Entropic force of a fluctuating semiflexible polymer exerted on a nanoparticle

doi:10.1088/1674-1056/ae2d31

中国物理B ›› 2026, Vol. 35 ›› Issue (4): 46101-046101.doi: 10.1088/1674-1056/ae2d31

Entropic force of a fluctuating semiflexible polymer exerted on a nanoparticle

Shi-Qiang Li(李世强)†, Yu-Shan Zheng(郑玉山)†, Xiao-Jing Wan(万晓静), and Kai Li(李凯)‡

College of Mechanical Engineering, Xinjiang University, Urumqi 830002, China

收稿日期:2025-09-17 修回日期:2025-12-04 接受日期:2025-12-16 发布日期:2026-04-07
通讯作者: Kai Li E-mail:likai@xju.edu.cn
基金资助:
This work was financially supported by Xinjiang Autonomous Region Science and Technology Programme of China (Grant No. 2024B04007-2), Xinjiang Tianchi PhD Project (Grant No. TCBS202113), the Natural Science Foundation of Xinjiang Autonomous Region of China (Grant No. 2022D01C34), and Xinjiang Basic Research Funds for Universities (Grant No. XJEDU2022P017). The authors thank Professor Ji-Zeng Wang for his revision and suggestions.

Entropic force of a fluctuating semiflexible polymer exerted on a nanoparticle

Shi-Qiang Li(李世强)†, Yu-Shan Zheng(郑玉山)†, Xiao-Jing Wan(万晓静), and Kai Li(李凯)‡

College of Mechanical Engineering, Xinjiang University, Urumqi 830002, China

Received:2025-09-17 Revised:2025-12-04 Accepted:2025-12-16 Published:2026-04-07
Contact: Kai Li E-mail:likai@xju.edu.cn
Supported by:
This work was financially supported by Xinjiang Autonomous Region Science and Technology Programme of China (Grant No. 2024B04007-2), Xinjiang Tianchi PhD Project (Grant No. TCBS202113), the Natural Science Foundation of Xinjiang Autonomous Region of China (Grant No. 2022D01C34), and Xinjiang Basic Research Funds for Universities (Grant No. XJEDU2022P017). The authors thank Professor Ji-Zeng Wang for his revision and suggestions.

摘要/Abstract

摘要： This study theoretically investigates the force exerted on a nanoparticle (NP) by a clamped semiflexible chain in solution. The force exerted by the semiflexible chain on the NP is related to the chain's conformational entropy, known as the entropic force. Under the weakly bending approximation, we derive an analytical formula for the entropic force using perturbation theory. This force can be divided into two components: parallel ($f_{\rho }$) and perpendicular ($f_{z} $, lifting the NP) to the initial vector at the clamped end. These two components are correlated with the local slope of the NP's cross-section, with the component $f_{z} $ additionally linked to the local curvature. We compare the magnitude of force $f_{z} $ with the Euler buckling threshold $f_{\rm c} $. The study reveals that as the chain becomes more compressed, $f_{z} $ initially peaks at a value exceeding the mechanical limit and subsequently decreases to a steady-state value lower than $f_{\rm c} $. This behavior significantly differs from the entropic force derived under flat wall confinement. In three dimensions, $f_{z} $ always stays below the Euler buckling threshold and in two dimensions it is larger than $f_{\rm c} $ for most of the parameter space.

关键词: semiflexible chain, entropic force, perturbation theory, Euler buckling

Abstract: This study theoretically investigates the force exerted on a nanoparticle (NP) by a clamped semiflexible chain in solution. The force exerted by the semiflexible chain on the NP is related to the chain's conformational entropy, known as the entropic force. Under the weakly bending approximation, we derive an analytical formula for the entropic force using perturbation theory. This force can be divided into two components: parallel ($f_{\rho }$) and perpendicular ($f_{z} $, lifting the NP) to the initial vector at the clamped end. These two components are correlated with the local slope of the NP's cross-section, with the component $f_{z} $ additionally linked to the local curvature. We compare the magnitude of force $f_{z} $ with the Euler buckling threshold $f_{\rm c} $. The study reveals that as the chain becomes more compressed, $f_{z} $ initially peaks at a value exceeding the mechanical limit and subsequently decreases to a steady-state value lower than $f_{\rm c} $. This behavior significantly differs from the entropic force derived under flat wall confinement. In three dimensions, $f_{z} $ always stays below the Euler buckling threshold and in two dimensions it is larger than $f_{\rm c} $ for most of the parameter space.

Key words: semiflexible chain, entropic force, perturbation theory, Euler buckling

中图分类号: (Polymers, organic compounds)

61.82.Pv

82.35.Gh (Polymers on surfaces; adhesion)

Shi-Qiang Li(李世强), Yu-Shan Zheng(郑玉山), Xiao-Jing Wan(万晓静), and Kai Li(李凯). Entropic force of a fluctuating semiflexible polymer exerted on a nanoparticle[J]. 中国物理B, 2026, 35(4): 46101-046101.

Shi-Qiang Li(李世强), Yu-Shan Zheng(郑玉山), Xiao-Jing Wan(万晓静), and Kai Li(李凯). Entropic force of a fluctuating semiflexible polymer exerted on a nanoparticle[J]. Chin. Phys. B, 2026, 35(4): 46101-046101.

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Entropic force of a fluctuating semiflexible polymer exerted on a nanoparticle

Entropic force of a fluctuating semiflexible polymer exerted on a nanoparticle

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