A kinetic model of a polyelectrolyte gel undergoing phase separation

TL;DR

This paper develops a comprehensive kinetic phase-field model for polyelectrolyte gels undergoing phase separation, capturing multi-scale dynamics, solvent flux, and pattern formation through numerical simulations.

Contribution

It introduces a coupled thermodynamic and hydrodynamic model for polyelectrolyte gels, incorporating interface energy, nonlinear elasticity, and multi-component diffusion, which advances understanding of gel phase behavior.

Findings

Rapid volume changes during phase transition

Spinodal decomposition triggers inhomogeneous stress patterns

Model predicts observable pattern formation in gels

Abstract

In this study we use non-equilibrium thermodynamics to systematically derive a phase-field model of a polyelectrolyte gel coupled to a hydrodynamic model for a salt solution surrounding the gel. The governing equations for the gel account for the free energy of the internal interfaces which form upon phase separation, the nonlinear elasticity of the polyelectrolyte network, and multi-component diffusive transport following a Stefan--Maxwell approach. The time-dependent model describes the evolution of the gel across multiple time and spatial scales and so is able to capture the large-scale solvent flux and the emergence of long-time pattern formation in the system. We explore the model for the case of a constrained gel undergoing uni-axial deformations. Numerical simulations show that rapid changes in the gel volume occur once the volume phase transition sets in, as well as the triggering of spinodal decomposition that leads to strong inhomogeneities in the lateral stresses, potentially leading to experimentally visible patterns.