Atomistic Simulation To Understand Anisotropic Growth Behavior of

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Cite This: Cryst. Growth Des. 2019, 19, 3768−3776

Atomistic Simulation To Understand Anisotropic Growth Behavior of Naproxen Crystal in the Presence of Polymeric Additives Krishna M. Gupta,* Yin Yani, Sendhil K. Poornachary, and Pui Shan Chow* Institute of Chemical & Engineering Sciences, A*STAR (Agency for Science, Technology and Research), 1 Pesek Road, Jurong Island, Singapore 627833

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S Supporting Information *

ABSTRACT: Polymeric additives can either inhibit or promote the growth of a crystal. While crystal growth inhibition by additives/impurities has been widely documented, the molecular-level mechanisms by which additives promote crystal growth are largely elusive. In this study, we use molecular dynamics simulations to model the interactions among a polymeric additive (polyvinylpyrrolidone), solute (naproxen), and solvent (ethanol/water mixture) molecules occurring at the crystal/solution interface. At the (01̅1) surface, solvent interactions with the crystal surface and solute molecules are diminished in the presence of the additive, thereby lowering the solvation barrier to crystal growth. Besides, the interaction of solute molecules with this surface is enhanced, leading to crystal growth promotion along the −b axis. On the contrary, the additive preferentially interacts with the (011) face and the solute−solvent interaction is stronger at this crystal face. These two factors lower the adsorption rate of solute molecules onto this face and consequently retard crystal growth along the +b direction. Further, in the presence of the additive, mobility of the solute is slowed down at the (01̅1) face (supports the promotion event); in contrast, at the (011) face, the solute exhibits a larger mobility (supports the inhibition event). The simulation results, while providing insights into the anisotropic growth behavior of naproxen crystals in the presence of polymeric additives, have implications on the selection of additives for crystallization inhibition in pharmaceutical and agrochemical formulations, as well as for modulation of undesired crystal shapes to enable better downstream processing.

1. INTRODUCTION Crystallization is one of the most important unit operations for the efficient separation and purification of active pharmaceutical ingredients (APIs); in recent years, development of pharmaceutical crystallization has gained significant attention in both academic and industrial research.1,2 In the context of pharmaceutical crystallization, additives (compounds that are being intentionally added to the crystallizing solution precisely either to modify the crystal habits3−5 or to stabilize a metastable polymorph6,7) and impurities (synthesis/reaction byproducts originating from the upstream process) have shown significant impact over the crystallization processes in their abilities to tune the morphology of a crystal.8,9 They can influence the nucleation and growth rates,8,10,11 leading to a change in polymorph or crystal habit.3,4,9,12,13 Usually, additives and impurities have great potential to inhibit the crystal growth,6,14−16 but in a few situations, they are known to promote the crystal growth.17,18 Various types of additives have been employed to exercise control over crystal habits, e.g., polymers, surfactants, and organic molecules with similar moieties as the solute molecules.19−21 Solvents are also known to affect crystal habits.22 The effect of “tailor-made” additives on crystal morphology has been examined and rationalized by the stereoselective interactions between the additives and the crystal surface.3,4 Kuznetsov et al. have studied experimentally © 2019 American Chemical Society

the influence of organic impurities on the growth rates of different faces of potassium acid phthalate (KAP) and potassium dihydrogen phosphate (KDP) crystals. The presence of impurities first led to an increase in growth rate. With increasing impurity concentrations, the growth rate increased and reached a maximum, and then decreased.19 To modify the paracetamol crystal habit, various additives such as agar, gelatin, polyvinylpyrrolidone (PVP), and hydroxypropylmethyl cellulose (HPMC) were used. It was observed that the crystal habit changed from polygonal prismatic to rod-shaped, ellipsoidal, or spherical crystals depending on the concentration of additives.23 Xie et al. produced micrometer-sized salbutamol sulfate using surfactant and polymeric additives. Among additives studied, PVP K25 was found to be the most effective in inhibiting crystal growth.21 Simone et al. tailored the crystal shape and polymorphism of ortho-aminobenzoic acid (OABA) using a combination of solvents and a structurally related additive (benzoic acid). It was observed that the nucleation of OABA Form III dominated in the examined solvents at a particular concentration of benzoic acid.24 In a separate study, the authors further investigated the effect of a polymeric additive (HPMC) on the morphology and Received: February 10, 2019 Revised: May 30, 2019 Published: June 3, 2019 3768

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Figure 1. (a) Crystal morphology, (b) two faces of naproxen crystal (color code: O, red; H, white; C, gray), and (c) molecular structures of PVP and HPMC.

polymeric additives (PVP and HPMC) with naproxen crystal faces were modeled primarily. However, those simulations were performed in vacuum, and hence did not account for the interactions between the solute, solvent, and naproxen molecules on the crystal face. Further, most of the literature studies for understanding crystal growth rate in the presence of polymeric additives were modeled in the absence of either solute28,31,32 or solvent.27 These studies illustrate the crystal growth rate in the presence of polymeric additives to a certain extent, but would not be able to capture the actual scenario because models without solute would not incorporate solute− polymer, solute−interface, and solute−solvent interactions, whereas, in the case of modeling without solvent, the solvent− interface, solvent−solute, and solvent−polymer interactions would be missing. Additionally, they were focused on crystal growth inhibition, rather than promotion by polymeric additives. Although crystal growth inhibition by additives/ impurities is relatively well understood, the molecular-level mechanisms by which additives promote crystal growth have not been widely reported in the literature. In our recent study,30 it was observed that a naproxen crystal shows anisotropic growth behavior in the presence of PVP, that is, growth promotion in the −b direction and inhibition in the +b direction. The objective of this study is to provide molecular-level insights into the experimentally observed effect of PVP on naproxen crystal growth. To this end, molecular dynamics (MD) simulations were performed to probe the interaction of PVP with naproxen crystal faces in a solution environment. Additionally, simulations were performed in the presence of a mixture of polymeric additives (PVP and HPMC). On the basis of these results, we propose a possible mechanism by which the additive simultaneously promotes and inhibits growth at the hemihedral faces along the b axis of naproxen crystal.

polymorphism of OABA crystals; it was found that HPMC not only inhibits nucleation and growth of Form I but also increases the time for the polymorphic transformation from Form II to I.25 Recently, the presence of triblock copolymer Pluronic P123 (PP123) has been shown to modify the crystal morphology of succinic acid from plate-like crystals to blocklike crystals.26 Besides experimental investigations, efforts have also been made to understand the crystal growth at the molecular level in the presence of additives or impurities using molecular modeling and simulation. With rapidly growing computational resources, molecular simulation has become an indispensable tool, which can provide microscopic insight that is otherwise experimentally intractable. Duffy and Rodger conducted molecular simulations to model the effect of poly(octadecyl acrylate) (PA-18) on an n-octacosane crystal. They showed that dimer units of PA-18 strongly adsorbed onto the noctacosane crystal surfaces with only localized disruption to the structure.15 Yani et al. provided atomistic level insights into the interaction between salbutamol sulfate crystal faces and various additives including PVP, HPMC, and lecithin and suggested that PVP is the most effective for crystal inhibition.27 Yang et al. explored the unusual promotion effect of L-valine on the growth of the (011) L-alanine crystal surface by molecular simulation. Without L-valine, the mobility of L-alanine is hindered due to hydrogen bonding (H-bonding) interaction with water, thus inhibiting crystal growth. At higher concentration of L-valine, L-alanine becomes free due to preferential interaction between L-valine and water; thus crystal growth is promoted.14 Gao et al. examined the crystal growth of tolazamide (TLZ) in the presence of diblock copolymer, poly(ethylene glycol)-block-poly(lactic acid) (PEG-b-PLA), which changes its morphology from needle to plate in aqueous media. It was predicted that strong hydrophobic and van der Waals interactions of polymer might be more effective in inhibiting crystallization of poorly water-soluble and hydrophobic drugs in aqueous media compared to H-bonding capability.28 Recently, by combining molecular modeling and experiments, the influence of solvent composition on the crystal morphology and structure of p-aminobenzoic acid was investigated, and the changes in crystalline form and morphology were explained by solute−solvent interactions.29 To access the degree of interaction between the additive and the crystal face, in our previous study,30 interactions of the

2. SIMULATION MODELS AND METHODS Figure 1 depicts the crystal morphology, molecular models of the (01̅1) and (011) faces of a naproxen crystal, and molecular structures of the polymeric additives. Molecular models of the naproxen crystal surfaces were built by cleaving the (hkl) faces from the crystal structure to a depth of 1−3 unit cells, and extending the surface to m × n unit cells. Naproxen is a chiral molecule and crystallizes in a noncentrosymmetric, P21 space group. The polar axis in the crystal structure runs along the crystallographic b axis as shown in Figure 1b. Therefore, the two ends of the packing diagram are different. A 3769

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vacuum slab of appropriate thickness was built above the crystal face, with periodic boundary conditions imposed on the system. The solute (naproxen), solvent (a mixture of ethanol and water), and additive molecules (PVP or HPMC) were placed randomly near the crystal surface. Likewise, systems with different ratios of solute to PVP, viz., 8/0, 8/2, and 8/6, respectively, were built. In our previous experimental work,30 a mixture of ethanol and water was used as the solvent for naproxen crystal growth to mimic the solution conditions prevailing during an antisolvent precipitation process.18 Hence, we have chosen an ethanol−water mixture (100 ethanol molecules and 300 water molecules) as the solvent to be consistent with the solvent composition used in previous experimental work. In our previous work,30 in addition to experiments, the interactions of polymeric additives (PVP and HPMC) with naproxen crystal faces were also modeled in the absence of solvent. The objective of that study was to assess the degree of interaction between the polymeric additive and a given crystal face and, in turn, link it to the growth inhibition along that crystallographic axis. As opposed to that, the current study investigates complex intermolecular interactions, including solute−crystal, solvent−crystal, and solute−solvent, both in the absence and in the presence of the additive molecule (systems corresponding to solute/PVP ratios of 8/0 and 8/2). Note that, in a solution environment, modeling the polymer additive with a large number of monomer unitsto match the molecular weight of the polymer used in the experiments30will considerably increase the computational time for MD simulation; hence, we modeled the polymer additive with two monomer units. Further, by using six such additive molecules in a simulation run (system corresponding to solute/PVP ratio of 8/6), we aim to verify if the observed molecular phenomenon is reproducible in the presence of a larger number of repeat units. In the subsequent text, PVP refers to a PVP molecule containing two monomer units (see Figure 1c), 2 PVP refers to two PVP molecules each containing two monomer units, and 6 PVP indicates six PVP molecules each containing two monomer units. By increasing the number of PVP molecules, the polymeric nature of the additive molecule is qualitatively simulated. However, in this modeling approach, the effect of polymer conformation on interaction of the additive with the crystal surface may not be accurately assessed. Prior to the above simulations, which were conducted in the presence of solvent (ethanol/water mixture), an additional set of simulations was also performed with two PVP molecules without solvent at both the crystal surfaces to validate the suitability of two monomer units in a chain. These simulations were similar to our previous study,30 but only different in the chain length. In the additional set of simulations, 2 PVP were placed near the (01̅1) and (011) faces and results were compared. The PVP molecules interact strongly with the (011) face compared to the (01̅1) face. In addition, there is no H-bond forming between PVP and the (01̅1) face, but a few H-bonds (−COPVP···H−Onaproxen) are observed with the (011) face. These observations/events are consistent with our previous studies wherein we have used a very long chain and thus, to a certain extent, provide support to the use of a short chain in this current study (Figure S1 in the Supporting Information). Representing a polymer chain with only a few repeat units to account for the interfacial interaction of polymers (HPMC and Pullulan) on the drug crystal (fenofibrate and griseofulvin) surfaces in the presence of solvent has previously been reported in the literature.31,32 Figure 2 represents a snapshot of the simulation system. The atoms of the naproxen crystal were represented by Lennard-Jones (LJ) and electrostatic potentials É ÅÄÅ 0 9 6Ñ ÅÅ ij r yz ij rij0 yz ÑÑÑÑ qiqj Å jj ij zz j z Å ∑ εijÅÅÅÅ2jjj zzz − 3jjjj zzzz ÑÑÑÑÑ + ∑ r r ÅÅ k rij { i>j k ij { ÑÑÑÖ i > j ij ÅÇ (1)

Figure 2. A snapshot of the simulation system with the (011) face. Color code: naproxen, green; PVP, red; water, blue; ethanol, orange. In the naproxen crystal: C, gray; O, red; H, white. Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS)33 force field (with force field-assigned partial atomic charges) was used to model atomic interactions in the crystal structure of naproxen, PVP, HPMC, as well as in water and ethanol. All the systems were initially subjected to energy minimization in order to avoid unwanted overlap between the atoms and to reduce the thermal noise in the system; then velocities were generated according to the Maxwell−Boltzmann distribution. Finally, isothermal and isochoric (NVT) MD simulations were conducted at 300 K. The temperature was controlled by the Nose−Hoover34 thermostat with a relaxation time of 0.1 ps, and Ewald summation was used to incorporate the long-range interactions. The equations of motion were integrated by the Verlet velocity algorithm with a time step of 1 fs for a simulation duration of 500 ps, and trajectories were saved at every 0.5 ps. The equilibration state was determined by observing the change in the thermodynamic properties such as energy and temperature as a function of time. It was found that all the systems reach equilibrium within 100 ps of simulation; thus all the properties were estimated using trajectory after 100 ps. The initial placements of the molecules near the crystal surface give close results, gauged by interaction of the solute around the (011) crystal surface in the presence and absence of polymeric additives as g(r)’s are found to be similar (Figure S2 in the Supporting Information). All the MD simulations were performed in Materials Studio (Version 8.0).35

3. RESULTS AND DISCUSSION 3.1. Pure Polymeric Additive. To characterize how solute, additive, and solvent molecules interact with both the interfaces of naproxen crystal, the radial distribution functions g(r), based on all atoms to all atoms, were evaluated. The g(r) describes how the particle density of a system varies with a distance measured from a reference particle and indicates the interaction behavior between molecules/atoms. Generally, three types of interactions, (1) solute−interfacial layer, (2) solvent−interfacial layer, and (3) solute−solvents, are present in a system without polymeric additive. First, we examine the solute−interfacial layer interaction. Figure 3 shows the g(r) of solute around the interfacial layer of the crystal with various PVP concentrations. In the absence of

where εij and r0ij are the corresponding LJ parameters for the ij ion pair, rij is the distance between atoms i and j, and qi is the atomic charge of the atom i. During simulations, the crystal structure was kept fixed. Consistent with our previous work,30 the Condensed-phase 3770

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Figure 3. Radial distribution functions g(r) of solute around the interfacial layers of the crystal.

Figure 4. Radial distribution functions g(r) of solvent around the interfacial layers of the crystal.

Figure 5. Radial distribution functions g(r) of solute around solvent.

PVP, pronounced peaks are seen at a distance r ∼ 8 Å at both the faces, indicating favorable interaction between the solute and the crystal faces. However, the strength of interaction of the solute with the (01̅1) face is weaker (as seen by lower peak height) than with the (011) face. Upon addition of PVP, the peak height decreases (2.29 without additive and 1.67 with 6 PVP) at the (011) face, indicating decreased interaction between solute and interfacial layer. The reversed is noticed at the (01̅1) face. This can be explained by the different surface chemistry on the two crystal faces. On the (011) face (see Figure 1b), polar carboxylic acid functional groups of naproxen

interact favorably with the −CO groups of PVP molecules; thus the solute−interfacial layer interaction is reduced. On the other hand, nonpolar methyl and naphthyl functional groups on the (01̅1) face do not interact favorably with PVP. However, this is insufficient to explain the increase in solute− interfacial layer interaction at the (01̅1) face upon addition of PVP. This suggests that other types of interactions are also having a role in the observed phenomenon. Further, to evaluate the interaction between solvent and the interfacial layer of the crystal, Figure 4 displays the g(r) of solvent around the interfacial layer. Interestingly, at both faces, 3771

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the g(r) decreases when PVP is introduced, indicating that the interactions between solvent and crystal faces are weakened. This suggests the removal of the solvent layer near the interfacial region, thereby lowering the solvation barrier for a molecule (solute or additive) to reach the surface. This explains why the solute−interfacial layer interaction is enhanced in the presence of PVP at the (01̅1) face as observed in Figure 3 and crystal growth is promoted along the −b direction. Similar phenomena, i.e., the role of additive in promoting crystal growth by disrupting the solvation layer, are also reported in the literature.36,37 To quantify the interaction between solute and solvent, Figure 5 depicts the g(r) of the solute around the solvent in the crystal faces. At the (011) face, two peaks are observed at r ∼ 1.6 and 1.9 Å, indicating the possibility of H-bond formation between solute and solvent. Nevertheless, at the (01̅1) face, only one small peak is seen at r ∼ 1.83 Å. This represents that the solvent interacts strongly with the solute at the (011) face compared to the (01̅1) face. In general, in the presence of PVP, the solute−solvent interaction becomes weaker at the (01̅1) face but stronger at the (011) face. To further investigate the interaction between solute and solvent, H-bonds are calculated. Two geometrical criteria were implemented to define a Hbond: (1) the distance between a donor and an acceptor (H··· O) ≤ 0.34 nm and (2) the angle of donor−hydrogen−acceptor (O−H···O) ≥ 120°.38−40 Specifically, to calculate H-bonds, the last 100 ps trajectory was used. Figure 6 shows the number

decreases at the (01̅1) face, particularly toward lower lifetimes. In general, the number of H-bonds of various lifetimes in the presence of PVP is always greater compared to that without PVP at the (011) face, but the reversed is observed at the (01̅1) face. The analysis of the above molecular interactions indicates that solute interactions with the interfaces are affected by the presence of PVP differently on the +b and −b surfaces, suggesting that there is a possible competition between the solute−interfacial layer interaction and PVP−interfacial layer interaction. To examine such a competitive behavior, Figure 7 shows the g(r) of solute and PVP around the interfacial layer corresponding to a solute/PVP ratio of 8/2. On the (011) face, the peak height of the g(r) of PVP at r ∼ 7.55 Å is higher than that of solute, reflecting that the interaction of PVP with the interfacial layer is greater than that of solute with the interfacial layer. However, at the (01̅1) face, naproxen solute displays a higher g(r) peak r ∼ 7.85 Å compared to PVP; thus the solute is interacting with the interfacial layer stronger than PVP. To quantify the interaction strength of solute and PVP with the interfacial layer, interaction energies (van der Waals, electrostatic, and total) on the basis of per molecule (PVP or naproxen) with the first layer of the crystal face are calculated (Table 1). It should be noted that usually a negative value for the interaction energy indicates favorable interactions and a higher absolute value of interaction energy denotes stronger intermolecular interactions. The total interaction energies of PVP and naproxen with the first layer of the crystal face are −45.72 and −37.69 kJ/mol, respectively, at the (011) face, and −33.77 and −48.57 kJ/mol, respectively, at the (01̅1) face. Consistent with g(r) calculations, the naproxen solutes exhibit higher interaction energies compared to PVP at the (01̅1) face and vice versa at the other face. In addition, the energy contributions by van der Waals and electrostatic interaction forces to the total energy are evaluated. Similar to previous findings (without solvent),30 herein, the total energies are dominated by van der Waals contribution at both faces, and also the polymeric additive interacts strongly with the (011) face compared to the (01̅1) face. Furthermore, the dynamics of solute and PVP are quantified by mean square displacements (MSDs) MSD(t ) =

1 N

N

∑ ⟨|ri(t ) − ri(0)|2 ⟩ i=1

(2)

where N is the number of molecules and ri(t) is the position of the ith molecule at time t. As shown in Figure 8, the hierarchy of MSDs of naproxen solute is 0 PVP < 2 PVP < 6 PVP near the (011) face. The weaker interaction of solute with the crystal face upon addition of PVP compared to that without PVP (as discussed in Figure 3) leads to a larger mobility of solute. In contrast, at the (01̅1) face, the solute exhibits a smaller MSD in the presence of PVP because of the relatively stronger interactions of the solute with the crystal face. More specifically, solutes display extremely low mobility in the presence of 6 PVP, reflecting that, once solutes are adsorbed on the (01̅1) face, they tend to remain, thereby promoting the crystal growth. On the other hand, solutes move faster near the (011) face. Thus the chances of them being adsorbed on the crystal face are lower; therefore, crystal growth is retarded. The mobility of the polymeric additive is also evaluated after investigating the dynamics of naproxen solute in order to envision the surface effect on the dynamics of PVP. At both

Figure 6. Lifetime distribution of H-bonds between solute and solvent.

of H-bonds of various lifetimes in the system at both the crystal faces. The number of H-bonds of lifetime 0.5 ps in the presence of 0, 2, and 6 PVP is 52, 58, and 62 at the (011) face, whereas at the (01̅1) face is 54, 48, and 46, respectively. Supportive to g(r) calculations, with an increase in PVP concentration from 0 to 6 PVP, the number of H-bonds between solute and solvents increases at the (011) face but 3772

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Figure 7. Radial distribution function g(r) of PVP and naproxen (solute) around the interfacial layer of the crystal.

interaction of solvent with the interfacial layer decreases, but the interaction between solute and solvent increases. As a consequence, the mobility of the solute is hindered by the solvent (not freely available). Due to higher interaction energy of PVP with the interfacial layer compared to the solute, adsorption of solute to the surface is hindered as well; thus growth on this face is inhibited. To visualize such competitive events on the crystal faces, Figure 9 illustrates the simulation snapshots with time. Initially (t = 0 ps), solvent molecules are attached to the surface, and solute and PVP are near to the surface. As time lapses, solvent molecules are being freed at both the faces and a competitive behavior between PVP and solute is observed. Finally (t = 500 ps), PVP is favorably adsorbed on the (011) face, whereas solute naproxen is adsorbed favorably at the (01̅1) face. 3.2. Mixture of Polymeric Additives. In our previous study, it was also observed that crystal growth rate on the (01̅1) face was reduced by the addition of a mixture of PVP and HPMC but improved in the presence of PVP alone.30 To understand these interesting phenomena, Figure 10 plots the g(r) of the solute around the interfacial layer of the crystal. The g(r) peak is amplified with the presence of PVP alone, but diminished in the mixture of PVP and HPMC. This, in turn, indicates that solute interaction with the interfacial layer is enhanced in the presence of PVP alone, but weakened in the mixture. Further, the solvent−interfacial layer interaction is decreased in the presence of PVP alone, but enhanced in the mixture of PVP and HPMC (Figure S4 in the Supporting

Table 1. Interaction Energies between Polymeric Additive and Solute Naproxen with the Crystal Faces interaction energy (kJ/mol) total PVP naproxen

−45.72 −37.69

PVP naproxen

−33.77 −48.57

van der Waals (011) −42.82 −28.65 (01̅1) −31.21 −38.36

electrostatic −1.91 −8.09 −1.56 −9.27

PVP concentrations, the MSD of PVP is lower at the (011) face than the (01̅1) face (Figure S3 in the Supporting Information). The strong interaction between PVP and the (011) face is attributed to a lower mobility, but weak interaction between PVP and the (01̅1) face leads to a higher mobility. From the above analysis, it can be seen that the crystal growth promotion and inhibition phenomenon of naproxen in the presence of PVP is due to the competition among the different types of interactions. In summary, at the (01̅1) face, in the presence of PVP, the interactions of the solvent with the interfacial layer and solute decrease; consequently, solute molecules are freely available. Due to higher interaction energy of the solute with the interfacial layer compared to PVP, solute molecules are adsorbed quickly and, thus, growth is promoted on this face. At the (011) face, upon addition of PVP, the

Figure 8. Mean square displacements (MSDs) of solute with and without PVP in the crystal faces. 3773

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Figure 9. Time evaluation simulation snapshots in the crystal faces. Black dotted lines indicate the solution/crystal interface. Color code near the interface: naproxen, green; PVP, red; ball scheme, solvent. White, solvent away from interface. For clarity, only one molecule of each PVP or solute naproxen is shown.

Figure 10. Radial distribution functions g(r) of solute around interfacial layer of the crystal.

Figure 11. Radial distribution functions g(r) among various pairs. Note that the first layer indicates the interfacial layer.

Information). Additionally, Figure 11 shows the various interactions that are present in the system with mixture of additives. Among these interactions, the solute interacts most strongly with HPMC, followed by PVP, as indicated by the highest and second highest peaks in the g(r) at r ∼ 5.53 Å. Overall, in the presence of PVP alone, solute interaction increases, whereas solvent interaction decreases with the interfacial layer. On the other hand, upon addition of a mixture of PVP and HPMC, solute interaction decreases, but solvent interaction increases with the interfacial layer. Besides, the solute interacts strongly with HPMC, which hinders the motion of the solute to reach the interface, thus retarding the growth.

three different competing molecular phenomena occur at the (01̅1) and (011) faces, leading to growth promotion and inhibition in the −b and +b directions, respectively. First, the degree of solvent (ethanol/water mixture) interaction with either of these two facets drops in the presence of the additive; second, the interaction of the solute (naproxen) with the (01̅1) surface is increased; and, last, solute−solvent interaction at the (01̅ 1) face is reduced, thereby enhancing the rate of attachment of the solute molecules onto this face. In contrast, at the (011) face, the interaction of solute molecules with the crystal surface decreases and, at the same time, the solute− solvent interactions become stronger: overall, these two factors retard crystal growth. Additionally, calculation of mean square displacement illustrates that the additive also influences the mobility of solute molecules present at the interface. This result is supportive of the effect of the additive on crystal growth promotion and inhibition. Furthermore, in the presence of a mixture of additives (PVP and HPMC), molecular interactions among the solute, solvent, and additives

4. CONCLUSIONS We have carried out MD simulations to gain insights into the mechanism underlying the effect of a polymeric additive (PVP) on a naproxen crystal growth along the fast-growing b axis. The simulation results reveal that, in the presence of the additive, 3774

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Crystal Growth & Design

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at the crystal/solution interface lead to growth inhibition at the (01̅1) faces. These results are consistent with the experimental observations and helpful in explaining the anisotropic growth behavior of a naproxen crystal in the presence of polymeric additives.30

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.9b00193. Radial distribution functions g(r) of PVP around the interfacial layer, mean square displacements (MSDs) of PVP, and g(r) of solvent around the interfacial layer (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (K.M.G.). *E-mail: [email protected] (P.S.C.). ORCID

Krishna M. Gupta: 0000-0003-4839-5980 Yin Yani: 0000-0001-7602-084X Sendhil K. Poornachary: 0000-0003-4139-1549 Pui Shan Chow: 0000-0002-5100-2677 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Science and Engineering Research Council of A*STAR (Agency for Science, Technology and Research), Singapore.

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REFERENCES

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Crystal Growth & Design

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DOI: 10.1021/acs.cgd.9b00193 Cryst. Growth Des. 2019, 19, 3768−3776