Macromolecular complex viscosity from space-filling equilibrium structure

Abstract

Macromolecular theory for the rheology of polymer liquids usually proceeds from a scale much larger than chemical bonding. For instance, a bead in a general rigid bead-rod theory can represent a length of the polymer. This is why we sculpt the shape of the macromolecule with a rigid bead-rod model. From the macromolecular hydrodynamics that follow, we then discover that the rheology of polymeric liquids depends on the macromolecular moments of inertia. In this paper, we use this discovery to arrive at a way of proceeding directly from the chemical bonding diagram to dimensionless complex viscosity curves. From the equilibrium conformation of the macromolecule, its atomic masses and positions, we first arrive at the macromolecular principal moments of inertia. From these, we then get the shapes of the complex viscosity curves from first principles thusly. We call this the macromolecular moment method. The zero-shear viscosity and relaxation time must still be fit to measurement. Using space-filling equilibrium structures, we explore the roles of (i) end group type, (ii) degree of polymerization, and (iii) pendant group type. We compare our results with complex viscosity measurements of molten atactic polystyrene.