Abstract
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.
Highlights
Phase separation is a useful technique for fabricating functional binary materials
This method is used in a variety of applications such as in polymer-dispersed liquid crystal films for electro-optical devices [1,2], porous polymeric membranes for separation processes [3,4], the paper, paint and pharmaceutical industries [5,6], biophysics [7,8], nanocomposite materials [9], fabricating electrodes for lithium ion batteries [10], energy storage devices [11], fuel cells [12], scaffolds for tissue engineering [13], and molecular biology to produce protein crystals [14,15]
If phase separation is spontaneous it is said that the binary solution is in the unstable state, and phase separation occurs by spinodal decomposition
Summary
Phase separation is a useful technique for fabricating functional binary materials. This method is used in a variety of applications such as in polymer-dispersed liquid crystal films for electro-optical devices [1,2], porous polymeric membranes for separation processes [3,4], the paper, paint and pharmaceutical industries [5,6], biophysics [7,8], nanocomposite materials [9], fabricating electrodes for lithium ion batteries [10], energy storage devices [11], fuel cells [12], scaffolds for tissue engineering [13], and molecular biology to produce protein crystals [14,15]. The purpose of this paper is to investigate the phase separation behavior of binary solutions that spans both the metastable and unstable regions using the Cahn-Hilliard theory for phase separation incorporating the Flory–Huggins (F–H) free energy function [30]. During spinodal decomposition in the unstable region, high-amplitude structure factors correspond to a ring-shape light-scattering pattern, while such ring is absent during nucleation and growth in the metastable region. We hope that these investigations will give a more complete understanding of using the C–H theory in both the metastable and unstable regions
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