Analytical sphere–thin rod interaction potential

Junwen Wang; Shengfeng Cheng

doi:10.1140/epje/s10189-025-00480-9

2023 Impact factor 1.8

Soft Matter and Biological Physics

Open Access

Eur. Phys. J. E (2025) 48: 15
https://doi.org/10.1140/epje/s10189-025-00480-9

Regular Article - Soft Matter

Analytical sphere–thin rod interaction potential

Junwen Wang¹^,2^,3 and Shengfeng Cheng¹^,2^,3^,4^a

¹ Department of Mechanical Engineering, Virginia Tech, 24061, Blacksburg, VA, USA
² Center for Soft Matter and Biological Physics, Virginia Tech, 24061, Blacksburg, VA, USA
³ Macromolecules Innovation Institute, Virginia Tech, 24061, Blacksburg, VA, USA
⁴ Department of Physics, Virginia Tech, 24061, Blacksburg, VA, USA

^a chengsf@vt.edu

Received: 27 October 2024
Accepted: 28 February 2025
Published online: 7 April 2025

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 $a + 0.787 σ$ $a+0.787\sigma$ , where a is the radius of the sphere and $σ$ $\sigma$ is the unit of length of the Lennard–Jones potential. Furthermore, the adhesion between the two is found to scale with $\sqrt{a}$ $\sqrt{a}$ .

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epje/s10189-025-00480-9.

© The Author(s) 2025

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