  Statistical mechanics is an important tool for understanding polymer
electroelasticity because the elasticity of polymers is primarily due to
entropy. However, a common approach for the statistical mechanics of polymer
chains, the Gaussian chain approximation, misses key physics. By considering
the nonlinearities of the problem, we show a strong coupling between the
deformation of a polymer chain and its dielectric response; that is, its net
dipole. When chains with this coupling are cross-linked in an elastomer network
and an electric field is applied, the field breaks the symmetry of the
elastomer's elastic properties, and, combined with electrostatic torque and
incompressibility, leads to intrinsic electrostriction. Conversely, deformation
can break the symmetry of the dielectric response leading to volumetric torque
(i.e., a couple stress or torque per unit volume) and asymmetric actuation.
Both phenomena have important implications for designing high-efficiency soft
actuators and soft electroactive materials; and the presence of mechanisms for
volumetric torque, in particular, can be used to develop higher degree of
freedom actuators and to achieve bioinspired locomotion.
