KINETICALLY STABLE STRUCTURES IN THE NONLINEAR-THEORY OF SPINODAL DECOMPOSITION

A nonlinear diffusion equation is used to study the spinodal decomposition of binary polymer mixtures. The structure of steady‐state solutions is analyzed. The free energy of the system for the solutions is shown to be a nonincreasing time function. The solution with the minimum free energy is the only stable solution and corresponds to complete phase separation in the system. A numerical analysis shows that transition to complete equilibrium takes place through a succession of fast concentration structure changes interspersed by periods in which the process is abruptly showed down. The free energy of the system is almost constant in the kinetically stable periods. All these facts indicate a relaxation process of an absolutely new type. Slow variables are introduced to describe the spinodal decomposition in macroscopic regions. These variables govern the spatial transformation of the forms and sizes of microphases. The perturbation theory is used to derive the equations for slow variables. The final relations of the simplest type give an exponential time dependence of the average size of a microphase. The problem of a contact of two pure components that are not compatible in the entire composition range is set. Copyright © 1990 John Wiley & Sons, Inc.