FOKKER-PLANCK EQUATION FOR THE ONE-MOLECULE DISTRIBUTION FUNCTION IN POLYMER MIXTURES AND ITS SOLUTION

It is shown how a Fokker-Planck equation in the phase space of a singl e polymer molecule in a multicomponent mixture can be obtained from th e Liouville equation in the phase space of a mixture of polymeric liqu ids. This result is a generalization of the Schieber-Ottinger equation for a dilute solution of a single polymer species in a solvent, or th e Ottinger-Petrillo equation for nonisothermal systems. The Fokker-Pla nck equation is solved as a series in powers of a small parameter epsi lon, thereby displaying quantitatively the deviation of the velocity d istribution from the Maxwellian. It is then shown how moments of the s inglet distribution function needed for the evaluation of the transpor t coefficients can be obtained. In addition, expressions for the first three moments of the Brownian force are developed. It is further show n how the present discussion is related to the Curtiss-Bird theory for multicomponent diffusion. Throughout the development the polymer mole cules are modeled as arbitrary bead-spring structures, with all inter- bead forces (representing both intra- and intermolecular forces) deriv able from a potential and directed along the bead-bead vectors. These models can describe flexible chain macromolecules, ring-shaped polymer s, starlike polymers, and branched polymers. (C) 1997 American Institu te of Physics.