Abstract
Abstract Originally derived by Walther Nernst more than a century ago, the Nernst equation for the open-circuit voltage is a cornerstone in the analysis of electrochemical systems. Unfortunately, the assumptions behind its derivation are often overlooked in the literature, leading to incorrect forms of the equation when applied to complex systems (for example, those with ion-exchange membranes or involving mixed potentials). Such flaws can be avoided by applying a correct thermodynamic derivation independently of the form in which the electrochemical reactions are written. The proper derivation of the Nernst equation becomes important, for instance, in modeling of vanadium redox flow batteries or zinc-air batteries. The rigorous path towards the Nernst equation derivation starts in non-equilibrium thermodynamics.
Highlights
Derived by Walther Nernst more than a century ago, the Nernst equation for the opencircuit voltage is a cornerstone in the analysis of electrochemical systems
Assuming that the cell is in a steady state and that no current is passing through the external circuit, the electrochemical reactions do not proceed and there is no ionic transport through the electrolyte or the membrane
Which is compatible with the usual formula [17]. We have included this example to demonstrate the thermodynamic derivation of the open-circuit voltage (OCV) on the simple example where it coincides with the usual formula from the literature
Summary
To properly interpret the measured value, a formula relating it to the cell properties is required: the so-called Nernst equation It was Helmholtz who first derived a formula relating voltage and dissolved species concentrations [3], Nernst formulated the relation in a general thermodynamic way: the Gibbs energy of the overall reaction (written down with no charge imbalance) will be equal to the maximal electrical work that can be obtained (cf [4, 5]), which determines the OCV. We focus on the operational definition of the OCV that is given by the first plateau in the voltage/time curve, which means that we only consider the relaxation of the most relevant processes Such analysis requires the application of both equilibrium and non-equilibrium thermodynamics. It is shown that for instance in vanadium and zinc-air redox flow batteries the thermodynamic derivation of Nernst relation gives better results than the simplified one
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