IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Phase Transitions of Macromolecular Microsphere Composite Hydrogels Based on the Stochastic Cahn-Hilliard Equation

  • Oct. 12, 2015
  • 1:15 p.m.
  • LeConte 312

Abstract

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.

© Interdisciplinary Mathematics Institute | The University of South Carolina Board of Trustees | Webmaster
USC