## On the Teaching of Modern Polymer Physics: Free Energy of a Single Polymer Chain in Polymer Solutions

Liu Yi-Xin, Li Jianfeng,, Zhang Hongdong

Abstract

Free energy of a single polymer chain in polymer solutions is critical for the derivation and understanding of the scaling law between the polymer size and its degree of polymerization. This work provides a novel derivation of the single-chain free energy based on the Flory lattice model.

Keywords： Single chain ; Polymer solution ; Scaling law ; Free energy

Liu Yi-Xin. On the Teaching of Modern Polymer Physics: Free Energy of a Single Polymer Chain in Polymer Solutions. University Chemistry[J], 2022, 37(1): 2103041-0 doi:10.3866/PKU.DXHX202103041

## 1 修正高斯链模型简介

${\mathit{\Phi }} ({\bf{h}}, N) = {{\mathit{\Phi }} _0}({\bf{h}}, N){\mathit{\Omega }} {{(}}h{{)}}{\rm{\exp}} [ - \frac{{E(h)}}{{{k_{\rm{B}}}T}}]$

${\mathit{\Omega }} (h) \approx \prod\nolimits_{k = 1}^N {(1 - k{l^3}/{h^3})} \approx \exp [ - {l^3}{N^2}/2{h^3} - {l^6}{N^3}/6{h^6}].$

$F(R)/{k_{\rm{B}}}T = \frac{{3{R^2}}}{{2N{l^2}}} + \frac{{{N^2}\tau {v_0}}}{{2{R^3}}} + \frac{{{N^3}v_0^2}}{{6{R^6}}} + {\rm{const}}$

## 3 单链自由能

### 图1

${F}_{单链}={F}_{\rm{G}}+{F}_{\rm{s}}+\Delta {F}_{\rm{m}}$

## 参考文献 原文顺序 文献年度倒序 文中引用次数倒序 被引期刊影响因子

Doi M. Introduction to Polymer Physics Oxford, UK: Clarendon Press, 1996, pp. 10- 16.

Rubinstein M. ; Colby R. H. Polymer Physics Oxford, UK: Oxford University Press, 2003, pp. 25- 101.

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