# Theoretical model for the structural relaxation time in co-amorphous drugs

## TL;DR

This paper introduces a theoretical model that predicts the structural relaxation time in co-amorphous drugs by mapping real materials to hard sphere fluids, aligning well with experimental data.

## Contribution

It presents a novel thermal mapping approach combined with the Elastically Collective Nonlinear Langevin Equation theory to model glass transition in amorphous pharmaceuticals.

## Key findings

- Quantitative agreement with experimental relaxation times
- Successful application to ezetimibe-simvastatin mixture
- Provides a comprehensive description of glassy dynamics

## Abstract

We propose a simple approach to investigate the structural relaxation time and glass transition of amorphous drugs. Amorphous materials are modeled as a set of equal sized hard spheres. The structural relaxation time over many decades in hard sphere fluids is theoretically calculated using the Elastically Collective Nonlinear Langevin Equation theory associated with Kramer's theory. Then, a new thermal mapping from a real material to an effective hard sphere fluid provides temperature-dependent relaxation time, which can compare to experiments. Numerical results quantitatively agree with previous experiments for pharmaceutical binary mixtures having different weight ratios. We carry out experiments to test our calculations for an ezetimibe-simvastatin-Kollidon VA64 mixture. Our approach would provide a simple but comprehensive description of glassy dynamics in amorphous composites.