On the theory of late-stage phase separation in off-critically quenched binary systems

The late stage of phase separation in off-critically quenched binary systems is studied from an unifying viewpoint by numerically solving not only the kinetic equation for the single droplet distribution function ƒ(R,t) but also the linear equation with the source term for the structure function S(k,t), both of which were recently derived by the present authors to study the dynamics of phase separation. The scaling behaviors, ƒ(R,t) ≈ 〈R〉(t)−4FL(R〈R〉(t)) and S(k,t) ≈ kM(t)−3ΨL(kkM(t)), are thus recovered, where 〈R〉(t) is the average droplet radius, and kM(t) the peak position of S(k,t) as a function of k. The temporal power behavior of 〈R〉 and kM are also shown to agree with those expected on the basis of the Lifshitz-Slyozov-Wagner theory. The universal features of the time-independent scaling functions FL(ρ) and ΨL(x) are thus investigated explicitly, including their volume fraction dependence, and the x4 dependence of ΨL(x) for small x. The results are in good agreement with experiments for both scaling functions.