Cottrell equation (original) (raw)
In electrochemistry, the Cottrell equation describes the change in electric current with respect to time in a controlled potential experiment, such as chronoamperometry. Specifically it describes the current response when the potential is a step function in time. It was derived by Frederick Gardner Cottrell in 1903. For a simple redox event, such as the ferrocene/ferrocenium couple, the current measured depends on the rate at which the analyte diffuses to the electrode. That is, the current is said to be "diffusion controlled." The Cottrell equation describes the case for an electrode that is planar but can also be derived for spherical, cylindrical, and rectangular geometries by using the corresponding Laplace operator and boundary conditions in conjunction with Fick's second law of diffu
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| dbo:abstract | In electrochemistry, the Cottrell equation describes the change in electric current with respect to time in a controlled potential experiment, such as chronoamperometry. Specifically it describes the current response when the potential is a step function in time. It was derived by Frederick Gardner Cottrell in 1903. For a simple redox event, such as the ferrocene/ferrocenium couple, the current measured depends on the rate at which the analyte diffuses to the electrode. That is, the current is said to be "diffusion controlled." The Cottrell equation describes the case for an electrode that is planar but can also be derived for spherical, cylindrical, and rectangular geometries by using the corresponding Laplace operator and boundary conditions in conjunction with Fick's second law of diffusion. where, = current, in units of A = number of electrons (to reduce/oxidize one molecule of analyte , for example) = Faraday constant, 96485 C/mol = area of the (planar) electrode in cm2 = initial concentration of the reducible analyte in mol/cm3; = diffusion coefficient for species in cm2/s = time in s. Deviations from linearity in the plot of sometimes indicate that the redox event is associated with other processes, such as association of a ligand, dissociation of a ligand, or a change in geometry. In practice, the Cottrell equation simplifies to , where is the collection of constants for a given system. (en) L'équation de Cottrell (du nom de l'Américain Frederick Gardner Cottrell) concerne les techniques d'électrochimie transitoire. Elle montre que, lorsqu'un saut de potentiel est imposé à une électrode, le courant électrique décroît selon l'inverse de la racine carrée du temps. Dans le cas d'une réaction d'oxydo-réduction du type R → O + ne−, où R est le réducteur et O l'oxydant d'un couple rédox, l'équation de Cottrell s'écrit : Avec : * I : courant (A) ; * t : temps (s) ; * n : nombre d'électrons échangés (mol) ; * F : constante de Faraday (96485 C.mol-1) ; * A : surface de l'électrode (cm2) ; * cR : concentration interfaciale de R (mol.cm-3) ; * DR : coefficient de diffusion de R (cm2.s-1) . (fr) In elettrochimica, l'equazione di Cottrel descrive il cambiamento in corrente elettrica rispetto al tempo in un esperimento a potenziale controllato, come nella cronoamperometria. Per un semplice processo redox, come nel caso della coppia ferrocene/ferrocenio, la corrente misurata dipende dalla velocità con la quale l'analita diffonde all'elettrodo. Vale a dire, la corrente si definisce come "controllata dalla diffusione". L'equazione di Cottrell tratta il caso di un elettrodo piano ma può essere applicata anche a geometrie sferiche, cilindriche, e rettangolari, utilizzando il corrispondente operatore di Laplace e condizioni al contorno insieme con la seconda legge di Fick: dove * i è la corrente elettrica; * n il numero di elettroni implicati; * F la costante di Faraday; * A l'area dell'elettrodo piano; * cjO la concentrazione molecolare iniziale di analita; * Dj la diffusività di materia della specie j-esima; * t tempo in s. Riportando in un grafico l'andamento della corrente i contro Δt-1/2 è anche possibile mettere in evidenza eventuali deviazioni dalla linearità che indicano la concomitanza con l'evento redox di altri processi, come l'associazione o dissociazione di un ligando, oppure un cambiamento della geometria. (it) |
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| rdfs:comment | In electrochemistry, the Cottrell equation describes the change in electric current with respect to time in a controlled potential experiment, such as chronoamperometry. Specifically it describes the current response when the potential is a step function in time. It was derived by Frederick Gardner Cottrell in 1903. For a simple redox event, such as the ferrocene/ferrocenium couple, the current measured depends on the rate at which the analyte diffuses to the electrode. That is, the current is said to be "diffusion controlled." The Cottrell equation describes the case for an electrode that is planar but can also be derived for spherical, cylindrical, and rectangular geometries by using the corresponding Laplace operator and boundary conditions in conjunction with Fick's second law of diffu (en) L'équation de Cottrell (du nom de l'Américain Frederick Gardner Cottrell) concerne les techniques d'électrochimie transitoire. Elle montre que, lorsqu'un saut de potentiel est imposé à une électrode, le courant électrique décroît selon l'inverse de la racine carrée du temps. Dans le cas d'une réaction d'oxydo-réduction du type R → O + ne−, où R est le réducteur et O l'oxydant d'un couple rédox, l'équation de Cottrell s'écrit : Avec : (fr) In elettrochimica, l'equazione di Cottrel descrive il cambiamento in corrente elettrica rispetto al tempo in un esperimento a potenziale controllato, come nella cronoamperometria. Per un semplice processo redox, come nel caso della coppia ferrocene/ferrocenio, la corrente misurata dipende dalla velocità con la quale l'analita diffonde all'elettrodo. Vale a dire, la corrente si definisce come "controllata dalla diffusione". dove (it) |
| rdfs:label | Cottrell equation (en) Équation de Cottrell (fr) Equazione di Cottrell (it) |
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