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 â. 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 X̃c that determines the onset of intermolecular entanglements, where X̃c=πNAρLcâ/3ML for semiflexible polymers with â≪L, with ρ the polymer density, ML the mass per unit length of the chain, and Lc the value of L for the onset of entanglement effects in undiluted polymer; X̃c≊100 for a number of systems, including rodlike chains.