (see Table 5.2) Similarly, the molecules at the (011) crystal side of the interface (Figure 5.4b) are of Types 2 and 3, with the corresponding growth units being the solute molecules in interfacial region with orientations close to those of Types 4 and 1 molecules (see Figure 5.1) on the crystal surface Of these two molecules, the center of mass for Type 4

molecule (with θ CC =156˚, CC = 48˚ and θ CN = 92˚) lies slightly closer to the interface, and Type 4 molecule would certainly be expected to be a growth unit, but Type 1 molecules can also contribute to the growth (The dipole vectors for all the molecules on the unit cell of glycine are listed in Table 5.2.) For each surface we define the region of the first prominent peak in the glycine density profile at the interface as the interfacial region, as marked in Figure 5.4

One can now calculate the fraction of molecules having the proper orientation to become crystal-like molecules based on the orientational distribution functions and the corresponding free Gibbs energy landscapes Typical orientational density distributions

of the dipole vectors of the interfacial glycine molecules at the (010) and (011) interfaces are shown in Figures 5.5a and 5.5b The distributions are calculated as per Equation

(3.25) and are plotted as functions of θ CC and θ CN and the azimuthal angle CC for both the surfaces The corresponding Gibbs energy distributions calculated from Equation (3.26) are shown in Figures 5.6a and 5.6b Since the probability distributions and the

Gibbs energy landscape are functions of the three angles θ CC , θ CN and CC, the results illustrated in the above figures correspond to a few typical slices for the third angle (e.g.,

the p vs θ CC and CC and the G vs θ CC and CC in Figures 5.5a and 5.6a correspond to

fixed values of θ CN , and the p vs θ CN and CC and the G vs θ CN and CC in Figures 5.5b

and 5.6b correspond to fixed values of θ CC, as indicated in the captions and the remaining slices for the other angles are given in Appendix A) The corresponding contour diagrams shown in each case also show the orientations corresponding to the F1 growth unit on the crystal lattice Constructions such as these may be then used to identify orientation ranges

of interfacial molecules that are within the favorable Gibbs energy landscape

corresponding to the growth units, and such an examination leads to {θ CC  [0˚, 180˚];

CC  [0˚, 190˚]; and θCN  [90˚, 180˚]}for the (010) face and {θCC  [110˚, 180˚]; CC 

[0˚, 75˚] & [280˚, 360˚]; and θ CN  [0˚, 180˚]} for the (011) face The fractions of molecules (i.e., the fractions of growth units) corresponding to these ranges are then easily determined from the probability distributions and lead to 0.24 for the (010) face and 0.13 for the (011) face

The effective concentrations are then calculated from the product of fractions (’s) calculated and the concentrations of solute molecules in the interfacial region

Fig r 5.5 Pro abi ty densi y distrib t o for he (0 0) sur a e as a fu ct o of θ C an C atθ C = 1 6˚

(cor esp n in o he growth u i Ty e 3 mole ule n Fig re 5.1 an Table 5.2, wi h θ C =

9 ˚, C = 1 0˚, an θ C = 1 6˚ The co to r plot sh wn cor esp n s o he pro abi ty sur a e n he 3D plot The growth u i (Ty e 3 mole ule) s represented b

Fig r 5.5 Pro abi ty densi y distrib t o for he (0 1) sur a e as a fu ct o of θ C an C atθ C = 1 6˚

(cor esp n in o he growth u i Ty e 4 mole ule n Fig re 5.1 an Table 5.2, wi h θ C =

1 6˚, C = 4 ˚, an θ C = 9 ˚ The co to r plot sh wn cor esp n s o he pro abi ty sur a e

in he 3D plot The growth u i s (Ty e 4 & 1 mole ule) are represented b an

Fig r 5.6 Gib s f e energ distrib t o for he (0 0) sur a e as a fu ct o of θ C an C atθ C = 1 6˚

(cor esp n in o he growth u i Ty e 3 mole ule n Fig re 5.1 an Table 5.2, wi h θ C =

9 ˚, C = 1 0˚, an θ C = 1 6˚ The co to r plot sh wn cor esp n s o he Gib s f e energ sur a e n he 3D plot The growth u i (Ty e 3 mole ule) s represented b

Fig r 5.6 Gib s f e energ densi y distrib t o for he (0 1) sur a e as a fu ct o of θ C an C atθ C

= 1 6˚ (cor esp n in o he growth u i Ty e 4 mole ule n Fig re 5.1 an Table 5.2, wi h

θ C = 1 6˚, C = 4 ˚, an θ C = 9 ˚ The co to r plot sh wn cor esp n s o he pro abi ty sur a e n he 3D plot The growth u i s (Ty e 4 & 1 mole ule) are represented b an

The reduction in  for the (011) surface relative to  for the (010) surface appears

to arise from the presence of a large fraction of molecules (close to about 0.25; in the

range {θ CC  [90˚, 120˚]; CC  [160˚, 240˚]; and θCN  [0˚, 70˚] & [160˚, 180˚]}) which

can form hydrogen bonds with molecules of Type 2 (with orientations θ CC = 24˚; CC =

228˚; and θ CN = 88˚) at the (011) crystal face This decreases the probability of such solution-bound molecules assuming the orientations necessary for becoming growth units

5.3.2 Relative Growth Rates

We use the molecular crystallographic properties (listed in Table 5.3) and the dependent parameters at the fluid-solid interface calculated from EISA (listed in Table 5.4) and Equation (3.14) to evaluate the relative growth rate The results show that the growth rate for the (011) surface is 2.88 ± 0.5 times greater than that of the surface (010), implying that the latter is the more stable of the two, indicates a result consistent with experimental studies on the growth kinetics of glycine crystals in aqueous solutions (Li and Rodriguez-Hornedo 1992)

solvent-As discussed below, previous calculations based on attachment theory, which does not consider the effects of the solvent, lead to growth rates for the (011) face that are about 4 to 7 times that of the (010) face An indication of the reason for the decrease in relative growth rate in the presence of solvent is provided by an examination of the structure of the crystal surface

Ta le 5.3.Mole ular evel crystal o rap ic pro ert es for he relat ve growth rate o he (0 0) an (0 1)

planes of glycine crystal

Plane Interplanar

distance

d(hkl) (Ǻ)

Coordination number

n(hkl)

Slice Energy

slice hkl E

(kJ/mol)

Crystallographic orientation factor

slice hkl

E E

 

Note that, E cr refers to the lattice energy of the crystal and is equal to –306.018 kJ/mol

Ta le 5.4.S lvent-depen ent pro ert es an relat ve growth rate for he (0 0) an (0 1) planes of glycine crystal

Plane Effective concentration

lnln

X



Relative growth rate

rel hkl

the hydration shell to form a growth layer Further, as notedearlier in the last section, we found from our simulations that, in the case of the (011) surface, there is a possibility for the formation of hydrogen bonds between some of the molecules at the interfacial region

on the solution side and molecules of Type 2 on the crystal side of the interface (see Figure 5.7 for a typical example) An analysis of the molecular trajectories shows that such bonding behavior is consistently seen during the course of the simulations The

substantial number of molecules we observe in the range {θ CC  [90˚, 120˚]; CC  [160˚,

240˚]; and θ CN  [0˚, 70˚] & [160˚, 180˚]} in the orientational distribution function indicates that a fairly good number of molecules in the interfacial region form hydrogen bonds with the crystal molecules at the interface

Fig r 5.7.A snapsh t n ic t n he existenc of h dro en b n in betwe n a mole ule of Ty e 2 o he

(0 1) sur a e an wi h a mole ule n he nter a ial regio o he solut o side This fig re s the same as he ex an ed p rt o of Fig re 5.2(b) Blue: Ni ro en; Metal c Aq a: Carb n; Red: Ox gen; Lig t Gray: Hy ro en Al the other mole ules (inclu in he mole ules n he

ba k ro n n his wo-dimensio al proje t o ) are n shad w Water mole ules are n t sh wn.

The growth of the (011) face is therefore impeded, as a result of the formation of such hydrogen bonds and the consequent “mis-orientation” of the molecules at the

interface This could be the cause of the reduction in the growth rate ofthe (011) surface relative to what was observed using the attachment energy calculations

The morphology predicted from our results provide further proof of the above influence of the solvent and are consistent with previous experimental results The morphology of the crystal predicted using the Wulff plot from our calculations is shown

in Figure 5.8a, along with the morphologies observed in experiments (Figure 5.8b) and predicted from the attachment energy theory (Figure 5.8c), the only theoretical attempt available in the literature for predicting the morphology of glycine crystals Poornachary

et al (Poornachary et al 2008) studied the morphology of glycine crystals in aqueous

solutions and reported the aspect ratio (c/b) to be 2.62 ± 0.5 In addition, the experimental crystal habit they observed had prismatic bipyramidical shape, elongated along the c-axis

(see Figure 5.8b)

Fig r 5.8.Compariso betwe n he ex erimental an he predicted morp olo y of glycine n aq eo s

solut o s (A) Morp olo y of glycine crystal n aq eo s solut o predicted f om simulat o s (this work) (B) Ex erimental y o served morp olo y of glycine n aq eo s solut o s (P orna hary et al 2 0 ) (C) Morp olo y predicted b at a hment energ theory (P orna hary et al 2 0 ).

B

C A

The relative growth rate of 2.88 ± 0.5 we predict using EISA agrees very well with theabove reported experimental results Moreover, our predicted morphology is also similar10 to the one seen in the experiments More importantly, the relative growth rate

we predict is also consistent with, and supports, the observations of Lavah and Leiserowitz (Lahav and Leiserowitz 2001) for glycine crystals grown in aqueous media

Lavah and Leiserowitz (Lahav and Leiserowitz 2001) also reported a bipyramidical shape with large (011) and (110) faces (as did Poornachary et al (Poornachary et al 2008)), but with a less well-developed (010) surface (as a result of its slower growth) In support of their observations, these authors suggest that the (011) surface is likely to grow more slowly because of its hydrophilic nature (as a hydrophilic surface would be expected to present an additional energy cost for growth due to reasons

we mentioned earlier) This suggestion by Lavah and Leiserowitz (Lahav and Leiserowitz 2001) is consistent with our own observations discussed earlier in this section Correspondingly, our result in Figure 8a shows that our calculations capture the same morphological shape observed by Lavah and Leiserowitz (Lahav and Leiserowitz 2001)

In contrast, as noted above, the attachment energy theory (Bisker-Leib and Doherty 2003; Poornachary et al 2008) predicts a relative growth rate between 4 and 7, as it does not consider the effects of solvent and the potential implications of the affinities of surface-bound chemical groups on the solvent (In the approach based on attachment energy, one calculates the growth rate purely on the basis of the energy needed to attach a crystal slice

of thickness d hkl to the surface in vacuum, and the solvent does not enter the picture.) Our

10 Similarity is based on the overall shape of the crystal as well as on the aspect ratio (b/c) Both the

predicted and experimentally observed glycine crystals have bipyramidical shape and also have almost equal aspect ratio

results and discussions thus illustrate and emphasize the need for the type of analysis we use here for assessing accurately the growth (and dissolution) rates and morphology of solution-grown crystals

In summary, we have presented a molecular level analysis for the effect of solvent on the morphology of α-glycine crystals grown in aqueous solutions, using an extended interface structure analysis for interfacial orientational distributions of solute molecules obtained from molecular dynamics The approach allows one to account for the effects of exposed groups and their interactions with the solvents and the effects of the interactions

of the solution-bound solute molecules with those on the crystal surfaces As a result, the relative growth rate is calculated by taking into account not only the crystallographic features of the growing surfaces but also the interaction and influence of the solvent on the crystal/solution interface The relative growth rate for the morphologically important (010) and (011) surfaces is predicted (2.88 ± 0.5) and compared well with recent experiments (2.62 ± 0.5) Moreover, the crystal shape and morphology are also consistent with the experimental observations Comparison with the results from approximate analyses in the literature based on attachment energy calculations shows that neglecting solvent effects could lead to unrealistic predictions for morphology Equally important is the approach used here, allows one to examine interfacial phenomena at the crystal/solution interface more closely and rigorously As a result, the approach used paves the way for systematic examination of the effects of different solvents and the

presence of impurities on crystal morphology One such attempt is made in methanol/water mixture and will be discussed in detail in the next chapter

6 Prediction of α-Glycine Crystals Morphology

in Methanol/Water Mixtures

_ 6.1 Introduction: Importance of Solvent in Changing the Crystal

Shape

As emphasized earlier, the shape of pharmaceutical crystals plays a key role in drug manufacturing as it influences process parameters as well as the desired properties of active pharmaceutical ingredients Such process properties include powder flowability, compressibility, suspension stability and bulk density Most importantly, in the case of drugs administered in high doses, particle shape plays an important role in the tableting behavior of drugs As crystal faces have a direct link to the surface chemistry and surface free energy, different physicochemical properties are observed for crystals with different habits The role of a mixture of solvents in directing such morphological development, however, remains elusive despite the many advances in crystallization techniques and related theoretical analyses In order to shed light on this area, we take glycine crystals as

an example here and examine and also testing our computational formalism (discussed in Chapter 3), whether the effect of using a solvent mixture on the shape of the resulting crystal can be predicted

The crystalline form of glycine has received significant attention in studies of crystal morphology For instance, the prediction of morphology of glycine crystals grown

in vacuum (Berkovitch-Yellin 1985; Boek et al 1991; Bisker-Leib and Doherty 2003)

and in water (Bisker-Leib and Doherty 2003) has been addressed both experimentally and theoretically in the literature It is well-known that a crystal form known as -glycine occurs in stable form in aqueous solutions of glycine; this polymorph has a bipyramidical crystal shape with less developed (010) face and dominant (011) and (110) faces in aqueous solutions (Berkovitch-Yellin 1985; Boek et al 1991; Bisker-Leib and Doherty 2003)

In contrast, relatively very little is known about how mixtures of solvents affect glycine crystallization, and only a few, experimental, investigations have been reported and no theoretical examination exists For example, it has been shown experimentally (shown in Figure 6.1) that glycine forms a well-developed (010) surface in ethanol-water mixtures (Weissbuch et al 2005), in contrast to the less-developed (010) surface seen in pure aqueous solutions Presence of alcohol in the solution suppresses the solubility of glycine significantly While, as mentioned earlier, this suppression allows a high degree

of supersaturation to be used for crystal growth (thereby increasing the yield), the reduced solubility changes the growth rates of morphologically important (MI) faces and hence changes the morphology of the crystals

Fig r 6.1.Morp olo y of glycine n 1: 9 ethan l water mixture (Weis b ch et al 2 0 ).

We focus here on a predictive methodology capable of determining crystal shapes and morphology from the relevant intermolecular interactions using a systematic examination of interfacial structure, types of growth units, and the relative growth rates

of morphologically important faces of the crystals as discussed in Chapters 3 & 5 As a result, the approach can examine any given solvent and mixture of solvent Here, we are interested in the prediction of morphology for glycine crystals in 50:50 (v/v) water/methanol mixtures Methanol is chosen here since it is a simple enough alcohol with the needed –OH functional group (as glycine is soluble in only alcohol water mixtures) Moreover, glycine’s solubility in methanol/water mixtures is higher than in higher-order alcohols, and this allows one to use a sufficiently large number of glycine molecules in the solution without a need for very large demand on the computational needs For the same reasons, we use an equi-volume mixture of methanol and water in order to (i) have a sufficient level of solubility of glycine in the mixture and (ii) assure a level of (potential) difference in the growth rate relative to the one in pure water, so that the effect of the presence of the alcohol can be assessed meaningfully Successful demonstration of the computational method, i.e., EISA, using the simple alcohol could then pave the way for more elaborate materials and computations

6.2 Models and Methodology

As discussed in Chapter 4, we choose the zwitterionic model for glycine and SPC/E model for water The force field and the partial charges are identical to those used in our earlier work, as they have been tested for their suitability pertaining to glycine crystal growth studies (Gnanasambandam et al 2009) For methanol, we use RESP partial charges and amber ff03 force field (Caldwell and Kollman 1995) The partial charges are

given in Table 6.1 A methanol molecule with the atom name is shown in Figure 6.2 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

Table 6.1 ESP charges for Methanol

Atom index

OH

HO

0.1166 0.3720 0.3720 0.3720 –0.6497 0.4215

Fig r 6.2. Representat o for a methan l mole ule Label Red-Ox gen, Cyan-Carb n an Whi

e-Hy ro en.

6.2.1 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 The second step has two major tasks, one is mixing methanol and water in a particular volume percentage and the other is the creation of glycine/methanol/water saturated solution These two are then incorporated into the simulation box

The first step, i.e., constructing the crystal surface is done as we explained in our previous chapter The lower part of the box consists of the crystal, with a thickness of atleast 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

The first step in preparing saturated bulk solutions is the preparation of equivolume mixture of methanol and water (50/50 volume %) The mixture is prepared

by randomly adding methanol and water molecules in the simulation box, and the mole fraction of methanol in the bulk solution is set at a value of 0.39 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 1 atm with a relaxation time

of 1 ps An anisotropic pressure coupling in the y-direction is applied to the system The

time step for the simulation is 2 fs The particle-mesh 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 1 nm The bulk solution is initially subjected to energy minimization for 400 steps Thereafter, the velocities of all molecules including methanol and water are assigned according to the Boltzmann distribution at 100

K Then the system is heated up and equilibrated for 1ns, and an additional NPT

simulation (anisotropic pressure coupling in the y-direction) of 5 ns is performed

Then saturated bulk solution is prepared by randomly adding glycine in the mixture of methanol/water in the simulation box, and the mole fraction of glycine in the bulk solution is set at a value of 0.026 Then, the above described MD simulation

procedure is followed with the same parameters for the bulk solution which consists of glycine/methanol/water molecules

The saturated bulk solution thus obtained is then added to the box with the crystal slice The number of crystalline glycine, solute glycine, methanol and water molecules used in the simulations are listed along with the dimensions of the simulation box in Table 6.2 The simulation parameters are the 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 1 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

1 bar The reason for employing pressure coupling, with 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

Table 6.2 Glycine/methanol/water mixtures for the crystal/bulk solution

6.3 Results & Discussions

As we discussed in Chapters 3 & 5, crystal morphology of glycine crystals in a mixture

of methanol/water is predicted by three steps First, molecular dynamics simulation is

performed on crystal/fluid interface to know the orientations of the interfacial molecules

The next step is to find the effective concentration of properly orientated molecules using

extended interface structure analysis (EISA) Then the crystal structural and solvent

dependent properties obtained from EISA are used in the relative growth rate expression

developed by Liu et al (1995) Finally, the morphology of glycine crystals in the mixture

of solvents is predicted using Wulff plot

6.3.1 Solution at Interface

Typical snapshots of the (010) and (011) faces at the end of a 10-ns MD simulation are

shown in Figure 6.3 In general, an examination of a large number of such snapshots

System dimension (Ǻ) x: 40.84

y: 135.91 z: 40.62

x: 52.63 y: 132.08 z: 35.31

reveals that on an average there are more glycine molecules in the solution at the vicinity

of the (011) face than near the (010) face, thereby suggesting that the (011) face is likely

(a)

(b)

Fig r 6.3.Ty ic l snapsh ts of he crystal solut o nter a e of an α-glycine crystal f om he simulat o s

(a) (0 0) plane (b) (0 1) plane Glycine mole ules n he solut o an at the nter a e are

sh wn bal s an st cks n blue Water an methan l mole ules are n ic ted b blue an gre n

st cks, respe t vely.

Fig r 6.4.Densi y profi es for crystal ne glycine, glycine n solut o an water mole ule as a fu ct o of

distanc f om (a) (0 0) plane an (b) (0 1) plane.

to grow faster than the (010) face While these snapshots provide an insight of what can

be expected, a more quantitative analysis of the solution structure at the interface is needed to establish the available growth units and the relative growth rates at the respective faces Such an analysis, based on solute density profiles and solute orientational distribution functions obtained by configurational-averaging of the generated coordinates has been discussed below

Figure 6.4 shows the density profiles of glycine molecules in the crystal and in the solution and the density profiles of water and methanol molecules, respectively, all normal to the (010) and (011) faces, with the centers-of-mass as locator points The prominent peaks in the glycine density profiles at both the (010) and (011) surfaces indicate the accumulation of the molecules at each surface, with the larger magnitude of the peak at the (011) surface suggesting that it is likely to grow faster than the (010) surface.The interfacial region can be identified from the first prominent peak in the bulk glycine density profile shown in Figure 6.4

We use extended interface structure analysis on the interfacial molecules to identifythe growth units based on the orientations and azimuthal angle of the interfacial solute molecules for both the surfaces The orientations under consideration are the Cα→C and the Cα→N dipole vectors with reference to the surface normal (θ CC and θ CN, respectively) and the azimuthal angle for the Cα→C dipole vector (CC) are availed to predict the growth units (Table 5.2 shows the orientations of glycine in a unit cell) The growth units for (010) face are those molecules with orientations close to Type 3 molecules in the crystal shown in Table 5.2 (i.e., those molecules in the interfacial region without

significant Gibbs energy barriers separating them from the needed orientation) Similarly, the growth units for the (011) surface are those close to Type 4 and Type 1 molecules Note that Type 4 molecules have centers of mass closer to the interface, whereas Type 1 molecules lie a little farther but can, nevertheless, contribute to the growth of the surface

We calculate the fraction of molecules (δ) lying within the acceptable ranges of orientations using the orientational distribution functions and the corresponding free Gibbs energy landscapes The acceptable range of orientation is determined as mentioned

in the methodology section The acceptable range of orientation includes the growth unit orientation and other orientations close to growth unit orientations that do not have significant Gibbs energy barrier to become growth unit

The orientational probability distributions of the interfacial glycine molecules at the (010) and (011) interfaces are calculated using Equation (3.25) Typical orientational density distributions of the dipole vectors of the interfacial glycine molecules at the (010) and (011) interfaces are shown in Figures 6.5a and 6.5b The required Gibbs free energy

of the molecules at state τ follows readily from the probability distribution through Equation (3.26) and are shown in Figures 6.6a and 6.6b for both the surfaces Since the probability distributions and the Gibbs energy landscape are functions of the three angles

θ CC , θ CN and CC, the results illustrated in the above figures correspond to a few typical

slices for the third angle (e.g., the p vs θ CN and CC and the G vs θ CN and CC in Figures

6.5a-b and 6.6a-b correspond to fixed values of θ CC, as indicated in the captions) The corresponding contour diagrams shown in each case also show the orientations corresponding to the F1 growth unit on the crystal lattice Constructions such as these may be then used to identify orientation ranges of interfacial molecules that are within the

favorable Gibbs energy landscape corresponding to the growth units, and such an

examination leads to {θ CC  [0˚, 180˚]; CC  [0˚, 180˚]; and θCN  [90˚, 180˚]}for the

(010) face and {θ CC  [110˚, 180˚]; CC  [0˚, 75˚] & [280˚, 360˚]; and θCN  [0˚, 180˚]}

for the (011) face

Fig r 6.5 Pro abi ty densi y distrib t o for he (0 0) sur a e as a fu ct o of θ C an C atθ C = 9 ˚

(cor esp n in o he growth u i Ty e 3 mole ule wi h θ C = 9 ˚, C = 1 0˚, an θ C =

1 6˚ The co to r plot sh wn cor esp n s o he pro abi ty sur a e n he 3D plot The growth u i (Ty e 3 mole ule) s represented b