General Rigid Bead-Rod Macromolecular Theory

Abstract

In the general rigid bead-rod theory, we explain the elasticity of a polymeric liquid by considering just the orientation of a suspension of macromolecules. With the general rigid bead-rod theory, we construct macromolecules from sets of beads whose positions, relative to one another, are fixed. The general rigid bead-rod theory is, thus, not to be confused with a freely jointed chain, where the beads are rigidly separated but the joints rotate freely. Our macromolecular bead-rod models are suspended in a Newtonian solvent. In this work, we neglect interactions of the solvent velocity fields, be they between the nearest beads (Stewart and Sørensen, 1972; and Piette et al., 2019b)1 or the nearestmacromolecules. With the general rigid bead-rod theory, we, thus, locate beads and their dimensionless massless rods along molecular chains, including rings, backbones, or branches. In this way, we can model anymacromolecular architecture. To any such collection of masses, we can associate a moment of inertia ellipsoid (MIE) whose center is the center of mass and whose principal moments of inertia match those of the macromolecule. The MIE determines the orientability of the macromolecules and, thus, the polymer contribution to the rheological properties.