Determination of Young's modulus of active pharmaceutical ingredients by relaxation dynamics at elevated pressures

TL;DR

This paper introduces a theoretical method to determine the elastic modulus of amorphous pharmaceutical ingredients by analyzing their relaxation dynamics under high pressure, aligning well with experimental data.

Contribution

It develops a new theoretical framework combining elastic barriers and thermal expansion mapping to study glass transition and relaxation in amorphous materials under pressure.

Findings

Effective elastic modulus estimates match experimental results

The model captures effects of molecular conformation on relaxation

Pressure and temperature dependence of relaxation are accurately described

Abstract

A new approach is theoretically proposed to study the glass transition of active pharmaceutical ingredients and a glass-forming anisotropic molecular liquid at high pressures. We describe amorphous materials as a fluid of hard spheres. Effects of nearest-neighbor interactions and cooperative motions of particles on glassy dynamics are quantified through a local and collective elastic barrier calculated using the Elastically Collective Nonlinear Langevin Equation theory. Inserting two barriers into Kramer's theory gives structural relaxation time. Then, we formulate a new mapping based on the thermal expansion process under pressure to intercorrelate particle density, temperature, and pressure. This analysis allows us to determine the pressure and temperature dependence of alpha relaxation. From this, we estimate an effective elastic modulus of amorphous materials and capture effects of conformation on the relaxation process. Remarkably, our theoretical results agree well with experiments.