Experimental and Mechanistic Study of the Heterogeneous Nucleation

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Experimental and mechanistic study of the heterogeneous nucleation and epitaxy of acetaminophen with biocompatible crystalline substrates Tharanga K. Wijethunga, Fahimeh Baftizadeh, Jelena Stojakovic, Allan S. Myerson, and Bernhardt L Trout Cryst. Growth Des., Just Accepted Manuscript • Publication Date (Web): 24 May 2017 Downloaded from http://pubs.acs.org on May 25, 2017

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Crystal Growth & Design

Experimental and mechanistic study of the heterogeneous nucleation and epitaxy of acetaminophen with biocompatible crystalline substrates Tharanga K. Wijethunga,+ Fahimeh Baftizadeh,+ Jelena Stojaković, Allan S. Myerson and Bernhardt L. Trout* Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States. ABSTRACT: The presence of different heterogeneous surfaces can directly influence the nucleation kinetics, crystal growth and morphology of active pharmaceutical ingredients (APIs). However, a mechanistic understanding of heterogeneous nucleation remains lacking. Herein, we report the use of biocompatible crystalline heterogeneous surfaces to enhance the nucleation rates of the model API compound acetaminophen (APAP). We also report experimental and computational studies of the epitaxial growth mechanism of APAP on different substrates. Five crystalline substrates namely, D-galactose (DGAL), the α and β forms of D-mannitol (DMAN), α-lactose monohydrate (LMH) and xylitol (XYL) were selected because they contain a similar functionality: a high density of hydroxyl groups per molecule. We measured the induction times in the presence of the substrates and used the results to rank the substrates based on their ability to enhance the nucleation of APAP. While all selected substrates enhanced the nucleation rates, XYL was particularly effective and enhanced the nucleation rate by a factor of 10 (average induction time: 85 minutes) relative to bulk crystallization (average induction time: 885 minutes). To determine the mechanism underlying the enhanced heterogeneous nucleation, we analyzed grown crystals using single crystal X-ray diffraction (SCXRD) and developed computational models of APAP-substrate interactions. Previously developed computational techniques, which are based solely on the level of lattice matching (geometric term) and ignore the importance of chemical interactions (energy term) between the crystallizing API and the substrate were not effective in predicting and explaining our experimental results. Herein, we present a novel computational method that contains both energy and geometry terms to describe the nucleation of APAP on different crystalline substrates. First, we studied the energetics of the association of a single APAP molecule and a substrate. We found that an increase in the association energy is related to an increase in the effectiveness of the substrate for enhancing the nucleation rate. We next developed a method based on molecular dynamics (MD) simulations of the interaction between the different crystal faces of APAP and the substrates. The method predicted the epitaxial growth of the crystal face (001)APAP on top of the selected substrates based on strong hydrogen bond interactions with the substrates. The growth of the crystal face (001)APAP was confirmed by SCXRD.

INTODUCTION Crystals are ubiquitous in nature, and crystallization is an important process in the pharmaceutical, food and chemical industries. Crystallization can be divided into two broad stages: nucleation and crystal growth.1 Nucleation is the initial step during which the new phase is formed and is crucial for the control of all important product properties, such as the crystal form and particle size distribution.2,3 There are two distinct nucleation mechanisms: homogeneous and heterogeneous nucleation. In homogeneous nucleation, a nucleus is formed by the random aggregation of particles from the solution, which is energetically unfavorable because of the high surface tension of the prenucleation aggregates.4 In contrast, in heterogeneous nucleation, the high energy barrier for the formation of the prenucleation aggregates is reduced by the presence of foreign surfaces that decrease the surface tension of the newly formed nuclei.5 As a result, almost all nucleation events in practice are influenced to some degree by different foreign surfaces (often referred to as heterosurfaces) present in the crystallization environment. Both the chemistry (compatible functional groups and intermolecular interactions) and geometry (naturally occurring roughness, crystal lattice parameters and imprinted features) of heterosurfaces determine the crystalliza-

tion outcome, and these features can control the morphology,6,7 orientation,8,9 polymorphism,10–12 crystal size distribution13 and nucleation kinetics14,15 of the newly forming crystal. However, heterogeneous nucleation is a complex process, and a fundamental understanding of the effects of heterosurfaces on nucleation remains lacking,16 which also hinders the design and direct utilization of heterosurfaces for the control of crystallization. Enormous amounts of effort have been directed toward understanding the effects of different heterosurfaces on nucleation processes, such as self-assembled monolayers (SAMs),17,18 polymers,19,20 microgels21 and inorganic crystalline surfaces.22 During nucleation on crystalline surfaces, the substrate crystal has been demonstrated to determine the orientation of the newly forming crystal (overlayer), and this concept is known as epitaxy.23 The success of the epitaxial mechanism is governed by the ability of the substrate crystal to interact and order the prenucleation aggregates and thereby reduce the unfavorable energetics. Hence, a rational approach to selecting crystalline heterosurfaces for a crystallization process can directly influence the structure of the prenucleation aggregates, leading to the directed self-assembly of molecular components into nuclei and crystals with predetermined structures and properties. How-

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ever, organic molecular crystalline surfaces have attracted considerably less attention as substrates, probably because of their inherently complex surfaces, which require the combined analysis of the contributions from intermolecular interactions with surface functionalities, surface topography and crystal lattice matching. Previous studies on the epitaxial nucleation mechanism have primarily focused on understanding the influence of the lattice match between the heterosurface and the underlying overlayer surface in enhancing the nucleation process.24,25 Three categories of lattice registry modes have been defined namely, total (commensurate), partial (coincident) and lattice mismatch (incommensurism) that have different effects on epitaxial growth.26 A total or partial lattice registry between two opposing planes has been shown to lower the nucleation free energy barrier by successfully absorbing the prenucleation aggregates in the systems such as Langmuir monolayers27 and inorganic crystalline surfaces22. However, with organic crystalline substrates, crystal nucleation has been found to be highly sensitive to the substrate’s surface functionalities, which may be more important than the effect of lattice match.28 Such functional groups on heterosurfaces can participate in intermolecular interactions, such as hydrogen bonding,29 potentially lowering the free energy barrier to nucleation. This concept has been successfully exploited to create organic crystalline substrates able to enhance the nucleation rates of an active pharmaceutical ingredient (API)30 and control polymorphism.31–33 In contrast, seeding can be introduced as a process involving an epitaxial interaction mechanism between seed crystals acting as substrates and newly forming crystal nuclei. This method is widely used to control crystallization in industrial processes. However, for crystalline substrates, the effect of molecular functionality is comparatively underexplored. Acetaminophen (APAP) is an important analgesic and antipyretic agent that is commonly known as paracetamol.34 It has three reported polymorphs, of which form I is the most stable.35 Of its two metastable polymorphs, form II has been fully characterized and shown to have attractive tableting properties compared to form I.36 APAP is very soluble in many solvents, including United States Pharmacopeia (USP) Convention class III solvents, such as ethanol.37 Apart from these physical properties, the structure of APAP is simple and includes potential hydrogen bonding sites, such as hydroxyl, amide and carbonyl functional groups (Fig. 1). These facts make APAP an ideal candidate to study the underlying mechanistic effects of crystalline heterosurfaces and their substrate functionalities in promoting heterogeneous nucleation. Hence, we opted to measure the nucleation rate of APAP to evaluate the effectiveness of different biocompatible crystalline substrates as heterosurfaces. To this end, a set of four biocompatible substrates that are rich in hydroxyl groups were selected for the primary investigation: D-galactose (DGAL), D-mannitol (DMAN), α-lactose monohydrate (LMH) and xylitol (XYL), Fig. 1. Furthermore, considering the importance of epitaxy in industrial settings, developing a method that can reliably predict whether a certain substrate will facilitate the crystallization of the solute and in what orientation would be useful. To achieve epitaxy predictions, Ward’s group has developed methods based on geometric lattice match, which are known as EpiCalc24,38 and global real-space analysis of crystal epitaxy (GRACE).33 These methods calculate the degree of lattice match between two two-dimensional (2D) lattices as a dimensionless potential energy term, V/V0, which represents a “goodness-of-fit” between the lattices of the overlayer and the substrate. Such calculations require information about the 2D lattice parameters for the overlayer and substrate, the range and step size of θ (the

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azimuthal angle between the overlayer and substrate unit cells) to be tested, and the size of the overlayer. In GRACE, rather than searching for exact matches between lattices (EpiCalc criteria) and determining the mode of epitaxy, both exact and near-coinciding points are considered to produce an “epitaxy score” that reflects the density and precision of lattice coincidence within a predefined search area.33 Over the years, these methods have proven to be effective in cases where predominantly geometrical factors are important, such as when a Van der Waals (VdW) crystalline overlayer grows on a VdW crystalline substrate.38 A question remains as to whether these methods can predict the epitaxial growth when the surface chemistry of the substrate and overlayer is likely the major contributor to nucleation.

Fig. 1: Chemical structure of a) APAP and the substrates b) DGAL, c) DMAN, d) LMH and e) XYL.

Herein, we present the key results and conclusions of our nucleation studies of APAP on biocompatible crystalline heterosurfaces. The purpose of this work was to expand the fundamental understanding of how compatible functionalities and intermolecular interactions between functional crystalline heterosurfaces and API would manifest in the enhancement of the nucleation kinetics. All of the selected substrates are rich in hydroxyl functional groups because it is presumed that hydroxyl groups can easily form hydrogen bonds with APAP. As predicted all the substrates were effective in enhancing the nucleation rates of APAP. We observed complex probability distributions of the nucleation induction time with LMH, and further studying this phenomenon confirmed that LMH undergoes surface changes in ethanol, producing two dominant types of nucleation sites. We also investigated the effect of the substrate polymorphism on the nucleation using two polymorphs of DMAN (α and β forms). This is, to our best knowledge, the first study of this type. Induction experiments proved that these two polymorphs are equally effective in enhancing the nucleation kinetics, possibly because they contain nearly identical DMAN molecules, which only differ in the intermolecular interactions between them, in the crystal lattice. Thus, we expect our results to be applicable to a wide range of crystallization processes. In addition to the experimental study, we present a computational method used to rationalize the effectiveness of XYL in enhancing APAP nucleation and to predict the epitaxy of APAP on different crystalline substrates. Our method contains both energy and geometric terms. We postulated that the crystal face of APAP that has the highest energy of interaction (EOI) with the substrate will eptaxially grow on the exposed face of the substrate. For the studied substrates, our method calculated that the crystal face (001)APAP has the highest EOI with the substrates and will, therefore, grow on these substrates. Our predictions were confirmed by single crystal X-ray


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diffraction (SCXRD) analysis. We also showed that this high EOI is the result of the high number of strong hydrogen bonds formed between APAP and the substrate face. The presented method is generic and can predict epitaxial growth when both geometric and energetic terms play important roles in nucleation.39

the polymorphism of the material using HighScore Plus software (see the Supplementary Information [SI S1]). The CSD codes for the crystal structures utilized in the powder pattern simulations were ADGALA01 (DGAL),45 DMANTL01 (-DMAN),46 DMANTL07 (-DMAN),47 LACTOS03 (LMH)48 and XYLTOL01 (XYL)49.

METHODS

Then, the selected excipient substrates were sieved through two sieves with pore sizes of 125 μm and 250 μm to control the crystal size distribution (125 - 250 μm) in the induction time experiments. These sieved crystals were then analyzed using PXRD using the above mentioned experimental settings to extract preferred orientation information. A minimum of three PXRD patterns were collected from different samples of each substrate (see SI S2).

Experimental methods Materials APAP, DMAN and XYL were purchased from Sigma-Aldrich (St. Louis, MO). LMH was purchased from DFE Pharma (Paramus, NJ). DGAL was purchased from Acros Organics (Geel, Belgium). Ethanol (absolute, 200 proof) was purchased from VWR International (Edison, NJ). One-milliliter shell vials with clear caps were obtained from Cole Parmer Instrument Co. (Vernon Hills, IL). Preparation of shell vials The shell vials used for the induction time experiments may have contained particulate matter, which could act as potential nucleation sites. To minimize the influence of these foreign substances on nucleation, the vials were submerged in ethanol for a few hours (~2 hrs), washed thoroughly with ethanol, and dried overnight in a hot (50 ºC) vacuum oven to remove any particulate matter. Substrate selection and preparation Previous studies demonstrated the use of interfaces with similar molecular functionality and hydrogen-bonding capability to induce fast nucleation.30,40,41 APAP has hydroxyl and amide functional groups, which are favorable for the formation of hydrogen bond interactions. Therefore, it was predicted that crystalline substrates whose crystal faces are rich in hydroxyl groups should promote nucleation through preferential interactions with the APAP nuclei. Therefore, all of the selected substrates are rich in hydroxyl functional groups. Furthermore, all of these selected substrates are biocompatible and frequently used in pharmaceutical formulations, and they display no detectable solubility in ethanol, which was the preferred solvent in the current study. Considering these factors, LMH, DGAL, XYL and β-DMAN were selected as substrates and were used directly without any treatment. These were the initially investigated substrates. Subsequently, -DMAN was introduced as a substrate to study the effect of the substrate polymorphism on the nucleation kinetics of APAP. For this purpose, -DMAN was obtained by slowly cooling a saturated solution of commercially available DMAN at 50 ºC in 70% ethanol. Long, needle-shaped crystals of DMAN were obtained after 24 hours. Often, different polymorphs can be present concomitantly in different substrates, such as DMAN,42,43 and can act as different heterosurfaces, giving rise to multiple regimes or complex probability distributions in induction time experiments. Hence, it was necessary to confirm the polymorphic purity of the selected substrates before using them in the induction time experiments. To this end, powder XRD (PXRD) was performed, and powder patterns were collected at room temperature with a PANalytical X’Pert PRO Theta/Theta PXRD system with a CuKα X-ray source at 40 kV and 40 mA and an X’Celerator high-speed detector. The substrate samples were finely ground and spread evenly onto standard zero-background sample holders, and PXRD patterns were obtained for a 2θ range from 3° to 35°. The data obtained were compared to the simulated powder patterns from the Cambridge Structural Database44 (CSD) to ascertain

Optimizing the experimental parameters and conditions Ethanol was selected as the solvent of choice for the induction time measurements because APAP is highly soluble in ethanol, whereas the selected substrates displayed no detectable solubility in ethanol. Furthermore, ethanol is a biocompatible USP class III solvent. The reference temperature was selected to be 15 ºC for the calculation of the supersaturation. The supersaturation (S) was defined as S = C/C*, where C is the solution concentration of the hot solution, and C* is the saturated concentration at the reference temperature. To select a suitable supersaturation, homogeneous/bulk induction time experiments of APAP were conducted without any substrate in the system with selected supersaturations of 1.5, 1.6, 1.7 and 1.8. For each supersaturation, a set of 80 experiments was conducted to obtain the average nucleation induction time (see SI S3). A supersaturation of 1.7 was found to be optimal to obtain a reasonable number of crystallizations while maintaining a reasonable induction time. When the supersaturation is too low (1.7) value facilitates homogeneous nucleation even if the substrates are present in the system. Induction time measurements Various methods, such as microscopy,20 light-scattering spectroscopy,50 turbidimetry,21 pulsed nuclear magnetic resonance, electrodynamic levitation51 and conductivity measurements52, have successfully been utilized in induction time experiments, and each has its own advantages and disadvantages.53 We opted to use an automated microscopic method for these experiments because this method facilitated visually observing the onset of nucleation. First, a solution of APAP in ethanol with the concentration needed (229.89 mg/ml) to achieve the target supersaturation (1.7) was prepared on a hot stirring plate at 50 ºC. Once the APAP had dissolved completely, the hot solution was filtered into four pre-heated 25-ml vials kept on a heating block at 50 °C through a polytetrafluoroethylene (PTFE) membrane with 0.2-μm pores. This filtration ensured the elimination of suspended foreign particles, which can act as potential nucleation sites. Furthermore, precautionary steps were taken to minimize solvent evaporation during the transfer to ensure that the targeted supersaturation was achieved. The solution was divided into four vials to minimize the evaporation during pipetting, and the vials were then tightly capped and allowed to equilibrate. The pretreated shell vials were loaded onto heating blocks and kept at 50 °C for equilibration. For the experiments with substrates, 2 mg (± 0.1 mg) of substrate was measured and added to each shell vial before the vials were transferred to the heating blocks. An attempt was made to evenly distribute the substrate to cover the bottom of each



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shell vial. A control experiment was conducted without any substrate to measure the homogeneous nucleation rate of APAP at the selected supersaturation. In a typical induction time experiment, 80 vials were used, and 400-μL aliquots of filtered and equilibrated solution were hot-pipetted into each vial, which was then capped immediately to prevent evaporation. These shell vials were kept on the heating blocks for approximately ten minutes to ensure the complete dissolution of any APAP nucleates before being transferred to a cooling block kept at 15 °C. The cooling block was mounted on the top of a Zeiss Axio Observer inverted microscope (Carl Zeiss International, USA) equipped with a motorized stage. The sudden decrease in temperature resulting from the contact of the vials with the cooling block ensured that the target supersaturation was achieved via quench cooling. The image collection was fully automated and controlled via AxioVision software (Carl Zeiss Microscopy GmbH). Once the samples were transferred to the cooling block, they remained undisturbed aside from minor vibrations related to microscope stage movements for the duration of the image collection. This ensured that possible secondary nucleation pathways would be minimized. The stage was moved so that the bottom of each vial came into focus every 3 minutes, at which point an image was captured. Image collection was initiated as soon as the vials were transferred to the cooling block, and the data were collected for a total period of 24 hours. The time required for each sample to nucleate was determined based on the recorded images by calculating the time lapsed from the start of the imaging, which corresponds to the time when a supersaturation of 1.7 at 15 °C was achieved, and the time at which the first appearance of a visible crystal was captured. The results of this technique are based on the assumption that the growth rate of the APAP crystals was fast enough so that the time between nucleation and the crystals growing to a visible size was negligible. Furthermore, it was assumed that the time taken to generate the desired supersaturation was negligible. Previous studies have suggested investigating the nucleation induction times based on experimentally determined probability distributions considering the random and independent nature of nucleation.54 For this purpose, a large number of identical experiments is required to obtain a statistically significant result. Thus, several attempts were made for each experimental condition. Only the first nucleation event observed in each sample was considered because, if the first formed single crystal is large enough, it can cause secondary nucleation55,56, as commonly observed in these systems. Moreover, the vials were carefully monitored for any significant solvent loss at the end of each experimental session because solvent evaporation would increase the supersaturation and, thereby, decrease the induction time. However, no significant solvent evaporation was noted in the crystallization vials during the experimental period. Following the above-described method, induction time measurements of APAP were conducted under six different conditions: without substrate (bulk/homogeneous nucleation) and on DGAL, -DMAN, -DMAN, LMH and XYL. Determination of the effective surface areas of substrates for APAP induction To ensure that using the same weights of different substrates led to comparable surface coverages on the bottom of each vial, Brunauer–Emmett–Teller (BET) analysis was conducted. The surface areas of the substrates were determined by BET nitrogen-adsorption measurements using a Micromeritics ASAP 2020 instrument. Approximately 200 mg of each sample was degassed for 5 hours at 70 °C prior to the analysis, followed by N2 adsorption at 196 °C. N2-adsorption isotherms were collected in triplicate for all

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substrates, analyzed using the ASAP 2020 software (Micromeritics) and reported as average values. For XYL, BET analyses of two additionally size-distributed crystal samples (75-125 µm and 250-300 µm) were performed in triplicate. Effect of the surface area on the average induction time Two separate sets of induction time experiments were conducted with XYL as the substrate to investigate the effect of changing the substrate surface area on the average induction time of APAP. In the first set of experiments, three different masses (1 mg, 2 mg and 3 mg) of XYL with the same size distribution (125-250 µm) were introduced into each vial, and 80 experiments were conducted for each mass, as described above. In the second set of experiments, equal masses (2 mg) of three differently size-distributed (75-125 µm, 125250 µm and 250-300 µm) crystal samples of XYL were introduced into crystallization vials, and induction time measurements were performed. In each experiment, the effective surface area of XYL for the induction of APAP nucleation was controlled by changing either the amount of substrate or the size distribution of the substrate crystals. PXRD analysis after nucleation experiments After the nucleation experiments were complete, the APAP crystals obtained from each set of experiments were analyzed using PXRD. For each experimental condition, at least five vials were randomly selected, and XRD powder patterns were collected from the finely ground powder to identify the APAP polymorph that had crystallized. All the samples were kept on standard zero-background sample holders, and XRD powder patterns were obtained over the 2θ range from 3° to 35° using a PANalytical X’pert Pro diffractometer and analyzed with HighScore Plus software. The patterns were compared to the simulated powder pattern of APAP Form I (CSD code HXACAN0157). The PXRD data confirmed that in each experimental setting, APAP Form I was produced exclusively, regardless of the presence of different substrates in the system (see SI S4). To determine whether the substrates underwent any polymorphic conversions or considerable changes in ethanol under the induction experimental conditions, a separate set of experiments was conducted. Initial PXRD patterns were collected from finely ground substrates, and then, the powders were immersed in absolute ethanol for 24 hours at room temperature. After 24 hours, the powders were filtered and dried, and PXRD patterns were recorded. These final PXRD patterns were then compared with the initial powder patterns and the simulated powder patterns from the CSD reported structures. This comparison confirmed that the substrates were stable under the experimental conditions, thereby eliminating the potential for complications resulting from polymorphic conversion or other changes to the substrates in ethanol (see SI S5). Atomic force microscopy (AFM) analysis of LMH crystals Single crystals (1-2 mm) of LMH were analyzed with AFM to observe any surface changes. AFM images were obtained with a Dimension 3100 XY closed-loop scanner (Nanoscope IV, VEECO) equipped with Nanoscope software (Veeco Instruments, Inc.). Height and phase images were obtained in tapping mode in ambient air with silicon tips (VEECO), and roughness and phase changes were analyzed using Nanoscope software. Initial AFM images of a selected face of the LMH crystals were recorded, and the crystals were then immersed in absolute ethanol for 24 hours at room temperature, carefully removed and dried before re-analyzing the same face with AFM.


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Growing single crystals of excipients LMH single crystals were grown from a solution of 10% aqueous LMH by adding acetone as an antisolvent until an LMH solution-toacetone ratio of 13:7 was reached.58 The mixed solution was kept undisturbed, and tomahawk-shaped single crystals of LMH appeared within a day. Thin pad-shaped single crystals of DGAL were obtained by slowly cooling a 70% ethanolic solution of DGAL. Long needle-shaped -DMAN crystals were obtained by slowly evaporating an aqueous solution over a week.30 XYL crystals were produced from a saturated solution of 95% ethanol by slow evaporation at room temperature.49 Crystals of -DMAN were acquired by slowly cooling a saturated solution of DMAN at 50 °C in 70% ethanol, which yielded long, flexible, fine needles of the polymorph after three days.59 Unfortunately, these crystals were bundled together, and the single crystals appeared to be too thin and fragile for further experimentation. Thus, -DMAN was not included in the face-indexing experiments. Approximately ten single crystals of each substrate were combined to produce one sample and subjected to PXRD to determine their preferred orientations. To this end, the selected crystals were kept on a standard zero-background sample holder, and PXRD patterns were collected. Experiments were conducted in triplicate by changing the random orientation of the crystals using the previously mentioned settings. These PXRD patterns were then compared with simulated powder patterns to index the preferred orientations (see SI S6). Growing epitaxic crystals for face indexing To grow epitaxic single crystals of APAP on selected substrates, single crystals of the substrates were first picked under a Nikon Eclipse ME600 optical microscope equipped with a polarizer and placed in 20-ml scintillation vials. Then, a saturated APAP solution in ethanol (3 mL) at 30 °C was carefully pipetted into these vials, and single crystals of APAP were grown on the substrate single crystals by inducing supersaturation by allowing the solutions to cool slowly to room temperature. All crystallizations were performed without stirring. Once APAP crystals were observed to have formed in the vials, the solution was filtered, and the substrate crystals were recovered. These crystals were then analyzed under an optical microscope to identify the presence of APAP crystals bound with substrate crystals. Subsequently, these substrate-bound crystals were analyzed by Raman microscopy to ensure that the substrate-bound crystals were indeed APAP crystals. A Kaiser Raman microscope equipped with a 785-nm excitation laser and a 20× microscope objective was used for this purpose. The Raman spectroscope was manually focused to locate the surface of each counterpart of the crystal pairs, and spectra were collected in the range of 100 to 4000 cm−1 and compared with the literature-reported Raman spectroscopic details for each compound. Face indexing with SCXRD Once good-quality crystals were identified by microscopic and Raman analyses, the unit cell dimensions were determined for each counterpart of a crystal pair, and the Miller indices of the substrate and APAP crystal faces were measured to identify which crystal faces were bound together. Each substrate-based crystal pair was subjected to multiple attempts to confirm the reproducibility of the results. For each crystal pair, low-temperature diffraction data were collected on a Bruker-AXS X8 Kappa diffractometer coupled to a Bruker APEX2 CCD detector using Mo Kα radiation (lambda =

0.71073 Å) from an IμS microsource. Omega-scans were performed by focusing the X-ray beam on one component at a time. The orientation matrices and unit cell parameters for each component were determined with the program cell_now (Bruker AXS, Inc.), and the crystal faces were determined using the face-indexing plug-in of APEX2 (Bruker AXS, Inc.). Computational methods DFT calculations of association energies The initial atom coordinates for the molecular models of APAP, DGAL, DMAN, LMH and XYL were taken from the respective crystal structures. The crystal structures were retrieved using Mercury software (Mercury CSD 3.6, last updated July 1st, 2015), and the atom types were assigned using the COMPASSII force field in Materials Studio (Accelrys Inc.). The geometry of each molecule was optimized using the Smart algorithm in Materials Studio. The Smart algorithm is a cascade of the steepest descent, adopted basis Newton-Raphson (ABNR) and quasi-Newton methods. Next, using the optimized structures, the models of four molecular complexes were built: APAP···DGAL, APAP···DMAN, APAP···LMH, and APAP···XYL. To minimize the bias introduced by the initial orientation of the molecules, the molecules were systematically rotated with respect to each other. In cases where different initial orientations yielded different optimized structures, the structure with the minimum energy was accepted. Following the described optimizations, the obtained atom coordinates were used in gas-phase density functional theory (DFT) calculations. The geometries of all individual molecules and complexes were optimized, and the energy was calculated using the M06/6-31+G(d) level of theory in the GAUSSIAN 09 computer program. See SI S7 for relevant figures and the energies of the optimized individual molecules. The association energy was calculated as the difference in energy of the optimized complexes and the combined energy of the optimized individual molecules, ΔE = E_cmplx – (E_APAP + E_substrate)

(1)

where E_cmplx is the energy of the optimized molecular complex, E_APAP is the energy of the optimized APAP molecule, and E_substrate is the energy of the optimized substrate molecule. Overview of the molecular dynamics (MD) simulations The “goodness of fit” in this method is based on the value of the EOI between the APAP overlayer and the substrate, which includes a geometric factor, electrostatic interactions and hydrogen bonding. To accurately compute the EOI, it is important to note that there are numerous possible ways for two surfaces to approach and interact with each other. For each of the possible poses of the overlayer with respect to the substrate, the EOI depends on how well their functional groups interact with each other at the interface. The best possible pose is the one in which there are good lattice and chemistry matches between the two surfaces at the interface. Therefore, finding the best possible coordinates and azimuthal angle for the overlayer with respect to the substrate for which the EOI is highest (i.e., has the largest negative value) is important. In another word, the global minimum in a coarse energy landscape must be found which is a difficult task. Here we proposed the following procedure to search for the global minimum energy of interaction between APAP and each substrate: 1.

Generate lists of the important crystal faces for the APAP and each substrate.

2.

Prepare a slab of each APAP crystal face.



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3.

Prepare a slab of each substrate face. The substrate surface area should be reasonably larger than APAP surface area.

4.

Generate a large pool of all possible relative orientations of the APAP surface with respect to the substrate surface.

5.

For each of the possible orientations, perform 100ps MD simulations at a low temperature (10 K) to allow the overlayer to relax on top of the substrate surface and form interactions with the substrate at the overlayer/substrate interface. (MD simulations are performed at low temperature to prevent major disruptions of the crystal structures.)

6.

For each of the relaxed poses of the APAP on top of the substrate (after the MD simulation), perform an energy minimization to further relax the system into a local minimum.

7.

Compute the EOI between the substrate and APAP at the interface for each relaxed pose after energy minimization.

8.

Find the pose for which the EOI is highest (this energy is the representative EOI of that specific face of the APAP with the substrate).

9.

Repeat the above steps for each APAP crystal face on each face of each substrate.

10. Rank the APAP crystal faces based on the EOI with respect to each substrate.

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odicity of the overlayer and substrate surfaces. Therefore, all possible poses of a crystalline overlayer on a crystalline substrate can be generated by translating and rotating the overlayer on top of the substrate surface within a confined area (substrate unit cell). To achieve this, a confined area on top of the substrate surface is considered and then divided into small grids. Then, the center of surface of the overlayer is placed on top of the center of each grid and rotated around the azimuthal angle from 0 to 360 degrees. Next, the center of surface of the overlayer is translated to the next grid point and rotated to generate new poses. A sufficiently fine grid for translating and rotating the overlayer on top of the substrate must be selected to ensure that all possible poses are considered. For example, for the (010)XYL face, the 2D unit cell on the surface is a= 8.27 Å, b= 8.9 Å and α = 90 degrees. The overlayer was translated and rotated on top of the substrate on a surface area of 12 Å 12 Å. This larger surface area was chosen instead of the smaller unit cell of the substrate (8.27 Å 8.9 Å) to ensure that simulations were performed for all possible configurations. The grid size used for translation along the sides of the rectangles was 2 Å, and the grid size for rotation around the azimuthal angle at each point was 10 degrees. Therefore, almost 1296 configurations were generated for that face of the APAP with respect to this substrate face. In Fig. 2, a schematic representation of our method is provided.

Generating the list of the important crystal faces for the APAP and each substrate For APAP, we chose all faces that were identified by XRD and predicted with non-zero morphological importance using the BravaisFriedel-Donnay-Harker (BFDH),60 Growth61 and Equilibrium morphology prediction methods available in Materials Studio. Ultimately, the following faces of APAP were chosen for this study: 001, 011, 11-1, 20-1, 110, 10-1 and 1-10. The selection of the important crystal faces of the substrates was based on SCXRD face indexing. Preparation of the crystal slabs Using Mercury software and crystal structure data (DMANTL07, LACTOS03, ADGALA01, and XYLTOL01) retrieved from CSD, substrate slabs with surface dimensions of 100 Å 100 Å and thicknesses of 25 Å were prepared. The APAP crystal slabs were generated using the same method but with surface dimensions of 50 Å 50 Å and thicknesses of 25 Å. The substrate slab was made significantly larger than the overlayer slab to ensure that the overlayer molecules do not interact with their periodic images during the MD simulations. Generation of the possible relative orientations of the overlayer on top of the substrate In our simulations, the substrate and overlayer surfaces were both crystalline, and their surface areas were larger than their corresponding unit cell surface areas. Thus, both the overlayer and substrate include several unit cells at their interface. Let us assume that the unit vectors of the overlayer surface are b1 and b2 and that the unit vectors of the substrate surface are a1 and a2 at the interface. If an overlayer is placed parallel to and on top of the substrate and if the center of surface of the overlayer is placed on the center of surface of the substrate (Fig. 2), a specific pose (pose A) of these two slabs will be generated. Now, if the overlayer is moved on top of the substrate surface along vector a1 or a2 (unit vectors of the substrate), another pose will be generated that is identical to pose A because of the peri-

Fig. 2: Schematic representation of the generation of all possible configurations of the overlayer with respect to the substrate. a1 and a2 are the unit cell vectors of the crystalline substrate, and b1 and b2 are the unit cell vectors of the crystalline overlayer. Black dots indicate the centers of the unit cells of the substrate (if the overlayer is moved to any of these black dots, an identical configuration will be created by symmetry), and red dots indicate the grid points on one unit cell of the substrate (the center of the overlayer is translated on these points to generate all the “different” configurations of the overlayer on the substrate).

Calculation of the partial charges The following procedure was used to derive the partial charges: First, the xyz coordinates of APAP, DMAN, LMN, DGAL and XYL were taken from CSD, and the coordinates of these structures were relaxed to a local minimum on the potential energy surface (zeroimaginary frequencies) using the B3-LYP/6-31G(d) level of theory. The electrostatic potentials (ESPs) and partial charges of the APAP, DMAN, LMN, DGAL and XYL were derived by performing a singlepoint energy calculation on the resultant structures at the HF/631G(d) level of theory.62,63 All quantum chemistry calculations were conducted using the Gaussian03 program package.64 Details of the MD simulations The CHARMM3662 force field parameters were used to describe the bonds, angles, dihedrals and VdW potentials of APAP, DMAN,


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LMH, DGAL and XYL. All MD simulations were performed using GROMACS 4.5.6 and a Nose-Hoover thermostat with a relaxation time of 1 ps. The particle-mesh Ewald method65 was applied for longrange electrostatics with a short-range cutoff of 1 nm; a cutoff of 1 nm was also used for the Lennard-Jones interactions. All bonds were constrained to their equilibrium length with the LINear Constraint Solver (LINCS) algorithm.66 Force field validation Extensive tests were performed previously by our group to examine whether CHARMM36 is a good force field for APAP.39 CHARMM3662 was also adopted for DMAN, LMH, DGAL and XYL, and crystal slabs were built and minimized using steepest descent with periodic boundary conditions. The particle mesh Ewald summation method65 was applied to correct for the long-range electrostatic interactions. Subsequently, the percentage change of lattice parameters (PLCP) and root mean squared differences (rmsd) compared to the experimental X-ray structures were calculated. The PCLP value is within 5%, and the rmsd value is within 1 Å, suggesting that the CHARMM36 force field is suitable for simulating these substrates. Calculation of EOI The EOI between the overlayer and substrate was computed for each relaxed pose as EOI = Esubstrate +overlayer - Eoverlayer - Esubstrate

(2)

where EOI is the energy of interaction, and Eoverlayer and Esubstrate are the energies of the relaxed overlayer and substrate, respectively. All energy values computed for all the poses of each face of APAP with respect to each substrate face were sorted to obtain the lowest energy value explored by our simulations for each face. Analysis of hydrogen bonds Using a geometric definition for the existence of a hydrogen bond, we computed the number of hydrogen bonds formed between the overlayer and substrate for all simulations using a GROMACS tool (g_hbond). Hydrogen bonds were identified using cutoffs for the angle (hydrogen-donor-acceptor) and the distance (donor-acceptor). The distance cutoff was 3.5 Å, and the angular cutoff was 30°. The number of hydrogen bonds was computed between the overlayer and substrate molecules only; hydrogen bonds between overlayer molecules and between substrate molecules were not included.

RESULTS AND DISCUSSION Nucleation induction times for APAP crystallizations The nucleation induction time (τ) was used to determine the effectiveness of the chosen substrates at promoting APAP nucleation because it is a suitable measure and can be reduced if the substrate of choice is effective in lowering the free energy barrier to nucleation or affecting the nucleation kinetics by increasing the local APAP concentration near the substrate surface.30 τ can be defined as the time elapsed from the attainment of the target supersaturation until the nucleation event occurs.67 All precautions were taken to eliminate other possible pathways to nucleation to demonstrate that any alteration in τ was an effect of the substrate. Furthermore, a large number of identical experiments were performed under each experimental condition to obtain a significant probability distribution. Fig. 3a depicts the formation of an APAP crystal on top of XYL crystals at the end of the induction time experiments, and Fig. 3b shows the growth process of APAP crystals in the presence of XYL as the substrate. In

all vials, except for the control bulk crystallization, the crystallization of APAP was initiated on the surface of the substrate crystals, indicating that the selected substrates promoted heterogeneous nucleation.

Fig. 3: a) APAP grown on XYL crystals and b) microscope images of APAP growth over time

Once the induction times were obtained for a sufficient number of individual samples, the number of vials crystallized was plotted as a function of time to obtain the cumulative probability distributions of the nucleation induction time for each system tested. Fig. 4a shows the representative cumulative probability distributions for the bulk nucleation of APAP from ethanol and with LMH, DGAL, XYL and -DMAN. Average induction times were obtained based on Poisson distributions (Equation 3), assuming the stochastic nature of each nucleation throughout the experimental series,

= (3) where P is the probability of not observing nucleation at time t, and τ is the average nucleation induction time extracted from the slope of the straight-line fit (Fig. 4b) (see SI S8 for the full data sets). The complete data series obtained with XYL followed a Poisson distribution and provided a τ of 85 minutes; thus, XYL was most effective substrate at reducing the induction time of APAP, achieving a ten-fold enhancement relative to the bulk nucleation of APAP. As shown in Fig. 4b, for the APAP bulk nucleation and those in the presence of DGAL and -DMAN, two distinct nucleation time scale regimes were observed. In previous studies, the existence of multiple induction time scales was attributed to nucleation from different types of heterosurfaces10 or the formation of different polymorphs of the crystallizing product.15 Because precautionary steps were followed to minimize the presence of other heterogeneous surfaces (e.g., dust particles), it was unlikely that the presence of different heterosurfaces gave rise to this multi-regime formation. Examining some selected APAP crystals obtained from the second nucleation regime in detail revealed that their morphological features were similar to those of APAP Form II, but a subsequent Raman spectroscopic analysis of these crystals confirmed that they were an elongated morphology of APAP Form I. APAP Form II may have formed initially in these regimes before undergoing a solvent-mediated transformation to Form I.



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Fig. 4: a) Cumulative probability distributions of induction data for APAP in ethanol and b) a plot of ln(P) vs. t, where P is the probability of not observing nucleation at time t

Therefore, in these three systems, only the first induction time scale was fitted to determine the average nucleation induction time, and τ values (in minutes) of 885, 510 and 327 were found for bulk APAP, DGAL and -DMAN, respectively. DGAL enhanced the nucleation of APAP by a factor of 1.7, whereas -DMAN enhanced it by a factor of 2.7. All the data series obtained, with the exception of the LMH data, followed an exponential decay of P(t), indicating a well-defined and time-independent nucleation rate. Thus, they corresponded to class I68 nucleation, at least in the first nucleation time scale regime. The LMH data could not be explained with a simple Poisson distribution, even when only a portion of the data scale was considered. Kinetics of heterogeneous nucleation on LMH The nucleation of APAP on LMH crystals appeared to follow a different mechanism than that of the nucleation on DGAL, XYL and DMAN. Specifically, the nucleation induction times could not be described using a single-process Poisson distribution because multiple regimes appear to be involved. The slope in the first regime suggests that nucleation was faster than on any other substrate, whereas in the second regime, the nucleation appears to be slower. To extract the average nucleation, we used a two-exponential model, as described in Equation 4,21 ⁄ = + (1 − ) ⁄ (4) where P is the probability of observing no nucleation at time t, and a is a constant. Based on this equation, two nucleation induction time scales—τ1 = 39 min and τ2 = 1758 min—were identified (Fig. 5). The other models did not provide good fits to the experimental data (see SI S9). The described model explains the nucleation mechanism, which is often referred to as a Class 2 mechanism, with two distinct nucleation times that correspond to nucleation on two different heterogeneous surfaces.68 Considering that all APAP crystals formed on LMH crystals with uniform compositions prior to the crystallization experiments, the observed mechanism implies that LMH changed, resulting in the formation of a second type of heterogeneous surface that subsequently served as a second type of active nucleation site. LMH has been reported to convert to its α-stable anhydrous form in alcoholic media because of the removal of water molecules from the crystal lattice.69 To determine whether these changes occurred in the LMH crystals during our crystallization experiments, we analyzed the LMH crystals before and after immersion in ethanol for 24 hours. The PXRD pattern did not indicate any changes in the composition of the LMH upon immersion (SI S5).

However, the PXRD patterns provide information on the bulk composition and may not be sensitive enough to detect localized changes on the surfaces of the crystals. 70 Hence, AFM imaging was performed to analyze the possible surface changes of LMH under the induction experimental conditions. The AFM images of the initial crystal surface (before immersion in ethanol) show that the LMH crystals had smooth flat surfaces, comprising only atomic-scale steps, with a single uniform phase (Fig. 6a). In contrast, the AFM images taken after immersion in ethanol show significantly rougher surfaces (Fig. 6b). The roughness analysis of the surfaces is provided in SI S10. Additionally, the phase analysis revealed that two distinct phases are present on the surface of the crystals, indicative of a surface phase transformation and recrystallization. The AFM observations provide the basis for two distinct types of nucleation sites, consistent with the two observed nucleation regimes in the induction time measurements. The first type of nucleation site, which resulted in the fastest nucleation, is most likely the initial, unchanged LMH surface. Upon immersion in ethanol, the second type of nucleation sites appear, most likely anhydrous lactose.69 Deceleration of the nucleation rate is as a result of several factors. Due to the conversion to anhydrous form, the effective surface area of LMH is reduced resulting in smaller number of active nucleation sites. Also, the second type of nucleation site may not be as effective as LMH in promoting heterogeneous nucleation. In addition, during the conversion, water was released into the solution which may have negative impact on nucleation.

Fig. 5: Plot of the fractions of vials not crystallized vs. time (min). The data are fitted with the two-exponential model.


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Fig. 6: a) Initial AFM images of the LMH surface and b) AFM images of the LMH surface after immersion in ethanol.

Fig. 7: a) Effect of substrate polymorphism on the cumulative probability distribution of the induction data for APAP and b) plot of ln(P) vs. t for the induction data of APAP in the presence of α- and β-mannitol.

Effect of DMAN polymorphism on the APAP induction time The effect of the different polymorphs of a single compound on the nucleation kinetics is one area that has not been investigated previously. Thus, to explore this issue, α-DMAN was introduced as a substrate because it a metastable polymorph of DMAN. DMAN has three fully characterized polymorphs, known as α, β and δ;59 among them, -DMAN is stable under ambient conditions. For the α and β forms, the polymorphism relates to different hydrogen-bonding arrangements.59 Induction time experiments of APAP were conducted in the presence of α-DMAN under identical experimental conditions to those used for the other substrates. Fig. 7 depicts the cumulative probability distribution and linear regression of the induction time data of APAP in the presence of α-DMAN with respect to those collected with -DMAN and for bulk nucleation. The induction time values obtained with α-DMAN (τ = 316) and -DMAN (τ = 327) were very similar, and α-DMAN seemed to outperform -DMAN by only a few minutes. Physico-chemical properties, such as the heat of fusion and melting point, hardly differ between these two DMAN polymorphs. For example, α-DMAN melts at 166 °C, and -DMAN melts at 166.5 °C. Thus, small energetic differences exist between these two forms, which have been characterized to conform to the same space group (orthorhombic P212121).71 Furthermore, both polymorphs have a similar needle-like morphology,72 and as mentioned earlier, the only difference between the two polymorphs is in the hydrogen bond arrangement in the crystal structures. Because these two polymorphs exhibit such similar properties, their comparable behaviors in inducing APAP nucleation are not surprising.

In summary, all the experimental conditions provided reasonably good fits (R2 > 90) with the selected models, and all the selected substrates reduced τ compared to that of bulk nucleation, Table 1. When comparing the substrates that exhibit class 1 nucleation, XYL had the largest impact on reducing the induction time, followed by both polymorphs of DMAN; DGAL exhibited the poorest performance. XYL resulted in an approximately ten-fold reduction in the nucleation time compared to the bulk nucleation of APAP, and it was four times more effective than the DMAN polymorphs and six times more effective than DGAL; thus, it is one of the best substrates for facilitating APAP nucleation reported to date. Although a direct comparison between these substrates and LMH may not be valid (because of the use of different models to fit the induction time data), examining the induction times of LMH in depth reveals that it is, initially, the best of the tested substrates, but subsequently, the nucleation induction time drastically decreases. Thus, LMH can be assumed to be the second best performing substrate overall (Fig. 4). Therefore, as predicted, all the selected substrates could greatly enhance the nucleation rate of APAP because of the favorable interactions between APAP and each selected substrate.



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Table 1: Comparison of the average nucleation induction times for APAP in the presence of different crystalline substrates. Nucleation following Class 1 (exponential P(t)) mechanism Excipient Average induction time R2 τ (min) APAP-Bulk 885±20 0.95 DGAL 510±14 0.91 α-DMAN 316±5 0.94 β-DMAN 327±8 0.96 XYL 85±1 0.98 Nucleation following Class 2 mechanism (decreasing effective nucleation rate with time) Excipient Fitted parameters R2 τ1 – 39 min LMH τ2 – 1758 min 0.97 a – 0.40

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and, thus, in enhancing the nucleation rate. In other words, the enhanced nucleation rates are macroscopic manifestations of the strong interactions between APAP and the substrates. To test this hypothesis, we calculated the association energies for four molecular complexes expected to form on the substrate/solution interface: APAP···DGAL, APAP···DMAN, APAP···LMH, and APAP···XYL. The results, which are summarized in Table 3, indicate that XYL should be particularly effective in enhancing the nucleation rate of APAP. Indeed, the APAP···XYL molecular complex is ~20 kcal/mol more stable than similar complexes based on DGAL and DMAN. This finding is in agreement with the nucleation time in the presence of XYL, which was several orders of magnitude shorter than those observed for the other systems. The APAP and XYL molecules assemble into a particularly stable cyclic assembly (APAP···XYL), which is sustained by a series of hydrogen bonds (Fig. 8).

BET analysis and the effect of surface area on the average induction time measurements BET measurements were performed to determine the surface areas of the 125-250-µm crystals and whether a considerable difference between the surface areas of the selected substrates existed. The results are summarized in Table 2. Table 2: Summary of the BET analysis of the surface area. Substrate β-DMAN α-DMAN LMH DGAL XYL

BET surface area (m2/g) 1.734±0.007 1.427±0.014 1.666±0.050 1.775±0.016 1.846±0.010

Normalized average induction times τ (min) 307 242 τ1 – 35, τ2 – 1587 490 85

All the substrates appeared to have comparable surface areas, but a closer look suggests that XYL, which was also the best substrate for promoting the APAP nucleation rate, has a slightly higher surface area. Thus, a separate set of induction time experiments was conducted with XYL as the substrate. In these experiments, the amount of XYL used in each crystallization vial or the size distribution of the XYL crystals used was changed. Probability distribution plots and the induction time data are provided in SI S11. Based on the results of these experiments, regardless of the effect of the surface area on the average induction time (as the surface area increases, the induction time decreases), XYL is the best substrate, even when its surface area was smaller than those of the other substrates. Table 2 also presents the normalized average induction times for each substrate (normalized with respect to the surface area of XYL) for comparison. DFT predictions of the EOIs between APAP and selected substrates To rationalize the effectiveness of XYL in enhancing the nucleation of APAP, we performed a series of DFT energy calculations. We assumed that the variations in the observed nucleation rates can be attributed to differences in the interactions of APAP with different substrates. Specifically, the substrates that have the strongest interactions with APAP should be the most effective in stabilizing the prenucleation clusters and locally increasing the APAP concentration

Fig. 8: Cyclic molecular complex of APAP···XYL sustained by hydrogen bonds (indicated by blue dashed lines).

Because of the changes in the LMH surface induced by immersion in ethanol, we prepared two different molecular complexes based on LMH: APAP···LMH and APAP···LMH ···H2O. The crystals used for the induction time measurements consist of the hydrated form of lactose; thus, water molecules are included in the crystal lattice. However, upon immersion in ethanol, the surface of the LMH changes: Water leaves, and an anhydrous lactose layer is formed. The changes of the surface of the LMH substrate are also reflected in the nucleation kinetics, and two apparent nucleation regimes are detected. During the first regime, while water is still present, the nucleation is particularly fast, and LMH is the most effective substrate. In contrast, in the second regime, the nucleation slows down, and XYL is a better substrate. These observations can be rationalized based on the association energies. Specifically, the molecular complex APAP···LMH···H2O is more stable than APAP···XYL. However, when the water molecule is removed from the complex with LMH, the association energy is less than that of APAP···XYL. In summary, the relatively simple and fast computational modeling method implemented here seems to provide good guidelines for selecting substrates able to enhance the nucleation rate of APAP. Table 3: Summary of the energetics of APAP interactions with different substrates. Complex APAP···XYL APAP···DGAL APAP···DMAN APAP···LMH···H2O APAP···LMH


E(kcal/mole) -24.6 -6.2 -5.1 -30.7 -20.3

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XRD face indexing To further understand the epitaxial growth of APAP on selected substrates, we performed an extensive XRD analysis to identify the face of the substrate on which the APAP was deposited during crystallization and the face of the APAP that was attached to the exposed face of the substrate. To this end, we grew single crystals of APAP onto single crystals of the substrate and used SCXRD to index the crystal faces (Fig. 9 and SI S12). α-DMAN was not used in the indexing experiments because of the difficulty of obtaining good-quality single crystals. Apart from LMH, the other three systems produced consistent results over multiple attempts. In each instance, APAP was determined to be on the {010}DMAN, {00-1}DGAL and {0-10}XYL faces (Table 5). In contrast, for LMH, three crystal pairs were analyzed, but coherent results were not obtained (see SI S12). The reason for this inconsistency is unclear, but all the LMH faces that were identified via the face indexing of the LMH/APAP crystal pairs had potential hydrogen bonding sites, making them competitive with each other (see SI S13). The tomahawk shape of the LMH crystals also introduced complications in the face indexing. For instance, this asymmetric morphology led to difficulty in centering the crystal while focusing the X-ray beam and when attempting to index these crystals accurately. The surface changes of LMH that occurred in ethanol might also have contributed to these inconsistencies. APAP showed preferential binding to each substrate surface via a {001}APAP family face, except for the {0-10}APAP or {-10-1}APAP family face in LMH (Table 5 and SI S12).

Fig. 9: Miller indices of crystal faces determined by SCXRD for an XYLAPAP pair: (a) XYL and (b) APAP.

By carefully examining the experimentally obtained faces, one common feature could be extracted: The abundance of possible hydrogen bonding sites on these faces stabilized the prenucleation aggregates via strong interactions between the substrate and APAP nuclei (Fig. 10). Thus, we attempted to explain the observed results through a simple hydrogen bond density analysis of the observed faces; the method is described in SI S14. {001}APAP was among the best faces predicted by this method and was observed experimentally in the presence of XYL, DGAL and DMAN. For the two APAP faces observed with LMH, {-10-1}APAP was as effective as {001}APAP; both faces had the same number of hydrogen bonding sites per unit area. However, the {0-10}APAP face is one of the worst faces predicted by this method because it contains only methyl functional groups. Despite this prediction, in the experiments, APAP was observed to be attached to this face of LMH in two out of the three attempts. Indeed, the experimentally observed substrate faces were not the best ones predicted by this simple method. Hence, this simple predictive approach is not adequate to rationally explain the experimentally observed selection between particular APAP-substrate faces.

Fig. 10: Hydrogen bonding sites extending out from face {00-1}APAP and face {0-10}XYL.

Furthermore, for DGAL and XYL, a direct correlation was observed between the SCXRD-identified faces on which the APAP was bound and the preferred orientations extracted by PXRD. For βDMAN, PXRD revealed no prominent preferred orientation, and thus, a direct correlation was not possible. In contrast, this simple relationship could not be applied to LMH because of the inconsistent results obtained for this particular substrate. Overall, these observations can be explained because the preferred orientation of a particular substrate is the most highly populated face in a crystallization system, and the probability of the incoming nuclei to attach to this face is high. Thus, when all substrate faces contain possible interacting sites, if a good lattice match between these faces is not evident, the most abundant face of the substrate (i.e., that with the highest surface area) is the most probable face on which the nuclei attachment should occur. Thus, a delicate balance among various factors, such as the hydrogen bond density and type, lattice match, size match of the two molecules and surface area, appears to contribute to the final manifestation of the attachment of the overlayer to a particular substrate face. Epitaxy prediction using GRACE Although DFT calculations predicted an observed trend in the substrate efficacy, such calculations are too simplistic to reveal the mechanism of epitaxy and identify which crystal faces are important. Thus, we attempted to apply a previously developed epitaxy prediction tool: GRACE.33 We calculated the epitaxy score between the experimentally observed substrate faces and all the possible faces for APAP with a maximum Miller index limit of three (145 faces). The best APAP face that exhibited the highest epitaxy scores with the respective substrate faces is provided in Table 5, and the complete results are included in SI S15. When comparing the predictions to the experimental results, the method did not produce good predictions. It is possible that, in our system, both the overlayer and the substrates crystallize in low-symmetry groups, making it likely that the geometric match is overshadowed by the strong contributions of the energy terms. MD simulations of APAP-substrate interactions We performed MD simulations of APAP as the overlayer, on experimentally observed substrate faces and calculated the EOI to elucidate the mechanism of epitaxy and identify which APAP crystal faces would crystallize on these substrates. We generated thousands of relative orientations in which the APAP overlayer can approach and interact with the substrate. For each of these orientations, 100 ps MD simulations at T=10K were performed to relax the overlayer on top of the substrate and allow them to interact via hydrogen



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bonds and VdW interactions. Next, we performed 2000 steps of energy minimization to further relax the system. Fig. 11 presents a representative MD simulation of APAP on top of the XYL substrate face (010)XYL. Following the MD simulations, the interfacial layer of APAP undergoes changes and rearranges to allow the two slabs to interact and form hydrogen bonds.

Fig. 11: APAP crystal on top of an XYL crystal a) before and b) after the MD simulations.

We next calculated the EOI for each orientation of the APAP layer with respect to the substrate surface. This procedure was repeated for all important faces of APAP with respect to the given face of XYL. Finally, all the EOI values for each pair of substrate and APAP faces were sorted, and the lowest value was taken as the EOI for that specific face of APAP with respect to face (010)XYL. Interestingly, we found that for face (010)XYL, the crystal face (001)APAP had lower energy values or a higher EOI with the substrate (i.e., high negative energy values) compared to all tested APAP faces (i.e., faces 001, 011, 11-1, 20-1, 110, 10-1, and 1-10) (Table 4). In effect, our simulations predict that during the heterogeneous nucleation of APAP on the tested substrates, the crystal face (001)APAP will grow on the substrate, regardless of the face index (see SI). Table 4: The APAP crystalline faces are listed in the first column, and the second and third columns present the whole-layer and perAPAP molecule EOIs with respect to face (010)XYL, respectively. The fourth and fifth columns list the total number of hydrogen bonds in the whole layer and per molecule of APAP with respect to each substrate face. hkl

EOI (kj/mol)

001 11-1 011 10-1 20-1 1-10 110

-5493.97 -5115.43 -4497.40 -4886.32 -4521.02 -4473.48 -4435.22

EOI (kj/mol*molecule) -20.81 -18.94 -17.58 -16.18 -16.09 -14.86 -14.69

#H bonds

#H bonds per molecule

115 86 82 95 79 86 82

0.44 0.32 0.32 0.35 0.28 0.27 0.28

To investigate the origin of this distinct difference between the EOIs of the different faces of APAP with each substrate surface, we analyzed the formation of hydrogen bonds at the interface of the two layers in detail by performing MD simulations. We hypothesized that the hydrogen bonds are the major contributor to favorable EOIs. APAP has three functional groups that can form hydrogen bonds: hydroxyl (-OH), carbonyl (–C=O) and amide (-NH) groups. Additionally, the substrate has hydroxyl groups that can form hydrogen bonds with the overlayer molecules. Using a geometric definition for the existence of a hydrogen bond (explained in the

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Methods section), we computed the number of hydrogen bonds between the overlayer and substrate for all simulations using GROMACS tools. Histograms of the number of hydrogen bonds for all simulations are presented in SI S16. Also the corresponding values are reported in Table 4. The histogram related to the number of hydrogen bonds that face (001)APAP forms with the substrate is located at higher values, and its tail extends to the highest value found for all other faces of APAP. This is in agreement with the EOI values presented in Table 4, indicating that the highest EOI with the substrate corresponds to face (001)APAP because of the more numerous and stronger hydrogen bonds between APAP and the substrate surface. To investigate exactly which type of hydrogen bond has the most important effect, we analyzed the numbers of hydrogen bonds between the hydroxyl groups, carbonyl groups and amide groups of the APAP with the hydroxyl groups of the substrates individually. We found that the hydroxyl groups of the APAP crystal faces create more hydrogen bonds with the substrate than the other two groups analyzed. Indeed, investigating the hydrogen bonds in the crystal structure of APAP reveals that face (001)APAP has the highest number of hydroxyl groups among all the considered faces of APAP (see SI S16). This procedure was also used to successfully predict the epitaxial growth of APAP on β-DMAN and DGAL. Similar calculations involving LMH were attempted. However, because of the changes exhibited by LMH in ethanol, which were confirmed by AFM, and the reproducibility issues observed in the face-indexing experiments, accurate MD simulations were not possible. The experimental results and different prediction methods are compared in Table 5. For all of the tested substrates, our computational technique predicted that face (001)APAP would have the highest EOI with the given face of the substrate. Indeed, in all cases, face (001)APAP had the highest number of strong hydrogen bonds with the substrate (the EOIs of the various faces of APAP with these substrates and a hydrogen bond analysis are provided in SI S16). Most importantly (001)APAP face was the experimentally observed face to preferentially grow on XYL, β-DMAN and DGAL. Table 5: Summary and comparison of experimentally obtained substrate and APAP faces and the predicted APAP faces for each substrate Substrate face Substrate

β-DMAN DGAL XYL

Bound APAP face

From SCXRD

From SCXRD

{010} {00-1} {0-10}

{001} {00-1} {00-1}

Face predicted by GRACE (100) (100) (011), (01-1)

Face predicted by our method (001) (001) (001)

For APAP (001) and (00-1) faces are equivalent, for DGAL (001) and (00-1) faces are equivalent, for XYL (010) and (0-10) faces are equivalent and for β-DMAN (010) and (0-10) faces are equivalent.

CONCLUSION The experiments presented revealed that XYL is a particularly effective substrate in enhancing the nucleation of APAP and reduced the average nucleation induction time by a factor of 10. In fact, all of the studied substrates effectively enhanced the nucleation of APAP, and we determined that the observed epitaxial growth is likely governed by the formation of hydrogen bonds between APAP and the


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substrates. This study represents the first instance in which two polymorphs of the same substrate (i.e., the α and β forms of DMAN) were used in induction experiments. Both forms were found to be equally effective in enhancing the nucleation rate of APAP. Moreover, as indicated by AFM, LMH was converted to anhydrous α-lactose under the experimental conditions, giving rise to two dominant types of heterosurfaces in the system and, thereby, leading to the splitting of the nucleation time scales. We also observed that the crystal face (001)APAP preferentially grows on top of XYL and other substrates that are rich in hydroxyl groups, except for LMH. Using DFT studies, we found that APAP and XYL could form a very stable molecular complex sustained by a cyclic series of hydrogen bonds. The detailed MD method presented here correctly revealed that (001)APAP preferentially grows on top of the studied substrates because it interacts via strong hydrogen bonds with the exposed substrate faces. This is an important improvement to the previous computational techniques which were not able to explain our experimental results. This method can be generalized to be used for noncrystalline surfaces as well. In that case, geometrical factor is negligible and the most important factor in nucleation is the level of functional group matching at the interface which is directly defined in our technique. In summary, our results provide insight into the utilization of crystalline heterosurfaces to facilitate the directed nucleation of APIs. These organic, biocompatible, functional, crystalline heterosurfaces are understudied because of their complex surface functionalities and topographies, but our work provides some guidelines for selecting heterosurfaces for use in crystallization. Thus, we expect our results contribute to widening the range of crystallization processes used to control the polymorphism, crystal morphology, nucleation kinetics and other crystal-related properties. Furthermore, we believe that our findings will set the stage for the exploration of crystalline heterosurfaces as seeds in industrial settings.

ASSOCIATED CONTENT Supplementary Information (SI) available: [PXRD data, induction time data, DFT calculation models, AFM data, face-indexing data, H-bond density analysis, GRACE calculations and data from MD simulations. “This material is available free of charge via the Internet at http://pubs.acs.org.”]

AUTHOR INFORMATION

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Corresponding Author (30)

**E-mail: [email protected].

Author Contributions

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The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. +These authors contributed equally. TW conducted all the experiments and wrote the sections related to the experimental work. FB conducted all the MD simulations and wrote the related sections. JS conducted the DFT calculations and wrote the related sections.

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ACKNOWLEDGMENT

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The authors would like to thank Dr. Peter Mueller and Dr. Jonathan Becker (Department of Chemistry, Massachusetts Institute of technology) for their assistance with the SCXRD work and Novartis for funding.

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Insert Table of Contents artwork here We demonstrate the use of biocompatible, functional and crystalline heterogeneous surfaces as substrates to enhance the nucleation rates of acetaminophen. A molecular dynamic simulation method to determine the interacting faces of acetaminophen and substrates is also reported.


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Experimental and Mechanistic Study of the Heterogeneous Nucleation

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