一种推导相分离热力学中xc与φc的方法
A Derivation Method of xc and φc
卢大伟 1徐渤钧1
作者信息
- 1. 北京化工大学材料科学与工程学院,北京 102299
- 折叠
摘要
聚合物相分离热力学是高分子物理中重要的教学内容,相图临界点的相关参数xc与φc是该部分理论教学的难点和重点之一.本文基于自由能-组成曲线本身的数学特点,刍议传统推导方法在教学方面的缺陷与不足.运用导数与基本不等式两种基本的数学工具,展现了一种新的xc与φc的推导方法,该法更加简单,角度新颖,利于学生掌握,并加深学生对相分离临界点相关理论的认识和理解.
Abstract
The thermodynamics of polymer phase separation constitutes a crucial topic in polymer physics,and the associated parameters pertaining to the critical point of the phase diagram,namely,xc and φc,present a challenge and a pivotal aspect in this area of study.This paper aims to address the inadequacies and insufficiencies of conventional derivative methods employed in teaching,based on the mathematical properties of the free energy-composition curve itself.We present a new approach to derive xc and φc using two fundamental mathematical tools,derivatives,and elementary inequalities,which not only simplifies the process but also offers a fresh perspective,thereby enhancing students'comprehension and knowledge of the theory associated with the critical point of phase separation.
关键词
相分离/临界点/基本不等式/自由能-组成曲线/导数Key words
Phase separation/Critical point/Basic Inequality/Free energy-composition curve/Derivatives引用本文复制引用
出版年
2024
NETL
NSTL
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