Complex viscosity of poly[n]catenanes including olympiadanes

Abstract

Chains of mechanically interlocking or intersecting organic rings, called poly[[Formula: see text]]catenanes, afford interesting opportunities to study the role of orientation in suspensions. We call poly[[Formula: see text]]catenanes olympiadanes. In this work, we use general rigid bead-rod theory to arrive at general expressions, from first principles, for the complex viscosity of poly[[Formula: see text]]catenane suspensions. General rigid bead-rod theory relies entirely on suspension orientation to explain the elasticity of the liquid. We obtain analytical expressions for the complex viscosity of poly[n]catenanes for both [Formula: see text] even and odd, for both mechanically interlocking and intersecting rings, and for identically sized rings. We restrict our analysis to evenly spaced poly[n]catenanes of orthogonal adjacency. We find that the parts of the complex viscosity for intersecting and interlocking rings, when made dimensionless with the polymer contribution to the zero-shear viscosity, match. We find good agreement with the available complex viscosity measurements for molten intersecting polystyrene poly[1,3]catenanes, but not so for poly[2]catenanes. We next calculate space filling equilibrium structures of these poly[[Formula: see text]]catenanes, only to discover that each polystyrene ring looks more like a bead. We find that, for these polystyrene poly[[Formula: see text]]catenanes and for good agreement with the available complex viscosity measurements, the shish-kebab theory suffices.