A solution may be in one of three states: stable, unstable, or metastable. If the solution is unstable, phase separation is spontaneous and proceeds by spinodal decomposition. If the solution is metastable, the solution must overcome an activation barrier for phase separation to proceed spontaneously. This mechanism is called nucleation and growth. Manipulating morphology using phase separation has been of great research interest because of its practical use to fabricate functional materials. The Cahn-Hilliard theory, incorporating Flory-Huggins free energy, has been used widely and successfully to model phase separation by spinodal decomposition in the unstable region. This model is used in this paper to mathematically model and numerically simulate the phase separation by nucleation and growth in the metastable state for a binary solution. Our numerical results indicate that Cahn-Hilliard theory is able to predict phase separation in the metastable region but in a region near the spinodal line.

Binary phase polymer solution is interesting in that they expresses double-well local energy behavior, which means phase separation is preferred when condition is right. It is a feature that has been used to fabricate functional polymeric materials such as PDLC films for electro-optical devices (e.g. flat-panel displays and switchable windows). A uniformly mixed solution may be in one of three state: unstable, stable, or metastable. If the solution is unstable, then phase separation is spontaneous and proceeds by spinodal decomposition. If the solution is metastable, then the solution must overcome certain activation barrier for phase separation to proceed spontaneously. The activation barrier is usually the thermal noise or the fluctuation created by some external influence. This mechanism is called nucleation-and-growth. Manipulating morphology of phase separation has been of some great research interest because of its practical use. While spinodal decomposition has been well-studied, there are several other methods to further control morphology. For this thesis, the following methods are considered: double quench, anisotropic quenching with varying temperature or polymerization, surface-directed wetting, and concentration gradient. The methods are carried out within metastable or unstable regions or both. To numerically model, Cahn-Hilliard theory and FloryHuggins’ theory are used. This thesis is to also demonstrate that, present numerical method is very efficient and can work on complex geometry.

Binary phase polymer solution is interesting in that they expresses double-well local energy behavior, which means phase separation is preferred when condition is right. It is a feature that has been used to fabricate functional polymeric materials such as PDLC films for electro-optical devices (e.g. flat-panel displays and switchable windows). A uniformly mixed solution may be in one of three state: unstable, stable, or metastable. If the solution is unstable, then phase separation is spontaneous and proceeds by spinodal decomposition. If the solution is metastable, then the solution must overcome certain activation barrier for phase separation to proceed spontaneously. The activation barrier is usually the thermal noise or the fluctuation created by some external influence. This mechanism is called nucleation-and-growth. Manipulating morphology of phase separation has been of some great research interest because of its practical use. While spinodal decomposition has been well-studied, there are several other methods to further control morphology. For this thesis, the following methods are considered: double quench, anisotropic quenching with varying temperature or polymerization, surface-directed wetting, and concentration gradient. The methods are carried out within metastable or unstable regions or both. To numerically model, Cahn-Hilliard theory and FloryHuggins’ theory are used. This thesis is to also demonstrate that, present numerical method is very efficient and can work on complex geometry.