The surface-directed phase separation (SDPS) phenomena of a model binary polymer blend quenched into the unstable region of its binary symmetric upper critical solution temperature phase diagram is numerically investigated using a mathematical model composed of the nonlinear Cahn–Hilliard (CH) theory for phase separation along with the Flory–Huggins–de Gennes (FHdG) free energy functional. The SDPS occurs in a square domain with a linear temperature gradient along the horizontal direction and with all sides having short range surface potential h1. The effects of different quench depth, diffusion coefficient, surface potential, and temperature gradient were studied numerically. The numerical results indicate that there is a simultaneous competition between the four surfaces in attracting the preferred polymer. The side with a higher surface potential would win the competition against the side with a lower surface attraction in the case of a uniform quench. The numerical results also indicated a later transition time for higher values of h1. As surface potential increased, the transition time from complete wetting to partial wetting occurred at a later time on the surface. The impact of different temperature gradient ΔT*/Δx* values on the surface enrichment rate with fixed temperature at one surface and higher temperature at the opposite surface was studied for the first time within a multiple surface potential set up. The results showed that higher values of ΔT*/Δx* increased the growth rate of the preferred polymer on the surface adding to the thickness of the wetting layer. The transition time from complete wetting to partial wetting occurred slightly later at the lower temperature side.
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