Analysis of the Rouse model in extensional flow. I. A general solution of the distribution function in an arbitrary flow field

Abstract

The statistical mechanics of the Rouse model for a macromolecule are analyzed by the use of Laplace transform techniques. The analysis leads to the known constitutive equation for a dilute solution of Rouse-type molecules and to the general solution for the distribution function ψ in an arbitrary flow field. The form of the general solution is different from that presented by Lodge and Wu and appears to be easier to use. In particular, the new solution makes it straightforward to calculate average molecular quantities like deformation because there is a simple relation between the quantity and the Laplace transform of ψ. This capability is shown by calculations of molecular size, shape, and elastic storage for a general flow field. The deformation of a submolecule unit is also calculated for an assessment of the validity of the Rouse model. The assessment shows that the model is valid per se even at high rates of pure extension.