Beyond Debye–Hückel: A Spectral–Curvature Theory of Activity Coefficients

Beyond Debye–Hückel: A Spectral–Curvature Theory of Activity Coefficients | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Beyond Debye–Hückel: A Spectral–Curvature Theory of Activity Coefficients Cesar A. Cohen de Mello This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8303565/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The classical Debye–Hückel (DH) theory remains the foundational framework for dilute electrolytes, yet itsmathematical structure imposes strict topological and spectral constraints incompatible with experimental dataabove ionic strengths 𝐼 ≳ 10−2 mol kg−1. Here a rigorous operator formulation is developed for the linearisedPoisson–Boltzmann equation,LDH = −Δ + 𝜅2, 𝜅2 = 2𝑒2 𝐼𝜀𝑘𝐵𝑇 ,acting on H = 𝐻1 (R3). The DH prediction for the mean activity coefficient, log 𝛾± ∝ −√𝐼, belongs to aone-dimensional functional manifold whose curvature is identically zero. Any experimental profile with nonzerosecond derivative,𝐾 (𝐼) = d2d𝐼2 log 𝛾± (𝐼) ≠ 0,cannot be generated by LDH under the assumptions of homogeneous permittivity, point-ion structure, and linearisedresponse. A spectral decomposition of L𝜀 with spatially varying dielectric field 𝜀(x) shows that realistic solvationintroduces nontrivial curvature via eigenvalue modulation 𝜆𝑛 (𝐼), producing experimentally observed inflectionpoints and salting-in/out regimes. Thus DH failure is structural: the theory lacks the degrees of freedom requiredto reproduce the topology of measured activity-coefficient curves. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8303565","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":585135566,"identity":"bc90cf33-5707-44bf-8289-24731b5508fd","order_by":0,"name":"Cesar A. 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