Statistical mechanics of a dielectric polymer chain in the force ensemble

Dear colleagues,

We invite you to see the preprint of our new paper "Statistical mechanics of a dielectric polymer chain in the force ensemble" that will appear in Journal of the Mechanics and Physics of Solids. Here we investigate the electroelasticity of single polymer chains using both analytical approximations and novel MCMC techniques. Working in the fixed force ensemble facilitates the derivation of the analytical approximations, which are shown to agree well with the MCMC results. This work complements prior work on the statistical mechanics of dielectric polymers chains obtained in a different ensemble. (https://doi.org/10.1016/j.jmps.2021.104658).

Statistical mechanics of a dielectric polymer chain in the force ensemble

Matthew Grasinger, Kaushik Dayal, Gal deBotton, and Prashant K. Purohit

Abstract

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.