| Issue |
J. Phys. I France
Volume 4, Number 12, December 1994
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|
|---|---|---|
| Page(s) | 1791 - 1812 | |
| DOI | https://doi.org/10.1051/jp1:1994221 | |
J. Phys. I France 4 (1994) 1791-1812
Projection of the Rouse model onto macroscopic equations of motion for polymers under shear
H.-P. Wittmann and G. H. FiedricksonDepartment of Chemical Engineering and Materials Department, University of Califorma, Santa Barbara, CA 93106, U.S.A
(Receveid 30 May 1994, received in final form 18 August 1994, accepted 1 September 1994)
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.
© Les Editions de Physique 1994