Electroelasticity of polymer networks

A multiscale analysis of the electromechanical coupling in elastic dielectrics is conducted, starting from the discrete monomer level through the polymer chain and up to the macroscopic level. Three models for the local relations between the molecular dipoles and the electric field that can fit a variety of dipolar monomers are considered. The entropy of the network is accounted for within the framework of statistical mechanics with appropriate kinematic and energetic constraints. At the macroscopic level closed-form explicit expressions for the behaviors of amorphous dielectrics and isotropic polymer networks are determined, none of which admits the commonly assumed linear relation between the polarization and the electric field. The analysis reveals the dependence of the macroscopic coupled behavior on three primary microscopic parameters: the model assumed for the local behavior, the intensity of the local dipole, and the length of the chain. We show how these parameters influence the directional distributions of the monomers and the hence the resulting overall response of the network. In particular, the dependences of the polarization and the polarization induced stress on the deformation of the dielectric are illustrated. More surprisingly, we also reveal a dependence of the stress on the electric field which stems from the kinematic constraint imposed on the chains.