An application of the generalized Fokker–Planck equation to the dynamics of dilute polymer solutions

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Abstract
The nonlinear formalism developed by Zwanzig and Mori is utilized to derive a kinetic equation for the distribution of monomer phase space coordinates and a coarse-grained momentum density. Several simplifying approximations are then introduced into the exact kinetic equation. The resulting approximate description is shown to be closely related to the starting equations of the Freed–Edwards theory. The former differs, however, due to the presence of a non-Stoke’s frictional term which accounts for dissipation of monomer momentum fluctuations relative to the local velocity field of the solvent. Two applications of the approximate description are considered. A derivation of an equation for the two-time configuration space distribution function ψ (y, y′, t) is presented, where y denotes the collection of monomer position vectors. It is demonstrated that ψ (y,y′,t ) satisfies an equation similar to the Kirkwood–Riseman equation. Nonlinear couplings of the polymer distribution function to monomer momenta and the momentum density of the solvent lead to a diffusion tensor in which hydrodynamic interactions are characterized by a coarse-grained Oseen tensor. The correlation function formulation of the intrinsic viscosity proposed by Stockmayer et al. is extended to finite wavevectors and polymer concentrations. The specific viscosity is identified as the sum of two terms involving the mechanical contribution to the polymer momentum flux tensor and the diffusion current of chain segments.

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