改进的Marquardt算法研究制膜液三元相图

Improved Marquart algorithm in studying on ternary phase diagram of casting solution

在制膜液三元相图的计算研究中,非线性方程组解经常出现无意义解。为了避免该问题,本工作以Flory-Huggins理论为基础,推导出浊点线(binodal)方程和旋节线(spinodal)方程,先确定富相中聚合物体积分数为独立变量,然后应用更新雅可比矩阵及其逆的技巧,并应用本工作改进了的Marquardt算法,得出非线性方程组的有意义解。本工作还推导出成膜过程连续相组成迹线(pathline)方程。通过计算绘出了浊点线、旋节线和连续相组成迹线,并用于分析聚合物膜的成膜机理。

Meaningless solutions for a nonlinear equations set were often appeared in studying on ternary phase diagram of casting solution. In order to avoid the problem, a new method, improved Marquart algorithm, was developed. The method, based on the modified Flory-Huggins theory, derived binodal curve equation and spinodal curve equation. It firstly determined the volume fraction of polymer in rich phase as an independent variable and then, by means of renewing Jacob matrix and its inverse and improved Marquart algorithm, obtained the solution which was in agreement with the nonlinear equations set for the ternary phase diagram of casting solution. For a membrane-forming process, continuous phase composition pathline equation was derived. Binodal curve, spinodal curve and continuous phase composition pathline were drawn for the use of analyzing the mechanism of membrane formation.