A Computational Study into Thermally Induced Phase Separation in Polymer Solutions under a Temperature Gradient

Abstract

The influence of spatial temperature on the morphological development in polymer solutions undergoing thermally induced phase separation was studied using mathematical modeling and computer simulation. The one-dimensional mathermatical model describing this phenomenon incorporates the nonlinear Cahn-Hilliard theory for spinodal decomposition (SD), the Flory-Huggins theory for polymer solution thermodynamics, and the slow-mode theory and Rouse-law for polymer diffusion. The resulting governing equation and auxiliary conditions were solved using the Galerkin finite element method. The temporal evolution of the spatial concentration profile from the computer simulation illustrates that an anisotropic morphology (see Figure) results when a temperature gradient is maintained along the polymer solution sample. The final anisotorpic morphology depends on the overali phase separation time. If phase separation is terminated at very early stages, smaller (larger droplets are formed in the lower (higher) temperature regions due to be deep (shallow) quench effect. On the other hand, if phase separation is allowed to proceed for a long period of time. then larger droplets are formed in the low-temperature regions, whereas smaller droplets are developed at higher temperatures. This is due to the fact that the low-temperature regions have entered the late stage of SD. while the high temperture regions are still in the early stage of SD.The presence of a temperature gradient during thermally induced phase separation introduced spatial variations in the change of chemical potential, which is the driving force for phase separation. These numerical results provide a better understanding or the control and optimization during the fabrication of anisotropic polymeric materials using the thermally induced phase separation technique.