Cell Model Approaches for Predicting the Swelling and Mechanical Properties of Polyelectrolyte Gels

TL;DR

This paper introduces two simplified mean-field models for predicting the swelling and mechanical properties of polyelectrolyte gels, achieving high accuracy with significantly reduced computational complexity compared to detailed molecular simulations.

Contribution

The authors develop a two-step mean-field approximation framework that simplifies the complex gel system into an efficient Poisson-Boltzmann cell-gel model, outperforming previous models especially for highly charged chains.

Findings

Models agree well with molecular dynamics simulations.

The approach predicts bulk moduli more accurately than traditional models.

Robust across parameter variations and chain polydispersity.

Abstract

We present two successive mean-field approximations for describing the mechanical properties and the swelling equilibrium of polyelectrolyte gels in contact with a salt solution. The first mean-field approximation reduces the many-chain problem of a gel to a corresponding single chain problem. The second mean-field step integrates out the degrees of freedom of the flexible chain and the ions. It replaces the particle-based description of the polyelectrolyte with suitable charge distributions and an effective elasticity term. These simplifications result in a computationally very efficient Poisson-Boltzmann cell-gel description. Despite their simplicity, the single chain cell-gel model shows excellent and the PB model very good agreement with explicit molecular dynamics simulations of the reference periodic monodisperse network model for varying chain length, polymer charge fraction, and external reservoir salt concentrations. Comparisons of our models to the Katchalsky model reveal that our approach is superior for strongly charged chains and can also predict the bulk moduli more accurately. We further discuss chain length polydispersity effects, investigate changes in the solvent permittivity, and demonstrate the robustness of our approach to parameter variations coming from several modeling assumptions.