Rheo-Dielectrics and Diffusion of Type-A Rouse Chain under Fast Shear Flow: Method of Evaluation of Non-Equilibrium Parameters for FENE, Friction-Reduction, and Brownian Force Intensity Variation

Abstract

Rouse model is the basic molecular model for unentangled linear polymer chains in melts. Recent studies suggest that the Rouse parameters characterizing the unentangled melts, the spring strength κ , the segmental friction coefficient ζ, and the mean-square Brownian force intensity B, change under fast flow thereby providing significant rheological nonlinearities with those melts (Matsumiya et al., Macromolecules, 51, 9710 (2018)). This article theoretically analyzes effects of the flow-induced changes of these parameters on the dielectric and diffusion behavior of the Rouse chain having so-called type-A dipoles parallel along the chain backbone. It turned out that the dielectric behavior under steady shear is determined by non-equilibrium parameters, rκ = κ/κeq and rζ,ij = ζij/ζeq but irrelevant to rB,ij = B ij/Beq, where the subscript “eq” stands for the quantities at equilibrium and the subscripts “ij” denote the spatial direction under shear flow: i and/or j = x, y, and z for the velocity, velocity gradient, and vorticity directions, respectively. Specifically, the complex dielectric permittivity ε* is analytically expressed in terms of the parameters rκ and rζ,ij, which in turn enables us to evaluate these parameters from data of the dielectric relaxation time and intensity under steady shear (obtained in future experiments). In contrast, the advective diffusion behavior under steady shear is determined by rζ,ij and rB,ij but irrelevant to rκ. The mean-square displacement ‹Δr2CM› of the center of mass defined with respect to the known non-diffusive advection point is analytically expressed in terms of rζ,ij and rB,ij, thereby allowing us to evaluate rB,ij from the diffusion data under steady shear and the dielectrically determined rζ,ij. The method of experimental evaluation of the non-equilibrium parameters presented in this article provides us with a complementary basis for analyzing nonlinear rheological behavior of unentangled melts.