Non-linear dynamics of spinodal decomposition

Abstract

A new approach is proposed to describe the spinodal decomposition, in particular, in polymer binary blends. In the framework of this approach, the spinodal decomposition is described as a relaxation of one-time structure factor S(q,t) treated as an independent dynamic object (a peculiar two-point order parameter). The dynamic equation for S(q,t), including the explicit expression for the corresponding effective kinetic coefficient, is derived. In the first approximation this equation is identical to the Langer equation. We first solved it both in terms of higher transcendental functions and numerically. The asymptotic behaviour of S(q,t) at large (from the onset of spinodal decomposition) times is analytically described. The values obtained for the power-law growth exponent for the large-time peak value and position of S(q,t) are in good agreement with experimental data and results of numerical integration of the Cahn-Hilliard equation.