Anomalous Water-Sorption Kinetics in ASDs

Abstract

Anomalous water-sorption kinetics in amorphous solid dispersions (ASDs) are caused by the slow swelling of the polymer. In this work, we used a diffusion-relaxation model with the Williams-Landel-Ferry (WLF) equation and the Arrhenius equation to predict the anomalous water-sorption kinetics in ASDs of poly(vinyl-pyrrolidone)-co-vinyl-acetate (PVPVA) and indomethacin (IND) at 25 °C. These predictions were based on the viscosities of pure PVPVA and pure IND, as well as on the water-sorption kinetics in pure PVPVA. The diffusion-relaxation model was able to predict the different types of anomalous behavior leading to a qualitative and quantitative agreement with the experimental data. Predictions and experiments indicated more pronounced anomalous two-stage water-sorption behavior in the ASDs than in pure PVPVA. This was caused by a higher viscosity of glassy ASD-water mixtures compared to glassy PVPVA-water mixtures at the same distance from their glass transition temperature. These results suggest that this ASD swells more slowly than the polymer it is composed of. The modeling approach applied in this work can be used in the future for predicting diffusion-controlled release behavior or swelling-controlled release behavior of ASDs.

Keywords: ASDs; diffusion; relaxation; swelling controlled; water-sorption kinetics.

Figure 1

(a) Schematic representation of the temperature dependency of viscosity. The solid lines describe the viscosity of a polymer or API modeled via the WLF equation or Arrhenius equation. The dashed line is the extrapolation of the WLF equation to the Arrhenius region. The point marks the temperature $T^{\alpha \beta }$ at which the temperature dependency switches from WLF to Arrhenius behavior. The distance $\Delta T^{\alpha \beta }$ of the switching temperature $T^{\alpha \beta }$ to the glass transition temperature $T_g$ is indicated as a gray box. (b) Schematic representation of viscosity as a function of the glass transition temperature $T_g$. Drug load and relative humidity (RH) alter the glass transition temperature of the mixture and decrease its viscosity. The glass transition occurs when the glass transition temperature $T_g$ is equal to the temperature $T$.

Figure 2

Water-sorption kinetics in PVPVA films at T = 25 °C for (a) step change from 0.75 to 0.9 RH (case A) as hexagons and (b) step change from 0.6 to 0.75 RH (case B) as downside triangles. The experimental data from previous work [13] are displayed as symbols. The modeling of the diffusion–relaxation model (Equation (1)) using the WLF equation (Equation (8)) is indicated as dotted lines. The dash-dotted line in (b) marks the water weight fraction at which the glass transition temperature of the PVPVA–water mixture reaches 25 °C, as derived from [31].

Figure 3

Water-sorption kinetics in PVPVA films at 25 °C during (a) an RH step of 0.45–0.6 RH (case C) as stars and of 0.30.45 RH (case D) as upside triangles. The experimental data from previous work [13] are displayed as symbols. The modeling of the diffusion–relaxation model (Equation (1)) using the WLF equation alone (Equation (8)) is indicated as dashed lines. The modeling of the diffusion–relaxation model (Equation (1)) using the combination of the WLF equation (Equation (8)) with the Arrhenius equation (Equation (9)) is indicated as dotted lines. The right diagram (b) shows the modeled viscosities of PVPVA–water mixtures via the WLF equation (Equation (8)) as a dashed line and via the combination of WLF equation (Equation (8)) and Arrhenius equation (Equation (9)) as a dotted line. The viscosities of PVPVA–water mixtures derived from the zero-shear viscosities by Wolbert et al. [16] are displayed as squares. The vertical markers denote the viscosity ranges relevant to the models of each water-sorption curve (cases A, B, C, and D, respectively).

Figure 4

Water-sorption kinetics in PVPVA–IND ASD films at 25 °C with drug load 0.2 (a) step changes during RH steps of 0.3–0.45 RH (case E) as upside triangles and 0.45–0.6 RH (case F) as stars. The experimental data from previous work [14] are displayed as symbols. The modeling of the diffusion–relaxation model (Equation (1)) using Equations (9)–(11) is displayed as solid lines. (b) The predicted viscosities of the corresponding ASD–water mixtures, whereas the WLF equation (Equation (8)) corresponds to the dashed line and the combination of WLF equation (Equation (8)) and Arrhenius equation (Equation (9)) corresponds to the solid line. The modeled viscosities of PVPVA–water mixtures via WLF equation (Equation (8)) and Arrhenius equation (Equation (9)) are displayed as dotted lines. The experimental viscosities of PVPVA–water mixtures derived from the zero-shear viscosities by Wolbert et al. [16] are displayed as squares. The vertical markers correspond to the ranges of viscosities relevant to the models of each water-sorption curve (cases E, F, G, and H, respectively).

Figure 5

Water-sorption kinetics in PVPVA–IND ASD films at 25 °C with drug load 0.2 and RH steps of (a) 0.6–0.75 RH (case G) as downside triangles and (b) 0.75–0.9 RH (case H) as hexagons. The experimental data from previous work [14] are displayed as symbols. The modeling of the diffusion–relaxation model (Equation (1)) using the combination of WLF equation (Equation (8)) and Arrhenius equation (Equation (9)) is displayed as solid lines.

Figure 6

Water-sorption kinetics in PVPVA–IND ASD films at 25 °C with drug load 0.5 and (a) RH steps of 0.3–0.45 RH (case I) as upside triangles, 0.45–0.6 RH (case J) as stars, 0.6–0.75 RH (case K) as downside triangles, and 0.75–0.9 RH (case L) as hexagons. The experimental data from previous work [14] are displayed as symbols. The prediction via the diffusion–relaxation model (Equation (1)) using the combination of the WLF equation (Equation (8)) and Arrhenius equation (Equation (9)) is displayed as solid lines. (b) Viscosities of the corresponding ASD–water mixtures predicted via the WLF equation (Equation (8)) as dashed lines and via the combination of the WLF equation (Equation (8)) and Arrhenius equation (Equation (9)) as solid lines. The modeled viscosities of the PVPVA–water mixtures by the WLF equation (Equation (8)) and Arrhenius equation (Equation (9)) are displayed as dotted lines. The experimental viscosities of PVPVA–water mixtures derived from the zero-shear viscosities by Wolbert et al. [16] are displayed as squares. The vertical markers correspond to the ranges of viscosities relevant to the models of each water-sorption curve (cases I, J, K, and L, respectively).