Hartree self-consistent field approach towards dilute polymer solutions

Abstract

The presence of elastic forces in the spring and bead model of polymer solutions suggests a discussion in terms of modes rather than of beads. The transition from a many-mode picture to a one-mode picture is effected by a factorization of the many-mode probability density into one-mode probability densities. These obey a system of coupled integro-differential equations of the Hartree type. Working in the Rouse mode representation and beginning with the longmolecule free-draining approximation good one-mode probability densities were derived which take into account Oseen's hydrodynamic interactions in an average fashion and form the starting basis for the well-known Hartree self-consistent procedure which goes beyond the approximation of the averaged Oseen tensor. This procedure can be used to improve the values of the viscosity and normal stress functions which we have calculated for the case of simple shear flow. The shear stress and the two relevant normal stress differences are non-zero and depend on the velocity gradient in a non-linear manner. The calculation of explicit numerical results requires computer work of moderate extent for which all required formulae are given in the appendix.