Cole–Cole relation for long-chain branching from general rigid bead–rod theory

Abstract

Empirically, we find that the parametric plots of the imaginary vs real parts of the complex viscosity may depend neither on temperature nor on average molecular weight. Moreover, for a fixed polydispersity, these viscosity Cole–Cole curves amplify both rightward and upward with long-chain branching content. In this paper, we find that general rigid bead–rod theory [O. Hassager, “Kinetic theory and rheology of bead–rod models for macromolecular solutions. II. Linear unsteady flow properties,” J. Chem. Phys. 60(10), 4001–4008 (1974)] can explain these rightward and upward amplifications. We explore the effects of branching along a straight chain in small-amplitude oscillatory shear flow. Specifically, we explore the number of branches, branch length, branch position, and branch distribution.