Non-linear dynamics of spinodal decomposition

A new approach is proposed to describe the spinodal decomposition, in parti cular, in polymer binary blends. In the framework of this approach, the spi nodal decomposition is described as a relaxation of one-time structure fact or S(q,t) treated as an independent dynamic object (a peculiar two-point or der parameter). The dynamic equation for S(q,t), including the explicit exp ression 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 nu merically. The asymptotic behaviour of S(q,t) at large (from the onset of s pinodal decomposition) times is analytically described. The values obtained for the power-law growth exponent for the large-time peak value and positi on of S(q,t) are in good agreement with experimental data and results of nu merical integration of the Cahn-Hilliard equation.