Butler-Volmer equation

The Butler-Volmer equation describes the reaction kinetics in electrochemistry in the vicinity of the equilibrium potential. The current density , which corresponds to a reaction rate in electrochemistry, is related to the potential difference by the Butler-Volmer equation . This potential difference to the equilibrium potential is often referred to in the literature as the transmission overvoltage . This equation forms the basis of the electrochemical reaction kinetics in the equilibrium between oxidation and reduction reactions. ${\displaystyle E_{\mathrm {eq} }.}$ ${\displaystyle j}$ ${\displaystyle E-E_{\mathrm {eq} }}$ ${\displaystyle \eta }$

${\displaystyle j=j_{0}\cdot \left\{\exp \left[{\frac {\alpha _{\mathrm {a} }\cdot z\cdot F}{R\cdot T}}\cdot (E-E_{\mathrm {eq} })\right]-\exp \left[-{\frac {\alpha _{\mathrm {k} }\cdot z\cdot F}{R\cdot T}}\cdot (E-E_{\mathrm {eq} })\right]\right\}}$

This plot shows the anodic and cathodic branches as well as the sum of the current densities according to the Butler-Volmer equation for an exchange current density of and a charge transfer coefficient of ${\displaystyle j_{0}}$ ${\displaystyle 1\,\mathrm {mAcm^{-2}} }$ ${\displaystyle \alpha }$ ${\displaystyle 0.5.}$

with the following parameters:

${\displaystyle j}$: Current density [A / m ² ], defined as the current per electrode surface

${\displaystyle j_{0}}$: Exchange current density [A / m ² ] based on the electrode surface

${\displaystyle E}$: Electrode potential [V]

${\displaystyle E_{\mathrm {eq} }}$: Equilibrium potential [V]

${\displaystyle T}$: Temperature [K]

${\displaystyle z}$: Number of charges (electrons transferred per metabolic rate of the transition reaction)

${\displaystyle F}$: Faraday constant

${\displaystyle R}$: universal gas constant

${\displaystyle \alpha _{\mathrm {a} },\,\alpha _{\mathrm {k} }}$: Charge transfer coefficient for the oxidation reaction (at the anode) and for the reduction reaction (at the cathode).

The simplified form of the Butler-Volmer equation is often used, in which it is assumed that the sum of the anodic charge transfer coefficient and the cathodic charge transfer coefficient is 1. ${\displaystyle \alpha _{\mathrm {a} }}$ ${\displaystyle \alpha _{\mathrm {k} }}$

This can be used in the above equation and it results with : ${\displaystyle \alpha _{\mathrm {k} }=1-\alpha _{\mathrm {a} }}$ ${\displaystyle \eta =(E-E_{\mathrm {eq} })}$

${\displaystyle j=j_{0}\cdot \left\{\exp \left[{\frac {\alpha _{\mathrm {a} }\cdot z\cdot F\cdot \eta }{R\cdot T}}\right]-\exp \left[-{\frac {(1-\alpha _{\mathrm {a} })\cdot z\cdot F\cdot \eta }{R\cdot T}}\right]\right\}}$

The Butler-Volmer equation can be derived from the kinetics . To simplify matters, it describes that the speed of an (electrochemical) reaction depends exponentially on the “driving force” of the reaction.

The relationship, mostly known today as the Butler-Volmer equation, was first published in 1930 in a decisive paper by the chemists Tibor Erdey-Grúz and Max Volmer . John Alfred Valentine Butler published a corresponding work in 1932, although he had already done preliminary work in 1924. There have been discussions about the naming of this equation which can be found in the American Chemical Society's Journal of Chemical Education.

See also

• Nernst equation , electrochemical equivalent , Tafel equation , electrochemical kinetics

Individual evidence

1. ↑ Volkmar M. Schmidt: Electrochemical process engineering: Fundamentals, reaction engineering, process optimization . Wiley-VCH, Weinheim 2003, OCLC 85820545 , p. 94 .
2. ↑ T. Erdey-Grúz, M. Volmer: On the theory of hydrogen overvoltage . In: Journal of Physical Chemistry . 150A, 1930, p. 203-213 , doi : 10.1515 / zpch-1930-15020 ( PDF ).
3. ^ Robert de Levie: What's in a Name? In: Journal of Chemical Education . tape 77 , no. 5 , May 1, 2000, doi : 10.1021 / ed077p610 .
4. ^ Robert de Levie: Correction What's in a Name? In: Journal of Chemical Education . tape 88 , no. 6 , 2011, doi : 10.1021 / ed100894x .

Web links

Wiktionary: Elektrochemie  - explanations of meanings, word origins, synonyms, translations

• Butler-Volmer visualization in the form of a GNU Octave script file
• Short biography of Max Volmer