Exact Screening-Ranged Expansions for Many-Body Electrostatics
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| author | Siryk, Sergii V. Rocchia, Walter |
| author_facet | Siryk, Sergii V. Rocchia, Walter |
| contents | We present an exact many-body framework for electrostatic interactions among $N$ arbitrarily charged spheres in an electrolyte, modeled by the linearized Poisson--Boltzmann equation. Building on a spectral analysis of nonstandard Neumann--Poincaré-type operators introduced in a companion mathematical work arXiv:2512.08684, we construct convergent screening-ranged series for the potential, interaction energy, and forces, where each term is associated with a well-defined Debye--Hückel screening order and can be obtained evaluating an analytical expression rather than numerically solving an infinitely dimensional linear system. This formulation unifies and extends classical and recent approaches, providing a rigorous basis for electrostatic interactions among heterogeneously charged particles (including Janus colloids) and yielding many-body generalizations of analytical explicit-form results previously available only for two-body systems. The framework captures and clarifies complex effects such as asymmetric dielectric screening, opposite-charge repulsion, and like-charge attraction, which remain largely analytically elusive in existing treatments. Beyond its fundamental significance, the method leads to numerically efficient schemes, offering a versatile tool for modeling colloids and soft/biological matter in electrolytic solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09421 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact Screening-Ranged Expansions for Many-Body Electrostatics Siryk, Sergii V. Rocchia, Walter Soft Condensed Matter Mathematical Physics Biological Physics Chemical Physics Computational Physics We present an exact many-body framework for electrostatic interactions among $N$ arbitrarily charged spheres in an electrolyte, modeled by the linearized Poisson--Boltzmann equation. Building on a spectral analysis of nonstandard Neumann--Poincaré-type operators introduced in a companion mathematical work arXiv:2512.08684, we construct convergent screening-ranged series for the potential, interaction energy, and forces, where each term is associated with a well-defined Debye--Hückel screening order and can be obtained evaluating an analytical expression rather than numerically solving an infinitely dimensional linear system. This formulation unifies and extends classical and recent approaches, providing a rigorous basis for electrostatic interactions among heterogeneously charged particles (including Janus colloids) and yielding many-body generalizations of analytical explicit-form results previously available only for two-body systems. The framework captures and clarifies complex effects such as asymmetric dielectric screening, opposite-charge repulsion, and like-charge attraction, which remain largely analytically elusive in existing treatments. Beyond its fundamental significance, the method leads to numerically efficient schemes, offering a versatile tool for modeling colloids and soft/biological matter in electrolytic solution. |
| title | Exact Screening-Ranged Expansions for Many-Body Electrostatics |
| topic | Soft Condensed Matter Mathematical Physics Biological Physics Chemical Physics Computational Physics |
| url | https://arxiv.org/abs/2512.09421 |