Physical behavior of electrostrictive polymers. Part 1: Polarization forces

The electrostrictive response of soft elastomers with the same stiffness, strongly depends on their chemical nature and their typically multiphase microstructure. Moreover, some elastomers exhibit a strongly time dependent electrostriction over tens of minutes, and up to now, no theoretical approach has been proposed to analyze experimental data on local parameters like the dielectric constants, conductivities and viscoelastic moduli of these composite-like materials. We consider the phenomenon where the deformation of a polymeric sample between two electrodes is proportional to the square of the applied field, which is known as electrostriction. The electrostatic attraction of charged electrodes is Maxwell electrostriction. In cases, such as block co-polymers with phase separation, the observed electrostriction reaches magnitudes more than 10 times higher than those achieved via the Maxwell process. Phenomenological analyses of experimental data are usually performed but few physical have been proposed to explain the difference. Therefore, we analyze the electric forces inside a composite-like polymer and estimate the corresponding deformation. Using data sets for polyurethane-based materials that exhibit phase separation during their processing, we propose a microstructural model corresponding to a composite where spherical particles randomly fill a matrix. The particles and matrix exhibit different values of physical parameters such as the (i) dielectric constant and electrical conductivity, which determine the local electric field and (ii) viscoelastic modulus, which determine the local stiffness. Because the phases are different, the electric field is not homogenous and the field gradient generates forces around the interfaces. Developing a 2D model, we compare simulation results to experimental literature and other modeling approaches, and discuss them in detail. The polarization forces are found to be responsible for 20% of the deformation in a material with 35% inhomogeneity. Though the time constants are consistent with experimental data, their contribution is smaller than the Maxwell contribution, and therefore other mechanisms are involved in the large electromechanical activity of polymers like polyurethanes.