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.
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.
- Quantities, Units and Symbols in Physical Chemistry, 3rd edition, 2nd printing
IUPAC · 2011
Topic background · Physical-chemistry notation, thermodynamics, electrochemistry and transport quantities.