Advancing amorphous solid dispersions through empirical and hybrid modeling of drug-polymer solubility and miscibility: A case study using Ibuprofen

Abstract

This study investigates the solubility and miscibility of ibuprofen (IBU) with four pharmaceutical polymers, KOLVA64®, KOL17PF®, HPMCAS, and Eudragit® EPO, using a combination of empirical and hybrid modeling approaches, supported by differential scanning calorimetry (DSC) experiments. Traditional group contribution methods based on Hildebrand and Hansen solubility parameters (Fedors, Hoftyzer-van Krevelen, and Just-Breitkreutz) showed variability in solubility predictions but consistently classified all polymer-API blends as miscible (Δδ < 7 MPa^½). Bagley plots reinforced these findings, although borderline miscibility was indicated for HPMCAS and EPO depending on the method used. A novel attempt to derive the Flory-Huggins (FH) interaction parameter (χ) from solubility parameters at near-melting temperatures showed poor agreement with experimental data, underscoring the limitations of such extrapolations and the semi-empirical nature of the FH model. Phase diagrams were constructed from DSC-based melting point depression data using three modeling strategies: FH theory, the empirical approach by Kyeremateng (with two fitting methods), and the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state, both in pure predictions and with fitted binary interaction parameters (k_ij). The glass transition temperature (T_g) of the mixtures was modeled using the Gordon-Taylor and Kwei equations. All models provided a consistent polymer ranking based on their solubilizing capacity, with KOL17PF as the most compatible and HPMCAS as the least. Demixing zones (liquid-liquid equilibrium - LLE) predicted by FH and PC-SAFT models suggest that for HPMCAS-based ASDs only very low drug loadings (< 5 % w/w) could potentially be stable at room temperature. In contrast, higher drug loadings (> 10 % w/w) fall under a meta-stable zone with the other polymers, making them better candidates for IBU formulation. HPMCAS also exhibited consistently prediction errors across all T_g models, (AARD ∼4.5 %), indicating poorer agreement with experimental data. By integrating empirical and hybrid modeling approaches, this study highlights the strengths and limitations of commonly used solubility prediction methods and advocates for a shift toward a harmonized framework.

Keywords: Amorphous Solid Dispersion (ASD); Glass transition; Melting Point Depression (MPD); Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT); Phase Diagram.

Graphical abstract

Fig. 1

Ibuprofen (IBU), Kollidon® VA64 (KOL VA64), Kollidon® 17PF (KOL 17PF), HPMCAS and Eudragit EPO (EPO) molecular structures.

Fig. 2

Total solubility parameter Δδ_t obtained using Fedors, Hoftyzer van-Krevelen and Just-Breitkreutz methods.

Fig. 3

Bagley plots depicting R_av parameter obtained using a) HVK and b) JB methods.

Fig. 4

DSC data at different API-polymer compositions, showing melting point depression (1 °C/min). A) KOL VA64. B) KOL 17PF. C) HPMCAS. D) EPO.

Fig. 5

Linear fitting from MPD data for the different compositions evaluated for (A) KOL VA64, (B) KOL 17PF, (C) HPMCAS and (D) EPO.

Fig. 6

High temperature interaction parameter (χ) plots for the compositions tested (A) KOL VA64, (B) KOL 17PF, (C) HPMCAS and (D) EPO.

Fig. 7

Interaction parameter calculated using experimental data and GC as a function of the inverted melting temperature in K (10³) for (A) KOL VA64, (B) KOL 17PF, (C) HPMCAS and (D) EPO. The solid line represents the best linear fitting for the data.

Fig. 8

Δ_mixG/RT as a function IBU volume fraction in different polymers: (A) KOL VA64, (B) KOL 17PF, (C) HPMCAS and (D) EPO at temperatures between 25 °C and 150 °C.

Fig. 9

SLE curves extrapolated from MPD data using Kyemerateng empirical equation (One-Step and Two-Steps fitting). (A) KOL VA64, (B) KOL 17PF, (C) HPMCAS and (D) EPO.

Fig. 10

SLE curves extrapolated from MPD PC-SAFT (k_ij = 0 and k_ij ≠ 0) for (A) KOL VA64, (B) KOL 17PF, (C) HPMCAS and (D) EPO.

Fig. 11

T_g modeling using GT (Simha-Boyer rule), GT (fitted k) and Kwei (fitted q) equations for IBU and (A) KOL VA64, (B) KOL 17PF, (C) HPMCAS and (D) EPO.

Fig. 12

Phase diagrams of binary blends (A) KOL VA64, (B) KOL 17PF, (C) HPMCAS and (D) EPO, comparing experimental data, SLE and LLE curves modeled using FH, Kyeremateng empirical equation and PC-SAFT.