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A similar resistance to electrolyte resistance is formed by a single kinetically-controlled electrochemical reaction. In this case we do not have a mixed potential, but rather a single reaction at equilibrium.
Consider a metal substrate in contact with an electrolyte. The metal molecules can electrolytically dissolve into the electrolyte, according to:
or more generally:
In the forward reaction in the first equation, electrons enter the metal and metal ions diffuse into the electrolyte. Charge is transferred. This charge-transfer reaction has a certain speed. The speed depends on the kind of reaction, the temperature, the concentration of the reaction products, and the potential. The general relation between the potential and the current, which is directly related to the amount of electrons and so the charge transfer via Faraday's law, is:
with the exchange-current density i0 in A/cm2, concentration of oxidant at the electrode surface () and in the bulk solution (), concentration of reductant at the electrode surface () and in the bulk solution (), Faraday's constant F, temperature T, gas constant R, reaction order α, number n of electrons involved, and the overpotential η (Eapplied - EOC).
The overpotential η measures the degree of polarization. It is the electrode potential minus the equilibrium potential for the reaction. When the concentration in the bulk is the same as at the electrode surface, and , the equation can be simplified into:
This equation is called the Butler-Volmer equation. It is applicable when the polarization depends only on the charge-transfer kinetics. Stirring the solution to minimize the diffusion layer thickness can help minimize concentration polarization.
If the overpotential η is very small and the electrochemical system is at equilibrium, the expression for the charge-transfer resistance Rct changes to:
From this equation the exchange-current density i0 can be calculated if Rct is known.