Irreversible Statistical Mechanics of Polymer Chains. II. Viscosity

The Fokker–Planck diffusion equation derived in the previous paper is applied to Erpenbeck–Kirkwood theory on the viscosity of polymer solutions. The Newtonian viscosity for ring polymers is given by ηN = 2ckT ∑ σ = 1N τσ / (1 + iωτσ), where τσ is the relaxation time, c is the number of polymers in unit volume, and kT has the usual meaning. Without hydrodynamic interactions among monomer units, the relaxation time is given by τσ = γσ2 / 2Dσ, where γσ and Dσ are, respectively, the expansion parameter and the diffusion constant in regard to the normal coordinate Qσ. With hydrodynamic interactions, the relaxation time is modified as τσ′ = τσ(1 + kTT̃σ / Dσ), where T̃σ is the σth eigenvalue of Kirkwood–Riseman tensor.