A statistical mechanical model for the electrostriction of polymers

Dielectric elastomers (DEs) are soft materials that polarize in the presence of an electric field. Using statistical mechanics, the thermodynamics of a DE chain subject to electrical loading and kinematic constraints is investigated. The equations of the monomer orientation density and the approximate chain free energy are derived. Solutions are presented in the small chain stretch limit and near the fully stretched limit. A closed-form approximation for the free energy of a DE chain is developed using asymptotic matching and shown to agree well with the numerical solutions. Next, averaging over chain orientations, the chain-scale response is built up to an electromechanically coupled DE constitutive model. Some preliminary results from the constitutive model are presented, which includes a contribution, at the macromolecular scale, to the electrostriction of DEs. The contribution to electrostriction is shown to be dependent on the lengths and orientations of chains in the DE network.