A Theory on the Relationship between Viscosity and Molecular Weight in Bulk Polymers

Abstract

A statistical mechanical theory of steady viscosity in bulk polymers is presented. In slowly relaxing phenomena such as steady viscosity, the inter-chain relaxation is predominant and the segmental conformation of each polymer molecule attains to a state of dynamic equilibrium. It is assumed that the intermolecular force between two molecules consists of two parts: the force derived from potential and the friction due to entanglements between them. The general expression of viscosity is derived from the fundamental equation for the velocity distribution function of a polymer molecule, using Born-Green's method. The molecular weight dependence of viscosity η is roughly estimated by taking into account the inner structure and conformation of polymer molecules. The result is η= C 1 N + C 2 N 3 , where N is the number of segments constituting a polymer molecule, C 1 and C 2 are constants, and C 1 ≫ C 2 . This prediction agrees semi-quantitatively with experiment.