The electric double layer at the interface between a polyelectrolyte gel and salt bath

TL;DR

This paper models the electric double layer at a polyelectrolyte gel-salt bath interface, revealing conditions for phase separation and the limits of electroneutrality assumptions using asymptotic and numerical methods.

Contribution

It develops a comprehensive asymptotic and numerical framework for analyzing the EDL at gel interfaces, including phase separation effects and the validity of electroneutrality.

Findings

Electroneutral models match solutions when Kuhn length exceeds Debye length.

Phase separation leads to periodic charged domains when Debye length is large.

Electroneutrality assumption is valid only when Debye length is much smaller than Kuhn length.

Abstract

The electric double layer (EDL) that forms at the interface between a polyelectrolyte gel and a salt bath is studied using asymptotic and numerical methods. Specifically, matched asymptotic expansions, based on the smallness of the Debye length relative to the typical gel dimensions, are used to construct solutions of the governing equations and derive electroneutral models with consistent jump conditions across the gel-bath interface. A general approach for solving the equations of incompressible nonlinear elasticity in a curved boundary layer is developed and used to resolve the gel mechanics in the EDL. A critical feature of the model is that it accounts for phase separation within the gel, which gives rise to diffuse interfaces with a characteristic thickness described by the Kuhn length. We show that the solutions of the electroneutral model can only be asymptotically matched to the solutions in the EDL, in general, when the Kuhn length greatly exceeds the Debye length. Conversely, if the Debye length is similar to or larger than the Kuhn length, then the entire gel can self-organise into periodic, electrically charged domains via phase separation. The breakdown of electroneutrality demonstrates that the commonly invoked electroneutral assumption must be used with caution, as it generally only applies when the Debye length is much smaller than the Kuhn length.