Electro-viscoelasticity of polymer melts in continuum theory

TL;DR

The paper addresses how electric fields modify the viscoelastic response of charged polymer melts across scales. It extends the Rouse model to include backbone charges and an external field, deriving a polarization-driven stress and introducing the upper-convected electro-Maxwell (UCEM) continuum framework, which assigns polarization stresses to the E-field dyadic and transports them via the upper-convected derivative. Across scales, it demonstrates that viscosity can increase anisotropically with field orientation in a manner governed by a mode-specific relaxation time, a behavior captured by the UCEM model but missed by traditional electrorheological formulations. The findings establish a frame-indifferent, cross-scale description of electroviscoelasticity that aligns with steady Couette, pressure-driven, and SAOS observations, and harmonizes molecular-level simulations with continuum theory and experimental trends such as those reported for PMMA.

Abstract

Electro-viscoelastic polymers have been studied experimentally for the past century, primarily for manufacturing purposes; however, the mechanisms governing their behavior in combined flow and electric fields remain poorly understood. To address this, we model charged polymers across scales. We extend the Rouse model to include charge density along the polymer chain and ambient electric fields, deriving the shear stress under homogeneous shear and electric fields. Viscosity exhibits anisotropic enhancement dependent on field-flow orientation with a scaling factor dependent on a charge sequence relaxation time, dielectric constant, and quadratic electric field term. These results inform a new continuum model--the upper-convected electro-Maxwell (UCEM) model--resembling an upper-convected Maxwell model with polarization stresses expressed through an electric field dyadic subject to upper-convected time derivatives. Coarse-grained molecular dynamics simulations of Kremer-Grest chains with charge sequences reveal distinct relaxation timescales for overall chain dynamics versus charge redistribution, manifested in shear and normal stress responses. Critically, upper-convected time derivatives of the electric field dyadic reproduce the viscosity scaling observed in both the Rouse and MD results; while standard continuum formulations without these terms fail to capture the scaling. Analysis of the dynamic rheological properties show that the phase shift is unaffected by the electric field, in agreement with recent PMMA experiments.

Figures (4)

• Figure 1: A visual representation of the linear polymer chain made using the Kremer-Grest model. The monomer coloring of red, blue, and gray represents a negatively charged, positively charged, and neutral monomer, respectively.
• Figure 2: Polarization stress as shown in equations \ref{['eq:PolarSigma22']}-\ref{['eq:PolarSigma33']} for a constant shear rate of $\dot{\gamma}=0.00259$. The best fit values for the $\sigma_{22}$, $\sigma_{12}$, and $\sigma_{11}$ polarizations are shown, respectively, relative to the quadratic scaling with the electric field.
• Figure 3: Transient shear stress response of a step strain rate of $\dot{\gamma}=0.00259$ under an $E_2=0.9$ electric field.
• Figure 4: A normalization of the pressure-driven velocity profile for an increasing $E_2$ from the molecular dynamics results. A best fit was performed with equation \ref{['eq:BestFitFunc']} to find the coefficient $\frac{\tau_f\epsilon_{dielec}}{\eta}$.