Viscosity of Entangling Polydisperse Polymers

Abstract

This paper presents a theory of viscosity in steady shearing flow for bulk polymers and concentrated polymer solutions. The basis for the theory is the supposition that intermolecular chain entanglements control the magnitude of the viscosity and that the decrease in viscosity with increasing shear rate is caused by shear-induced changes in the network of entanglements. It was found possible to represent the effect of entanglements by an additional term in the segmental friction coefficient, and to incorporate the effects of polymer concentration, molecular weight distribution, and shear rate in the final result. At low shear rates (γ̇→0) the viscosity reduces to η0=(const) (φn̄x)3.5 for highly entangled chains, where φ is the volume fraction of polymer and n̄x is an average chain length slightly greater than the weight average. The form of the viscosity—shear rate master curve was found to depend on the chain-length distribution of the polymer. Departures from Newtonian behavior occur at lower shear rates the broader the distribution, but at sufficiently high shear rates the behavior becomes similar for all distributions. The master curve for monodisperse polymers was in good agreement with measurements on solutions of narrow distribution polystyrene. The limiting power-law exponent in η=k|γ̇|−a was found to be 9/11 rather than ¾ as given by an earlier theory. The master curve calculated for most-probable distributions (M̄w/M̄n=2) agreed moderately well with the empirical master curve of Bueche and Harding and with data on solutions of unfractionated polystyrene.