Multi-scale Modeling of the Electro-viscoelasticity of Charged Polymers in Combined Flow and Electric Fields

Abstract

The behavior of polymers in combined flow and electric fields underlies many manufacturing processes but remains poorly understood. To address this, we model charged polymers across scales. We extend the original Rouse model for a bead-spring chain to include a charge density distributed along the polymer chain, and derive the viscoelastic stress under homogeneous shear and electric fields. The viscosity increase depends on field-flow orientation and scales quadratically with select components of the electric field strength, modulated by the effective charge sequence relaxation time and dielectric constant. Inspired by this result, a new continuum model--the upper-convected electro-Maxwell (UCEM) model--is proposed, resembling an upper-convected Maxwell model with polarization stresses expressed through an electric field dyadic subject to upper-convected time derivatives. We analyze the constitutive response for several flows and electric field strengths, discussing limitations and demonstrating compliance with the second law of thermodynamics. Lastly, coarse-grained molecular dynamics (MD) simulations of Kremer-Grest chains with a defined charge sequence confirm the existence of distinct relaxation timescales for overall chain dynamics versus charge redistribution, consistent with the UCEM model predictions. Critically, we demonstrate that the upper-convected time derivative of the electric field dyadic is required in the evolution of stress to account for stretching and rotation of the charge pairs in flow, reproducing the viscosity scaling observed in both the Rouse and MD results; whereas standard continuum formulations without these terms fail to capture this observed scaling.