Relation de Butler-Volmer

In electrochemistry, the Butler–Volmer equation (named after John Alfred Valentine Butler and Max Volmer), also known as Erdey-Grúz–Volmer equation, 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: The Butler–Volmer equation is: or in a more compact form: where: electrode current density, A/m2 (defined as j = I/S) exchange current density, A/m2 electrode potential, V equilibrium potential, V absolute temperature, K number of electrons involved in the electrode reaction Faraday constant universal gas constant so-called cathodic charge transfer coefficient, dimensionless so-called anodic charge transfer coefficient, dimensionless activation overpotential (defined as ). The right hand figure shows plots valid for . There are two limiting cases of the Butler–Volmer equation: the low overpotential region (called "polarization resistance", i.e., when E ≈ Eeq), where the Butler–Volmer equation simplifies to: the high overpotential region, where the Butler–Volmer equation simplifies to the Tafel equation. When , the first term dominates, and when , the second term dominates. for a cathodic reaction, when E < Eeq, or for an anodic reaction, when E >> Eeq where and are constants (for a given reaction and temperature) and are called the Tafel equation constants. The theoretical values of the Tafel equation constants are different for the cathodic and anodic processes. However, the Tafel slope can be defined as: where is the faradaic current, expressed as , being and the cathodic and anodic partial currents, respectively. The more general form of the Butler–Volmer equation, applicable to the mass transfer-influenced conditions, can be written as: where: j is the current density, A/m2, co and cr refer to the concentration of the species to be oxidized and to be reduced, respectively, c(0,t) is the time-dependent concentration at the distance zero from the surface of the electrode.