Quantitative Theory for Critical Conditions of Like-Charge Attraction Between Polarizable Spheres
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913746832588800 |
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| author | Duan, Yanyu Gan, Zecheng |
| author_facet | Duan, Yanyu Gan, Zecheng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_10516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative Theory for Critical Conditions of Like-Charge Attraction Between Polarizable Spheres Duan, Yanyu Gan, Zecheng Soft Condensed Matter Chemical Physics 70E50 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. |
| title | Quantitative Theory for Critical Conditions of Like-Charge Attraction Between Polarizable Spheres |
| topic | Soft Condensed Matter Chemical Physics 70E50 |
| url | https://arxiv.org/abs/2501.10516 |