electrochemistry Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an outc ...

, the Cottrell equation describes the change in

electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The movin ...

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 Frederick Gardner Cottrell (January 10, 1877 – November 16, 1948) was an American physical chemist, inventor and philanthropist. He is best known for his invention of the electrostatic precipitator, one of the first inventions designed to ...

in 1903. For a simple

redox Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate (chemistry), substrate change. Oxidation is the loss of Electron, electrons or an increase in the oxidation state, while reduction ...

event, such as the

ferrocene Ferrocene is an organometallic compound with the formula . The molecule is a complex consisting of two cyclopentadienyl rings bound to a central iron atom. It is an orange solid with a camphor-like odor, that sublimes above room temperature, ...

/ferrocenium couple, the current measured depends on the rate at which the

analyte An analyte, component (in clinical chemistry), or chemical species is a substance or chemical constituent that is of interest in an analytical procedure. The purest substances are referred to as analytes, such as 24 karat gold, NaCl, water, et ...

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 In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is t ...

and boundary conditions in conjunction with Fick's second law of diffusion.Bard, A. J.; Faulkner, L. R. “Electrochemical Methods. Fundamentals and Applications” 2nd Ed. Wiley, New York. 2001. :

i = \frac

where, :

i

= current, in units of A :

n

= number of electrons (to reduce/oxidize one molecule of analyte

j

, for example) :

F

Faraday constant In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of S ...

, 96485 C/mol :

A

= area of the (planar) electrode in cm² :

c_j^0

= initial concentration of the reducible analyte

j

in mol/cm³; :

D_j

diffusion coefficient Diffusivity, mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). Diffusivity is enco ...

for species

j

in cm²/s :

t

= time in s. Deviations from linearity in the plot of

i\; vs\; t^

sometimes indicate that the redox event is associated with other processes, such as association of a

ligand In coordination chemistry, a ligand is an ion or molecule ( functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's ele ...

, dissociation of a ligand, or a change in geometry. In practice, the Cottrell equation simplifies to

i = kt^

, where

k

is the collection of constants for a given system (

n, F, A, c_j^0, D_j

References

Electrochemical equations {{electrochem-stub

See also

References