The time-dependent Ginzburg-Landau (TDGL) mesoscopic method is utilized to simulate the phase separation of the poly($N$-isopropylacrylamide)–clay nanocomposite hydrogel in the three-dimensional case, where the Cahn-Hilliard-Cook equation with a proposed free energy, which consists of the stretching and mixing energy based on Flory's mean theory, is considered. The main features of the presently proposed model include the following: (i) the proposed free energy consists of both the stretching and mixing energy; (ii) the processes of polymer chains detaching from and reattaching on crosslinks are considered in the proposed free energy; (iii) polymer chains have inhomogeneous chain lengths, which are divided into different types. A stabilized semi-implicit difference scheme is used to numerically solve the corresponding Cahn-Hilliard-Cook equation. Numerical results show the process of the phase separation and are consistent with morphology of the nanocomposite hydrogel.

• Received 29 December 2019
• Revised 12 March 2020
• Accepted 28 April 2020

DOI:https://doi.org/10.1103/PhysRevE.101.062118