Radius of Gyration in Shear Gradient Direction Governs Steady Shear Viscosity of Rouse-Type Model

TL;DR

This paper derives general relations between stress and gyration tensors in a Rouse-type polymer model, showing that the steady shear viscosity is determined by the gyration radius in the shear gradient direction.

Contribution

It provides new, exact relations linking stress and gyration tensors in a Rouse model without approximations, highlighting the role of the gyration radius in shear viscosity.

Findings

Steady shear viscosity depends on the gyration radius in the shear gradient direction.

Derived general relations between stress and gyration tensors for Rouse-type models.

Formulated rheological quantities in terms of the gyration tensor.

Abstract

We analyze the stress tensor and the gyration tensor of an unentangled polymer melt under flow by using a Rouse-type single chain model. We employ the bead-spring type single chain model, in which beads interact each other via nonlinear potentials such as the finite-extensible nonlinear elasticity (FENE) potential. Beads are assumed to obey the Langevin equation with a constant friction coefficient. We derive simple yet general relations between the stress tensor and the gyration tensor for this Rouse-type model, without any additional approximations. Various formulae for rheological quantities in terms of the gyration tensor can be derived from the general relations. For example, the steady shear viscosity is governed by the gyration radius in the shear gradient direction.