Phase transitions of macromolecular microsphere composite hydrogels based on the stochastic Cahn-Hilliard equation
Phase transitions of macromolecular microsphere composite hydrogels based on the stochastic Cahn-Hilliard equation
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DOI：
10.1016/j.jcp.2014.11.032
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发表时间：
2015-02
期刊：
影响因子：
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通讯作者：
Xiao Li;Guanghua Ji;Hui Zhang
中科院分区：
文献类型：
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作者：
Xiao Li;Guanghua Ji;Hui Zhang
利用随机Cahn-Hilliard方程模拟了随机扰动下大分子微球复合材料（MMC）水凝胶的相变。基于Flory-Huggins晶格模型和Boltzmann熵定理，我们建立了一套适用于MMC水凝胶网络结构的网状自由能模型。考虑到随机因素，采用时变Ginzburg-Landau （TDGL）介观模拟方法，建立随机Cahn-Hilliard方程，本文称之为MMC-TDGL方程。方程中的随机项适当地构造以满足涨落耗散定理，并在空间网格上离散化以进行模拟。采用半隐式差分格式对MMC-TDGL方程进行数值求解。在不同参数下进行了数值实验。结果与物理现象一致，验证了随机项的良好模拟效果。
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.