Projection of the Rouse model onto macroscopic equations of motion for polymers under shear

Abstract

A projection operator technique is used to show how the Onsager coefficients among collective polymer variables can be expressed in terras of correlation and response functions. For a collection of noninteracting Rouse polymers, and with no external shear imposed, the matrix of Onsager coefficients is calculated for the collective variables of concentration and stress. By including appropriate convective ternis, these Onsager coefficients are used to systematically formulate Langevin equations for concentration and stress variables. Due to memory effects, these equations are non-local in both space and time. Moreover, they can be used to compute the dynamical response functions and the Green functions in the presence of shear flow. The resulting coupled equations for concentration and stress variables turn out to be appropriate generalizations of those obtained from simple phenomenological constitutive equations, such as the upper convected Maxwell model and the second order fluid model.