Molecular Dynamics Simulation of Amorphous Hydroxypropyl

Article pubs.acs.org/molecularpharmaceutics

Molecular Dynamics Simulation of Amorphous HydroxypropylMethylcellulose Acetate Succinate (HPMCAS): Polymer Model Development, Water Distribution, and Plasticization Tian-Xiang Xiang and Bradley D. Anderson* Department of Pharmaceutical Sciences, College of Pharmacy, University of Kentucky, Lexington, Kentucky 40536, United States ABSTRACT: Molecular models for HPMCAS polymer have been developed for molecular dynamics (MD) simulation that attempt to mimic the complex substitution patterns in HPMCAS observed experimentally. These molecular models were utilized to create amorphous HPMCAS solids by cooling of the polymeric melts at different water contents to explore the influence of water on molecular mobility, which plays a critical role in stability and drug release from HPMCAS-based solid matrices. The densities found for the simulated amorphous HPMCAS were 1.295, 1.287, and 1.276 g/cm3 at 0.7, 5.7, and 13.2% w/w water, indicating swelling of the polymer with increasing water content. These densities compare favorably with the experimental density of 1.285 g/cm3 for commercial HPMCAS-(AQOAT AS-MF) supporting the present HPMCAS models as a realistic representation of amorphous HPMCAS solids. Water molecules were observed to be mostly isolated from each other at a low water content (0.7% w/w), while clusters or strands of water were pervasive and broadly distributed in size at 13.2% w/w water. The average number of first-shell water molecules (nw) increased from 0.17 to 3.5, though the latter is still far below that (8.9) expected for the onset of a separate water phase. Increasing water content from 0.7 to 13.2% w/w was found to reduce the Tg by ∼81 K, similar to experimental observations. Plasticization with increasing water content resulted in increasing polymer mobility and water diffusivity. From 0.7 to 13.2% w/w water, the apparent water diffusivity increased from 1.1 × 10−9 to 7.0 × 10−8 cm2/s, though non-Einsteinian behavior persisted at all water contents explored. This and the water trajectories in the polymers suggest that water diffusion at 0.7% w/w water follows a “hopping” mechanism. At a higher water content (13.2% w/w) water diffusion follows dual diffusive processes: (1) fast water motions within water clusters; and (2) slower diffusion through the more rigid polymer matrix. KEYWORDS: solid state, pharmaceuticals, molecular dynamics simulations, HPMCAS, amorphous polymers, glass transition, water distribution, water diffusion

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INTRODUCTION Interest in amorphous solid drug dispersions has been increasing over the past decade because of their potential advantages in enhancing solubility and dissolution rates of poorly soluble drugs.1−6 Dispersions of therapeutic agents in polymeric matrices have also proven useful for controlled release applications7,8 and as a means of further improving dissolution and oral bioavailability by inhibiting drug crystallization.9−11 Hydroxypropylmethylcellulose acetate succinate (HPMCAS) is a common polymer that is often used for enteric coating of pharmaceutical dosage forms12−15 and in extended drug release matrices.13,16 It has a high glass transition temperature (Tg) in its un-ionized state,17 which tends to reduce molecular mobility and improve the physical stability of HPMCAS-based solid dispersions. HPMCAS has also been chosen as a tablet matrix former for drug release, because it is water-insoluble at low, and water-soluble at high, pH values, which can be utilized for bimodal drug release.8 Its amphiphilic properties allow its hydrophobic regions to associate with those poorly water-soluble but lipophilic drugs while its hydrophilic regions may facilitate © XXXX American Chemical Society

the formation of hydrated nanosized colloidal structures after oral administration that can inhibit formation of drug crystals. Indeed, drug/HPMCAS solid dispersions were recently found to be more effective at maintaining drug supersaturation in the GI milieu than other polymers investigated18−20 and to provide large bioavailability increases in vivo.9,17 Polymers used to form amorphous drug−polymer dispersions exhibit a high level of disorder, which enhances their tendency to absorb a larger quantity of water (e.g., 0−12% w/w water in 0− 95% relative humidity for HPMCAS).21,22 This increased hygroscopicity can result in a large decrease in Tg and enhancement of molecular mobility, which may lead to a more rapid crystallization of the dispersed drug. Water can also act as a reactant, and this type of reaction may also be limited by diffusivity of water. For example, dissolution of delavirdine Received: February 14, 2014 Revised: May 11, 2014 Accepted: May 28, 2014

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dx.doi.org/10.1021/mp500135f | Mol. Pharmaceutics XXXX, XXX, XXX−XXX

Molecular Pharmaceutics

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mesylate tablet is substantially reduced after exposure to high humidity due to occurrence of a solid-state reaction between the free methanesulfonic acid and the carboxyl sites on the croscarmellose sodium disintegrant.23 While the role of water in this disproportionation process (reactant or plasticizer) is not entirely clear, water in the polymer could increase acid mobility and allow the reaction to proceed. Apart from the well-known effects of molecular mobility on drug phase transition and chemical reaction in amorphous drug−polymer tablets, understanding the underlying diffusion mechanisms is also imperative for developing polymer systems for controlled release applications and for controlling the effects of water vapor transmission through film coatings, solid tablets, and packaging materials. For HPMCAS-based matrix tablets, water imbibition into the tablets and subsequent polymer swelling and drug diffusion out of the tablet play a critical role in the drug release profile.8 Thus, it is important to understand water distribution and associated plasticization effects on molecular mobility in HPMCAS polymer. Unfortunately, few experimental methods are well suited to determine molecular mobility in amorphous solids and understand the underlying microscopic dynamic processes. In particular, water diffusivity and associated diffusion mechanism(s) in amorphous HPMCAS remain to be determined both experimentally and computationally. Molecular dynamics (MD) simulations are ideally suited to explore various atomic-level structures and dynamic processes that are of importance in determining molecular mobility and physical stability in amorphous solids but are not easily monitored experimentally. Although progress has been made in recent years using ab initio calculations in small-scale molecular systems, MD simulations based on a classicalmechanics force field remain more realistic for polymeric systems and have been widely used for investigation of various structural and dynamic properties of polymers and other condensed materials of pharmaceutical interest.24−31 Significant progress has been made toward understanding the glass transition,32 miscibility and solubility of drugs,27,30,33,34 moisture uptake,28 and molecular motions accompanying relaxation and diffusion processes.24,27,28,35 Nevertheless, computational studies on cellulose-based polymers with polar side-chain substitutions are still rare, and to the authors’ knowledge, no MD simulation of amorphous HPMCAS solids has been reported in the literature. This may be due to the complex polymer structure as a result of multiple substitution sites (i.e., O2, O3, O6 in Table 1) and substituent groups (e.g., Me, HP, HPMe, Ac, Su, etc.) and their somewhat random substitution patterns. Thus, our first goal in this study was to develop molecular models for HPMCAS and then use these molecular models to construct HPMCAS polymer assemblies varying in water content (0.7−13.2% w/w). The polymers built were then cooled from the melt to a temperature (200 K) well below their Tg to generate the amorphous polymer glasses. We then shifted our focus to the examination of water distribution and its plasticization effects on the polymer as characterized by changes in polymer Tg, swelling, relaxation rate, and water diffusivity.

Table 1. Various Substituent Groups Present in HPMCAS

R

chemical composition

Me HP HPMe Ac Su HPAc HPSu

−CH3 −CH2CH(CH3)OH −CH2CH(CH3)OCH3 −COCH3 −COCH2CH2COOH −CH2CH(CH3)OCOCH3 −CH2CH(CH3)OCOCH2CH2COOH

models were first built based on the molar distributions for all of the detectable substituent patterns in HPMC by Adden et al.36 The results for HPMC polymer will be discussed in a separate study. Once the HPMC molecular models were constructed, HPMCAS molecular models could be constructed. Experimentally, HPMCAS can be synthesized by treating O-(hydroxypropyl)-O-methylcellulose with acetic anhydride and succinic anhydride, as set forth by Tezuka et al.37 and Onda et al.38 Although such derivatives of cellulose are often considered in the literature as simply having varying average percentages of the four substituents (Me, HP, Ac, Su in Table 1) attached to the three hydroxyl groups on each of the glucose repeat units of cellulose, 13C NMR research suggests that most of the hydroxyl groups initially present on the 2-hydroxypropyl groups are also substituted by methyl, acetyl, succinoyl, or a second 2hydroxypropyl group.38 Using 13C NMR, Tezuka et al.39 found that the degrees of substitution of the two ester substituents (acetyl and butyrate) are close to each other at the O2, O3, and O6 positions in cellulose acetate butanoate (CAB). As a first approximation, we therefore assumed that acyl substitutions at O2, O3, and O6 have the same probabilities (P2 = P3 = P6) independent of previous substitution patterns. Thus, for each substitution site of every monomer unit in HPMC, if the site was not occupied by a Me, HP, or HPMe group, an acetyl or succinyl would occupy this site with the following probabilities calculated from the 13C NMR data by Tezuka et al.:37 Pac = 0.51, Psu = 0.29 and Pun = 0.20, where Pun is the probability that this site remains unoccupied. If searching indicated occupation of a site by HP, 65% of it was randomly replaced with HPAc and 35% with HPSu. A program was written to facilitate the process described above which was repeated multiple times for each glucose unit in the HPMCAS polymer. The basic glucose unit structure from the Amber database, glycam04.dat, was adopted as a template in building the HPMCAS backbone. The standard AMBER all-atom force field (ff03) was used for these calculations. The atom types and associated force-field parameters (bond, angle, and torsion) for the glucose unit and the substituent groups shown in Table 1 were assigned by analogy with existing parameters in the Amber database. Since up to 50 different residue patterns could be present in HPMCAS as shown in Table 2, we adopted a simplification strategy for determining the atomic partial charges

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COMPUTATIONAL METHODS HPMCAS is a cellulose derivative consisting of a backbone of cellulose with certain functional groups (cf. Table 1) substituted onto the glucose units at position O2, O3, or O6. The first three substituents in Table 1 were used in the construction of hydroxypropylmethylcellulose (HPMC), and since HPMCAS is commonly manufactured from HPMC, HPMC molecular B



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correlation functionals with the ccpVTZ30 basis set were used, and the IEFPCM continuum solvent model41,42 was applied to mimic an organic solvent environment (ε = 4).43 Effective atomic charges were obtained by fitting the electrostatic potential using the RESP method.44 From the unit patterns built, six individual HPMCAS polymer chains each consisting of 20 randomly selected monomer patterns were constructed by using xLeap. The six HPMCAS chains were then visually combined with a certain number (12, 100, or 250) of water molecules (TIP3P) in a cubic box to minimize the degree of bad atomic contacts. The number of water molecules was chosen such that the percentage water by weight in the polymer (0.7, 5.7, and 13.2% w/w) was close to the experimental range of 0−13% w/w for HPMCAS polymers (AQOAT AS-MF, Shin Etsu Chemical Co., Tokyo, Japan) over the entire relative humidity range (0−100%).21 Once constructed, the assemblies were energy minimized (300/700 iterations of steepest descent and conjugate gradient) to eliminate any bad contacts and equilibrated in their molten state (>500 K) at 1 bar by a dynamic run (1−3 ns) subjected to periodic boundary conditions. The equilibrated systems were then subjected to a cooling dynamic run during which the system temperature was lowered at a constant rate of 0.033 K/ps to a final temperature of 200 K. After the completion of the cooling run, a selected microstructure corresponding to a certain temperature (i.e., 298 K) was selected from the acquired trajectory file as a restarting configuration for a prolonged aging dynamic run (up to 100 ns) at the same temperature and pressure to acquire system trajectories at 10 ps intervals for subsequent analyses. The above minimization and dynamic runs were performed using Sander 11, in which Newton’s equations of motion are evolved using the Verlet leapfrog algorithm45 with a time step of 1 fs. The dielectric constant was set at 1.0. Constant temperature and pressure were maintained by coupling to external thermal baths.46 Electrostatic interactions were calculated using the particle mesh Ewald method47 with a cutoff of 10 Å. The SHAKE algorithm was used to constrain all covalent bonds involving hydrogen. The ptraj programs in Amber 11, VMD 1.9.1,48 and numerous computer programs developed in house were utilized to calculate numerically and analyze visually various structural and dynamic properties of the simulated HPMCAS systems. Calculations were performed on a Lipscomb HPC cluster (Dell Inc.) rated at >40 teraflops at the High Performance Computing complex, University of Kentucky, and PCs in the authors’ laboratory.

Table 2. Substitution patterns Used in Building the HPMCAS Molecular Model pattern ID

pattern

pattern ID

pattern

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

236-Me 26-Me 36-Me 23-Me 6-Me 2-Me 3-Me 26-Me-3HPMe 36-Me-2-HPMe Un 23-Me-6-HPMe 6-Me-2-HPMe 2-Me-6-HPMe 26-Me-3-HP 3-Me-2HPMe 36-Me-2HP 6-HPMe 23-Me-6-HP 2-Me-3-HP 2-Me-6-HP 23-HP 2-Me-3-HP-6-HPMe 2-Me-66-HP 26-Me-3Ac 3-Su-6-HPMe

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

26-Me-3Su 2-Me-36Ac 2-Me-3-Ac-6-HPMe 23-Me-6-HPAc 236-Ac 2-Me-3-Ac-6-Su 23-Me-6-Su 2-Me-36-Su 2-Me-3-Ac 6-Me-2-HPMe-3Ac 2-Su-36-Me 2-Su-3-Ac-6-Me 23-Me −6-Ac 2-Ac-3-Me 2-Me-3-Su 36-Su 3Me-26-Ac 2-Me-3HPAc-6HPSu 2-Me-3HPSu-6-HPAc 2-HPSu-36-Me 2-Me-3-HPAc-6-Su 2-Me-3-Su-6-Ac 23-HPAc 2-Su-3-Ac-6-Me 2-Me-6-Ac

for these residues. The atomic partial charges for atoms in the basic glucose unit were obtained from the Amber database and, unless specified, largely unchanged. To determine the atomic partial charges for various substituent groups used in building the HPMCAS polymers, a glucose trimer was first built with xLeap. Various substituent groups of interest were then covalently attached to selected positions (O2, O3, O6) in the central glucose unit of the trimer as shown in Figure 1.

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RESULTS AND DISCUSSION Construction of HPMCAS Molecular Models. Since no MD simulations of HPMCAS polymer have been reported in the literature, our first effort was focused on developing an HPMCAS

Table 3. Substituent Compositions (% by Weight) in Model and Commercial HPMCAS Polymers

Figure 1. A representative structure for substitution of an acetyl group at O6 in the central glucose residue.

To account for polarization effects that are important in the condensed phase where the local electrostatic environment is significantly different from that in the gas phase due to the presence of neighboring atoms,40 the electrostatic potential for the optimized triglucose structure was calculated with Gaussian 03. In the ab initio quantum mechanical calculation,40 density functional theory (DFT) and the B3LYP exchange and

substance

methoxy

hydroxypropoxy

acetyl

succinoyl

model HPMCASa AS-Lb AS-Mb AS-Hb

25 20−24 21−25 22−26

4 5−9 5−9 6−10

11 5−9 7−11 10−14

13 14−18 10−14 4−8

a

Present molecular model. bCommercial products AQOAT from Shin-Etsu Chemical Co. (http://www.elementoorganika.ru/files/ aqoat.pdf).

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weight for commercial HPMCAS products varies with lot and grade but is approximately in the range of 17000−20000 with the number-average molecular weight around 13000.49 In the present case, the HP groups are mostly substituted by methyl (HPMe), acetyl (HPAc), and succinoyl (HPSu), consistent with a previous 13C NMR study by Onda.38 If each of these groups is counted as consisting of one HP and one Me, Ac, or Su group, the percentages of the methoxy, hydroxypropoxy, acetyl, and succinoyl substituents in the present HPMCAS polymer are 25, 4, 11, 13% by weight, respectively. Table 3 compares the substituent compositions in the present HPMCAS model with those reported for commercial products (AQOAT) from ShinEtsu Chemical Co. Although essentially any degree of substitution of the various groups can be used as long as the resulting polymer is soluble at the pH of the small intestine (e.g., pH 5 to 7) the amounts of the substituents methoxy, hydroxypropoxy, acetyl, and succinoyl used in the synthesis of HPMCAS are generally in the range of 10−35%, 3−15%, 3−20%, and 2−30% by weight, respectively, and preferably in the range of 15−30%, 4−11%, 4−15%, and 3− 20% by weight, respectively.50 The substituent distribution in our present HPMCAS model lies within the preferable range and is also close to typical values (23% methoxy, 7% hydroxypropoxy, 9% acetyl, and 11% succinoyl20 in the popular HPMCAS-MF product (Shin Etsu Chemical Co.)). The atom types and associated force-field parameters (bond, angle, and torsion) for the glucose unit and the substituent groups shown in Table 1 were assigned by analogy with existing parameters in the Amber force-field (ff03). To determine the atomic partial charges for various substituent groups used in HPMCAS, they were covalently attached to selected positions (O2, O3, O6) in the central glucose unit of a glucose trimer as shown in Figure 1 and Gaussian calculations as described in the preceding section were conducted on these substituted trimers. We found that the partial atomic charges for various substituent groups are generally not sensitive to the substituent location. Thus, for simplification, a single set of atomic charges was used for each substituent regardless of the substitution pattern. We also noted that except for HP, HPMe, and Su groups (cf. Table 1), the net charges for all other substituents, some of which (i.e., Me and Ac) are the primary contributors to the substitution patterns, are close to the value necessary (0.194) to maintain charge neutrality for the whole glucose residue after the substitution(s). Thus, atomic charges for these substituents were finely adjusted to ensure exact charge neutrality for the underlying residues. For HP, HPMe, and Su groups, the atomic partial charges from the quantum mechanical calculation were such that their net charges were 0.05−0.095 lower than 0.194, and for those cases the charges of the adjacent oxygen atoms (O2, O3, or O6) were finely adjusted to maintain charge neutrality for the whole residue. Table 4 presents the atomic partial charges used for the relevant substituent groups. For unsubstituted −OH groups, the oxygen atom was assigned a charge of −0.7 based on the present ab initio calculations. Accordingly, to maintain charge neutrality for a whole residue, the partial charges for hydrogen atoms in −OH were assigned values of 0.418−0.437. Similar values were reported for the −OH group (−0.735, 0.404) in heparin.51 The partial charges for the −COOH groups in Su (0.64, −0.56, −0.64, 0.49) and HPSu (0.67, −0.58, −0.63, 0.48) are slightly larger (in the absolute values) than those (0.55, −0.50, −0.58, 0.45) covalently attached to a carbon nanotube obtained by Zheng et al.52 and those used by Li et al.53 for hydrophobic graphite-COOH plates. For comparison, we also

Table 4. Atomic Names, Types, and Partial Charges for Various HPMCAS Substituents name

type

partial charge

HP

name

type

partial charge

C10 H11 H12 H13

CT HC HC HC

−0.046 0.08 0.08 0.08

C38 H64 H65 C39 H66 C40 H67 H68 H69 O43 C41 O44 C42 H70 H71 H72

CT HC HC CT HC CT HC HC HC OS C OS CT HC HC HC

−0.177 0.12 0.12 0.588 0.023 −0.55 0.14 0.14 0.14 −0.54 0.844 −0.614 −0.325 0.095 0.095 0.095

C61 H10 H11 C62 H12 C63 H13 H14 H15 O49 C64 O50 C65 C66 C67 O51 O52 H16 H17 H18 H19 H20

CT HC HC CT HC CT HC HC HC OS C O CT CT C O OH HC HC HO HC HC

0.038 0.057 0.057 0.13 0.17 −0.42 0.12 0.12 0.12 −0.42 0.68 −0.53 0.05 −0.18 0.671 −0.58 −0.63 0.056 0.056 0.475 0.077 0.077

Me C13 H21 H22 C14 H23 C15 H24 H25 H26 O27 H28

CT HC HC CT HC CT HC HC HC OH HO

−0.18 0.08 0.08 0.44 −0.019 −0.46 0.116 0.116 0.116 −0.69 0.42

C49 H87 H88 C50 H89 C51 H90 H91 H92 O46 C52 H93 H94 H95

CT HC HC CT HC CT HC HC HC OS CT HC HC HC

−0.22 0.12 0.12 0.36 0.041 −0.46 0.13 0.13 0.13 −0.4 0.14 0.015 0.015 0.015

C16 O29 C30 H31 H32 H33

CT O CT HC HC HC

0.88 −0.621 −0.53 0.155 0.155 0.155

C21 O32 C22 C23 C24 O33 O34 H40 H41 H42 H43 H44

C O CT CT C O OH HC HC HO HC HC

0.68 −0.55 −0.2 −0.02 0.64 −0.56 −0.64 0.09 0.09 0.49 0.062 0.062

HPAc

HPMe

Ac

Su

HPSu

molecular model that closely mimics HPMCAS commercial products such as AQOAT from Shin-Etsu Chemical Co. In this study, HPMCAS, which is commonly manufactured from HPMC, was constructed from HPMC molecular models developed in a separate study. The sequence of residue patterns for each of the six HPMCAS chains each consisting of 20 randomly selected monomer patterns was based on the probability values for occurrence of each substitution pattern. A total of 50 residue patterns as shown in Table 2 are present in these six HPMCAS polymer chains. The average molecular weight for the HPMCAS chains is 5213 Da. The molecular D



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Figure 2. Density−temperature (left) and atomic fluctuation−temperature (right) phase diagrams for the HPMCAS systems at 0.7% (black), 5.7% (dark gray), and 13.2% (light gray).

Figure 3. A microstructure of the HPMCAS glass (5.7% w/w water) formed at 298 K and 1 bar: The picture includes the central cell along with its ±x, ±y, ±z image cells.

high to low translational mobility of the polymer chains that occurs within a narrow range of decreasing temperature. It is of particular interest in the pharmaceutical sciences because of the often observed coupling of physical or chemical instability to either local mobility or global molecular mobility as reflected in the Tg.54−61 Experimentally, the glass can be formed by cooling

obtained the partial charges for acetic acid using the same ab initio method described above. The results for −COOH in acetic acid (0.80, −0.60, −0.66, 0.45) are close to those in the Su and HPSu groups. Formation and Aging of HPMCAS Glasses. The glass transition temperature (Tg) refers to the abrupt transition from E



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Figure 4. Evolution of density in the simulated HPMCAS systems containing 0.7, 5.7, and 13.2% w/w water at 298 K and 1 bar.

Figure 6. Radial distribution functions, g(r), between the oxygen atoms in water molecules and oxygen atoms on the HPMCAS polymers (solid circles) and hydrogen atoms in the HPMCAS polymers (open circles). Upper panel: 0.7% w/w water. Lower panel: 5.7% w/w water. In the lower panel, g(r) between the oxygen atom in a given water molecule and the oxygen atoms in the other water molecules (OW) is also plotted (gray circles).

faster cooling rate employed here (0.033 K/ps) compared with experiments is probably the main cause of the disparity, but it is currently not possible in all-atom MD simulations to approximate experimental time frames. This time scale for the cooling process is ∼10−13 orders of magnitude shorter than the relaxation time at the experimental Tg, and this, according to Barrat et al.,35 may shift Tg to a higher temperature by roughly 30−45 deg. Similar or even higher discrepancies have been reported in PVP and other amorphous polymers and silica glasses.24,65−67 A glass is “a liquid that has lost its ability to flow”68 due to an abrupt change in viscosity or, on a microscopic level, molecular mobility. Thus, the glass transition temperature can also be determined from changes in molecular mobility with temperature, though this method has rarely been used for a computational determination of Tg. In this study, molecular mobility was measured by the atomic fluctuations (= 8/3π2 Bfactor), a measure of how far each atom moves from its average position within a certain time interval.69 The atomic fluctuation is calculated as the root-mean-squared (RMS) distance of all atoms in the assembly from the average positions of these atoms in two adjacent snapshots separated, in this study, by 100 ps. The results for the HPMCAS polymers with different water contents during the entire cooling processes are presented in Figure 2. The mobilization of HPMCAS polymers by the addition of water is clearly apparent. The intersection of linear fits of the mobility profiles below and above the Tg gives estimates of 464, 430, and 380 K for the Tg at water contents of 0.7, 5.7, and 13.2% by weight, respectively. The observed plasticization effect (or the degree of Tg reduction) is similar to that obtained from the

Figure 5. Representative hydrogen bonding configurations in a simulated HPMCAS glass (0.7% w/w water) at 298 K.

the melt. The same technique was employed in the present MD simulations in which an HPMCAS glass was generated by fast cooling of the HPMCAS melt to 200 K at a constant cooling rate of 0.03 K/ps. Figure 2 shows the density−temperature phase diagrams for simulated HPMCAS polymers at three different water contents (0.7, 5.7, and 13.2% w/w). A distinct change in the slope as the polymer is cooled is evident in the phase diagrams. The glass transition temperature, Tg, can be determined from the intersection of linear fits of the density− temperature profiles below and above the Tg,62 which gives values of 442, 409, and 361 K at the water contents of 0.7, 5.7, and 13.2% by weight, respectively. As a manifestation of the classical plasticization effect of water,63 Tg decreases significantly at a higher water content. The magnitude of Tg reduction of ∼80 deg for a change in water content from 0 to 13% w/w is similar to experimental results for HPMCAS-LG and HPMCAS−MG.17 The calculated Tg values are generally higher than reported experimental values of ∼393−408 K for HPMCAS depending on the product grade (AS-LG, AS-MG, and AS-HG).64 The much F



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Figure 7. Spatial distributions of water molecules obtained from microstructures for newly formed HPMCAS glasses at 298 K: (A) 0.7%; (B) 5.7%; and (C) 13.2% w/w water by weight.

Figure 3 shows a representative three-dimensional image of an HPMCAS glass formed at 298 K and 5.7% w/w water. The polymer appears to be densely packed without unusual highenergy local microstructures, though a glass generated by rapid cooling is known to reside in a metastable thermodynamic state and its physical properties such as density will gradually drift toward an equilibrium value, a process referred to as structural relaxation or physical aging.62,70−72 The change in density at 298 K over 100 ns after the glass formation, shown in Figure 4, illustrates the aging process for the glass generated in the present study. Immediately after glass formation, the polymer densities at 298 K were found to be 1.295, 1.287, and 1.276 g/cm3 at water contents of 0.7, 5.7, and 12.3% w/w, respectively. These results compare favorably with the experimental value of 1.285 g/cm3 for commercial HPMCAS-(AQOAT AS-MF),22 supporting our present HPMCAS models as realistic representations of amorphous polymeric solids generated from industrial HPMCAS products. These results also indicate that the presence of water molecules reduces the polymer density, which is consistent with the swelling effect of water on amorphous HPMCAS.16 During 100 ns aging simulations, the polymer densities changed only slightly by 0.1−0.5% at 0.7 and 5.7, and 12.3% w/w water contents. Water Distribution and Associated Molecular Interactions in Amorphous HPMCAS Solids. Hydrogen bonding (HB) is known to affect stability of amorphous solid dispersions with respect to drug−excipient miscibility and inhibition of crystal growth.73 HPMCAS is commonly synthesized from HPMC, after which a large majority of the remaining hydrogen bonding donor sites in HPMC have been blocked, mostly by acetyl groups. In the HPMCAS polymer assembly constructed for these simulations, only 56 HB donor groups (−OH, Suc, HP) (0.47 per glucose unit or 0.16 per substituent site) were present. In a newly formed HPMCAS glass assembly at 0.7% w/w water, 38 HB donors were involved in a hydrogen bond (as defined by a proton-acceptor distance 120°). Among these HBs, 33 were formed within or between individual HPMCAS chains, and 5 HBs were between the HB donors in HPMCAS chains and water molecules. Two HB configurations in the HPMCAS glass are illustrated in Figure 5. Also, 24 HB donor groups in 12 water molecules are capable of forming HBs among themselves or with HB acceptors in HPMCAS. For the newly formed HPMCAS glass, 14 HB donors were hydrogen bonded to HB acceptors in

Figure 8. Probability distributions for the number of first-shell water molecules (nwater (nw)) surrounding a given water molecule in the simulated HPMCAS glasses at 298 K with different water contents.

Figure 9. Log−log plots of the mean-squared displacements, ⟨r2⟩, for water molecules in the HPMCAS glasses containing 0.72% (lower curve), 5.7% (middle curve), or 13.2% w/w (upper curve) water at 298 K and 1 bar versus time. The lines are the least-squares fits.

calculated density−T diagrams and experiment, though the calculated Tg values are 19−22 deg higher. This may suggest a somewhat higher temperature for the onset of the mobility freezing as predicted from the mode-coupling theory.35 G



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Figure 6 (lower panel), the g(r) distribution for the oxygen atoms in water with respect to other water molecules exhibits a large peak at 2.7 Å, supporting the notion that most water molecules exist in the form of water clusters with varying degree of size. This leads to substantially reduced interaction between water molecules and the polar oxygen atoms in HPMCAS chains as demonstrated by the much smaller first peak in the corresponding g(r) plot. Representative snapshots of the spatial distributions of water in simulated HPMCAS glasses containing different amounts of water are illustrated in Figure 7. The QuickSurf drawing method in VMD software,48 which computes an isosurface extracted from a volumetric Gaussian density map calculated from water atoms in the neighborhood of each lattice point, is used for the molecular representation. At 0.7% w/w water, water molecules are mostly isolated from each other, whereas clusters or strands of water molecules occupying channels between the polymer chains are found at a water content of ∼5.7% w/w, and a further elevation of water content from 5.7% w/w to 13.2% w/w greatly increases the size of these water clusters. This is in contrast to a more hydrophilic polymer such as poly(vinyl alcohol) in which the water distribution at 5.2% w/w water was found to be homogeneous.74 The degree of water self-aggregation in the polymer can be quantitatively evaluated by the probability distribution for the number of water molecules (nw) within the first shell (i.e., within a given distance of 3.4 Å in this study) of a given water molecule. The results are presented in Figure 8. Averages for the number of water neighbors surrounding a given water molecule were 0.17, 1.8, and 3.5, respectively, at water contents of 0.7, 5.7, and 13.2% w/w in the amorphous HPMCAS solids. Although nw increases with water content, at 13.2% w/w it is still well below the value of nw = 8.9 obtained in bulk liquid water using the same distance criteria (3.4 Å). Thus, there is no evidence, in the present MD simulation, for complete phase separation at water contents up to 13.2% w/w. Water Diffusion in HPMCAS Glasses. Solute mobility is one of the most important dynamic properties in amorphous pharmaceutical formulations due to potential coupling of molecular mobility and physical or chemical instability. The diffusion of water may be particularly important in formulations containing drugs that undergo diffusion-controlled chemical reactions with water or other water-related degradation processes as water is likely to be the more mobile reactant. Water mobility in HPMCAS can be characterized by its diffusivity (D) according to the Einstein relation:

Figure 10. Representative trajectories of relative displacements, |r(t) − r(0)|, for tagged water molecules in the simulated HPMCAS glasses at 0.7% w/w water (upper panel) and 13.2% w/w water (middle panel). The lower panel shows the corresponding number of first-shell water molecules (nw) for a given tagged water molecule at 13.2% w/w water.

HPMCAS and none formed HBs with other water molecules, suggesting that these water molecules were well isolated from each other. Strong HB interactions may induce nonrandom atomic/group distributions between HPMCAS and water molecules, which can be quantitatively investigated by certain radial distribution functions, g(r). Shown in Figure 6 are the radial distribution functions for the oxygen atoms in water molecules with respect to the polar oxygen atoms or hydrogen atoms in nonpolar methylene groups of HPMCAS. Although the distribution function for water with respect to the methylene hydrogen atoms in HPMCAS is roughly uniform beyond the close-contact distance (>2.6 Å), distinct peaks are evident near the first-shell distance for water with respect to the polar oxygen atoms of HPMCAS, suggesting their preferential location near these polar oxygen atoms. At the higher water content (5.7% w/w) shown in

D = lim Dt = lim t −∞

t →∞

|r(t0 + t ) − r(t0)|2 6t

Molecular diffusivity can be assessed by monitoring the meansquared displacement, ⟨|r(t) − r(0)|2⟩ (or ⟨r2⟩), over time (t). The results averaged over all the water molecules in HPMCAS glasses with 0.72%, 5.7%, and 13.2% w/w water are presented in Figure 9 as log−log plots. From the slopes of linear fits of the ⟨r2⟩ profiles near the long time limit (90−100 ns), the apparent diffusion coefficient for water could be estimated, according to the Einstein relation, to be 1.1 × 10−9, 2.3 × 10−8, and 7.0 × 10−8 cm2/s in HPMCAS polymers containing 0.72%, 5.7%, and 13.2% w/w water, respectively. These diffusivities are 3.1 × 104, 1.5 × 103, and 4.9 × 102 fold lower than that for water self-diffusion in liquid water (3.4 × 10−5 cm2/s),24 suggesting greatly reduced molecular mobility in these polymeric glasses. While an H



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Figure 11. A schematic depiction of water diffusion mechanisms in amorphous HPMCAS polymer: Left panel: Low water content where water molecules are isolated from each other and restrained, most of time, within a local cavity with a rare jump into another local cavity. Right panel: High water content where water molecules reside mostly within more fluid water clusters (light gray).

Representative trajectories at different water contents are plotted in Figure 10. At a low water content (0.72% w/w), water molecules are tightly constrained in a local cavity most of the time, (cf. D3 ∼ 0 in Figure 11) with infrequent jumps to another cavity (hopping mechanism) as shown in the top panel of Figure 10. At a higher water content (13.2% w/w), water displacement fluctuates over a much wider range with the average displacement rising fast initially (

Molecular Dynamics Simulation of Amorphous Hydroxypropyl

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