A model of multiscaling dynamics for spinodal decomposition

A model is developed for analysing small-angle scattering data for systems which are undergoing spinodal decomposition. This model is expressed as an integration of a series of Fourier components of the density fluctuation A(β)sin(βr + ϕ) based on Cahnʹs linear theory of spinodal decomposition. Hence the time evolution of the growth kinetics can be calculated analytically using a multiscaling function. The characteristic crossover phenomenon and the width of the crossover of the scaling function of the structure factor measured by small-angle scattering techniques are predicted to be associated with the maximum spinodal wave number βm and the correlation length ξm, respectively.