Crossover behavior in the viscosity of semiflexible polymers: Intermolecular interactions as a function of concentration and molecular weight

A simple relation is presented for the viscosity of isotropic solutions of flexible, semiflexible and rodlike chains over a range of concentration from dilute solutions to undiluted polymer, chain contour length L and persistence length (a) over cap. The expression is designed to account for the separate effects of screening of thermodynamic and hydrodynamic interactions, and the onset of intermolecular chain entanglements under Flory theta solvent conditions, or in ''good'' solvents, for which intramolecular excluded volume is important in dilute solutions. The relation includes a revised (dimensionless) Fox parameter <(X)over tilde (c)> that determines the onset of intermolecular entanglements, where <(X)over tilde (c)> = pi N-A rho L(c) (a) over cap/3M(L) for semiflexible polymers with (a) over cap much less than L, with rho the polymer density, M(L) the mass per unit length of the chain, and L(c) the value of L for the onset of entanglement effects in undiluted polymer; <(X)over tilde (c)> approximate to 100 for a number of systems, including rodlike chains. (C) 1996 Society of Rheology.