A Derivation Method of <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>χ</mi><mi>c</mi></msup></mrow></math><inline-graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1003-3726-2024-02-0270-I003.png"/><inline-graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1003-3726-2024-02-0270-I003c.png"/></alternatives></inline-formula> and <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>ϕ</mi><mi>c</mi></msup></mrow></math><inline-graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1003-3726-2024-02-0270-I004.png"/><inline-graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/1003-3726-2024-02-0270-I004c.png"/></alternatives></inline-formula>

LU Da-wei; XU Bo-jun

doi:10.14028/j.cnki.1003-3726.2024.23.134

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A Derivation Method of

χ^{c}

and

ϕ^{c}

更新时间：2024-01-25

- A Derivation Method of $χ^{c}$ and $ϕ^{c}$
- Polymer Bulletin Vol. 37, Issue 2, Pages: 270-272(2024)
- 作者机构：
  
  北京化工大学材料科学与工程学院，北京 102299
- 作者简介：
- 基金信息：
- DOI：10.14028/j.cnki.1003-3726.2024.23.134
  CLC：
- Published：20 February 2024，
  
  Received：13 April 2023，
  
  Accepted：23 May 2023
- 稿件说明：
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引用：卢大伟, 徐渤钧. 一种推导相分离热力学中χc与ϕc的方法. 高分子通报, 2024, 37(2), 270–272

Citation: Lu, D. W.; Xu, B. J. A derivation method of χc and ϕc. Polym. Bull. (in Chinese), 2024, 37(2), 270–272
引用：卢大伟, 徐渤钧. 一种推导相分离热力学中χc与ϕc的方法. 高分子通报, 2024, 37(2), 270–272 DOI： 10.14028/j.cnki.1003-3726.2024.23.134.

Citation: Lu, D. W.; Xu, B. J. A derivation method of χc and ϕc. Polym. Bull. (in Chinese), 2024, 37(2), 270–272 DOI： 10.14028/j.cnki.1003-3726.2024.23.134.

A Derivation Method of

χ^{c}

and

ϕ^{c}

PDF Download

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

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与

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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

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与

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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

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and

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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

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and

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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

Keywords

Phase separationCritical pointBasic InequalityFree energy-composition curveDerivatives

references

励杭泉, 武德珍, 张晨．高分子物理．2版．北京: 中国轻工业出版社, 2020.

华幼卿, 金日光．高分子物理．5版．北京: 化学工业出版社, 2019, 94.

吴其晔．高分子凝聚态物理学．北京: 科学出版社, 2012, 246–249.

王德海．高分子物理．北京: 化学工业出版社, 2010.

吴其晔, 张萍, 杨文君．高分子物理学．北京: 高等教育出版社, 2011.

何曼君, 张红东, 陈维孝．高分子物理．3版．上海: 复旦大学出版社, 2007.

赵孝彬, 杜磊, 张小平, 郑剑．聚合物共混物的相容性及相分离．高分子通报, 2001, (4), 75–81.

卢大伟, 徐渤钧．对高分子物理学中混合自由能-组成曲线与相图的讨论．高分子通报, 2023, 36(10), 1356–1361

Rubinstein, M. Colby, R. H．Polymer Physics．励杭泉．北京: 化学工业出版社, 2007.

贺昌城. “高分子物理”课程教学中进行完整数学推导举隅．高分子材料科学与工程, 2010, 26(12), 173–175.

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⁰

A Derivation Method of χc and ϕc

DOI：10.14028/j.cnki.1003-3726.2024.23.134

摘要

Abstract

关键词

Keywords

references

A Derivation Method of $χ^{c}$ and $ϕ^{c}$