Force-Extension Curve of an Entangled Polymer Chain: A Superspace Approach

Huan Gong; Jian-Feng Li; Hong-Dong Zhang; An-Chang Shi

doi:10.1007/s10118-021-2623-y

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Force-Extension Curve of an Entangled Polymer Chain: A Superspace Approach

RAPID COMMUNICATION | Updated：2021-07-23

- Force-Extension Curve of an Entangled Polymer Chain: A Superspace Approach
- Chinese Journal of Polymer Science Vol. 39, Issue 11, Pages: 1345-1350(2021)
- Affiliations：
  
  a.The State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
  b.Department of Physics and Astronomy, McMaster University, Hamilton, Ontario Canada L8S 4M1
  c.School of Computer Science and Technology, Fudan University, Shanghai 200433, China
- Author bio：
  
  lijf@fudan.edu.cn (J.F.L.)
  shi@mcmaster.ca (A.C.S.)
- Funds：
- DOI：10.1007/s10118-021-2623-y
  CLC：
- Received：09 May 2021，
  
  Revised：2021-6-16，
  
  Accepted：21 June 2021，
  
  Online First：23 July 2021，
  
  Published：18 September 2021
- Accepted：
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Gong, H.; Li, J. F.; Zhang, H. D.; Shi, A. C. Force-extension curve of an entangled polymer chain: a superspace approach. Chinese J. Polym. Sci. 2021, 39, 1345–1350

Huan Gong, Jian-Feng Li, Hong-Dong Zhang, et al. Force-Extension Curve of an Entangled Polymer Chain: A Superspace Approach[J]. Chinese Journal of Polymer Science, 2021, 39(11): 1345-1350.
Gong, H.; Li, J. F.; Zhang, H. D.; Shi, A. C. Force-extension curve of an entangled polymer chain: a superspace approach. Chinese J. Polym. Sci. 2021, 39, 1345–1350 DOI： 10.1007/s10118-021-2623-y.

Huan Gong, Jian-Feng Li, Hong-Dong Zhang, et al. Force-Extension Curve of an Entangled Polymer Chain: A Superspace Approach[J]. Chinese Journal of Polymer Science, 2021, 39(11): 1345-1350. DOI： 10.1007/s10118-021-2623-y.

摘要

Abstract

The statistical mechanics of an ideal polymer chain entangled with static topological constraints is studied using a superspace approach

in which the probability distribution of the polymer is obtained as solutions of the Fokker-Planck equation in a superspace with an inner structure characterized by the

-generator free group. The theory predicts that the force-extension curve of the polymer under the topological constraints has the generic form

where

is an effective extension. Aside from the elastic term that is linear in

the force-extension curve contains a universal term of the form

. The magnitude of this topological term is determined by the topological charge number

which characterizes the topological nature of the static constraints. The theoretical results are further verified by a scaling analysis based on a blob model of the chain conformations.

关键词

Keywords

references

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