# Modelling phase separation in amorphous solid dispersions

## TL;DR

This paper develops a comprehensive non-equilibrium PDE model for amorphous solid dispersions, enabling prediction of phase separation timescales and revealing complex phenomena like droplet formation and phase inversion through numerical simulations.

## Contribution

It introduces a multicomponent diffusion model for solid dispersions, derives an effective diffusion coefficient, and provides detailed numerical analysis of phase separation phenomena.

## Key findings

- Prediction of phase separation timescale.
- Observation of droplet and string formation.
- Identification of phase inversion and coarsening phenomena.

## Abstract

Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial differential equation non-equilibrium models that track the evolution of solid dispersions in time and space are lacking. Hence theoretical predictions for the timescale over which phase separation occurs in a solid dispersion are not available. In this paper, we address some of these deficiencies by (i) constructing a general multicomponent diffusion model for a dissolving solid dispersion; (ii) specializing the model to a binary drug/polymer system in storage; (iii) deriving an effective concentration dependent drug diffusion coefficient for the binary system, thereby obtaining a theoretical prediction for the timescale over which phase separation occurs; and (iv) presenting a detailed numerical investigation of the HPMCAS/Felodipine system assuming a Flory-Huggins activity coefficient. The numerical simulations exhibit numerous interesting phenomena, such as the formation of polymer droplets and strings, Ostwald ripening/coarsening, phase inversion, and droplet-to-string transitions.