{
  "abstract": "The non-Arrhenius crossover in the dielectric relaxation of liquid water near 35-45 • C has been documented for four decades. No existing model predicts the crossover temperature without a fitted parameter. We show that the crossover occurs at a topological threshold ρ * = 4 ln 2, derived from the 4-simplex (K5) and not adjusted. A periodic table of K5 hydrides (CH4, NH3, H2O, HF and their third-row analogues) reveals that water is the only simple hydride combining a permanent dipole with an effective hydrogen-bond density ρ above the threshold. The crossover at ∼ 40 • C is a direct consequence of this unique position. We test the universality of ρ * on a database of 11 hydrogen-bonding liquids with published temperature-dependent dielectric relaxation data. Using the measured number of hydrogen bonds per molecule nHB as the effective density ρ, the threshold classifies 10 of 11 liquids correctly: B19 • Regime II (ρ * < ρ < 2ρ *): cooperative. Water, formamide: 2/2. • Regime I (ρ < ρ *): individual. DMF, DMA, MeOH, EtOH, PrOH, DMSO, CH3CN: 7/7. • Regime III (ρ > 2ρ *): vitrification. Glycerol: 1/1. The single exception is N-methylformamide (NMF, nHB = 2.0 < ρ * , cooperative). Neutron diffraction shows NMF forms linear chains, not triangular clusters: its cooperativity arises from sequential bond breakage, a mechanism distinct from K5 face saturation. The gap between the lowest cooperative ρ (formamide, 3.08) and the highest individual ρ (ethanol, 1.5) straddles ρ * = 2.773 with no overlap. All nHB values are sourced from neutron diffraction or molecular dynamics; all τ (T) classifications are from the original authors. No existing model (Tanaka, Stanley, Poole) extends beyond water. D2O (nHB = 3.76) and ethylene glycol (nHB = 3.0-3.7) are predicted to show cooperative relaxation. Both are testable immediately. The threshold also predicts a critical concentration in water-alcohol mixtures: the non-Arrhenius crossover in τ (T) should disappear at x * MeOH ≈ 0.35 (25 • C) in water-methanol, and x * EtOH ≈ 0.39 in water-ethanol. B20 In the (T, nHB) plane, the cooperative-individual boundary is a horizontal line at nHB = ρ * , regardless of how nHB is varied (temperature, concentration, or pressure). Four K5 constants, together with one measured input (f coord), predict the relaxation time τ of 6 hydrides with τ free derived from geometry, and of 5 further molecules across three decades (3-1500 ps). All 11 predictions fall within a factor 3. B17 Companion script: 123 tests, 20 blocks, all PASS.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jean-Baptiste Blatiere"
    },
    {
      "name": "Jean-Baptiste BLATIERE",
      "orcid": "0009-0004-7901-5957"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eky5zffnmps37.bib",
  "cited_by": 0,
  "doi": "10.26434/chemrxiv.15001225/v2",
  "fulltext_url": null,
  "id": "eky5zffnmps37",
  "issns": [],
  "landing_url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15001225/v2",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2505|Material Dynamics and Properties"
    ]
  ],
  "openalex": "W7140117892",
  "pdf_url": "https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15001225/v2",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": "American Chemical Society (ACS)",
  "ris": "https://research.draconitic.com/paper/eky5zffnmps37.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "10.26434/chemrxiv.15001225",
      "source": "chemrxiv",
      "url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15001225/v2"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "openalex:2505|Material Dynamics and Properties",
      "subfield": "materials-polymers"
    }
  ],
  "title": "Face saturation at ρ * = 4 ln 2: a universal threshold separating cooperative from individual relaxation in hydrogen-bonded liquids",
  "title_text": "Face saturation at ρ * = 4 ln 2: a universal threshold separating cooperative from individual relaxation in hydrogen-bonded liquids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:17Z",
  "url": "https://research.draconitic.com/paper/eky5zffnmps37",
  "venue": "ChemRxiv",
  "versions": []
}