The Warburg coefficient (or Warburg constant; denoted or ) is the
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 ...
of
ions in
solution
Solution may refer to:
* Solution (chemistry), a mixture where one substance is dissolved in another
* Solution (equation), in mathematics
** Numerical solution, in numerical analysis, approximate solutions within specified error bounds
* Soluti ...
, associated to the
Warburg element
The Warburg diffusion element is an equivalent electrical circuit component that models the diffusion process in dielectric spectroscopy. That element is named after German physicist Emil Warburg.
A Warburg Electrical impedance, impedance element ...
, . The Warburg coefficient has units of
The value of can be obtained by the
gradient of the Warburg plot, a linear plot of the real
impedance () against the reciprocal of the square root of the
frequency (
). This relation should always yield a straight line, as it is unique for a Warburg.
Alternatively, the value of can be found by:
where
* is the
ideal gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
;
* is the
thermodynamic temperature;
* is the
Faraday constant;
* is the
valency;
* is the diffusion coefficient of the species, where subscripts and stand for the oxidized and reduced species respectively;
* is the concentration of the and species in the bulk;
* is the concentration of the electrolyte;
* denotes the surface area;
* denotes the fraction of the and species present.
The equation for applies to both reversible and quasi-reversible reactions for which both halves of the couple are soluble.
References
*
Electrochemistry
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