Academic Journal
Beyond Debye–Hückel: A Spectral–Curvature Theory of Activity Coefficients
| Τίτλος: | Beyond Debye–Hückel: A Spectral–Curvature Theory of Activity Coefficients |
|---|---|
| Συγγραφείς: | Cesar A. Cohen de Mello |
| Στοιχεία εκδότη: | Springer Science and Business Media LLC, 2026. |
| Έτος έκδοσης: | 2026 |
| Περιγραφή: | 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. |
| Τύπος εγγράφου: | Article |
| DOI: | 10.21203/rs.3.rs-8303565/v1 |
| Rights: | CC BY |
| Αριθμός Καταχώρησης: | edsair.doi...........2004fc3f3b83acbf60fefa75005c7b6b |
| Βάση Δεδομένων: | OpenAIRE |
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