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 vs complex shear modulus may depend neither on temperature [M. van Gurp and J. Palmen, "Time-temperature superposition for polymeric blends," Rheol. Bull. 67, 5-8 (1998)] nor on average molecular weight [S. Hatzikiriakos, "Long chain branching and polydispersity effects on the rheological properties of polyethylenes," Polym. 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 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 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.