Kontsevich quantization formula

The Warburg coefficient (or Warburg constant), $A_{W}$, is the diffusion coefficient of ions in solution, associated to the Warburg element, $Z_{W}$. The Warburg coefficient, $A_{W}$, also written as, ${\sigma }$, has the units of ${\Omega }/{\sqrt {seconds}}={\Omega }(s^{-1/2})$

The value of $A_{W}$ 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 (${1}/{\sqrt {\omega }}$). This relation should always yield a straight line, as it is unique for a Warburg.

Alternatively, the value of $A_{W}$ can be found by:

$A_{W}={\frac {RT}{An^{2}F^{2}{\sqrt {2}}}}{\left({\frac {1}{D_{O}^{1/2}C_{O}^{b}}}+{\frac {1}{D_{R}^{1/2}C_{R}^{b}}}\right)}={\frac {RT}{An^{2}F^{2}\Theta C{\sqrt {2D}}}}$

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, $C^{b}$ is the concentration of the $O$ and $R$ species in the bulk, C is the concentration of the electrolyte, $A$ denotes the surface area and $\Theta$ denotes the fraction of the $R$ and $O$ species present.

The equation for $A_{W}$ applies to both reversible and quasi-reversible reactions for which both halves of the couple are soluble.

References

• A. Ottova-Leitmannova, Advances in Planar Lipid Bilayers and Liposomes, Academic Press (2006)
• http://www.consultrsr.com/resources/eis/warburg2.htm#ref1