electrochemistry Electrochemistry is the branch of physical chemistry concerned with the relationship between Electric potential, electrical potential difference and identifiable chemical change. These reactions involve Electron, electrons moving via an electronic ...

, the Cottrell equation describes the change in

electric current An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...

with respect to time in a controlled

potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple r ...

experiment, such as

chronoamperometry In electrochemistry, chronoamperometry is an analytical technique in which the electric potential of the working electrode is step function, stepped and the resulting electric current, current from faradaic processes occurring at the electrode (c ...

. Specifically it describes the current response when the potential is a

step function In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having on ...

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 e ...

in 1903. For a simple

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

event, such as the

ferrocene Ferrocene is an organometallic chemistry, organometallic compound with the formula . The molecule is a Cyclopentadienyl complex, complex consisting of two Cyclopentadienyl anion, cyclopentadienyl rings sandwiching a central iron atom. It is an o ...

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

analyte An analyte, component (in clinical chemistry), titrand (in titrations), or chemical species is a substance or chemical constituent that is of interest in an analytical procedure. The remainder of the sample is called the matrix. The procedure ...

diffuses to the electrode. That is, the current is said to be " diffusion controlled". The Cottrell equation describes the case for an

electrode An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit (e.g. a semiconductor, an electrolyte, a vacuum or a gas). In electrochemical cells, electrodes are essential parts that can consist of a varie ...

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 field, scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \ ...

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, := current, in units of A : = number of electrons (to reduce/oxidize one molecule of analyte , for example) : =

Faraday constant In physical chemistry, the Faraday constant (symbol , sometimes stylized as ℱ) is a physical constant defined as the quotient of the total electric charge () by the amount () of elementary charge carriers in any given sample of matter: it ...

, 96485 C/mol : = area of the (planar) electrode in cm² :

c_j^0

= initial concentration of the reducible analyte

j

in mol/cm³; : =

diffusion coefficient Diffusivity, mass diffusivity or diffusion coefficient is usually written as the proportionality constant between the molar flux due to molecular diffusion and the negative value of the gradient in the concentration of the species. More accurate ...

for species in cm²/s : = time in s. Deviations from linearity in the plot of vs. 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 with a 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 el ...

, dissociation of a ligand, or a change in geometry. Deviations from linearity can be expected at very short time scales due to non-ideality in the potential step. At long time scales, buildup of the diffusion layer causes a shift from a linearly dominated to a radially dominated diffusion regime, which causes another deviation from linearity. In practice, the Cottrell equation simplifies to

i = kt^,

where is the collection of constants for a given system (, , ).

References

Electrochemical equations {{electrochem-stub

See also

References