The dynamics of a collapsing polyelectrolyte gel

TL;DR

This paper models the complex collapse dynamics of polyelectrolyte gels in ionic baths, revealing multiple collapse pathways, phase separation phenomena, and the influence of ion concentration on stability and heterogeneity.

Contribution

It introduces a comprehensive model combining non-linear elasticity, diffusion, and phase separation, and provides new analytical and numerical insights into gel collapse mechanisms.

Findings

Multiple solution branches at low ion concentrations

Existence of a depletion front during collapse

Spinodal decomposition leads to phase separation

Abstract

We analyse the dynamics of different routes to collapse of a constrained polyelectrolyte gel in contact with an ionic bath. The evolution of the gel is described by a model that incorporates non-linear elasticity, Stefan-Maxwell diffusion and interfacial gradient free energy to account for phase separation of the gel. A bifurcation analysis of the homogeneous equilibrium states reveals three solution branches at low ion concentrations in the bath, giving way to only one above a critical ion concentration. We present numerical solutions that capture both the spatial heterogeneity and the multiple time-scales involved in the process of collapse. These solutions are complemented by two analytical studies. Firstly, a phase-plane analysis that reveals the existence of a depletion front for the transition from the highly swollen to the new collapsed equilibrium state. This depletion front is initiated after the fast ionic diffusion has set the initial condition for this time regime. Secondly, we perform a linear stability analysis about the homogeneous states that show that for a range of ion concentrations in the bath, spinodal decomposition of the swollen state gives rise to localized solvent-rich(poor) and, due to the electro-neutrality condition, ion-poor(rich) phases that coarsen on the route to collapse. This dynamics of a collapsing polyelectrolyte gel has not been described before.