Journal
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
Volume 29, Issue 4, Pages 708-753Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0956792517000341
Keywords
Lippmann equation; electrochemistry; liquid-liquid interface; asymptotic analysis
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The Lippmann equation is considered as universal relationship between interfacial tension, double layer charge, and cell potential. Based on the framework of continuum thermo-electrodynamics, we provide some crucial new insights to this relation. For general interfaces such that the local curvature radius is large compared to the Debye length, we apply asymptotic analysis methods to obtain the Lippmann equation. We give precise definitions of the involved quantities and show that the interfacial tension of the Lippmann equation is composed of the surface tension of our general model, and contributions arising from the adjacent space charge layers that can only lower the interfacial tension. Moreover, it turns out that surface reactions can be consistently incorporated into the Lippmann equation, provided that there is no charge transfer from one side of the interface to the other. We apply the model to curved liquid metal electrodes and compare our model to experimental data of several mercury-electrolyte interfaces. We obtain qualitative and quantitative agreement in the 2 V potential range for various salt concentrations.
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