A coupled electro-chemo-mechanical theory for polyelectrolyte gels with application to modeling their chemical stimuli-driven swelling response

Abstract

Polyelectrolyte gels consist of a polymer network with charged functional side-groups, and a solvent with counter-ions filling the interstitial spaces in the network. Such gels respond to chemical signals such as the pH and the ionic strength of their external environment by substantial swelling or deswelling, which makes them attractive for use in a wide variety of applications including tissue engineering, drug-delivery, bioelectronics, valves and actuators for microfluidics, as well as small-scale soft-robotic applications. The physics driving the swelling and deswelling processes in these gels is complex because of the coupling of large deformations, simultaneous transport of solvent and ions into and within the gel, the influence of the ions in solution on the degree of ionization of the functional side-groups in the polymer network, and the cross-diffusion of the charged and neutral species. In this work we present a thermodynamically-consistent coupled electro-chemo-mechanical theory for polyelectrolyte gels which take these phenomena into account. We have numerically implemented our theory in a finite element program. Using this numerical capability, we present simulations of the transient swelling response of both anionic and cationic polyelectrolyte gels in response to variations in the pH and ionic strength of the environment, and show that our theory can quantitatively reproduce some corresponding experimental results available in the literature. We also show the practical utility of our theory and its attendant numerical capability by presenting simulation results for some interesting actuators made from polyelectrolyte gels.