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New insights on the interfacial tension of electrochemical interfaces and the Lippmann equation

Published online by Cambridge University Press:  13 December 2017

W. DREYER ,
C. GUHLKE ,
M. LANDSTORFER  and
R. MÜLLER
W. DREYER
Affiliation:
Weierstrass-Institute, Mohrenstr. 39, 10117 Berlin, Germany emails: Wolfgang.Dreyer@wias-berlin.de, Clemens.Guhlke@wias-berlin.de, Manuel.Landstrofer@wias-berlin.de, Ruediger.Mueller@wias-berlin.de
C. GUHLKE
Affiliation:
Weierstrass-Institute, Mohrenstr. 39, 10117 Berlin, Germany emails: Wolfgang.Dreyer@wias-berlin.de, Clemens.Guhlke@wias-berlin.de, Manuel.Landstrofer@wias-berlin.de, Ruediger.Mueller@wias-berlin.de
M. LANDSTORFER
Affiliation:
Weierstrass-Institute, Mohrenstr. 39, 10117 Berlin, Germany emails: Wolfgang.Dreyer@wias-berlin.de, Clemens.Guhlke@wias-berlin.de, Manuel.Landstrofer@wias-berlin.de, Ruediger.Mueller@wias-berlin.de
R. MÜLLER
Affiliation:
Weierstrass-Institute, Mohrenstr. 39, 10117 Berlin, Germany emails: Wolfgang.Dreyer@wias-berlin.de, Clemens.Guhlke@wias-berlin.de, Manuel.Landstrofer@wias-berlin.de, Ruediger.Mueller@wias-berlin.de
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Abstract

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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.

Keywords

Lippmann equationelectrochemistryliquid-liquid interfaceasymptotic analysis
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Issue 4 , August 2018 , pp. 708 - 753
Copyright
Copyright © Cambridge University Press 2017 

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