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A question about accuracy of Butler-Volmer kinetic equation

Posted Jun 4, 2018, 2:30 p.m. EDT Electromagnetics, Battery Design, Electrochemistry Version 5.2a 1 Reply

Waleed Zakri
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Hello, I have questions regarding how accurate butler-Volmer equation that applied for electrochemical reaction in batteries applications and models? if its accurate , Could you please provide a proof or explain how the accuracy been checked or tested? Thanks

1 Reply Last Post Jun 5, 2018, 1:45 a.m. EDT
Lasse Murtomäki
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Posted: 6 years ago Jun 5, 2018, 1:45 a.m. EDT

B-V kinetics is used because of its simplicity. The more pertinent Marcus or Marcus-Hush theories are more difficult to apply; an accurate quantum mechanical description of electron transfer has been derived by Ulstrup and Kuznetsov. The 'failure' of the B-V theory is seen in the potential dependence of the charge transfer coefficient α, for example. Also, the standard rate constant k° is an apparent one, including the effects of the double layer (Frumkin correction) that is also somewhat potential dependent. Yet another difficulty comes from multi-step reactions. The reaction rate is determined by the rate-determining step where the number of electrons certainly is different from the total number of the net reaction.

The convention that Comsol has adopted is to write in the exponentials (n - α) and α so that at equilibrium the B-V equation reduces to the Nernst equation. But now, α is not 0.5 for a multistep reaction! I wrote a brief analysis for my students (attached); it follows the nomenclature of the famous Bard & Faulkner textbook.

To summarize: B-V is a pragmatic choice, just accept that the rate constants are hiding this and that and are possibly potential dependent. Impedance experiments at varying dc potentials is a possible way of checking the theory.

BR Lasse

B-V kinetics is used because of its simplicity. The more pertinent Marcus or Marcus-Hush theories are more difficult to apply; an accurate quantum mechanical description of electron transfer has been derived by Ulstrup and Kuznetsov. The 'failure' of the B-V theory is seen in the potential dependence of the charge transfer coefficient α, for example. Also, the standard rate constant k° is an apparent one, including the effects of the double layer (Frumkin correction) that is also somewhat potential dependent. Yet another difficulty comes from multi-step reactions. The reaction rate is determined by the rate-determining step where the number of electrons certainly is different from the total number of the net reaction. The convention that Comsol has adopted is to write in the exponentials (n - α) and α so that at equilibrium the B-V equation reduces to the Nernst equation. But now, α is not 0.5 for a multistep reaction! I wrote a brief analysis for my students (attached); it follows the nomenclature of the famous Bard & Faulkner textbook. To summarize: B-V is a pragmatic choice, just accept that the rate constants are hiding this and that and are possibly potential dependent. Impedance experiments at varying dc potentials is a possible way of checking the theory. BR Lasse

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