Microscopic derivation and extension of the Cahn-Hilliard-Cook theory in polymer blends

A microscopic derivation, based on the linear response theory, of the Cahn--Hilliard--Cook (CHC) expression for the intensity of scattered radiation from binary polymer mixtures during transients following an initial perturbation is presented and compared with the conventional derivation. The microscopic approach leads to a more general expression for the intensity which allows a multicomponent description and non-exponential behavior. It shows that the time dependence of the intensity during the final stages of transients can be expressed quite generally in terms of the normalized dynamic scattering function in the final equilibrium state. An alternative macroscopic derivation based on the Markov assumption and the system-size expansion is also presented to clarify the validity of the inherent approximations in the generalized CHC form. These derivations do not require an incompressibility assumption or a model for the free energy of the mixture. Using a dynamic random phase approximation, an explicit form of the intensity is obtained in the case of an incompressible binary polymer mixture in terms of the interaction parameter. The new expression includes the effect of internal motions of segments on the time behavior of the intensity and extends the conventional theory to higher wavenumbers. Graphs. 23 ref.--AA