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Title: Phase transitions of macromolecular microsphere composite hydrogels based on the stochastic Cahn–Hilliard equation

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.

Authors:
; ;
Publication Date:
OSTI Identifier:
22382185
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 283; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPOSITE MATERIALS; COMPUTERIZED SIMULATION; ENTROPY; FLUCTUATIONS; FREE ENERGY; GINZBURG-LANDAU THEORY; HYDROGELS; PHASE TRANSFORMATIONS; RANDOMNESS; STOCHASTIC PROCESSES; TIME DEPENDENCE

Citation Formats

Li, Xiao, E-mail: lixiao1228@163.com, Ji, Guanghua, E-mail: ghji@bnu.edu.cn, and Zhang, Hui, E-mail: hzhang@bnu.edu.cn. Phase transitions of macromolecular microsphere composite hydrogels based on the stochastic Cahn–Hilliard equation. United States: N. p., 2015. Web. doi:10.1016/J.JCP.2014.11.032.
Li, Xiao, E-mail: lixiao1228@163.com, Ji, Guanghua, E-mail: ghji@bnu.edu.cn, & Zhang, Hui, E-mail: hzhang@bnu.edu.cn. Phase transitions of macromolecular microsphere composite hydrogels based on the stochastic Cahn–Hilliard equation. United States. doi:10.1016/J.JCP.2014.11.032.
Li, Xiao, E-mail: lixiao1228@163.com, Ji, Guanghua, E-mail: ghji@bnu.edu.cn, and Zhang, Hui, E-mail: hzhang@bnu.edu.cn. Sun . "Phase transitions of macromolecular microsphere composite hydrogels based on the stochastic Cahn–Hilliard equation". United States. doi:10.1016/J.JCP.2014.11.032.
@article{osti_22382185,
title = {Phase transitions of macromolecular microsphere composite hydrogels based on the stochastic Cahn–Hilliard equation},
author = {Li, Xiao, E-mail: lixiao1228@163.com and Ji, Guanghua, E-mail: ghji@bnu.edu.cn and Zhang, Hui, E-mail: hzhang@bnu.edu.cn},
abstractNote = {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.},
doi = {10.1016/J.JCP.2014.11.032},
journal = {Journal of Computational Physics},
number = ,
volume = 283,
place = {United States},
year = {Sun Feb 15 00:00:00 EST 2015},
month = {Sun Feb 15 00:00:00 EST 2015}
}
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