Irreversible Statistical Mechanics of Polymer Chains. II. Viscosity

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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.