Angle-Directed Nucleation of Paracetamol on Biocompatible

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Angle-directed nucleation of paracetamol on biocompatible nano-imprinted polymers Jelena Stojakovic, Fahimeh Baftizadeh, Michael A. Bellucci, Allan S. Myerson, and Bernhardt L Trout Cryst. Growth Des., Just Accepted Manuscript • Publication Date (Web): 09 May 2017 Downloaded from http://pubs.acs.org on May 11, 2017

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Crystal Growth & Design

Title: Angle-directed nucleation of paracetamol on biocompatible nano-imprinted polymers Author list: Jelena Stojaković, Fahimeh Baftizadeh, Michael A. Bellucci, Allan S. Myerson, and Bernhardt L. Trout* Affiliation: Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), 77 Massachusetts Avenue, E19-502, Cambridge MA 02130, USA, e-mail: [email protected] Abstract: Nucleation kinetics of small-molecule organics can be directed by heterogeneous surfaces imprinted with angular nano-patterns. In this work, we have utilized biocompatible polymer thin films to enhance the nucleation rates of paracetamol (APAP). We found that flat polymer films, without nano-imprinting, enabled crystallization of APAP two times faster than bulk crystallization. Nano-imprinting of polymer films led to further enhancement of the nucleation rates. Polymer films imprinted with a nano-pattern containing 40° angles were the most effective and enabled crystallization of APAP four times faster than bulk crystallization, and two times faster than crystallization with flat polymer films. The films imprinted with the nano-patterns containing 60°, 65°, 80° or 90° angles were more effective in enhancing crystallization of APAP than the flat films, but less effective compared to the 40° nano-pattern. We also performed molecular dynamics (MD) simulations and an analysis of the hydrogen bonding between crystal faces and the polymer surface. The results suggest that the 40° pattern, the smallest angle nanopattern, targets the (001) and (011) faces (intrinsic angle of 34°) due to the strong interaction of these crystal faces with the polymer. The computational results are supported by crystallographic studies and atomic force microscopy (AFM) images of a nano-crystal growing in the corners of the nano-patterns. Our findings indicate ways to rationally design the geometry of heterogeneous surfaces to enhance the nucleation of small-molecule organics. Moreover, considering that the only required input for this design is the chemical structure of the polymer, and the chemical and crystal structure of the crystallizing solute, we expect that our method is applicable to a wide range of crystallization processes. Most important illustration:

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Angle-Directed Nucleation of Paracetamol on Biocompatible Nano-Imprinted Polymers Jelena Stojaković, Fahimeh Baftizadeh, Michael A. Bellucci, Allan S. Myerson, and Bernhardt L. Trout * Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), 77 Massachusetts Avenue, E19-502, Cambridge MA 02130, USA, e-mail: [email protected]

Abstract

Nucleation kinetics of small-molecule organics can be directed by heterogeneous surfaces imprinted with angular nano-patterns. In this work, we have utilized biocompatible polymer thin films to enhance the nucleation rates of paracetamol (APAP). We found that flat polymer films, without nano-imprinting, enabled crystallization of APAP two times faster than bulk crystallization. Nano-imprinting of polymer films led to further enhancement of the nucleation rates. Polymer films imprinted with a nano-pattern containing 40° angles were the most effective and enabled crystallization of APAP four times faster than bulk crystallization, and two times faster than crystallization with flat polymer films. The films imprinted with the nano-patterns containing 60°, 65°, 80° or 90° angles were more effective in enhancing crystallization of APAP than the flat films, but less effective compared to the 40° nano-pattern. We also performed molecular dynamics (MD) simulations and an analysis of the hydrogen bonding between crystal faces and the polymer surface. The results suggest that the 40° pattern, the smallest angle nano-


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pattern, targets the (001) and (011) faces (intrinsic angle of 34°) due to the strong interaction of these crystal faces with the polymer. The computational results are supported by crystallographic studies and atomic force microscopy (AFM) images of a nano-crystal growing in the corners of the nano-patterns. Our findings indicate ways to rationally design the geometry of heterogeneous surfaces to enhance the nucleation of small-molecule organics. Moreover, considering that the only required input for this design is the chemical structure of the polymer, and the chemical and crystal structure of the crystallizing solute, we expect that our method is applicable to a wide range of crystallization processes.

1. Introduction Crystallization is the most widely used separation and purification process in pharmaceutical industry, and crystals are often incorporated in the small-molecule pharmaceutical products.1 In recent years, heterogeneous nucleation on polymer surfaces has attracted particular interest as it is proven to control effectively crystallization of small-molecule active pharmaceutical ingredients (APIs),2 as well as proteins,3 in terms of nucleation kinetics, morphology, size distribution and polymorph selection. Polymer surfaces probably promote nucleation by locally increasing the concentration of solute, as the solute molecules cluster near interface due to attractive solute/surface interactions, lowering the surface energy, and by matching the structures of the nucleating crystalline phase, an approach akin to epitaxy.4,5,6 In the field of semiconductors and integrated circuits, imprinted geometrical patterns on amorphous surfaces, such as diffraction gratings on glass substrate, have been used to direct oriented crystal growth of thin films.7,8 The approach is called artificial epitaxy or graphoepitaxy and it is based on the idea that micro-patterns provide “surface reliefs” if there is a geometrical match between imprints and growing crystalline phase.9 The design of micro-reliefs was guided by consideration of lattice


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symmetry and the growth shape of the crystallizing phase. More recently, a similar approach was used to template self-assembly of thin films of a block copolymer using nano-scale topographical elements of periodicity and spacing commensurate with periodicity of micro-domain lattice of copolymer.10 In addition to crystal growth, previous work in our group focused on understanding how the geometrical patterns on amorphous substrate affect nucleation, nucleation kinetics and polymorphism of APIs. More specifically, we showed that in addition to size,11,12 the shape of patterns affect nucleation rates and polymorph selection.13,14,15 In terms of nucleation rates, we demonstrated that spherical nano-patterns hinder nucleation while angular patterns accelerate it.13 Atomic force microscopy (AFM) and scanning electron microscopy (SEM) indicated that crystallization was initiated in the corners of imprinted nano-patterns as opposed to on flat sides, emphasizing the importance of angles. Prior to this work, the importance of dihedral angles on the substrate was recognized and exploited in “ledge directed epitaxy”. Freshly cleaved single crystals can provide planes, steps and angles that facilitate growth of molecular crystals, and even direct polymorph selection, depending on the exposed planes and angles.16,17 Although very important for fundamental understanding of directed heterogeneous nucleation, this approach is impractical and difficult to scale-up as it relies on good-quality single crystals that, as a substrate, expose well-defined faces upon cleaving. Independently of these experimental results, computer simulations of heterogeneous nucleation of Lennard-Jones model molecules in angular grooves found that nucleation rates depend on the size of the angle.18 The proposed explanation for above described effects of angles is the angle-directed nucleation mechanism which accounts for a geometrical match between angular shape and some important intrinsic angle of the growing crystalline phase as a nucleation-promoting factor. However, there is no systematic way to predict which intrinsic angle should be targeted, which greatly complicates the design of the best


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patterns to be imprinted on the surface of substrates. In our previous work, to find the best angular nano-pattern to promote nucleation of each API, all available angles were screened by performing tedious nucleation rate measurements.14,15 Moreover, the screening process required a library of imprinting masters which are expensive and time-consuming to prepare. For these reasons, it would be beneficial to develop a method that could guide design of imprints by predicting optimal angles based on the crystal structure of targeted form of API. Herein, we present a study of nucleation of APAP on films of a biocompatible hydroxyethylcellulose (HEC) polymer imprinted with angular nano-patterns. We quantified the effect of different angle sizes on nucleation by measuring the average induction times. To rationalize the observed angle-dependent variations in nucleation rates, we identified the most probable intrinsic angle of APAP using the analysis of exposed hydrogen bonds on different crystal faces and molecular dynamics (MD) simulations of HEC-APAP interaction. This is the first study that combines experimental and computational approach to angle-directed nucleation. The intrinsic angle identified using MD simulations as the most important angle for the nucleation enhancement is in agreement with the experimental results. Our findings open the door for rational design of imprinted polymer surfaces for directed crystallization that will circumvent tedious trial-and-error experimental screening of nano-patterns as it may be possible to predict the best angular imprints solely based on molecular and crystal structure of the targeted API forms. 2. Experimental section Materials. APAP (N-(4-hydroxyphenyl)ethanamide, C8H9NO2), HEC (2-hydroxyethyl cellulose, chemical formula variable) and all solvents were purchase from Sigma-Aldrich. All chemicals were used as received. Chemical structures of APAP and HEC are included in SI Fig. 3.


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Preparation of silicon masters with nano-imprints. Silicon wafers, premium grade polished 100 mm, were purchased from Silicon Valley Microelectronics, Inc. (Santa Clara, CA). Interference lithography was chosen as a method for creating nano-patterned masters as it can insure high-density, monodispersed patterning over relatively large area. The patterns were generated on round silicon wafers (100 mm in diameter) using two exposure−etch cycles. First, the wave-like patterns were produced on the photoresist by exposure to the interfering beam and then translated to straight ducts with sharp edges through several etching steps. Next, the second interference pattern was overlaid over the existing duct patterns, at the desired angle, using the same exposure-etching protocol. The pitch size of the features was controlled by the angle between mirrors that produce the interfering beams. The procedure yielded parallelogram-shaped nano-pillars with tunable angles with angle precision of 1° (based on the precision of the angle gauge on the customized interference lithography instrument). Such created patterns were analyzed using tapping mode AFM using Veeco Metrology Nanoscope IV instrument. Overall, the silicon masters with five different patterns were prepared containing 40°, 60°, 65°, 80° and 90° angles. Since the nano-patterns are pillars with bases in the shape of parallelograms, the other angles present are 140°, 120°, 115°, 100° and 90° respectively. AFM imaging was used to confirm the uniformity of nano-patterns and fidelity of imprints on HEC films (SI Fig. 4). Preparation of imprinted films. Imprinted polymer films were prepared by solution casting over nano-patterned silicon masters. The solution casting imprints on polymer surface the opposite or “negative” of the shapes on silicon masters. The convex shapes on silicon masters (parallelogram-shaped pillars) yields the concave shapes on polymer surface (pores with the base of the shape of parallelogram). 10% (w/w) aqueous stock solution of HEC was prepared by dissolving 10 g of HEC in 90 ml of DI water yielding a clear viscous liquid. 6 ml aliquots of


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solution were evenly spread over the silicon masters (100 mm in diameter). The solution was air-dried under a dust cover for two days to yield flexible clear films. The films were manually peeled off and cut out into round pieces 6 mm in diameter using a biopsy punch. The fidelity of pattern transfer was confirmed using AFM. Solvent selection. In addition to dissolving APAP, a good solvent had to be inert towards HEC films such that imprinted patterns are not changed during crystallization. To select appropriate solvent, the imprinted films were immersed in solvent for 1 day and imaged using AFM. Based on compatibility with HEC and APAP, we chose acetonitrile as crystallization solvent (SI Table 1 and SI Fig. 5). Solubility of APAP in acetonitrile. We measured the solubility of APAP in acetonitrile by turbidity measurements using Crystal16, in the temperature range 10 to 50 °C. We prepared 16 vials with 10-60 mg of APAP and added 1 ml of acetonitrile. The vials were subjected to three cycles of heating and cooling and stirring at 700 rpm. The obtained data is in good agreement (within 1mg/ml) with reported gravimetric solubility measurements.19 The solubility of APAP in acetonitrile at 10°C is 13.9 mg/ml (SI Fig. 6). Induction time measurements. All vials were pre-cleaned by immersing them in water, followed by ethanol and finally dried under vacuum at 80 °C. The films were cut into 6 mm pieces and placed on the bottom of the vial, except in the case of the control experiment. In the control experiment no films were used, as the purpose of the experiment was to measure the bulk nucleation rate. At all possible times, vials were covered to minimize intrusion of dust particles. From the solubility curve and screening experiments, the chosen concentration of APAP in acetonitrile was 25 mg/ml and the reference temperatures was 10 °C. The induction time measurements were conducted under supersaturation of 1.8. Solutions were prepared by


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dissolving 2500 (±10) mg of APAP in 100 ml of acetonitrile without stirring on a hot plate set at 50 °C. Once APAP dissolved, the hot solution was filtered through a polytetrafluoroethylene (PTFE) membrane with 0.2 µm pores into four pre-heated 25 ml vials. The solution was divided in four vials to minimize evaporation during pipetting later on. The vials were tightly capped and additionally sealed by wrapping with parafilm and let equilibrate at 50 °C. 80 aliquots of 1000 µL of solution were hot-pipetted into 1 ml vials and immediately capped to prevent evaporation. The solutions were kept on the 50 °C block for 10 min before transferring to a cooling block kept at 10 °C. The cooling block was mounted on the top of the Zeiss Axio Observer microscope equipped with the motorized stage. The stage was moving such that the bottom of each vial would come into focus every 5 min and at that point the image was taken. Images were taken for up to 72 h. Following the experiments, all vials were inspected for evaporation and/or crystals grown around the cap at the top, instead of the bottom, of the vial. Such crystallizations were observed very rarely and data collected on them was discarded. The induction time was estimated as the time lapsed from the start of the imaging, which corresponds to the time when supersaturation at 10 °C was achieved (within 2 min), and the time when the first crystal can be seen in an image. The induction time measurements were conducted under 7 different conditions: no polymer present (bulk nucleation), on flat polymer, and polymer imprinted with 40°, 60°, 65°, 80° and 90° patterns. Crystal growth. Observed crystal growth was fast compared to induction time. Estimated time for crystals to grow to visible size (~ 20 µm) was within minutes, which is negligible compared to induction times that are in hours. The scale of crystal growth rates was estimated by analyzing the change in crystal size across frames collected by the camera of the microscope. It is relatively difficult to determine accurate crystal growth rates. Crystals appear in different shapes and


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orientations, and different crystal faces grow with different rates. Moreover, from the collected images it is impossible to accurately capture all crystal faces and orientation of crystals at the moment when the image was captured. However, for our purposes, it is unnecessary to determine accurate crystal growth rates. We sought only to confirm the validity of the assumption that crystal growth is fast compared to induction time under experimental conditions described above. We chose to track over time the change in the length of the longest dimension of a crystal (most likely the fastest growing face). In the examples included in Supplementary Information (SI Fig. 1 and 2), within first 20 minutes of crystal growth, the rate of change of the longest crystal dimension vary between 30 and 60 µm/min. If we assume that the growth rates are on the order of ~ 50 µm/min, we can calculate that it will take 0.4 min for a crystal to grow to the visible size of 20 µm (time = (20 µm)/(50 µm/min)). Although this is a rough estimate, it is clear that the error introduced by our assumption is negligible considering that the fastest measured induction times were in hours. X-ray diffraction: powder, PO analysis and face indexing. Crystals obtained from induction time measurements were analyzed using powder X-ray diffraction (XRD). For each experimental condition, at least on fifth of vials was randomly selected for analysis. In each case, crystals were separated from solution and films, gently powdered and spread onto standard zero-background sample holders. XRD powder patterns were obtained for 2θ range between 3° and 35° using a Panalytical X’pert Pro diffractometer. The obtained patterns were compared to the simulated powder pattern of APAP Form I and Form II (CSD codes HXACAN0120 and HXACAN0721). The peaks were picked and assigned using standard parameters in High-score plus software. Preferred orientation of crystals and presumed interaction with films was determined by X-ray diffraction. Upon crystallization, the films with crystals were taken from the solution and


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mounted on the flat zero-background sample holder. An XRD pattern was obtained for 2θ range between 3° and 35° using a Panalytical X’pert Pro diffractometer. The amorphous phase originated from film was subtracted from the obtained patterns. From each set of nucleation conditions, a couple of crystals of suitable size was selected and mounted on a Bruker SMART APEX single crystal diffractometer. The unit cell and the orientation matrix were determined using a monochromatized Mo K-alpha source. For all mounted crystals, the unit cell data matched the un-solvated APAP (HXACAN01).20 It should be noted that this crystal structure is solved in a non-standard space group and different axes could have been chosen to result in P21/c or P21/n groups. For historical reasons and prevalence in literature, we proceeded with the unique axis being b = 9.386 Å and P21/a group. AFM imaging of the crystal in the nano-patterns. To obtain the image of a crystal inside the shapes, roughly less than 600 nm in size, we used the vial with a film and solution prepared as for induction time measurement. We chose a vial that has not yet crystallized based on the observations with optical microscope. Next, we gently shook the vial to initiate the crystallization and pulled out the polymer film. The surface of the film was then scanned in search for an isolated nano-crystal that is visible using AFM but still has not grown outside the walls of a single nano-pattern. This means that crystal had to be scanned sometimes during crystal growth while the longest dimension of the crystal is less than ~ 400 nm. Considering the crystal growth rater described in previous sections, an average crystal was of suitable size only for few seconds or less. Such procedure was necessary because otherwise we obtained only polymer films with crystals that have significantly overgrown the patterns and no useful information about the orientation of the crystals inside the shape could be obtained. 3. Computational methods


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Crystal Morphology Prediction. The crystal morphology of APAP was predicted using Morphology module of the Materials Studio 8.0 software of Accelrys Inc. on a Dell Latitude E6640 computer with Windows 10 pro, Intel® Core™ Xeon 2.70 GHz CPUs, and 8 GB of RAM. We used the crystal structure of APAP Form I (RefCode: HXACAN01).20 BFDH,22 Growth23 and Equilibrium24 morphology prediction methods were used. When necessary, prior to morphology calculations, the geometry of the unit cell was optimized using the PCFF force field and the default SMART algorithm, which utilizes a combination of steepest descent, quasiNewton, and ABNR methods. The hkl index was set to 2. Hydrogen-bond analysis of crystal faces. Combining crystal morphology prediction and experimentally observed faces (single-crystal face indexing and PO analysis), a list of most important faces was devised. Using Mercury software (Mercury CSD 3.6, last updated July 1st, 2015) we generated 20x20 Å slabs of each faces. The faces were analyzed and ranked based on number, density and type of hydrogen bonds. Hydrogen bonds were defined using default definition of Mercury software (contact distance range based on van der Waals distances). Polymer preparation for MD simulations. The polymer was prepared using the adapted softconfined method25 in Material Studio software. The backbone of the hydroxyethylcellulose polymer chains were built using eight 1,4-β-D-glucose repeat units, available in the library of Materials Studio, in head-to-tail orientation and isotactic tacticity. Next, the chains were modified by adding hydroxyethyl units such that final degree of substitution is two. This was followed by geometry optimization. The atom types were assigned by the COMPASS force field.26 Six molecules of the polymer were packed into a confined layer using Amorphous Cell. Initial density was set to 0.5 g/cm3 and target density to 1.5 g/cm3. The confined layer is then inserted between two slabs of xenon crystal, prepared in a separate window using the Build


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Crystal feature of Material Studio. Xenon crystal slabs are necessary as a confining surfaces during the optimization of a polymer model in order to prepare a smooth surface that closely mimic an actual surface of a polymer. The optimal confining surface does not attract or repulse the polymer, is flat, and solid at the optimization temperature. During optimizations, the position of xenon atoms were fixed. To adjust the density, NPT dynamics were performed. The polymer was further relaxed using NVT dynamics. The larger layer was built by expanding the prepared layer by 2 cell units in x and y direction and removing the xenon atoms. The larger layer was subjected to 5 cycles of annealing from 298 K to 500 K. Such prepared model was used to build the HEC polymer slab for MD simulations. To ensure that the polymer slab is a realistic model, we calculated the relative mass distribution (RMD), density, cohesive energy density (CED) and solubility parameter of polymer slab and compared them to the experimental values (See Results and discussion section). Calculation of charges. x, y, z- coordinates of APAP were taken from the crystal structure of APAP (RefCode: HXACAN01)20 and HEC chain structure was prepared using Materials Studio software, as described above. The geometry of the APAP molecule and the HEC chain were optimized separately to a local minimum on the potential energy surface (zero-imaginary frequencies) using HF/6-31G* level of theory. The electrostatic potentials (EPS) were derived the single-point energy calculations on the optimized structures using the same level of theory. The resultant EPSs were fitted using the RESP procedure to derive the partial atomic charges.27, 28

All quantum chemistry calculations were carried out using the Gaussian03 program package.29

Choice of the force field for the MD simulations. The initial HEC polymer slab was prepared using the COMPASS force field.26 COMPASS is a class II force field that contains additional cross-coupling terms for bonded interactions such as bond-bond, bond-angle and bond-torsion


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angle interactions. It also includes a LJ9-6 function for the van der Waals (vdW) term and a Coulombic function for an electrostatic interaction between pairs of atoms that are separated by two or more intervening atoms. The COMPASS force filed is more accurate than class I force fields but also substantially more expensive in terms of computational time. The purpose of this study was not to investigate the bulk properties of the polymer slab or to study the polymer dynamics. Instead, we were interested in estimating the energy of interaction (EOI) between the polymer surface and different crystal faces of APAP in the most efficient way. Therefore, we used CHARMM36 force field30,31 to perform MD simulations and compute EOI. CHARMM36 is a much faster force field for this type of massive computations. CHARMM36 is a class I force field and it is widely used for MD simulations of small molecules, biomolecules and carbohydrates. To confirm that the CHARMM36 force field is accurate enough for the purpose of the study, we performed several tests on both the HEC polymer slab and the APAP slabs. For the HEC polymer model, we analyzed the effect of force field on the EOI between HEC and APAP and the results are summarized in SI Table 5. For the APAP slabs, we had to develop a technique for modification and adjustment of the partial charges of APAP atoms to obtain the values of the lattice energy, heat of fusion, heat of sublimation, heat of vaporization and solvation free energy comparable with the experimental values (SI Table 7). The details of the method and modified charges for APAP (SI Table 6) are presented in SI. Details of the MD simulations. All MD simulations were performed using GROMACS-4.6.5.32 A Parrinello-Rahman barostat and Nosé-Hoover thermostat were used. Electrostatic interactions were calculated with particle mesh Ewald algorithm using a real space cutoff of 12 Å.33 Bonds were constrained using the LINCS algorithm34 and the time integration step was set to 1 fs. Crystal slabs of the following faces of APAP were generated: (001), (011), (11-1), (20-1), (200)


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and (110). All APAP crystal slabs had identical surface area of 50x50 Å. The surface area of the HEC polymer slab was 96x96 Å. The thickness of both slabs was 25 Å. The HEC polymer slab was first energy minimized using 1000 steps of steepest descent simulation. The structure was further relaxed by performing NPT simulations and slowly increasing the temperature from 10 K to 300 K. Periodic boundary condition was used in all directions. The final configuration was used for the calculation of EOI. To accurately calculate EOI, many possible configurations representing different relative orientation of the APAP crystal faces and the HEC polymer slab were generated by translating and rotating the center of the surface of the APAP slabs with respect to the center of surface of the HEC polymer slab. The procedure resulted in 7200 configurations for each crystal face (see SI for more details). For each configuration, 100ps of NVT MD simulations were performed. We used low temperature in order to overcome local energy barriers without causing major disruption of the relative lattice angles between APAP molecules. The configuration at the end of 100 ps of simulations was used for the analysis and calculation of EOI. EOI was calculated as: ‫ܧ = ܫܱܧ‬௧௢௧ − ‫ܧ‬஺௉஺௉ − ‫ܧ‬ுா஼ where EOI is energy of interaction, Etot is total energy of the APAP crystal face on top of the HEC polymer slab after MD simulation, EAPAP is energy of APAP crystal face and EHEC is energy of HEC polymer slab. The minimum energy value was considered as the best estimate for the global minimum For the hydrogen bond analysis, a geometric definition for the existence of a hydrogen bond was used. The acceptor-donor distance cutoff was set to 3.5 Å. The angular acceptor-hydrogendonor cutoff was set to 30º. The number of hydrogen bonds formed between the HEC polymer


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slab and the APAP slabs was calculated for each configuration using tools available in GROMACS. Finally, to analyze the effect of the force field on the results of simulations, we calculated EOI for one configuration for each face of APAP, using both COMPASS and CHARMM36 force fields. The absolute values of the energies were different, which is expected for simulations performed using different force fields (SI Table 5). However, the order of the faces based on EOI is identical for both force fields. This test confirms that using the CHARMM36 force filed instead of the expensive COMPASS force field was valid choice because the order of EOIs and, thus, main results of the simulations can be obtained using the significantly less expensive CHARMM36 force field. 4. Results and discussion Effect of polymer surfaces on average nucleation induction time. To quantify the effect of different polymer surfaces, we measured the average nucleation induction times for crystallization of APAP under exactly same conditions except that we varied the polymer surface present. The nucleation induction times were determined using optical microscopy. Upon crash cooling to achieve the targeted supersaturation, a set of 80 vials at once was monitored and induction times recorded using an inverted optical microscope. Induction time was defined as the time elapsed between achieving supersaturation and appearance of visible crystals. From observed crystal growth, we concluded that the time between the actual nucleation and appearance of visible crystals is negligible compared to the average induction times (SI Section 1.6). The average nucleation induction time, τ, was calculated based on the nucleation time for each vial and statistical analysis of the number of vials that nucleated at given time (N).35 Nucleation is a stochastic process that follows a Poisson distribution:


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ି௧

ܲሺ‫ݐ‬ሻ = ݁ ఛ where P is the probability that no nucleation event occurs within time, t. We first determined the effect of favorable surface chemistry of the polymer by comparing crystallization of APAP on the flat polymer surface to bulk crystallization (crystallization with no polymer present). We chose HEC polymer because of its molecular structure and biocompatibility.36 HEC powder readily makes clear flexible films that are soluble in water, but insoluble in many organic solvents, and can be used directly as an excipient.37 The monomer of HEC is D-glucose modified with hydroxyethyl groups. When prepared as a film, the surface of the polymer exposes hydroxyl (-OH) and ether groups, as observed in the model shown in Fig. 1, that can form interfacial hydrogen bonds with APAP (SI Fig. 3).

Figure 1. The HEC polymer surface prepared using the adapted soft-confined method.25 The nucleation induction time measurements show that at the same supersaturation level, the flat HEC films enhanced nucleation rate compared to the bulk crystallization and the average nucleation time is halved, from τ = 16 h to τ = 9 h (Fig. 2 and SI Table 2). Faster crystallization indicates attractive forces between functional groups on the HEC polymer surface and APAP molecules. The favorable polymer-APAP interactions likely have a positive effect on the nonspecific aggregation of solute molecules, the probable first step of heterogeneous nucleation, due to increased local concentration of APAP near the polymer surface.38 The polymer surface


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possibly affects the pre-exponential factor in the nucleation rate expression, instead of lowering the nucleation free energy barrier, by increasing the probability that a nucleus of a critical size will grow. The effect of functional groups present in the substrates has been previously noted in the field of self-assembled monolayers (SAMs) directed nucleation.39,40 For example, by employing SAMs terminated with complementary hydrogen bonding groups, accelerated nucleation and orientated crystal growth of several molecular crystals was achieved.41,42 The underlying mechanism seems to involve molecular recognition between SAMs and solute, and surface stabilization of prenucleation aggregates of solute via interfacial hydrogen bonding.

a)

b)

c)

Figure 2. Induction time measurements for a series of films: a) number of crystallized vials (N), b) ln(P) plotted against time t (the legend in the left plot applies to both plots) and, c) summary of the average induction times. We next measured the effect of different angle sizes present in nano-imprinted HEC polymer films on crystallization of APAP. Nano-patterns were imprinted by solution casting over inert solid masters prepared using interference lithography on smooth silicon wafers.43 We used for imprinting masters with nano-patterns containing 40°, 60°, 65°, 80° or 90° angles (Fig. 3).


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a)

b)

c)

d)

Page 18 of 34

e)

Figure 3. AFM images of imprinted silicon masters with pillars containing different angles a) 40°, b) 60°, c) 65°, d) 80° and e) 90° patterns. The measured average nucleation times show that the nucleation rate can be further improved by imprinting HEC polymer films with angular features and the nucleation rates are influenced by the imprinted angles (Fig. 2 and SI Table 2). The fastest crystallization occur when the HEC polymer imprinted with the 40° angle nano-patterns is used. Crystallization on the 40° angle nano-pattern (τ = 4 h) proceeds roughly four times faster than without the polymer (τ = 16 h) and two times faster compared to the flat polymer (τ = 9 h). Other patterns increased nucleation rates more than the flat films but less than the 40° angle pattern. The 80° angle pattern (τ = 5 h) was the second best, the 90° angle pattern (τ = 9 h) is comparable the flat polymer, and the 60° and 65° angle patterns are in between (τ = 6 h and τ = 8 h). The variations in the measured average nucleation time confirm that not only chemistry but also geometry of the polymer surfaces affect heterogeneous nucleation of APAP. Crystals obtained from described crystallization experiments were analyzed using XRD and we found that only pure Form I of APAP was present (SI Fig. 7).20 Diffractograms collected on crystals attached to the polymer films exhibit a high degree of preferred orientation (SI Fig. 8 and 9). The intensity of peaks associated with the {001} family of faces trump all other peaks, indicative of strong HEC-APAP interactions, particularly involving the face (001). The surface of the HEC polymer with the 40° angle was analyzed after crystallization using AFM imaging (SI Section 1.7). We observed a nanocrystal growing inside indentation formed by nano-patterns,


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and developing crystal faces are clearly visible (Fig. 4). The estimated angles between visible faces indicate that the face (001) and (011) align with the corners of the nano-pattern and the face (001) rise along the long side of the nano-pattern. Scans of a larger area of the polymer showed that nucleation initiated only in few nano-patterns.

a)

b)

Figure 4. AFM images of the APAP crystal grown on nano-patterned polymer: 3D-view (a), and crystal faces sitting in the angles of the nano-pattern (b). Polymer-crystal faces interactions: Hydrogen-bond analysis. To rationalize the observed enhanced nucleation of APAP, we attempted to identify the intrinsic angle that is targeted with the 40° angle nano-pattern in particular. We hypothesized that the most important intrinsic angle is the one between two crystal faces that interact the strongest with the polymer. Considering that hydrogen bonds are likely very significant in HEC-APAP interactions, we expect that the faces that have the greatest potential for forming hydrogen bonds will interact strongly with the polymer. We used morphology prediction methods to devise a list of crystal faces likely to appear during nucleation and crystallization. Crystal morphology is influenced both by internal crystal structure and interactions with environmental factors such as solvents, supersaturation and presence of heterogeneous surfaces. As a result, morphology prediction methods do not give perfect predictions, but the predicted faces in general appear at least as minor face at some stage


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Page 20 of 34

of crystallization process. We used Bravais-Friedel Donnay-Harker (BFDH),22 Growth (attachment energy)23 and Equilibrium morphology prediction methods24 (SI Table 3). All three methods predict the following six faces as major faces: (110), (001), (011), (20-1), (11-1) and (200). In comparison, the XRD analysis of crystals obtained in our experiments found that the crystal face (001) is the largest face in all analyzed crystals and the crystal faces (011), (20-1) and (110) are present with some variations in surface area from one crystal to another. We also surveyed literature for reports of morphology of APAP.44 Our survey did not find any faces that have not been predicted using above mentioned methods. To rank the faces based on their propensity to form hydrogen bonds with the HEC polymer, we analyzed number, orientation and type of functional groups for each crystal face. We also determined the density of hydrogen bonding groups for each face. Density of hydrogen bonds can be defined as number of hydrogen bonds on a plane per unit cell (δ1(HB)). However, different crystallographic planes cover different areas per one unit cell. For example, plane (001) covers area of 121.5 Å2 while plane (011) covers area of 113.5 Å2 per unit cell. To normalize the density, we also cut out slabs of each crystal faces with surface area of 20 x 20 Å (400 Å2) and counted hydrogen bonding groups within these slabs (δ2(HB)). Slabs were prepared using the Mercury software.45 The face (001) has eight exposed -OH groups originating from APAP molecules with aromatic rings in side-on orientation (Fig. 5a). -OH groups are protruding orthogonally out of the face which is expected to enable strong interactions with the polymer. Moreover, the face (001) has the highest density of hydrogen bonds (δ2(HB) = 2) among all analyzed faces. The face (011) has four aromatic rings and their four -OH groups exposed enabling a good interaction with the polymer surface (Fig. 5b). Additionally, there are two carbonyl (-C=O) groups exposed


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originating from two APAP molecules lying in (011) plane. The face (011) has the second highest density of hydrogen bonds (δ2(HB) = 1.5) behind the face (001). On the face (20-1) there are four exposed amino (-NH) and methyl (-CH3) groups originating from four APAP molecules orientated such that the long molecular axis is roughly parallel to the plane of the face (Fig. 5c). The exposed -NH groups are orientated such that bonding pattern is orthogonally protruding from the face. The four -CH3 groups are orientated in a same fashion. Since -CH3 groups are protruding ahead of -NH groups, it can be expected that the interaction of -NH groups with the polymer will be sterically hindered by -CH3 groups. The face (200) has four exposed -OH groups originating from APAP molecules tilted on to the plane of the face (Fig. 5d). The face (11-1) has three exposed -OH groups originating from APAP molecules with aromatic rings in side-on orientation (Fig. 5e). However, only oxygen of -OH group is exposed while hydrogen is locked in hydrogen bonds inside the bulk of the crystal. Thus, the -OH groups on face (11-1), without any significant rearrangement, can interact with the polymer only as hydrogen bond acceptors. On the face (110) there are three exposed hydroxyl (-OH) groups originating from three APAP molecules orientated such that the long molecular axis is roughly perpendicular to the plane of the face (Fig. 5f). The exposed -OH groups are orientated such that bonding pattern is parallel with the face which can be considered less optimal for interaction with polymer than if the you were protruding orthogonally towards a parallel polymer surface. The results of described analysis for all six faces are summarized in the Table 1. This analysis indicates that the crystal faces (001) and (011) interact the strongest with the HEC polymer. The angle between the face (001) and (011) is 34.19° (SI Table 4) which is close to the 40° angle imprinted on the HEC polymer film that enhanced the nucleation of APAP the most.


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Page 22 of 34

Table 1. Analysis of important crystal faces, in terms of number (N(HB)), density (δ(HB)) and type of hydrogen bonds (HB). face

δ1(HB) δ2(HB) N(HB) per 400 Å2

type of HB per 400 Å2

(001)

2

2

8

8x –OH as HB donor

(011)

2

1.5

6

4x –OH as HB donor 2x –C=O as HB acceptor

(20-1)

1

1

4

4x –NH as HB donor

(200)

1

1

4

4x –OH as HB donor and acceptor

(11-1)

1

0.75

3

3x –OH as HB acceptor

(110)

1

0.75

3

3x –OH as HB donor and acceptor

Figure 5. Slabs of crystal faces of APAP highlighting hydrogen bonds present on the surface area of 400 Å2 (red plane) of crystallographic planes (001), (011), (20-1), (200), (11-1), and (110). Polymer-crystal faces interactions: MD simulations.

A molecular model of the HEC

polymer slab was generated using the adapted soft-confined method25 and the properties of the relaxed polymer surface were validated by comparing the calculated values to the experimental


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values. For example, the relative mass distribution (RMD) of the polymer in the x and ydirections was monitored, and results demonstrated that the surface of the polymer slab is smooth and stable (SI Fig. 11). The calculated density is 1.13 g/cm3 which is in good agreement with reported density (1.1 - 1.3 g/cm3).46 The cohesive energy distribution (CED), a fundamental property of polymers which quantifies intermolecular interactions among the polymer molecules,47 was calculated to be 5.275x108 J/m3. The calculated solubility parameter (s) is 11.2 cal/cm3 which is in good agreement with reported experimental and simulated values (9.7-12.5 cal/cm3).48 Based on these results, we accepted our model as a realistic representation of thin films of HEC polymer used in crystallization experiments. The slabs of APAP crystal faces were generated for the following faces: (001), (011), (11-1), (20-1), (110) and (200). For each APAP crystal face, 7200 different configurations, with respect to the HEC polymer slab, were generated and relaxed to a local minimum by performing MD simulations. During MD simulations, the APAP crystal slabs move close to the surface of the HEC polymer slab and rearrange to form interfacial hydrogen bonds with the surface of HEC polymer (Fig. 6).

Figure 6. The configuration of the polymer and APAP face (001) slabs before (a) and after (b) MD simulations.


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Following MD simulations, EOI was calculated for each configuration of each crystal face/polymer system. The plotted sorted values of EOI (SI Fig. 12a) indicate that value of EOI is face-dependent. In particular, the crystal face (001) has the lowest minimum EOI, indicative of the strongest interaction with the HEC polymer slab. Based on EOI, the face (011) has 253 kJ/mol weaker interaction with the HEC slab relative to the face (001). The other considered crystal faces have comparable values of EOI and their interaction with the HEC slab is weaker by ~400 kJ/mol relative to the face (001) and ~150 kJ/mol relative to the face (011). The results indicate that the crystal faces (001) and (011) form significantly more favorable interactions with the HEC polymer compared to the other considered crystal faces. Table 2. Results of MD simulations: number of APAP molecules (N(APAP)) and hydrogen bonds (N(HB)), and total and per molecule EOI for the minimum energy configurations. face

N(APAP)

N(HB)

total EOI (kJ/mol)

EOI per molecule (kJ/mol)

(001)

264

67

-3674.197

-13.917

(011)

256

64

-3421.372

-13.364

(11-1)

270

59

-3281.855

-12.155

(20-1)

281

59

-3299.783

-11.827

(110)

302

57

-3202.742

-11.397

(200)

279

41

-3206.456

-10.617

To rationalize differences in EOI, we calculated the number of hydrogen bonds for each final configuration after 100 ps of MD simulations (SI Fig. 12b). Consistent with the analysis of hydrogen bonds and calculated EOIs, the face (001) forms the highest number of hydrogen bonds with the HEC polymer slab. However, the faces (011) and (110) form roughly the same


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number of hydrogen bonds with the HEC polymer slab. This is surprising considering that EOI of face (011) is significantly higher than that of the face (110). We assumed that type of hydrogen bonds formed between the face (011) and the HEC polymer slab must be stronger than the one between the face (110) and the same HEC polymer slab. To test this hypothesis, we searched for configurations were both faces form the same number of hydrogen bonds. We found that there are approximately 500 configurations in which both the face (011) and (110) formed 42 hydrogen bonds with the HEC polymer slab. We then calculated the short-range interactions (short-range Coulomb and van der Waals interactions) for these 500 configurations (SI Fig. 13). As expected, the average energy of the short-range interactions between the face (011) and the HEC polymer slab is shifted toward higher negative values by approximately 100 kJ/mol, compared to the face (110). The results confirmed that the face (011) indeed forms stronger hydrogen bonds with the HEC polymer slab than the face (110). Overall, the results of MD simulations indicate that the crystal faces (001) and (011) form energetically most favorable interactions with the HEC polymer. The number and type of hydrogen bonds formed is likely responsible for this effect. The combination of our experimental results and simulations provide new insights into understanding how angular shapes imprinted on amorphous polymer can direct nucleation. As already proposed in our previous work,13,14,15 nano-imprinted polymer surfaces influence the nucleation rate in two ways. First, the concentration of solute is increased near the polymer surface due to favorable solute-polymer interactions, and second, nano-imprints provide geometrical confinement that can facilitate orientational ordering of the solute molecules. If the geometry of nano-imprints resembles motifs in the crystal, nucleation will be further enhanced. In the case of APAP, the polymer imprinted with the 40° angle increased the nucleation rates to


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Page 26 of 34

the greatest extent. We propose that 40° angle is particularly efficient because it is close to the intrinsic angle between the (001) and (011) crystal face (34.19°). Based on MD simulations of crystal face-polymer interactions and hydrogen bond analysis, the crystal faces (001) and (011) interact stronger with the polymer relative to the other possible crystal faces. If this is true, then the nano-imprint that imposes the molecular arrangement that maximizes the interaction between the polymer and the crystal faces (001) and (011) should be the most effective. Although the match between the intrinsic angle and our nano-pattern is not exact (34° vs 40°), the pattern enables growing APAP crystals to be positioned such that two strongly favored crystal faces are simultaneously stabilized by interactions with the polymer. This arrangement is more energetically favorable than a random position with no polymer-APAP interaction or with only one crystal face interacting with the polymer. In addition, the interfacial layer is not perfectly flat or rigid, and it could likely adapt to the pattern within several degrees.9,49 5. Conclusion In summary, we improved the nucleation rate of APAP by employing polymer films imprinted with nano-patterns featuring different angle sizes. While all nano-patterns increased the nucleation rate, we found that the nano-pattern with the 40° angle is particularly efficient in promoting nucleation. These observations indicate that the underlying mechanism responsible for the enhancement of crystallization is angle-directed nucleation, based on a geometrical match between an intrinsic angle of crystal and an external angle of the nano-pattern. We propose that the intrinsic angle of APAP that is matched by the 40° angle pattern, and, thus, crucial for higher nucleation rate, is the angle between two crystal faces that interact the strongest with the HEC polymer. By analyzing the hydrogen bonds exposed on different crystal faces of APAP and performing a series of MD simulations of APAP-HEC interactions, we identified these faces as


26

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the crystal faces (001) and (011). Indeed, the measured intrinsic angle between the faces (001) and (011) is close to 40°. Our findings are important contribution to the fundamental understanding of directed heterogeneous nucleation. Moreover, our method has clear technological implications as it expedites the optimization of crystallization processes. Using our methods, the geometry of polymer surfaces can be quickly designed, without experimental screening of several possible angular patterns, because the important intrinsic angle can be identified based on computational work. We expect that our method can aid a wide range of crystallization processes, in particular those involving difficult-to-nucleate solids. ASSOCIATED CONTENT Supporting Information. Additional data for hydrogen bonds, AFM images, inductions time measurements, and crystal morphology analysis; solubility curve; XRD patterns; analysis of polymer model; additional computational results. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author Bernhardt L. Trout *E-mail: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT


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Page 28 of 34

We acknowledge the Novartis-MIT Center for Continuous Manufacturing for funding. We are grateful to Dr. T. Savas at MIT Research Laboratory of Electronics for fabricating the silicon masters used to imprint the nano-patterns. We are grateful to Dr. P. Müller at MIT X-Ray Diffraction Facility for help with indexing single crystals. We acknowledge Dr. Z. Zhu for initial work on screening possible solvents for induction time measurements. REFERENCES (1)

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For Table of Contents Use Only Angle-directed nucleation of paracetamol on biocompatible nano-imprinted polymers Jelena Stojaković, Fahimeh Baftizadeh, Michael A. Bellucci, Allan S. Myerson, and Bernhardt L. Trout*

Synopsis. We enhanced the nucleation rates of paracetamol using a biocompatible polymer imprinted with a nano-pattern with 40° angles. Using MD simulations and analysis of hydrogen bonds, we found that a 40° angle nano-pattern likely targets and stabilizes the (001) and (011) crystal faces of APAP by strong intermolecular interactions with the polymer.


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Angle-Directed Nucleation of Paracetamol on Biocompatible

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