Irreversible Statistical Mechanics of Polymer Chains. II. Viscosity

Abstract

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 η N = 2ckT ∑ σ = 1 N τ σ / (1 + iωτ σ ), where τ σ 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 τ σ = γ σ 2 / 2D σ , where γ σ and D σ are, respectively, the expansion parameter and the diffusion constant in regard to the normal coordinate Q σ . With hydrodynamic interactions, the relaxation time is modified as τ σ ′ = τ σ (1 + kTT̃ σ / D σ ), where T̃ σ is the σth eigenvalue of Kirkwood–Riseman tensor.