Complex viscosity of poly[n]catenanes including olympiadanes

Chains of mechanically interlocking or intersecting organic rings, called poly[n]catenanes, afford interesting opportunities to study the role of orientation in suspensions. We call poly[5]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[n]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 n 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[1–3]catenanes, only to discover that each polystyrene ring looks more like a bead. We find that, for these polystyrene poly[n]catenanes and for good agreement with the available complex viscosity measurements, the shish-kebab theory suffices.