The Warburg coefficient (or Warburg constant; denoted or ) is the diffusion coefficient of ions in solution, associated to the Warburg 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 angular 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; 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.
The Warburg coefficient is mainly used in engineering. Engineers can calculate how quickly ions are moving through a material by measuring the Warburg Coefficient: this enables them to characterise battery performance.
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