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| Home > Online First > Inconsistencies in the Debye-Hückel theory related to the Statistic Foundation and Permittivity |
| Home > Online First > Inconsistencies in the Debye-Hückel theory related to the Statistic Foundation and Permittivity |
| Contribution to a conference proceedings | FZJ-2025-03778 |
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2025
Abstract: The Debye-Hückel (DH) theory, a cornerstone in modeling ionic activities in electrolytes for over a century, remains widely applied like in equations of state and Onsager’s conductivity theory1. In the DH theory, the distribution of ions around a central ion is calculated assuming electrostatic interactions of point charges that are dispersed in a dielectric continuum2. To date, the parameterization of the DH theory is still being investigated, especially regarding the integration of the concentration-dependence of the relative static permittivity (dielectric constant), to improve the predictive capabilities of models3,4,5. In this presentation, we show that the theoretical foundation of the electrostatic interactions, namely the employed Poisson-Boltzmann framework, violates the statistical independence of states presumed for the Boltzmann theory. Hence, the physicochemical rigorosity of the DH theory is more restricted than often assumed in contemporary literature1. Even the DH limiting law, which is believed to be the most rigorous DH model, is subjected to this inconsistency. Additionally, the relative static permittivity of electrolytic solutions is critically examined, revealing inaccuracies in conventional extraction methods from experimental data obtained by dielectric spectroscopy. Consequently, the static permittivities of electrolytes and their concentration-dependences are subjected to unquantified uncertainties. To assess the impact of the uncertainties discussed, a sensitivity analysis demonstrates how a variation in the permittivity is overshadowed by adjusting the usual fitting parameters, the ionic radii, and arbitrary combinations of model extensions (such as models for the hard sphere contribution, Born term, and association). Ultimately, this presentation emphasizes that the theoretical foundations of the DH theory are fragile, restricting its applicability to fitting experimental data rather than enhancing predictive models. 6References:[1] G. M. Kontogeorgis, B. Maribo-Mogensen and K. Thomsen, Fluid Phase Equilibria, 2018, 462, 130–152.[2] P. Debye and E. Huckel, Phys Z, 1923, 24, 185–206. [3] G. M. Silva, X. Liang and G. M. Kontogeorgis, Fluid Phase, Equilibria, 2023, 566, 113671. [4] Rueben, P. Rehner, J. Gross and A. Bardow, Journal of Chemical & Engineering Data, 2024, 69, 3044–3054. [5] I. Y. Shilov and A. K. Lyashchenko, Journal of Solution Chemistry, 2019, 48, 234–247.[6] B. Janotta, M. Schalenbach, H. Tempel, R.-A. Eichel, Physical Chemistry Chemical Physics, 2025, DOI: 10.1039/D5CP00646E
Keyword(s): Chemistry (2nd)
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