A computational study of short-range surface-directed phase separation in polymer blends under a linear temperature gradient. (1st December 2015) - Tabatabaieyazdi, Mohammad; Chan, Philip K.; Wu, Jiangning
Abstract: The nonlinear Cahn–Hilliard theory and the Flory-Huggins-de-Gennes theory were used to study numerically the surface-directed phase separation phenomena of a model binary polymer blend quenched into the unstable region of its binary symmetric upper critical solution temperature phase diagram. Short-range surface potential within a square geometry, where one side of the binary polymer blend is exposed to a surface with preferential attraction to one component of the blend that is under a linear temperature gradient along the direction perpendicular to the surface, was integrated into the model. The structure factor analysis showed a faster exponential growth at the early stage of phase separation and a slower growth rate at the intermediate stage with a slope of 0.31 within the bulk, which is consistent with the Lifshitz–Slyozov growth law. The investigation of surface enrichment rate at the surface wall demonstrated faster growth rate at the early stage with the slope of 0.5. This growth rate became slower at the intermediate stage with a slope of 0.13 near the surface. The effect of various temperature gradient values on the surface enrichment rate with constant temperature T 1 * at the surface preferentially attracting one of the polymer components and different temperature T 2 * at the opposite surface, where T 1 *> T 2 *, was studied for the first time. The results showed that the thickness of the wetting layer increased with increasing temperature difference Δ T*, where Δ T *= T 1 *− T 2 *. The structure factor analysis of the surface potential h 1 effect on the phase separation within the bulk close to the surface showed earlier transition time for higher values of h 1 . However, there was no difference observed for transition time within the bulk at distances farther away from the surface. As the surface potential increased, spinodal wave became more visible in the bulk and the transition time from complete wetting to partial wetting occurred at a later time on the surface. Graphical abstract: Highlights: Model composed of Cahn–Hilliard and Flory-Huggins-deGennes theories is solved. Growth is fastest in the early stage of phase separation. Thickness of the wetting layer increased with increasing temperature. Transition time occurs earlier with higher surface potential. Spinodal wave became more visible in the bulk as the surface potential increased.