Large-Amplitude Oscillatory Shear Flow Loops for Long-Chain Branching From General Rigid Bead-Rod Theory

Abstract

General rigid bead-rod theory [Hassager, J Chem Phys, 60, 4001 (1974)] explains polymer viscoelasticity from macromolecular orientation. By means of this theory, we relate the complex viscosity of polymeric liquids to the architecture of axisymmetric branched macromolecules. In this work, we explore how adding long-chain branching to polymers affects the shapes of largeamplitude oscillatory shear flow (LAOS) loops. By loops, we mean plots of the alternant part of the shear stress response versus the cosinusoidal shear rate. When non-dimensionalized with the product of the zero-shear viscosity and the shear rate amplitude, the loop shapes depend upon the sole dimensionless architectural parameter, the macromolecular lopsidedness of the long-chain branched macromolecule. In this work, in this way, we compare and contrast the loop shapes of macromolecular chains that are straight, with those branched. Specifically, we explore symmetric branch multiplicity, branch functionality, branch length, branch position, branch distribution and multiple branch asymmetry. We find that adding branching collapses and distorts the loops. We then find that, so long as branch length, branch position and branch distribution are held constant, and so long as the branching is symmetric about the center of mass, the peak shear stress increases with branch multiplicity. We also find that branch functionality hardly affects the loops.