X-ray Diffraction of Water in Polyvinylpyrrolidone

Abstract

PVP is a hydrophilic polymer commonly used as an excipient in pharmaceutical formulations. Here we have performed time-resolved high-energy X-ray scattering experiments on pellets of PVP at different humidity conditions for 1–2 days. A two-phase exponential decay in water sorption is found with a peak in the differential pair distribution function at 2.85 Å, which is attributed to the average (hydrogen bonded) carbonyl oxygen–water oxygen distance. Additional scattering measurements on powders with fixed compositions ranging from 2 to 12.3 wt % H₂O were modeled with Empirical Potential Structure Refinement (EPSR). The models reveal approximately linear relations between the carbonyl oxygen–water oxygen coordination number $\left(n_{{\mathrm{O}}_{\mathrm{c}}-{\mathrm{O}}_{\mathrm{w}}}\right)$ and the water oxygen–water oxygen coordination number $\left(n_{{\mathrm{O}}_{\mathrm{w}}-{\mathrm{O}}_{\mathrm{w}}}\right)$ versus water content in PVP. A stronger preference for water–water hydrogen bonding over carbonyl–water bonding is found. At all the concentrations studied the majority of water molecules were found to be randomly isolated, but a wide distribution of coordination environments of water molecules is found within the PVP polymer strands at the highest concentrations. Overall, the EPSR models indicate a continuous evolution in structure versus water content with $n_{{\mathrm{O}}_{\mathrm{w}}-{\mathrm{O}}_{\mathrm{w}}}=1$ occurring at ~12 wt % H₂O, i.e., the composition where, on average, each water molecule is surrounded by one other water molecule.

Graphical Abstract

INTRODUCTION

Polyvinylpyrrolidone (PVP, povidone, trade name Kollidon)¹ is one of the most important substances in the pharmaceutical and cosmetic industries.^2–4 PVP is a highly soluble amorphous polymer consisting of a repeating chain of linear 1-vinyl-2-pyrrolidinone groups (C₆H₉NO)_n and is widely used as an excipient to enhance the solubility and bioavailability of an active pharmaceutical ingredient in amorphous solid dispersions.^5,6 The PVP polymer matrix traps the active pharmaceutical ingredient to inhibit crystallization at the molecular level,^7,8 which can alter the product’s physical properties and chemical stability and lead to an increased dissolution rate of the orally administered drug in the gastrointestinal tract.^9–11 Due to PVP’s excellent wetting properties it is commonly used as a binder in the manufacture of tablets, granules, capsules and in coating processes. PVP is also used in formulation matrices to provide controlled release dosages, including in treatments for COVID-19.¹²

The hydrophilic nature of PVP has been widely characterized and is largely independent of molecular weight; PVP can absorb up to ~45% by weight at 80% humidity at room temperature.² Assimilation of ambient water is useful to solubilize a product but also can lead to unwanted degradation that can decrease the efficacy of an amorphous formulation. Nevertheless, few experiments have probed the structural changes associated with the water absorption of PVP.⁵ The X-ray pair distribution function (PDF) method is one of the most powerful techniques for the characterization of both local and intermediate range ordering of disordered organic materials, shedding light on details of molecular structure at the atomic level. High-energy X-rays generated at intense synchrotron sources provide high-resolution PDFs and enable insight into variations in molecular packing arrangements.¹³

The main aims of this study are to quantify the nature and strength of hydrogen bonding between the absorbed water molecule and the polymer at low water contents,¹⁴ and identify the evolution from randomly isolated water molecules trapped within the PVP polymer, to chains and/or clusters of water molecules. Based on existing literature, we expect that this occurs at low water concentrations somewhere between 0.1 and 1 wt %, depending on molecular weight, whereby isolated water molecules will start to aggregate and form nanometer-sized strands.^3,6 We quantify these structural changes associated with increasing water content in PVP, by extracting the oxygen–oxygen coordination number from the differential pair distribution function as a function of both temperature and humidity using Empirical Potential Structure Refinement (EPSR)15,16 based on a 5-monomer unit PVP ‘molecule’ (C₆H₉NO)₅; see Figure 1.

Figure 1.

Structure of PVP K15 used in the EPSR simulation (see the “Materials and Methods” section) with the partial charges used on the nitrogen atoms (blue) and oxygen atoms (red). This amorphous polymer has the repeat unit (C₆H₉NO)_n and comprises of a 5-membered lactam linked to a vinyl group.

EPSR is a standard Monte Carlo simulation developed by Prof. Alan Soper^15–17 in which molecules are defined using harmonic force constants between all the atoms, as well as angular and dihedral angle constraints. Intermolecular forces are defined by a reference potential comprising of Lennard-Jones potentials and Coulombic terms. An additional empirical potential added later in the simulation. Once turned on, the empirical potential is determined from the difference between the experimental data and the model, perturbing the reference potential. It should be noted that these potentials are meaningless and are not transferable; they are just a means of driving the model toward the measured data. The simulation progresses via a random change in the coordinates of the atom or molecule, or a rotation of the molecule that results in a new configuration. A move is accepted if the change in potential energy is less or with some probability if it is more, to avoid local minima. The simulation is stopped once (or if) a good fit between the model and experimental structure factors are found. The EPSR code was primarily developed to interpret neutron diffraction data, but it has clear advantages in the area of X-ray diffraction from pharmaceuticals, where the scattering is dominated by the molecular skeleton rather than the interactions involving hydrogen atoms. High-energy X-ray diffraction pair distribution function measurements on amorphous organic molecules, conducted using synchrotron radiation in particular, has several advantages over laboratory X-ray sources, including, bulk studies, negligible attenuation corrections, and higher real space resolution.¹⁸

MATERIALS AND METHODS

Hydration studies were performed on Kollidon 15PF (BASF used as received), which has ~6% water content at 10% RH and 25 °C, a nominal bulk density of 1.18 g/mL, and average molecular weight of 8000.² Powder was pressed into a ca. 2 mm thick pill in a die that pressed them under 2 tons force to form 2 mm thick dense discs, which were mounted vertically in a Linkam humidity stage, model L-TMHS600-H. The pellets were dried at the lower limit of the stage 5–10% RH and 40 °C overnight and then exposed sequentially to (a) “normal” conditions of 35% RH and 27 °C for 30 h and (b) the FDA “accelerated” humidity conditions of 75% and 40 °C for 50 h, consistent with long-term stability testing.^19,20 In addition, steady state measurements were performed on PVP–water mixtures at concentrations of 2, 5, 10, and 12.3 wt % H₂O. These PVP samples were in the form of fluffy powder that had been dried and then exposed to air on a scale until the desired amount of water was absorbed from the atmosphere, at which point the powder was loaded into glass capillaries and immediately sealed with glue. The uncertainty in water content upon sealing was highest for the nominally 2 wt % water in PVP sample, which was estimated to be up to 0.4 wt % water, when accounting for the time it took to seal the tube. The errors were smaller for the lower hydration samples. We note that the glass transition in PVP can have a wide range of values that depend on many factors,²¹ including molecular weight and water content but this was not investigated in this study.

High-energy X-ray wide-angle scattering measurements were performed on beamline 6-ID-D at the Advanced Photon Source at Argonne National Laboratory. Experiments were carried out using a monochromatic X-ray beam, E = 100 keV (λ = 0.124 Å), collimated to a square 0.5 mm cross section, and the scattered X-rays were measured using a Varex (CT4343) area detector. The sample to detector distance was ~363 mm and the data reduction procedures were applied as described previously.²² Time resolved hydration measurements on the compressed pellets were taken every five minutes to follow the water absorption in PVP. For the higher concentration 2, 5, 10, and 12.3 wt % H₂O in PVP samples, both small- and wide-angle scattering (SAXS/WAXS) measurements were performed at 100 keV with a sample to detector distance of 2054 mm for SAXS covering 0.05 < Q (Å⁻¹) <2.7. The total X-ray scattering data were reduced using Fit2D²³ and PDFgetX2²⁴ with dark current, geometrical, polarization, background, and attenuation corrections applied to all data sets to yield the X-ray structure factors, S(Q).

Atomistic modeling was performed using EPSR. The EPSR simulation for pure PVP was performed on 50 PVP K15 molecules (comprising of 5 repeat units) using a cubic box under periodic boundary conditions, using an atomic number density of 0.118 atoms Å⁻³, corresponding to a cubic box size of ~30 Å. The K-value denotes the approximate molecular weight for different grades of polymer by using viscosity in aqueous solution relative to water, calculated using Fikentscher’s equation.^1,2 We note that although the nominal density of PVP (ρ = 1.18 g cm⁻³) corresponds to 0.109 atoms Å⁻³, this had to be refined in order to get a good fit between the EPSR model and the X-ray data for dry PVP in the region of first few intramolecular peaks in the X-ray PDF. The X-ray consistent density of dry, amorphous PVP was found to be 0.118 atoms Å⁻³ (1.28 g cm⁻³) significantly higher than the nominal value. A similar density refinement was also used for the samples containing different amounts of water.

For simplicity, the modeling was conducted as rigid molecule simulation, with limited flexibility introduced by relaxing constraints for bond angles and dihedral angles. Molecules were assigned partial charges and Lennard-Jones reference potentials as given in Table S1. Following initial Monte Carlo equilibration, the empirical potential term was refined to improve agreement between the model’s simulated scattering with the experimental data. Once the goodness-of-fit parameter was minimized between the model and the experimental S(Q), structural data were collected over an ensemble of at least 10,000 configurations. EPSR models were developed with the same approach for PVP with 2–12.3 wt % H₂O; see Table S2. While the EPSR fit to the data does not necessarily give a unique structural 3D configuration of molecules, it does provide an important insight into the types of interactions that are likely in the disordered state. Since X-rays are scattered by electrons, the S(Q)’s and corresponding PDF’s are most sensitive to the heavier atoms and in particular the orientations of the carbon, oxygen and nitrogen atoms.

RESULTS

Fixed PVP–Water Concentrations.

The SAXS/WAXS data and EPSR fits for the 2, 5, 10, and 12.3wt % H₂O in PVP are shown in Figures 2 and 3. Here we observe a first sharp diffraction peak (FSDP) in the range Q_P = 0.8–0.9 Å⁻¹ and a principal peak (PP) around 1.4–1.5 Å⁻¹. In addition, for these samples the high-energy SAXS measurements showed a small rise in the small angle scattering signal for Q < 0.1 Å⁻¹ due to long-range density fluctuations. The FSDP is typically located between 0.5 < Q (Å⁻¹) < 2 in the WAXS pattern and associated with medium range order (r > 5 Å in real space) in amorphous materials with a periodicity ~2π/Q_P = 6.2 Å.^25,26 The PP is often the second and tallest peak in S(Q). Oscillations in S(Q) for Q > 5Å⁻¹ are usually dominated by intramolecular bonds at short distances r < 5Å in real space. Therefore, water bonding to PVP molecules is expected to lead to changes at high-Q, and rearrangements of the polymer chains and formation of water clusters will affect the low-Q region. The differences between the experimental X-ray data and EPSR fit are most likely due to small variations in bond lengths and/or the relatively rigid body approximation used in constructing the model. However, the overall agreement suggests that the amorphous structure of dry PVP can be reasonably approximated by a random arrangement of intertwined K15 units shown in figure 1. A wireframe snapshot of the polymer chains in the dry PVP EPSR model is shown in figure S1.

Figure 2.

Overlap region between the high-energy X-ray SAXS and WAXS data.

Figure 3.

Combined experimental SAXS/WAXS structure factors S(Q) (black lines) and their EPSR model fits (red circles).

The corresponding total X-ray pair distribution functions with the density included is defined as $T\left(r\right)=4\pi \rho r\left[G\right(r)+1]$, where $G\left(r\right)$ is the weighted sum of the partial pair distribution functions $g_{\alpha \beta }\left(r\right)$, and was obtained through a Sine Fourier transform of $S\left(Q\right)$ using a $Q_{\mathrm{m}\mathrm{a}\mathrm{x}}=25{\mathrm{Å}}^{-1}$ with a Lorch modification function¹⁸ (see Figure 4). Vinylpyrrolidone is generally polymerized in aqueous solution using hydrogen peroxide, where it is believed to exist as a random coil.²⁷ There are no known crystal structures. For the dry T(r) in Figure 4, polymer backbone chain monomer correlations are found at 1.5 and 2.4 Å, and intermonomer interactions are found at 3, 3.6 and 4.5 Å. Oscillations for r < 1 Å are unphysical and due to inaccuracies in the assumed free-atom electron distribution and long wavelength systematic errors in the experiment. At higher r values, structural features decay rapidly after the second monomer unit. The effect of water sorption in the X-ray PDF is for the relative monomer peak intensity to decrease in height and there is a distinct increase in signal around distances of approximately 2.9, 3.6, and 4.7 Å (Figure 4 insert).

Figure 4.

Measured total X-ray pair distribution $T\left(r\right)$ of dry PVP compared to samples with 2, 5, 10, and 12.3 wt % H₂O in PVP. Insert: Example differences of water absorption given by $\mathrm{\Delta }T\left(r\right)=x\cdot T_{\text{wet}}\left(r\right)-T_{2\mathrm{w}\mathrm{t}\mathrm{\%}\mathrm{H}2\mathrm{O}}\left(r\right)$ (see text), where $T_{\text{wet}}=12.3$ wt % H₂O (solid line) and $T_{\text{wet}}=10$ wt % H₂O (dashed line).

Time-Resolved Hydration Experiments.

To investigate the uptake of water into PVP, two time-resolved X-ray PDF experiments were performed at different humidities and temperatures. The amount of absorbed water in the PVP polymer was calculated from the decrease in intensity of the 1.5 and 2.4 Å peaks that are due to the average “intramolecular” PVP momoner unit in the X-ray pair distribution function. As water is incorporated into the dry polymer, these peaks decrease in intensity because the overall contribution from the PVP to the total signal decreases. In the X-ray analysis an empirical adjustment of the composition is made to evaluate the water content present, by normalizing to the dry PVP monomer peaks in the PDF pattern, see Figure 5. A two-phase exponential increase in water sorption is found with time but becomes stretched at longer times. The final water contents correspond to (a) ~0.5 wt % water with 1 H₂O molecule to 34 PVP monomers for 35% RH 27 °C for 30 h and (b) ~0.8 wt % water with 1 H₂O molecule to 22 PVP monomers at 75% RH 40 °C for 50 h. These values are considerably lower than the equilibrium moisture contents of ~6 wt % water at 35% RH and 25 °C and ~30 wt % at 75% RH and 40 °C.² Diffusion measurements on PVP films have found an initial diffusivity of ~10⁻⁸ cm²/s for < 0.1 wt % H₂O, rising to ~10⁻⁶ cm²/s at 0.3 wt % H₂O.³ Therefore, in a 24 h period the diffusion distance should correspond to a penetration distance of ~1 mm. However, our measurements on a compressed pellet indicate that the water adsorption process in this experiment was diffusion limited, with a diffusivity closer to ~10⁻⁹ cm²/s. Similar X-ray experiments on fluffy powders showed greater water diffusivity but poor signal/noise.

Figure 5.

wt % water in a compressed pellet of PVP under different humidities and temperature with time on a log scale. The lines represent two-phase exponential decay functions, where y = −0.676·exp(−x/0.517) − 0.134·exp(−x/5.876) + 0.781 for 75% RH 40 °C, and y = −0.317·exp(−x/1.201) − 0.204·exp(−x/2.980) + 0.493 for 35% RH 27 °C.

To investigate the changes in PVP with absorbed water, the difference between the wet and dry pair distribution functions were calculated. Since the X-ray scattering from water is dominated by the oxygen–oxygen correlations,²⁸ by removing the dry polymer from the signal the difference function is dominated by the hydrogen bonded water oxygen–PVP interactions at low water contents. These difference functions shown in Figure 6 for the normal and accelerated humidity conditions were obtained using the formula $\mathrm{\Delta }T\left(r\right)=x\cdot T_{\text{wet}}\left(r\right)-T_{\mathrm{d}\mathrm{r}\mathrm{y}}\left(r\right)$, where x is chosen to eliminate the first two sharp peaks due to the 1.50 Å monomer and 2.41 Å polymer backbone. In both experiments the peak at 1.50 Å is found to shift slightly to shorter distances upon the absorption of water, indicating a slight compression of the monomer unit. At 35% RH and 27 °C and 75% RH and 40 °C, the ΔT(r) curves exhibit a peak at 2.85 Å that is very similar in shape and width to the nearest neighbor O–O peak observed in bulk water at 2.80 Å,²⁸ with a minima at 3.2 Å. This peak becomes more distinct over time, within the first 30–60 min, suggesting that the water structure may be disordered at first, but then water molecules find preferred locations to bond along the PVP chain. At longer distances in the 35% RH and 27 °C patterns, three peaks evolve over time with the two broader peaks at longer distances: ~3.6 Å peak likely associated with longer O_W–O_PVP hydrogen bonds and at ~4.8 Å. At 75% RH and 40 °C, the 3.6 Å becomes washed out, and the 4.8 Å increases more rapidly with time due to the larger water content.

Figure 6.

Difference curves ΔT(r) for (a) 35% RH and 27 °C and (b) 75% RH and 40 °C evolving with time. Curves are shown every 10 min for the first two hours and every hour subsequently.

Two structural scenarios have been suggested for the mechanism of the initial absorption process: (i) Water molecules first occupy the free volume space in the polymer, and then bond to specific chain segments or groups. (ii) Water molecules migrate through the bulk of the polymer network via jumping motions between carbonyl group sites.^29,30 Assuming an effective water radius is half the O–O distance in T(r), i.e., 1.425 Å, then there is ~25% void space in our dry PVP model that water molecules could occupy. Overall our results are consistent with elements of both scenarios. The disorder observed at early times in ΔT(r) is consistent with (i), while at later times the presence of distinct, moderately strong hydrogen bonds is in general agreement with scenario (ii). In-depth modeling is required to confirm the degree to which water preferentially bonds to the carbonyl group over other sites. This is in view of Rothschild’s findings that water binding takes place not only at the carbonyl bond of the lactams but also involves the C–N bond³¹ and will be addressed in the next section.

DISCUSSION

Hydrogen Bonding.

The EPSR oxygen water–oxygen carbonyl and oxygen water-nitrogen partial pair distribution functions, denoted $g_{{\mathrm{O}}_{\mathrm{w}}-{\mathrm{O}}_{\mathrm{C}}}\left(r\right)$ and $g_{{\mathrm{O}}_{\mathrm{w}}-\mathrm{N}}\left(r\right)$ respectively, provide an indication of the degree of hydrogen bonding between water and amorphous PVP; see Figure 7. The EPSR results suggest the presence of only very weak water interactions (if any) with the reactive C–N group as proposed by Rothschild,³¹ with an $r_{{\mathrm{O}}_{\mathrm{w}}-\mathrm{N}}$ peak distance of 4.9 Å in all the concentrations studied. The water–carbonyl interaction is much stronger, with a double peak arrangement at shorter distances of 2.9 and 3.9 Å.

Figure 7.

Oxygen-oxygen partial pair distribution functions $g_{{\mathrm{O}}_{\mathrm{w}}-{\mathrm{O}}_{\mathrm{C}}}\left(r\right)$ and $g_{{\mathrm{O}}_{\mathrm{w}}-\mathrm{N}}\left(r\right)$ at 2 wt % (dashed and dotted line), 5 wt % (dotted line), 10 wt % (dashed line), and 12.3 wt % H₂O (solid line) from the EPSR models.

Previous molecular dynamics simulations show that at 0.5 wt % water molecules are mainly isolated and uniformly distributed, but at 10 wt % water molecules form small, 1–3nm sized clusters and occupy channels between PVP chains.⁵ However, our EPSR results show considerably less clustering than this, and a much more disordered first oxygen–oxygen shell in the $g_{{\mathrm{O}}_{\mathrm{w}}-{\mathrm{O}}_{\mathrm{w}}}\left(r\right)$ and $g_{{\mathrm{O}}_{\mathrm{w}}-{\mathrm{O}}_{\mathrm{c}}}\left(r\right)$ functions at 10 wt % water in PVP in Figure 8(a). The differences between our EPSR Monte Carlo results and molecular dynamics simulations using a TIP3P water force field³² are unexpected from the point of view that TIP3P reproduces the first peak distance and approximate height in $g_{{\mathrm{O}}_{\mathrm{w}}{-\mathrm{O}}_{\mathrm{w}}}\left(r\right)$ for pure water,³³ when compared to the latest experimental data.³⁴ However, it should be noted that TIP3P fails to reproduce the second peak in $g_{{\mathrm{O}}_{\mathrm{w}}{-\mathrm{O}}_{\mathrm{w}}}\left(r\right)$ for pure water, which corresponds to the inherent tetrahedrality present in both water and ice phases,³³ making it more favorable for TIP3P water to form chains rather than 3D clusters.

Figure 8.

(a) Oxygen–oxygen partial pair distribution functions at 10 wt % H₂O, between the oxygen water OW and oxygen carbonyl OC atoms from the EPSR model compared to the MD model of Xiang et al.⁶ (b) EPSR oxygen–oxygen coordination numbers $n_{{\mathrm{O}}_{\mathrm{C}}-{\mathrm{O}}_{\mathrm{w}}}$ (red open diamonds) and $n_{{\mathrm{O}}_{\mathrm{w}}{-\mathrm{O}}_{\mathrm{w}}}$ (black closed circles) versus water content in PVP.

The EPSR oxygen–oxygen coordination numbers $n_{{\mathrm{O}}_{\mathrm{w}}-{\mathrm{O}}_{\mathrm{w}}}\left(r\right)$ and $n_{{\mathrm{O}}_{\mathrm{c}}-{\mathrm{O}}_{\mathrm{w}}}\left(r\right)$ are shown as a function of increasing water content in PVP in Figure 8(b), using the criteria of Xiang et al.,⁶ i.e., a water molecule was considered as being in a solvation shell if within a distance of 3.4 Å. The results indicate an approximately linear relation between $n_{\mathrm{O}-\mathrm{O}}$ and water content in PVP, with a stronger preference for water–water hydrogen bonding over carbonyl–water. The average number of hydrogen-bonded water molecules surrounding water in PVP from our 10 wt % H₂O EPSR model was found to be 0.90 ± 0.08 compared to the higher MD value of 2.0 ± 2.1⁶ and ~4.3 in bulk water.²⁸ Similarly, the average number of water molecules per carbonyl oxygen was found to be 0.48 ± 0.04 (EPSR) compared to 0.86 ± 1.2 (MD).⁶ Although our EPSR results are approximately half the absolute values proposed by Xiang et al. they are well within the MD standard deviations. One important finding of the EPSR modeling is that $n_{{\mathrm{O}}_{\mathrm{w}}{-\mathrm{O}}_{\mathrm{w}}}=1$ at ~12 wt % H₂O, which corresponds, mathematically at least, to the point at which the water molecules rapidly form chains and/or clusters. However, the EPSR results suggest a continuous evolution in structure with water content rather than any sort of abrupt structural transition.

Proton NMR measurements by Oksanen and Zografi³ show that the rotational and translational mobility of water molecules is hindered by the presence of the polymer chains, and there are two or more populations of water with different mobilities. The water molecules were found to be neither tightly bound or free as in bulk water, and it was surmised that water mobility increased with absorption content. Hydrogen bonds in bulk water with a nearest neighbor O–O distance of 2.8 Å are considered to be moderately strong, whereas longer O–O hydrogen bond distances are weak using Jeffery’s classification scheme.³⁵ Therefore, our EPSR results indicate a mixture of moderately strong and weak, bent hydrogen bonds is present over the range of water contents studied here,³⁶ in agreement with previous FTIR results.²⁹

Water Distributions.

Water is known to act as a plasticizer and at high water contents PVP proceeds toward a rubbery state. Previous MD simulations have predicted that at 10 wt % water the system is heterogeneous but not phase separated.⁶ Small-angle X-ray scattering (SAXS) measurements on PVP–water solutions at 60 wt % H₂O show phase separation at low temperatures through the formation of ice clusters on a length scale of 30 nm,³⁷ and on varying time scales indicating metastability.³⁸ However, our SAXS measurements between 2 and 12.3 wt % H₂O also show evidence of a small rise in small-angle scattering at much smaller length scales, which could be a density contrast due to the surface layer of water molecules attached to carbonyl oxygens on the PVP polymer, although further measurements into the Porod region at lower-Q values are needed to investigate the origin. A chain length distribution analysis of hydrogen bonded water molecules in the 2, 5, 10, and 12.3 wt % H₂O in PVP mixture EPSR models are shown in Figure 9. The chain length was calculated using the shortest path criterion which evaluates all the possible linked paths between two molecules, and counts only the one with the least number of linkages between the two molecules. The EPSR models all show that the majority of water molecules are randomly isolated, attached to carbonyl oxygens (Figure 10). Interestingly, once chains of water start to form they aggregate readily, forming ribbons with a wide distribution of lengths.

Figure 9.

Chain length distribution of hydrogen bonded water molecules for the 2, 5, 10, and 12.3 wt % H₂O in PVP mixture from EPSR model. Shown on a log scale as a function of chain length.

Figure 10.

Snapshot of the distribution of water molecules in the EPSR simulation boxes for the 2, 5, 10, and 12.3 wt % H₂O in PVP mixtures.

The EPSR probability distributions for the number of hydrogen bonds per molecule for O_C–O_W and O_W–O_W calculated up to distances within 3.4 Å for 2, 5, 10, and 12.3 wt % H₂O in PVP are shown in Figure 11. The majority of carbonyl oxygens are either nonbonded or only surrounded by a single water molecule even at the highest concentrations. There is a significant increase in $n_{{\mathrm{O}}_{\mathrm{C}}{-\mathrm{O}}_{\mathrm{w}}}$ between 2% and 5%, but >5% the distribution of waters around carbonyl oxygens is invariant. A direct comparison of $n_{{\mathrm{O}}_{\mathrm{C}}-{\mathrm{O}}_{\mathrm{w}}}$ from the EPSR and MD results of Xiang et al.⁶ at 10 wt % H₂O in PVP are found to be quantitatively similar. The distribution of water molecules surrounding other waters increases systematically with increasing water content and prefers to form chains ($n_{{\mathrm{O}}_{\mathrm{w}}-{\mathrm{O}}_{\mathrm{w}}}>1$) rather than dimers at the highest concentrations. However, the average value of $n_{{\mathrm{O}}_{\mathrm{w}}{-\mathrm{O}}_{\mathrm{w}}}$ is significantly lower than the maximum of 2 waters found in the previous MD simulation. Qualitatively, however, both EPSR and MD models indicate a wide distribution of coordination environments of water molecules at 10 wt % H₂O within the PVP polymer strands. Such information could be important in determining the phase behavior of PVP amorphous solid dispersions in wet conditions³⁹ or the interaction between water and mixed polymer systems.⁴⁰

Figure 11.

(a) and (b) EPSR model probability distributions for number of hydrogen bonds per molecule for O_C–O_W and O_W–O_W calculated up to distances within 3.4 Å for 2, 5, 10, and 12.3 wt % H₂O in PVP. (c) and (d) Comparison of the EPSR 10 wt % H₂O in PVP result with the existing MD results of Xiang et al.⁶

Comment on Use of EPSR to Model X-ray Data.

There has been much discussion on the uniqueness of using Monte Carlo algorithms to fit 3D models to diffraction data.^41,42 While, in theory, a particular S(Q) corresponds to a unique pair distribution function when assuming pairwise additive potentials,⁴³ in practice there might be several very different structures that provide reasonable fits to the scattering data.¹⁷ Given the complexity and large number of variables for large flexible molecules and polymers, this makes the task of fitting data over a wide range of length scales an almost intractable problem. However, we argue that models which fit the scattering data will often possess strong structural similarities, provided the salient features (such as the molecular backbone probed by X-ray diffraction) represent a significant fraction of the measured pattern. Therefore, the philosophy adopted here is to utilize the least number of constraints to reproduce the measured scattering data to extract the salient correlations. The S(Q) is after all excellent at eliminating a wide range of structures that do not fit the data, even for liquid and amorphous systems.⁴⁴ Moreover, from an experimental point of view a prerequisite for any model should be that it accurately reproduces the measured data. Here the molecular energy is minimized⁴⁵ to refine the preferred molecular geometry and the polymeric chains shortened to enable manageable sized simulations. This approach has allowed us to explore reasonable local and medium range interactions up to half the box size of ~15 Å. It may however be invalid in many other aspects and details of the structure, i.e., tacticity and longer length-scale polymer–polymer interactions.

CONCLUSIONS

Amorphous polymers in pharmaceutical formulations are used to improve solubility and bioavailability of active pharmaceutical ingredients over their pure crystalline forms. Time-resolved diffraction measurements on compressed PVP pellets show a two phase exponential uptake of water and a concomitant growth in a moderately strong hydrogen bonding peak at 2.85 Å attributed to the distance between (hydrogen-bonded) carbonyl oxygen–water oxygens. EPSR is an established method for the atomic scale modeling of molecular liquids, inorganic glasses and amorphous materials using neutron diffraction data,^15–17 but it is not as routinely used in the X-ray community. Here, EPSR models fitted to X-ray diffraction data from fixed compositions with 2–12.3 wt % H₂O show that the majority of water molecules are randomly isolated and attached to carbonyl oxygens. The results indicate an approximately linear relationship between the oxygen–oxygen coordination number $n_{\mathrm{O}-\mathrm{O}}$ and water content, with a stronger preference for water–water hydrogen bonding over carbonyl–water. The rapid formation of chains of water molecules occurs when $n_{{\mathrm{O}}_{\mathrm{w}}-{\mathrm{O}}_{\mathrm{w}}}>1$ at ~12 wt % H₂O, although the EPSR models indicate the existence of chains well before this and a continuous evolution in structure. Our EPSR results are in qualitative agreement with previous MD simulations, but the degree of water clustering is found to be quantitatively less than predicted by MD. It is anticipated that by characterizing the detailed structural aspects of water absorption in PVP these results may aid in the interpretation of the physical stability of PVP-based drug mixtures.⁴⁶