Geometrical Properties and Interface Dynamics: Time Evolution of Spinodal Interface in a Binary Polymer Mixture at the Critical Composition

Abstract

The time-evolution of a three-dimensional (3D), bicontinuous interface of a phase-separated polymer mixture in the late stage spinodal decomposition (SD) process has been studied by laser scanning confocal microscopy (LSCM) and time-resolved light scattering. The time evolution of the interface between two coexisting phases developed via SD (“spinodal interface”) was quantitatively captured in 3D by using LSCM. On the basis of the differential geometry, probability densities of the local curvatures, i.e., the mean and Gaussian curvatures, of the spinodal interface have been experimentally evaluated. We found that a large portion of the interface formed in the late stage SD consists of a saddle-shaped surface, i.e., a hyperbolic surface. The probability densities were used to predict the dynamics of the spinodal interface. Two basic mechanisms are found to be important for the system to reduce interface area during the late stage SD. In addition, the probability densities of the curvatures at various times were successfully scaled by a time-dependent characteristic wavenumber, i.e., interface area per unit volume. This clearly proves that the time evolution of the spinodal interface, which characterizes the local structure of the system, is dynamically self-similar.