Mean field theory of the hydrodynamics of concentrated polymer solutions

A self-consistent theory of the hydrodynamics of concentrated polymer solutions is derived. The lowest order approximation within this theory is equivalent to the result of a diagrammatic summation of the multiple scattering expansion carried out by Freed and Edwards, and it automatically provides the generalization to the case where chain interactions of a nonhydrodynamic nature are also present within and between the chains. The corrections to the Freed–Edwards theory are analyzed to establish the theory’s range of validity. It is explicitly demonstrated that the theory is valid when interchain correlations do not persist over macroscopic distances for times comparable to or greater than the inverse of the probing frequency. A simple heuristic derivation, which highlights the physical content of the Freed–Edwards theory, is also presented to complete and reinforce the conclusions of the mathematical discussion.