Entropic force of a fluctuating semiflexible polymer exerted on a nanoparticle

doi:10.1088/1674-1056/ae2d31

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.

Keywords: semiflexible chain entropic force perturbation theory Euler buckling

Received: 17 September 2025
Revised: 04 December 2025
Accepted manuscript online: 16 December 2025

PACS:	61.82.Pv	(Polymers, organic compounds)
	82.35.Gh	(Polymers on surfaces; adhesion)

Fund: 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.

Corresponding Authors: Kai Li
E-mail: likai@xju.edu.cn

Cite this article:

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 2026 Chin. Phys. B 35 046101

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