ButlerVolmerekvationen

The Butler-Volmer equation is a foundational relation in electrochemistry that describes how the current density at an electrode depends on the overpotential for a redox reaction. It arises from elementary charge-transfer steps coupled with transition-state arguments and is widely used to analyze electrode kinetics, including corrosion, electroplating, fuel cells, and sensors.

The commonly used form expresses the net current density i as a difference between the forward (anodic) and backward (cathodic) rates of electron transfer:

i = i0 [ exp( (αa n F η) / (R T) ) − exp( (−αc n F η) / (R T) ) ].

Here, i is the current density (A/m^2), i0 is the exchange current density, η is the overpotential (potential relative to the equilibrium potential), αa and αc are the anodic and cathodic transfer coefficients (0 < α < 1), n is the number of electrons transferred, F is the Faraday constant, R is the gas constant, and T is the absolute temperature. The sum αa + αc is often close to 1 for a simple one-step transfer.

Special cases include the high-overpotential (Tafel) limits, where one branch dominates and the equation reduces to i ≈ i0 exp((α n F η)/(R T)) for large positive η or i ≈ −i0 exp((αc n F |η|)/(R T)) for large negative η. The equation provides a practical means to extract kinetic parameters from polarization curves and to model electrochemical systems under varying driving forces.

Limitations include its assumption of a single rate-limiting step, negligible mass transport effects, and uniform surface conditions. More complex models integrate diffusion, multi-step mechanisms, and surface roughness. The Butler-Volmer equation is named after J. W. Butler and Max Volmer, who developed it in the 1930s.