Van Gurp-Palmen Relations for Long-Chain Branching From General Rigid Bead-Rod Theory

Abstract

Empirically, we find that parametric plots of mechanical loss angle versus complex shear modulus may depend neither on temperature [van Gurp and Palmen, Rheol Bull (SoR), 67, 5 (1998)], nor on average molecular weight [Hatzikiriakos (2000), Pol Eng Sci, 40, 2279 (2000)]. Moreover, Hatzikiriakos (2000) discovered that, for fixed polydispersity, these van Gurp-Palmen curves descend with long-chain branching content. In this paper, we find that general rigid beadrod theory [Hassager, J Chem Phys, 60, 4001 (1974)] can explain these descents. 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.