A Multi-Scale Theory of Electro-Viscoelasticity in Polymer Melts

Despite extensive experimental studies, a predictive theoretical framework for the electro-viscoelasticity of polymer melts remains underdeveloped. We address this gap by developing a multi-scale model that connects microscopic polymer dynamics to continuum mechanics. Starting from the Doi-Rouse model, we incorporate electrostatic forces acting on a chain with a prescribed cosine charge sequence along the chain backbone, which directly couples the electric field to a single Rouse mode. Analytical solution of the modified overdamped Langevin equations under homogeneous shear and electric fields predicts an anisotropic viscosity, dependent on the relative orientation of the flow and field. To bridge to the continuum scale, we derive a modified upper-convected electro-Maxwell (UCEM) model. This new model incorporates polarization stresses through two terms involving the upper-convected time derivative of the electric field dyadic and the electric field dyadic itself. The UCEM model and its underlying assumptions are validated against molecular dynamics (MD) simulations of Kremer-Grest melts with the specified charge sequence. The MD simulations confirm the theory's predictions for stress under various flow and field conditions. We show that the relaxation time of the charge distribution is distinct from the terminal relaxation time of the chain, which necessitates the use of the upper-convected derivative for the electric field dyadic to correctly capture the viscosity scaling.