Diffusive Evolution of Stable and Metastable Phases II: Theory of Non-Equilibrium Behaviour in Colloid-Polymer Mixtures

TL;DR

This paper develops a theoretical framework for understanding non-equilibrium behavior in colloid-polymer mixtures, revealing conditions under which metastable phases grow or become unbound, with implications for phase-ordering dynamics.

Contribution

It provides exact and approximate solutions for interface motion in phase-ordering kinetics, elucidating the onset of non-equilibrium phenomena in colloid-polymer systems.

Findings

Identifies a critical supersaturation threshold for metastable phase growth.

Derives an exact solution for planar interface motion driven by diffusion.

Predicts unbounded growth of metastable phases above critical supersaturation.

Abstract

By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics therefore impinges on many areas of thermodynamics and phase-ordering. An exact solution is found for the motion of a single, planar interface separating a growing phase of uniform high density from a supersaturated low density phase, whose diffusive depletion drives the interfacial motion. In addition, an approximate solution is found for the one-dimensional evolution of two interfaces, separated by a slab of a metastable phase at intermediate density. The theory predicts a critical supersaturation of the low-density phase, above which the two interfaces become unbound and the metastable phase grows ad infinitum. The growth of the stable phase is suppressed in this regime.