Predicting the Nucleation Induction Time Based on Preferred

Jul 26, 2017 - The utility of PETI has been tested using two model systems: (1) the .... PS, PVA, and PVC were ranked fourth, fifth, and sixth, respec...
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Predicting the Nucleation Induction Time Based on Preferred Intermolecular Interactions Mitulkumar A. Patel,*,† Brittany Nguyen,† and Keith Chadwick† †

Department of Industrial and Physical Pharmacy, College of Pharmacy, Purdue University, West Lafayette, Indiana 47906, United States

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S Supporting Information *

ABSTRACT: A key challenge in rationally designing heterogeneous surfaces for controlling crystallization is overcoming the lack of understanding the influence of surface properties has on nucleation. Previous studies have shown how surface chemistry can be used to control both nucleation rate and polymorphism. However, these approaches are often empirical and lack any predictive capability. Herein, a novel method, PETI (Predicting Efficacy Through Intermolecular Interactions), for predicting the effectiveness of different polymer surfaces in promoting heterogeneous nucleation is described. PETI utilizes the Cambridge Structural Database to determine the likelihood of forming an intermolecular interaction between solute chemical moieties and polymer surfaces. The concept for PETI is the more likely a solute/polymer interaction, the faster the rate of heterogeneous nucleation. PETI was tested by studying the nucleation of model compounds, benzocaine and 1,1′-bi-2-naphthol, on different polymer surfaces. Results showed that PETIs predictions for the effectiveness of the different polymers at promoting nucleation were in good agreement with experimental observations. This study represents a highly novel approach to predicting the effectiveness of surfaces in promoting crystal nucleation and shows the potential utility of using knowledge of solid-state intermolecular interactions as a tool for the rational design of polymer surfaces for controlling heterogeneous nucleation.

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role in directing the epitaxial mechanism.13,19,23,24 Previous studies have shown that modifying the surface chemistry of the heterosurface can have a significant impact on nucleation rate and polymorphism.20,25−27 However, these approaches are often empirical and lack any predictive capability. To our knowledge, no method exists for rationally selecting heterogeneous surfaces or predicting the efficacy of a surface for promoting heterogeneous nucleation. Herein, we discuss a novel method, named PETI (Predicting Efficacy Through Intermolecular Interactions), for predicting the relative effectiveness of different polymer surfaces in promoting the heterogeneous nucleation of organic compounds. This is a first attempt developing a predictive method for predicting the nucleation rate. Specifically, the aim of this work is to understand whether knowledge gained from the evaluation of solid-state intermolecular interactions (both hydrogen bonding and hydrophobic) from large crystallographic data sets in CSD could be used to predict (1) heterogeneous nucleation kinetics based on the favorability of an intermolecular interaction between a given functional group present on a molecule of interest and different polymer surfaces and (2) how molecules may orient themselves when adsorbed

INTRODUCTION Controlling crystallization is crucial for the production of better materials in the field of foods, pharmaceuticals, and electronics.1−5 Crystallization processes can be optimized by controlling nucleation and/or crystal growth.4,6 Controlling nucleation is of particular interest, as it during this step that the crystal form is determined. Nucleation can occur either homogeneously or heterogeneously at an interface.7 Both homogeneous and heterogeneous nucleation can be controlled using a variety of approaches. The use of additives, both soluble and insoluble, to control nucleation has received considerable interest.8−17 Soluble additives such as pH modifiers, surfactants, ionic strength modifiers, dissolved polymers, and structurally related compounds, have been shown to influence nucleation through direct interaction with a solute in solution.8−12 In contrast, insoluble additives such as polymers, glasses, organic crystals, metal surfaces, and self-assembled monolayers control nucleation by providing a heterogeneous surface (solid−liquid interface) upon which self-assembly can be templated through a variety of epitaxial mechanisms.13−17 The chemistry, crystallography, and topography of the surface have all been shown to affect heterogeneous nucleation.18−22 In particular, chemistry has been shown to play a significant role in controlling heterogeneous nucleation.13,17,19 Specifically, the intermolecular interactions between the functional groups of the solute and heterosurface play a key © 2017 American Chemical Society

Received: March 28, 2017 Revised: July 21, 2017 Published: July 26, 2017 4613

DOI: 10.1021/acs.cgd.7b00446 Cryst. Growth Des. 2017, 17, 4613−4621

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X-ray Powdered Diffraction (XRPD). X-ray powder diffraction patterns were collected using a Rigaku SmartLab XRD 6000 diffractometer (40 kV, 44 mA) using Bragg−Brentano mode. All data were collected at room temperature (∼25 °C) between 5 anf 40° 2θ and with a step size of 0.02°. Scanning Electron Microscopy (SEM). A Nova NanoSEM was used to collect images of the polymer particles and BZC crystals. The samples were fixed onto the sample holder using carbon tape, and then to reduce charging, the samples were coated with platinum (∼2 nm thickness) via a thermal evaporator as described previously.34 The coated samples were then mounted on the SEM stage, and the images were taken at an accelerating voltage of 5 kV. Heterogeneous Crystallization of BINOL on Polymer Surfaces. A solution of BINOL in hexane with concentrations of 0.50, 0.56, and 0.62 mg/mL was prepared and syringe filtered into a scintillation vial (10 mL) using a 0.2 μm PTFE membrane, in order to remove any solid impurities. A glass slide covered in films of PDMA and PS (50% each by area) was prepared by drop coating. The slide was inserted into the scintillation vial which was then quenched cooled to obtain a crystal of BINL. To visually confirm on which polymer the BINOL is being crystalliz first, a shorter induction time would be preferred. Furthermore, the boiling point of hexane being ∼70 °C, we used 60 °C as the saturation temperature, and to get faster crystallization we used 5 °C as the crystallization temperature (supersaturation of 4.20). Further, to compare the effect of various supersaturation values on crystallization of BINOL, lower supersaturation values of 3.66 and 3.16 were selected. Similar experiments were also done for different crystallization temperatures (keeping the supersaturation = 3.16). A BINOL solution in hexane with concentrations of 0.56 and 0.63 mg/mL was prepared (at 65 °C) and quench cooled to 18 and 21 °C, respectively. To ensure reproducibility, the experiment was performed in triplicate. After crystallization, the glass slides were removed from the vials and rinsed with cold hexane. Quantification of BINOL Crystal Mass on Polymer Surfaces. Each polymer film with BINOL crystals was collected and dissolved in ethanol. The concentration of the BINOL was measured using a SI Photonics UV/vis spectrometer (Tucson, AZ), to determine the mass of BINOL per unit area of each polymer.

to a polymer interface. Our hypothesis is that the stronger the interfacial interactions, the faster the rate of nucleation. In addition, heterogeneous nucleation on disordered polymer surfaces is governed by epitaxial mechanisms that orientate the nucleus such that strength of intermolecular interactions between the nucleus and surface is maximized. The utility of PETI has been tested using two model systems: (1) the nucleation of benzocaine on polyethylene, polypropylene, polyvinyl chloride, poly(vinyl alcohol), polystyrene, and poly(4-aminostyre) and (2) the nucleation of 1,1′-bi-2naphthol on polystyrene and poly(N,N-dimethylacrylamide). We shall discuss how PETI was used to predict the relative effectiveness of each polymer in promoting nucleation. Experimental data will be used to demonstrate that PETI was successful in predicting the most effective polymer surface for promoting the nucleation of both compounds. Finally, we shall describe the limitations of PETI in accurately predicting the order of effectiveness of a library of polymers.

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EXPERIMENTAL SECTION

Materials. Benzocaine (BZC), 1,1′-bi-2-naphthol (BINOL), poly(N,N-dimethylacrylamide) (PDMA), polyethylene (PE), polypropylene (PP), polyvinyl chloride (PVC), poly(vinyl alcohol) (PVA), and polystyrene (PS) were all purchased from Sigma-Aldrich (St. Louis, MO). Poly(4-aminostyre) (P4AS) was purchased from Polyscience, Inc. (Warrington, PA). Ethanol (200 proof) was purchased from Fisher Scientific Inc. Heterogeneous Crystallization of BZC. A stock solution of BZC in ethanol with concentrations of 375, 390, and 405 mg/mL was prepared and syringe filtered into scintillation vials (10 mL each) using a 0.2 μm polytetrafluoroethylene (PTFE) membrane, in order to remove any solid impurities. A preweighed amount (200 mg) of the insoluble polymers such as PE, PP, PVC, PVA, PS, and P4AS was added into these solutions, and the vials were then heated to 45 °C to ensure complete dissolution of BZC.28−33 Then the vials were quench cooled to 15 °C (supersaturation, σ = (c−csat)/csat = 1.64/1.75/1.85) and held at this temperature until crystallization. A similar experiment was done for different crystallization temperatures (keeping the supersaturation = 1.64). A BZC solution in ethanol with concentrations of 425 and 475 mg/mL was prepared (at 50 °C) and quench cooled to 18 and 21 °C, respectively. Induction Time Measurements. Nucleation induction time data for BZC with and without different polymer surfaces present were collected using a Crystal16.20 To observe and compare the differences in acceleration of nucleation kinetics on six heterosurfaces, the average induction time >100 min and 850,000 crystal structures)35,36 was searched using IsoStar37 (Version 2.2.4) to determine how many known occurrences (N) there are of an intermolecular interaction between each moiety of the solute and the functional group present on the polymer. It was hypothesized that the greater the value of N, the more favorable the interaction between the moiety and the polymer. Therefore, the moiety with the greater value of N is more likely to nucleate on the polymer. Table 1 is an example of a CSD search to

Table 2. Various Polymers with Predicted Relative Order and Experimentally Observed Order for Their Ability To Nucleate BZCa polymer (FGp) P4AS (uncharged amine) PP (methyl) PE (methylene) PS (phenyl) PVA (alcohol OH) PVC (terminal chloride)

Table 1. Number of Occurrences of Intermolecular Interactions between FGs with FGp for Various Polymersa

a

polymer (FGp)

N (AA)

N (AAE)

predicted interaction

P4AS (uncharged amine) PP (methyl) PE (methylene) PS (phenyl) PVA (alcohol OH) PVC (terminal chloride)

2924 1998 1703 1298 820 669

701 1966 1987 1427 490 824

AA AA AAE AAE AA AAE

predicted interaction

predicted order

observed order

AA

1

1

AA or AAE AAE AAE AA AAE

2 3 4 5 6

5 3 4 2 6

a

1 being most favorable to nucleate BZC and 6 being the least favorable to nucleate BZC.

BZC and BINOL do not alter the polymorphic outcome when crystallized with various heterosurfaces using different supersaturations. In addition, having no polymorphic variation, BZC and BINOL have amine group and aromatic group(s) which are common to many pharmaceutical compounds. Therefore, BZC and BINOL were selected for this study. First, PETI was used to rank the effectiveness of the polymers in promoting the nucleation of BZC. Six polymer heterosurfaces with differing chemical functionalities were selected for this test; PE, PP, PVC, PVA, PS, and P4AS (Figure 2). As discussed above, we hypothesized that the nucleation rate, J, is directly proportional to the number of occurrences, N, of an intermolecular interaction between solute moieties (FGs) and FGp in the CSD. The values of N for the interaction between different BZC moieties with FGp are shown in Table 1, and their rankings for promoting nucleation are shown in Table 2. P4AS (N = 2924) was predicted to be the most effective polymer for promoting the nucleation of BZC. It was also predicted that BZC would interact with P4AS through the AA moiety. After that, PP showed N = 1998 for the BZC AAE moiety, followed by PE which showed a value of N = 1987 for the BZC AA moiety. Therefore, PP was ranked second and PE third. PS, PVA, and PVC were ranked fourth, fifth, and sixth, respectively. To validate the predictions, the nucleation induction times of BZC in the presence of the different polymer heterosurfaces were then measured experimentally. Experimental Measurement of the Average Nucleation Induction Time of BZC in the Presence of Polymer Heterosurfaces. Nucleation induction time is defined as the time period between the generation of supersaturation and nucleation, where nucleation is measured indirectly as the first detectable crystal formation.42,43 Prior to measuring the heterogeneous nucleation induction times, it was necessary to verify that (1) all the polymer surfaces were capable of heterogeneously crystallizing BZC and (2) all polymers surface crystallized the same polymorph of BZC. For confirming the former, cooling crystallizations with the different polymers were carried out, and the resulting samples were analyzed by SEM.

1 = most effective, and 6 = least effective.

determine which BZC moieties (FGs) have the greatest value of N with 6 different polymer surfaces (FGp). Based on these results the PETI predicts that the BZC moiety AA is most likely to interact with P4AS, PP, and PVA, while the BZC moiety AAE is most likely to interact with PE, PS, and PVC.38,39 Predicting the Effect of Interaction between FGs and FGp on Nucleation Kinetics. To predict the efficacy of a polymer surface in promoting nucleation, we hypothesized that the more favorable the intermolecular interaction is between FGs and FGp, the greater the rate of nucleation. To determine the most favorable interaction, we used IsoStar. We propose that the rate of nucleation (J) is directly proportional to the number of occurrences (N) of an intermolecular interaction between FGs and FGp in the database (J ∝ N). Previous research also indicated that the specific complementary/ matching molecular functionality between the solute and the heterosurface influences the rate and the orientation of the nucleating crystal.19,25 Therefore, it is reasonable to hypothesize that the J is directly proportional to N.

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RESULTS AND DISCUSSION Testing the Effectiveness of PETI. To test the ability of PETI to predict the effectiveness of different polymer heterosurfaces on the nucleation rate, BZC and BINOL were selected as the model compounds being crystallized. Compounds such as ROY, carbamazepine, and acetaminophen are known to undergo polymorphic phase transformation when nucleated on various heterosurfaces.25,27,40,41 In our studies we wanted to study the nucleation kinetics for the same polymorph on different polymeric heterosurfaces. We found out that both 4615

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Figure 3. SEM micrographs of BZC crystallized on the different polymers: (A) PE, (B) PVA, (C) PP, (D) PVC, (E) PS, and (F) P4AS.

Effect of Supersaturation and Temperature of Crystallization on BZC Induction Time. To analyze the influence of supersaturation and temperature of crystallization on induction time and nucleating crystal plane, similar experiments were performed with higher supersaturations (1.75 and 1.85) and higher crystallization temperatures (18 and 21 °C, keeping supersaturation constant to 1.64). The results indicated that the average induction time decreases as the supersaturation and temperature of crystallization increase (Figure 4 and Table 3). However, the relative order of polymers for their ability to nucleate BZC did not change. These results suggest that the relative order of nucleation of BZC on the polymer surface was not changed over the range of supersaturation and temperature of the crystallization tested in this study. Mechanistic Investigation of the BZC Nucleation on Various Polymeric Heterosurfaces. As the predicted order of PVA for inducing crystallization of BZC does not match with that of the experimental order, further experiments were performed to analyze any effect of slightly dissolved PVA in ethanol. Briefly, the PVA was stirred in the ethanolic solution of BZC at conditions similar to that used for other crystallization experiments, to prepare a suspension. The supernatant from this suspension was syringe filtered into HPLC vials and analyzed for induction times. The results of the study showed that the average induction time for the PVA treated ethanolic solution of BZC was found to be similar to that of the nontreated bulk (Figure S2 and Table S1). This indicates that the slightly soluble PVA does not have any impact on induction time, and the observed effect is contribution from the insoluble PVA. To investigate the reason behind the slight perturbation in the predicted and observed nucleation rate of BZC on the PVA and PP, a mechanistic study of the nucleation of BZC on various polymers was carried out. A preferred orientation study by XRPD was performed to identify the plane of the BZC crystal nucleated on various polymers. The surface chemistry of the nucleated plane provides information regarding the specific polymer-BZC interaction responsible for heterogeneous crystallization of BZC on that polymer. The results of the study indicated that the (004) plane of the BZC Form I crystal

The results showed that all the polymers were capable of heterogeneously crystallizing BZC (Figure 3). To confirm that all BZC crystallized on all polymers is of the same form, XRPD analysis was performed. The results of the XRPD analysis showed that in all cases BZC Form I crystallized (Figure S1). Due to the stochastic nature of nucleation, for each polymer 80 induction times were measured (under identical experimental conditions) in order to calculate the average nucleation induction time. In determining nucleation induction times it was assumed that the time required to generate the desired supersaturation was negligible. It was also assumed that the time between primary and secondary nucleation occurring was negligible. Finally, it was also assumed that the growth rate of BZC Form I is sufficiently fast such that the time between nucleation occurring and the crystals becoming experimentally detectable is minimal.19 Once the experimental induction time data were collected, the average nucleation induction time for BZC Form I from the ethanol was calculated using eq 2. It was assumed that nucleation is a first order kinetic process and follows a Poisson distribution19,44−46 1 ln P = − t τ

(2)

where P is the probability that crystallization will not be observed during a time interval, t, and τ is the average nucleation induction time. The τ was obtained by plotting ln P against t (Figure 4). Using linear regression analysis, the values of τ and its associated error were calculated for BZC with and without the polymers (Table 3). From Table 3 it can be clearly seen that all the polymer heterosurfaces reduce the average nucleation induction time when compared to the bulk value. P4AS was found to be the most effective for promoting the nucleation of BZC, while the PVC was found to be the least effective. The experimental ranking of the polymer heterosurfaces was then compared with the ranking predicted by PETI (Table 2). The results of this study showed that the method was overall successful in predicting the relative nucleation rate of BZC on various polymeric heterogeneous surfaces. However, the order of nucleation of PP and PVA was found to change with each other. 4616

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Figure 4. A plot of ln P (obtained from induction time data) as a function of time for BZC in ethanol: (A) at 15 °C with supersaturation 1.64, (B) at 15 °C with supersaturation 1.75, (C) at 15 °C with supersaturation 1.85, (D) at 18 °C with supersaturation 1.64, and (E) at 21 °C with supersaturation 1.64. By utilizing the equation ln(P) = −t/τ (where P is the probability of not being crystallized within the fixed amount of time, t) the data are presented in the form of linear regression. The negative inverse of the slope (−1/τ) for the lines will give the values of the average induction time, τ.

Table 3. Average Induction Time, τ (min), for BZC Form I from Ethanol with or without the Presence of Various Polymeric Heterogeneous Substratesa substrate P4AS PVA PE PS PP PVC none (bulk)

σ = 1.64 at 15 °C 33 110 126 156 168 306 1238

± ± ± ± ± ± ±

1 2 3 2 3 3 31

σ = 1.75 at 15 °C 18 67 91 98 130 228 608

± ± ± ± ± ± ±

σ = 1.85 at 15 °C

1 3 2 4 3 5 18

13 38 55 68 77 106 398

± ± ± ± ± ± ±

1 2 4 3 2 2 12

σ = 1.64 at 18 °C 26 96 124 149 163 279 690

± ± ± ± ± ± ±

2 3 3 3 4 3 17

σ = 1.64 at 21 °C 22 47 66 76 95 183 424

± ± ± ± ± ± ±

1 3 2 2 3 3 10

R for linear regressions were found to be ≥0.95 for all conditions.

a 2

nucleated on PVA, PP, PVC, PE, and P4AS films, while the (011) plane of the BZC Form I crystal nucleated on PE films (Figure S3). Furthermore, the molecular chemistry of the (004) plane of the BZC Form I crystal showed the presence of the AA moiety (Figure 5A), which is in accordance with our preliminary prediction that the AA moiety of BZC has a higher potential to interact with P4AS and PP.

On the other hand, the molecular chemistry of the (011) plane of the BZC Form I crystal indicated the presence of mixed aromatic amine and aliphatic-aromatic ester functional moieties (Figure 5B). The PE indicated the presence of the (011) face on its surface, which was consistent with the predictions. Nevertheless, PS and PVC deviate from our predictions and nucleate on the (004) plane, indicating its interaction with the AA moiety. A meticulous look at the (004) 4617

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higher tendency to interact with the aromatic C−H (N = 4993), substituted aromatic carbon (N = 2496), and any C−Cl (N = 4993). Such types of interactions were not taken into consideration while predicting the most favorable interaction between solute and polymer. Similarly, to understand why the PVA was more effective than predicted, we also checked for possible aromatic interactions. An IsoStar search for the phenyl group indicated that it has a higher tendency to interact with the alcohol OH (N = 3321). In addition, the uncharged aliphatic hydroxyl group was also found to be prone to interact with the substituted aromatic carbon (N = 2481) as well as aromatic C−H (N = 4961). These results indicate that the interaction between BZC and the PVA not only involved the AA moiety but also a higher number of nonbonded aromatic interactions. These types of small aromatic moieties (phenyl and aromatic substituted carbon) of BZC were not considered while predicting using PETI. This was the reason why the PVA showed a higher preference over other polymers for enhancing the nucleation of BZC. The results of the study also indicated that the P4AS (containing 4-aminophenyl) has the greatest effect on enhancing the nucleation rate of BZC, which was due to their interaction with the BZC 4-aminophenyl group. These results were also consistent with the previous study, which indicated that the nucleation rate of the API is enhanced on the substrate with the same chemistry.19 Furthermore, according to these results, the primary amine containing polymer was shown to interact successfully with the amine functional group of BZC. In addition, the alcohol containing polymer was shown to interact successfully with the amine functional group of BZC. This result is also consistent with some of the experimental results for the cocrystal in general that showed that the alcohol (hydroxyl group) has a higher tendency to form a heterodimer with amine groups, while the primary amine is more prone to form a homodimer with the amine group.47 This indicates that the information from the CSD regarding solid-state intermolecular interactions can be used to predict the interactions between polymer and solute. Our method was successful for predicting relative nucleation rates as well as the most favorable interactions between a given compound and various polymer surfaces. In this method, while selecting the BZC moieties, BZC was broken down into only the hydrogen bonding moieties of BZC (AA and AAE) because they are the strongest interactions. However, other weak aromatic interactions that might play a role in influencing the nucleation of BZC were disregarded. To validate this argument that the aromatic carbon plays a significant role in the interactions, we selected a model compound BINOL as it has both aromatic moieties (for nonbonded interactions) as well as hydroxyl moieties (capable of making a hydrogen bond). Predicting BINOL Nucleation on Competing Polymer Films. To further validate the PETI, it was utilized for

Figure 5. (A) Molecular structures of the (004) plane of the BZC Form I crystals showing AA (dotted box) and AAE (solid box) groups and at the surface. (B) Molecular structures of the (011) plane of the BZC Form I crystal showing the presence of both AA (dotted box) and AAE (solid box) groups and at the surface. The solid line indicates the top surface of the corresponding plane.

Figure 6. Chemical structure of the material used for predicting the most favorable interaction between solute and a binary polymeric surface. Model compound 1,1′-bi-2-naphthol (BINOL) highlighting phenyl (dotted box) and phenol (solid box) functional groups. The binary polymeric surface has two polymers: polystyrene and poly(N,Ndimethylacrylamide).

Table 4. Number of Occurrences of Intermolecular Interactions between FGs (of BINOL) with FGp for Various Polymers polymer (FGp) PS (phenyl) PDMA (aliphatic dimethylamino)

N (phenol OH)

N (all aromatic) 8915 (aromatic C−H = 4993, substituted aromatic carbon = 2496, and phenyl = 1426) 6557 (aromatic C−H = 4966, substituted aromatic carbon = 807, and phenyl = 784)

3329 73

plane indicates that the phenyl group of BZC is always present near the surface. Moreover, PS and PVC form hydrophobic interactions with the aromatic portion (phenyl ring) of BZC. An IsoStar search for the phenyl group indicated that it has a

Table 5. Induction Time and Amount of BINOL Crystallized on PS and PDMA Film at Various Supersaturations supersaturation

temp of crystallization (°C)

4.20 3.66 3.16 3.16 3.16

5 5 5 7.5 10

induction time on PS (min) 7 12 29 22 15

± ± ± ± ±

induction time on PDMA (min)

2 3 5 2 2

15 28 74 62 49 4618

± ± ± ± ±

4 3 9 4 3

BINOL on PS (μg/cm2) 370 328 272 265 285

± ± ± ± ±

50 37 21 17 22

BINOL on PDMA (μg/cm2) 50 43 29 30 35

± ± ± ± ±

30 19 8 11 14

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Figure 7. Selective crystallization of BINOL on the binary polymeric surfaces. (A) Photograph of the binary polymeric surface consisting of the PDMA (left) and PS (right) films showing heterogeneous nucleation of the BINOL crystals after cooling crystallization. Optical micrograph of BINOL crystals growing on (B) PDMA and (C) PS surfaces.

tions, the nucleation of BINOL was then measured experimentally on both PS and PDMA films. Experimental Validation of Competitive BINOL Crystallization. To validate our predictions, crystallizations of BINOL in the presence of both polymers were carried out (supersaturation = 3.16). Visual inspection of the polymer surfaces during crystallization revealed that BINOL first crystallized on the PS film and then the PDMA film (Table 5). In addition, a significantly greater mass of BINOL crystallized on the PS film (Figure 7 and Table 5) compared to that on the PDMA film. To analyze the influence of supersaturation and temperature of crystallization on induction time and nucleating crystal plane, similar experiments were performed with higher supersaturations (3.66 and 4.20) and higher crystallization temperatures (7.5 and 10 °C, keeping supersaturation constant to 3.16). The results indicated that the induction time decreases as the supersaturation and temperature of crystallization increase (Table 5). However, in all cases the crystallization on PS was faster and produced more BINOL crystals compared to PDMA. These results suggest that the preference of nucleation of BINOL on PS and PDMA surfaces did not change over the range of supersaturation and temperature of the crystallization tested in this study. XRPD was used to identify the nucleating crystal plane(s) of BINOL on PS and PDMA (Figure S4A-E). The results of the study showed that the (200) crystal plane of BINOL nucleated on both surfaces for all different conditions. Analysis of the chemistry of the (200) face showed aromatic rings exposed to the surface, while the OH groups were not present (Figure 8). This is consistent with the PETI predictions that PS would be the most effective polymer for nucleating BINOL and that the nucleating crystal planes for both polymers would be aromatic rich and OH poor. In short, the PETI successfully predicted the effectiveness of polymers for nucleating BINOL. Further, this study also indicates that the aromatic interactions influence the result of the prediction.

Figure 8. Molecular structures of the (200) plane of BINOL crystal showing the presence of both phenyl (dotted box) and phenolic (solid box) groups. The solid line indicates the top surface of the corresponding plane.

predicting the nucleation of BINOL, a compound with both hydrogen bonding and nonbonding (aromatic) moieties. Further, to analyze the capability of BINOL to be attracted toward the surface containing aromatic FGp (hydrophobic) vs aliphatic FGp (hydrophilic) we have selected PS and PDMA (Figure 6) as polymeric heterosurfaces, respectively. The different conditions of this test is that the polymers are tested competitively rather than sequentially, i.e. the major goal of this study is to figure out with BINOL being a majorly aromatic molecule, what is more important for BINOL crystallization, aromatic surface or aliphatic surface. Therefore, only two polymers, PS and PDMA, were selected. For this study, first, BINOL was categorized as two distinct chemical moieties: (1) all aromatic interactions (aromatic C− H, substituted aromatic carbon, and phenyl) (Figure 6a, dottedline box) and (2) phenol OH (Figure 6b, solid-line box). The CSD was then searched using IsoStar to determine the value of N for each moiety with the functional groups of PDMA (aliphatic dimethylamino) and PS (phenyl). The search results showed that for the interaction with the functional group of PDMA, the N value for (1) all aromatic interactions was found to be 6432 and for (2) phenol OH it was found to be 70 (Table 4). On other hand, the search results for the interaction with the functional group of PS showed the N value for (1) all aromatic interactions was found to be 8915 and for (2) phenol OH it was found to be 3329 (Table 4). From these results, it was inferred that, for both chemical moieties of BINOL, the N values are greater for PS. Therefore, PETI predicts that the nucleation will be favored on PS. Furthermore, as the N values for aromatic moieties are greater in both PDMA and PS, PETI predicts that a nucleating crystal plane should consist of aromatic rich moieties for both polymers and a lesser chance of expecting OH−surface interactions. To validate our predic-

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CONCLUSIONS In conclusion, this study shows a novel approach to predict the efficiency of heterogeneous nucleation by developing a unique predictive method, PETI. Developing PETI is a first attempt to predict the most effective polymer, from a library of polymers, for promoting heterogeneous nucleation of organic compounds. This method was designed based on the favorability of intermolecular interactions between the functional group of the compound and the surface (according to CSD). PETI utilizes both hydrogen bonding and hydrophobic interactions 4619

DOI: 10.1021/acs.cgd.7b00446 Cryst. Growth Des. 2017, 17, 4613−4621

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existing in CSD to predict the relative order of heterogeneous nucleation kinetics and orientation of molecules interacting with the surface. PETI was overall successful in predicting the most effective heterosurface, which can maximize the nucleation rate of BZC on the polymer surface. In addition, the PETI was also successful when utilized for predicting the nucleation preference of the BINOL on competing surfaces. In both of these studies the molecules having one or two functional moieties were tested. Furthermore, PETI assumes that there is only one type of interaction involved in nucleation of solute on polymer. In the future, we will try to expand the ability of PETI to make successful predictions using more complex organic molecules containing wider varieties of chemical moieties. PETI could be applied to many different types of industries such as food, electronics, and pharmaceutical for finding the most effective polymer for controlling heterogeneous crystallization as well as the functional group present in the nucleating crystal plane. Application of PETI would help in improving the efficiency of the research and development involving crystallization on polymer heterosurfaces.

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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.7b00446.

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Materials and methods along with additional data (PDF)

AUTHOR INFORMATION

Corresponding Author

*Phone: 765-496-1693. Fax: 765-494-6545. E-mail: patel352@ purdue.edu. ORCID

Mitulkumar A. Patel: 0000-0002-9309-6288 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to thank Lilly Endowment, Inc. as this work was supported in part by a grant from the Lilly Endowment, Inc., to the College of Pharmacy, Purdue University, West Lafayette, IN 47906, USA.

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