# Modeling Gel Swelling Equilibrium in Mean-Field: From explicit Models to Poisson-Boltzmann

## TL;DR

This paper introduces a double mean-field model for charged macrogels that accurately predicts swelling behavior by combining explicit polymer sampling with a Poisson-Boltzmann approximation, extending to pH-sensitive gels.

## Contribution

It develops a computationally efficient double mean-field approach that bridges explicit polymer models and Poisson-Boltzmann theory for swelling predictions.

## Key findings

- Accurate swelling predictions with explicit coarse-grained models.
- Excellent agreement with molecular dynamics simulations.
- Effective extension to pH-sensitive gel systems.

## Abstract

We develop a double mean-field theory for charged macrogels immersed in electrolyte solutions in the spirit of the cell model approach. We first demonstrate that the equilibrium sampling of a single explicit coarse-grained charged polymer in a cell yields accurate predictions of the swelling equilibrium if the geometry is suitably chosen and all pressure contributions have been incorporated accurately. We then replace the explicit flexible chain by a suitably modeled penetrable charged rod that allows to compute all pressure terms within the Poisson-Boltzmann approximation. This model, albeit computationally cheap, yields excellent predictions of swelling equilibria under varying chain length, polymer charge fraction, and external reservoir salt concentrations when compared to coarse-grained molecular dynamics simulations of charged macrogels. We present an extension of the model to the experimentally relevant cases of pH-sensitive gels.