Equation of Cottrell

The equation of Cottrell (of the name of the American Frederick Gardner Cottrell) relates to the techniques of transitory electrochemistry. It shows that, when a jump of potential is imposed on a electrode, the Electric current decrease according to the Inverse of the square Racine of time.

In the case of a reaction of oxydoreduction of the type R → O + N e^-, where R is the reducer and O the oxidant of a redox cell, the equation of Cottrell is written:

I_ {(T)} = nFAc_R \ sqrt \ frac {D_R} {\ pi T}

With:

I : running (has);
T : time (S);
N : number of exchanged electrons (mol);
F : Constant of Faraday (96485 C .mol -1 );
has : surface electrode (cm 2 );
C : interfacial concentration of R (mol.cm -3 );
D : coefficient of diffusion of R (cm 2 .s -1 ).

Conditions of validity

The equation of Cottrell is established in the case of a reversible reaction redox (i.e. a reaction whose kinetics is very fast and whose current is controlled by the diffusion), on the assumption of a linear diffusion semi-infinite and perpendicular to the surface of the electrode. The potential of balance is such as the initial concentration in species O is negligible. Only a reagent is present in solution at balance, and it is completely oxidized following the application of the jump of potential.

References

Hubert H. Girault, physical and analytical Electrochemistry , ED. Polytechnic presses and French Academics, 2001

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