Dynamics of concentrated polymer systems. Part 2.—Molecular motion under flow.pdf

Dynamics of Concentrated Polymer Systems Part 2.-Molecular Motion under Flow BY MASAO Do1 j - AND S . F. EDWARDS* Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE Received 22nd March, 1978 The primitive chain model presented in Part 1 is extended to the case in which the system is macroscopically deformed. The molecular expression of the stress due to the primitive chain is given, and the stress relaxation after a sudden deformation is calculated as an example. 1. INTRODUCTION In the previous paper (Part l), we described the Brownian motion of the primitive chain in equilibrium. Now we discuss its dynamical behaviour when the system is macroscopically deformed. In the equilibrium state, the primitive chain model is constructed based on the following three assumptions : (A) the real polymer chains are moving in a mean field, called the cage. In this cage field each chain is confined in a tube-like region, the central line of which is the primitive chain, defined in Part 1 . (B) The equilibrium conformation of the primitive chain is a random walk with step length n and arc length L. (C) The primitive chain moves as one Brownian particle along itself with a curvilinear diffusion constant D. The purpose of this paper is to add a further assumption so that we can discuss dynamical properties under flow, particularly the rheological properties. The argu- ment of this paper is the basis of the next paper in which the rheological constitutive equation is constructed. The constitutive equation is obtained if we know (i) how the stress can be calculated from the primitive chain model and (ii) how the primitive chain deforms under the macroscopic flow. To answer these problems we follow the classical theory of rubber ela~ticity,~. which gives an important clue to the answer to the first problem. The success of the simple phantom chain model suggests that even in a condensed system the stress is mainly due to the intramolecular entropic f