No abstract

The influence of spatial temperature gradients on the morphological development in polymer solutions undergoing thermally induced phase separation was studied using mathematical modeling and computer simulation. The one‐dimensional mathematical 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 anisotropic morphology depends on the overall 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 the 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 temperature regions are still in the early stage of SD. The presence of a temperature gradient during thermally induced phase separation introduces spatial variations in the change of chemical potential, which is the driving force for phase separation. These numerical results provide a better understanding of the control and optimization during the fabrication of anisotropic polymeric materials using the thermally induced phase separation technique.

This paper studied the polymerization‐induced phase separation phenomenon (spinodal decomposition) in a model binary polymer solution under a linear spatial temperature gradient for the purpose of fabricating anisotropic polymeric materials by using mathematical modeling and computer simulation. Reaction kinetics were incorporated with the non‐linear Cahn‐Hilliard theory and the Flory‐Huggins free energy expression in the model. Moreover, the slow mode theory and Rouse law were used to account for polymer diffusion. It was found that an anisotropic morphology was obtained when a temperature gradient was imposed along the polymer solution sample. The direction of the structural anisotropy, however, depended significantly on the overall phase separation time. The presence of a temperature gradient along the polymer solution sample generated a spatial variation in polymerization rate, which resulted in a spatial variation of quench depth. Consequently, at a given instant, the phase separation at different locations of the polymer solution was at different stages of spinodal decomposition. The droplet size formed along the polymer solution was therefore dependent on the polymerization rate, the quench depth and the stage of spinodal decomposition. Furthermore, the spatial temperature gradient produced a spatial variation in the process induction time, which contains the polymerization induction time and phase separation induction time. It was also found that the polymerization induction time played a significant role on the spatial variation in the overall process induction time.image