Phase transitions of macromolecular microsphere composite hydrogels based on the stochastic Cahn-Hilliard equation

We use the stochastic Cahn-Hilliard equation to simulate the phase transitions of the macromolecular microsphere composite (MMC) hydrogels under a random disturbance. Based on the Flory-Huggins lattice model and the Boltzmann entropy theorem, we develop a reticular free energy suit for the network structure of MMC hydrogels. Taking the random factor into account, with the time-dependent Ginzburg-Landau (TDGL) mesoscopic simulation method, we set up a stochastic Cahn-Hilliard equation, designated herein as the MMC-TDGL equation. The stochastic term in the equation is constructed appropriately to satisfy the fluctuation-dissipation theorem and is discretized on a spatial grid for the simulation. A semi-implicit difference scheme is adopted to numerically solve the MMC-TDGL equation. Some numerical experiments are performed with different parameters. The results are consistent with the physical phenomenon, which verifies the good simulation of the stochastic term.