Warburg coefficient

The Warburg coefficient (or Warburg constant; denoted AW or σ) is the diffusion coefficient of ions in solution, associated to the Warburg element, ZW. The Warburg coefficient has units of

The value of AW can be obtained by the gradient of the Warburg plot, a linear plot of the real impedance (R) 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 AW can be found by:

where

  • R is the ideal gas constant;
  • T is the thermodynamic temperature;
  • F is the Faraday constant;
  • n is the valency;
  • D is the diffusion coefficient of the species, where subscripts O and R stand for the oxidized and reduced species respectively;
  • Cb is the concentration of the O and R species in the bulk;
  • C is the concentration of the electrolyte;
  • A denotes the surface area;
  • Θ denotes the fraction of the O and R species present.

The equation for AW applies to both reversible and quasi-reversible reactions for which both halves of the couple are soluble.

References

  • Ottova-Leitmannova, A. (2006). Advances in Planar Lipid Bilayers and Liposomes. Academic Press.


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