Recent Advances In Polymer Viscoelasticity From General Rigid Bead-Rod Theory

One good way to explain the elasticity of a polymeric liquid, is to just consider the

orientation distribution of the macromolecules. When exploring how macromolecular

architecture affects the elasticity of a polymeric liquid, we find general rigid bead-rod theory

to be both versatile and accurate. This theory sculpts macromolecules using beads and rods.

Whereas beads represent points of Stokes flow resistances, the rods represent rigid

separations. In this way, how the shape of the macromolecule affects its rheological behavior

in suspension is determined. Our work shows the recent advances in polymer viscoelasticity

using general rigid bead-rod theory, including the discovery of the first new materials

functions from general bead-rod theory since the first, the complex viscosity of Hassager

(1974). These include the steady shear material functions, large-amplitude oscillatory

shear flow material functions, and the steady uniaxial, biaxial and planar extensional

viscosities. We find each of these material functions to depend upon the same molecular

feature: the ratio of the macromolecular moment of inertia about the molecular axis to that

about the axes transverse to the molecular axis. We then use these new material functions

to bridge the Oldroyd 8-constant framework (and thus all of its many special cases) to

general bead-rod theory.