Analytical sphere–thin rod interaction potential

IF 1.8 4区物理与天体物理 Q4 CHEMISTRY, PHYSICAL

The European Physical Journal E Pub Date : 2025-04-07 DOI:10.1140/epje/s10189-025-00480-9

Junwen Wang, Shengfeng Cheng

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Abstract

A compact analytical form is derived through an integration approach for the interaction between a sphere and a thin rod of finite and infinite lengths, with each object treated as a continuous medium of material points interacting by the Lennard-Jones 12-6 potential and the total interaction potential as a summation of the pairwise potential between material points on the two objects. Expressions for the resultant force and torque are obtained. Various asymptotic limits of the analytical sphere–rod potential are discussed. The integrated potential is applied to investigate the adhesion between a sphere and a thin rod. When the rod is sufficiently long and the sphere sufficiently large, the equilibrium separation between the two (defined as the distance from the center of the sphere to the axis of the rod) is found to be well approximated as \(a+0.787\sigma \), where a is the radius of the sphere and \(\sigma \) is the unit of length of the Lennard–Jones potential. Furthermore, the adhesion between the two is found to scale with \(\sqrt{a}\).

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分析球-薄杆相互作用势

通过积分法得出了球体与有限长度和无限长度细杆之间相互作用的简洁分析形式，每个物体都被视为由通过伦纳德-琼斯 12-6 势相互作用的材料点组成的连续介质，总的相互作用势是两个物体上材料点之间成对势能的总和。得出了结果力和扭矩的表达式。讨论了分析球杆势的各种渐近极限。将积分势应用于研究球体和细杆之间的粘附。当杆足够长而球体足够大时，发现两者之间的平衡分离（定义为球体中心到杆轴线的距离）近似为\(a+0.787\sigma \)，其中 a 是球体的半径，\(\sigma \)是伦纳德-琼斯势的长度单位。此外，我们还发现两者之间的粘附力与\(\sqrt{a}\)成比例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

The European Physical Journal E CHEMISTRY, PHYSICAL-MATERIALS SCIENCE, MULTIDISCIPLINARY

CiteScore

2.60

自引率

5.60%

发文量

审稿时长

3 months

期刊介绍： EPJ E publishes papers describing advances in the understanding of physical aspects of Soft, Liquid and Living Systems. Soft matter is a generic term for a large group of condensed, often heterogeneous systems -- often also called complex fluids -- that display a large response to weak external perturbations and that possess properties governed by slow internal dynamics. Flowing matter refers to all systems that can actually flow, from simple to multiphase liquids, from foams to granular matter. Living matter concerns the new physics that emerges from novel insights into the properties and behaviours of living systems. Furthermore, it aims at developing new concepts and quantitative approaches for the study of biological phenomena. Approaches from soft matter physics and statistical physics play a key role in this research. The journal includes reports of experimental, computational and theoretical studies and appeals to the broad interdisciplinary communities including physics, chemistry, biology, mathematics and materials science.