Nonequilibrium statistical mechanics of the electrorheological effect in polymers*

We present a theoretical and computational investigation of the electrorheological effect in ionic polymer melts using the framework of nonequilibrium statistical mechanics. By analyzing the overdamped Langevin equation, we discover that the apparent viscosity's response to applied electric fields exhibits rich directional dependence relative to the shear flow. Notably, at low shear rates, the maximum electrorheological effects occur at ±45 degrees relative to the shear plane for charge distributions with high-frequency components along the polymer backbone. Our analysis reveals circumstances where the apparent viscosity can become negative, suggesting complex flow behavior. The theoretical framework suggests that the magnitude and directionality of the electrorheological effect can be controlled by modulating the charge sequence along the polymer backbone. These insights into the flow of polymers with ionic "beads" under electric fields have implications for electrically-assisted manufacturing processes such electrowetting, electrospinning, electrocoating, and electromagnetic alignment of composite fillers during additive manufacturing.