Elasticity in strongly interacting soft solids: polyelectrolyte network

TL;DR

This paper models the elastic behavior of weakly charged, crosslinked polyelectrolyte networks, revealing that their modulus comprises entropy elasticity and electrostatic interaction contributions, influenced by crosslink density and screening.

Contribution

It introduces a selfconsistent variational approach to quantify the combined entropy and electrostatic elasticity in polyelectrolyte networks.

Findings

Elastic modulus has two parts: entropy elasticity and electrostatic interaction.

Electrostatic contribution is proportional to crosslink density and screening parameter.

The model provides insight into the elastic response of weakly charged polyelectrolyte networks.

Abstract

This paper discusses the elastic behavior of a very long crosslinked polyelectrolyte chain (Debye-H\"uckel chain), which is weakly charged. Therefore the response of the crosslinked chain (network) on an external constant force $f$ acting on the ends of the chain is considered. A selfconsistent variational computation of an effective field theory is employed. It is shown, that the modulus of the polyelectrolyte network has two parts: the first term represents the usual entropy elasticity of connected flexible chains and the second term takes into account the electrostatic interaction of the monomers. It is proportional to the squared crosslink density and the Debye - screening parameter.