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.

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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 polymer. This is why we sculpt the shape of the macromolecule with a rigid bead-rod model. From the macromolecular hydrodynamics that follows, we then discover that the rheology of polymer liquids depends on the macromolecular moments of inertia. In this paper, we use this discovery to arrive 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.