# 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}

}