{
  "abstract": "Predicting the relationship between surface charge density and electrostatic potential for spherical particles remains a fundamental challenge in colloid science. Because the governing non-linear Poisson--Boltzmann equation lacks a general exact analytical solution, researchers typically rely on numerical calculations or various semi-empirical approximations. In this paper, we overcome these limitations by developing a dual-asymptotic framework that provides explicit, closed-form expressions for this surface charge--potential relationship across the entire spectrum of particle curvature. For weakly curved systems, where the Debye length $λ_D$ is much smaller than the particle radius $R$ ($λ_D/R \\ll 1$), a formal mathematical derivation rigorously establishes the Ohshima--Healy--White formula as an exact regular perturbation expansion. Conversely, for highly curved spheres ($R/λ_D \\ll 1$), we employ singular perturbation analysis using the scaled particle radius as the small parameter. This approach provides a first-principles mathematical justification for the spherical Debye--Hückel theory, proving that its leading-order expansion remains asymptotically exact within the full non-linear Poisson--Boltzmann framework due to the geometric deactivation of non-linearity. Crucially, we map the exact limits of this geometric regulation, demonstrating how non-linear screening re-emerges as the particle radius increases, with the breakdown threshold governed by the interplay between curvature and surface charge density.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03613",
  "author_total": 2,
  "authors": [
    {
      "name": "Olga I. Vinogradova"
    },
    {
      "name": "Elena F. Silkina"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5534yj8zdbtnr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03613",
  "fulltext_url": null,
  "id": "5534yj8zdbtnr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03613",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.soft"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "openalex",
      "1606|Electrostatics and Colloid Interactions"
    ]
  ],
  "openalex": "W7220417937",
  "pdf_url": "https://arxiv.org/pdf/2610.03613",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5534yj8zdbtnr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03613",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03613"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Surface Charge--Potential Relation for Spherical Particles in Electrolyte Solutions",
  "title_text": "Surface Charge--Potential Relation for Spherical Particles in Electrolyte Solutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/5534yj8zdbtnr",
  "venue": "arXiv",
  "versions": []
}