Statistical mechanics of a dielectric polymer chain in the force ensemble

Constitutive modeling of dielectric elastomers has been of long standing interest in mechanics. Over the last two decades rigorous constitutive models have been developed that couple the electrical response of these polymers with large deformations characteristic of soft solids. A drawback of these models is that unlike classic models of rubber elasticity they do not consider the coupled electromechanical response of single polymer chains which must be treated using statistical mechanics. The objective of this paper is to compute the stretch and polarization of single polymer chains subject to a fixed force and fixed electric field using statistical mechanics. We assume that the dipoles induced by the applied electric field at each link do not interact with each other and compute the partition function using standard techniques. We then calculate the stretch and polarization by taking appropriate derivatives of the partition function and obtain analytical results in various limits. We also perform Markov chain Monte Carlo simulations using the Metropolis and umbrella sampling methods, as well as develop a new sampling method which improves convergence by exploiting a symmetry inherent in dielectric polymer chains. The analytical expressions are shown to agree with the Monte Carlo results over a range of forces and electric fields. Our results complement recent work on the statistical mechanics of electro-responsive chains which obtains analytical expressions in a different ensemble.

Automated summary

Constitutive modeling of dielectric elastomers has been developed over the last two decades to couple the electrical response of polymers with large deformations, but lacks consideration of the coupled electromechanical response of single polymer chains, which can be addressed using statistical mechanics. This paper computes the stretch and polarization of single polymer chains subjected to fixed force and electric field through statistical mechanics, obtaining analytical results and validating them through Monte Carlo simulations. The study also introduces a new sampling method that improves convergence and shows agreement between analytical expressions and simulation results across a range of forces and electric fields.