Statistical field theory for the free energy of an electro-mechanical polymer chain: non-local dipole-dipole interactions in the fixed applied field ensemble

Existing theoretical approaches for polarizable polymers subject to a combined applied electric field and stretch are based on discrete monomer models. It is challenging to account for the non-local dipole-dipole interaction in this framework. The prior work typically considers only the interaction between the applied field and dipoles. To go beyond this approximation, we apply the statistical field theoretic framework that is based on a continuous description of the polymer chain in terms of density fields. We introduce a self-consistent formulation that enables us to address the setting of constant applied electric field ensembles that transforms the nonlocal interactions into a PDE constraint corresponding to Gauss’ equation. We implement the model in a finite element method to compute the free energy, average density, and average polarization distribution at equilibrium. We find that the presence of dipole-dipole interactions leads to qualitative changes in the dipole distributions, total polarization, and equilibrium electric field in the domain. We further notice a sharp instability leading to a collapse of the chain under the strong electric fields as a consequence of dipole-dipole interactions.