Numerical Simulation of Phase Separation Kinetic of Polymer Solutions Using the Spectral Discrete Cosine Transform Method

ABSTRACT

A spectral discrete cosine transform (DCT) method was used to solve numerically the spatio-temporal nonlinear Cahn-Hilliard equation for a temperature-induced phase separation process of a polymer solution. The properties of a high molecular weight polystyrene solution were used in the model to reflect the behavior of a real world polymer system. Based on the value of the initial concentration, three different final morphologies of the phase separated system, granular, interconnected, and microcellular, were identified. It was shown that the initial concentration is the main factor to determine the high rate of the phase separation when the phase separation time is the primary desired parameter. The degree of phase separation, as a quantitative measure of the phase separation process, indicates the rate and amount of separated polymer material for practical applications. The model is capable of providing quantitative information of morphology evolution during phase separation processes for microstructure control purposes. The structure factor profile was extracted as a theoretical output that enables comparison with scattering experiments observations as the finger-print of phase separation morphological evolution. It is shown that the DCT method is a very suitable and feasible method for solution of the nonlinear partial differential equation of phase separation kinetics.

KEYWORDS:

• Cahn-Hilliard theory
• Discrete cosine transform
• Flory-Huggins
• Polystyrene/cyclohexane
• Spectral method
• Temperature-induced phase separation