Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory

Abstract

With general rigid bead-rod modeling, we recreate shapes of complex macromolecular structures with beads, by rigidly fixing bead positions relative to one another. General rigid-bead rod theory then attributes the elasticity of polymeric liquids to the orientation that their macromolecules develop during flow. For linear viscoelastic behaviors, this theory has been evaluated for just a few very simple structures: rigid rings, the rigid tridumbbell, and three quadrafunctional branched structures. For oscillatory shear flow, the frequency dependencies of both parts of the complex viscosity are, at least qualitatively, predicted correctly. In this paper, we use general rigid-bead rod theory for the most complex macromolecular architectures to date. We thus explore the role of helix geometry on the complex viscosity of a helical polymeric liquid. Specifically, for both singly and doubly helical structures, we investigate the effects of helix radius, flight length, helix length, and the number of beads per flight on the complex viscosity function, the fluid relaxation time, and the zero-shear values of the steady shear viscosity and of the first normal stress coefficient. As a worked example, we examine specifically deoxyribonucleic acid (DNA). Using general rigid bead-rod theory, we dissect the DNA to see how the first helix, second helix, and then the base pairs each contribute to the complex viscosity. We next explore the rheological implications of gene replication to find that the unzipping of DNA into a pair of single strands is viscostatic.