Elasticity in strongly interacting soft solids: A polyelectrolyte network

This paper discusses the elastic behavior of a very long cross-linked polyelectrolyte chain (Debye-Hückel chain), which is weakly charged. Therefore the response of the cross-linked chain (network) on an external constant force f acting on the ends of the chain is considered. A self-consistent 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 cross-link density and the Debye-screening parameter.