Butler–Volmer equation
In electrochemistry, the Butler–Volmer equation (named after John Alfred Valentine Butler and Max Volmer), also known as Erdey-Grúz–Volmer equation (after Tibor Erdey-Grúz), is one of the most fundamental relationships in electrochemical kinetics. It describes how the electrical current through an electrode depends on the voltage difference between the electrode and the bulk electrolyte for a simple, unimolecular redox reaction, considering that both a cathodic and an anodic reaction occur on the same electrode: == Butler–Volmer equation == The Butler–Volmer equation is: j = j 0 ⋅ { exp [ α a z F R T ( E − E e q ) ] − exp [ − α c z F R T ( E − E e q ) ] } {\displaystyle j=j_{0}\cdot \left\{\exp \left[{\frac {\alpha _{\rm {a}}zF}{RT}}(E-E_{\rm {eq}})\right]-\exp \left[-{\frac {\alpha _{\rm {c}}zF}{RT}}(E-E_{\rm {eq}})\right]\right\}} or in a more compact form: j = j 0 ⋅ { exp [ α a z F η R T ] − exp [ − α c z F η R T ] } {\displaystyle j=j_{0}\cdot \left\{\exp \left[{\frac {\alpha _{\rm {a}}zF\eta }{RT}}\right]-\exp \left[-{\frac {\alpha _{\rm {c}}zF\eta }{RT}}\right]\right\}} where: j {\displaystyle j} : electrode current density, A/m2 (defined as j = I / S {\displaystyle j=I/S} ) j 0 {\displaystyle j_{0}} : exchange current density, A/m2 E {\displaystyle E} : electrode potential, V E e q {\displaystyle E_{\rm {eq}}} : equilibrium potential, V T {\displaystyle T} : absolute temperature, K z {\displaystyle z} : number of electrons involved in the electrode reaction F {\displaystyle F} : Faraday constant R {\displaystyle R} : universal gas constant α c {\displaystyle \alpha _{\rm {c}}} : so-called cathodic charge transfer coefficient, dimensionless α a {\displaystyle \alpha _{\rm {a}}} : so-called anodic charge transfer coefficient, dimensionless η {\displaystyle \eta } : activation overpotential (defined as η = E − E e q {\displaystyle \eta =E-E_{\rm {eq}}} ).