Battery knowledge · Electrochemistry fundamentals

Butler–Volmer equation

The kinetic law relating current density at an electrode to its overpotential: current grows exponentially with overpotential in each direction. It is the charge-transfer term in every physics-based cell model.

Relationship
i = i₀[exp(α_a·Fη/RT) − exp(−α_c·Fη/RT)]

Example

Compare equilibrium with a positive overpotential

For a symmetric one-electron example at 298.15 K, αa = αc = 0.5 and η = 25.7 mV give i/i₀ ≈ 1.04. At η = 0 the forward and reverse contributions cancel, so net current is zero.

Explore the graph

At equilibrium, forward and reverse reaction currents cancel.

Symmetric reaction kinetics at 25 °C
Symmetric reaction kinetics at 25 °COverpotential (V) versus Current density (A/m²). Net reaction current. Interpretation follows the graphs.-18.5-0.15-9.24-0.075009.240.07518.50.15Overpotential (V)Current density (A/m²)
Net reaction current

At equilibrium net current is zero. At +50 mV, current density is 2.268 A/m².

i = 2i₀ sinh(Fη / 2RT)

Illustrative model. Fixed concentrations, symmetric transfer coefficients and no transport limitation.

Use in Lemonergy

Connect reaction sites and transport paths.

This is a reference concept. No executable Lemonergy block has been verified for this term.

References & further reading

Further reading on this topic

These sources provide broader context; they are not presented as citations for every statement in this entry.

  1. Quantities, Units and Symbols in Physical Chemistry, 3rd edition, 2nd printing

    IUPAC · 2011

    Topic background · Physical-chemistry notation, thermodynamics, electrochemistry and transport quantities.