Quantitative Theory for Critical Conditions of Like-Charge Attraction Between Polarizable Spheres

Yanyu Duan; Zecheng Gan

doi:10.1021/acs.jctc.5c00144

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arXiv · 2501.10516

Quantitative Theory for Critical Conditions of Like-Charge Attraction Between Polarizable Spheres

Yanyu Duan·Zecheng Gan

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Abstract

Despite extensive experimental and theoretical efforts, a concise quantitative theory to predict the occurrence of like-charge attraction (LCA) between polarizable spheres remains elusive. In this work, we first derive a novel three-point image formula, based on a key observation that connects the classical Neumann's image principle with the incomplete beta function. This approach naturally yields simple yet precise critical conditions for LCA, with a relative discrepancy of less than $1\%$ compared to numerical simulations, validated across diverse parameter settings. The obtained critical conditions may provide physical insights into various processes potentially involving LCA, such as self-assembly, crystallization, and phase separation across different length scales. Additionally, the new image formula is directly applicable to enhance the efficiency of polarizable force field calculations involving polarizable spheres.

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Yanyu Duan, Zecheng Gan. 2025-01-17. Quantitative Theory for Critical Conditions of Like-Charge Attraction Between Polarizable Spheres. https://doi.org/10.1021/acs.jctc.5c00144

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