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Butler-Volmer kinetics

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As an electrochemist I cannot understand the formulation of the equation of the electrode reaction kinetics (attached). Why is there (n - eta) in the first exponent, instead of 1- eta? The formulation does return Nernst looking equation at zero current, but it neither agrees with the documentation of Comsol. Is this simply a cosmetic bug, or how is Comsol calculating reaction kinetics?

Note also that zero overpotential does not mean the C_Ox = C_red, as Comsol appears to define, but that the ratio (C_Ox/C_red) defines the value of the equilibrium potential.

The current-overpotential and the exchange current density equations are usually written in textbooks as in the other attachment. The formula that Comsol uses thus is a mixture of Butler-Volmer and current-overpotential equations. Literature is admittedly a bit confusing in these issues.; I follow the treatment of Bard & Faulkner.

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