Kinetics of the droplet formation at the early and intermediate stages of the spinodal decomposition in homopolymer blends - Aleksei Aksimentiev; Robert Hołyst; Krzysztof Moorthi (Macromolecular Theory and Simulations, 2000)
The kinetics of the droplet formation during the spinodal decomposition (SD) of the homopolymer blends has been studied by numerical integration of the Cahn-Hilliard-Cook equation. We have found that the droplet formation and growth occurs when the minority phase volume fraction, fm , approaches the percolation threshold value, fthr = 0.3 ± 0.01. The time for the formation of the disperse droplet morphology (coarsening time) depends only on the equilibrium minority phase volume fraction, fm . fm approaches its equilibrium value logarithmically at the late SD stages, and, therefore, the coarsening time decreases exponentially as the average volume fraction or the quench depth decrease. Since the temporal evolution of the total interfacial area does not depend on the quench conditions and blend morphology, the average droplet size and the droplet number density is determined by the coarsening time. Within the time scale studied, the droplet number density decreases with time as t–0.63±0.03; the average mean curvature decreases as t–0.35±0.05; the average Gaussian curvature decreases as t–0.42±0.03, and the average droplet compactness ˜V/S3/2 where S is the surface area and V is the volume) approaches a spherical limit logarithmically with time. The droplets with larger area have lower compactness and in the low compactness limit their area is a parabolic function of compactness. The size and shape distribution functions have been also investigated.