Chemistry: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 [math]\displaystyle{ {\Omega}/\sqrt{\text{seconds}}={\Omega}(s^{-1/2}) }[/math]
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 ([math]\displaystyle{ {1}/\sqrt{\omega} }[/math]). This relation should always yield a straight line, as it is unique for a Warburg.
Alternatively, the value of AW can be found by:
[math]\displaystyle{ A_W={\frac{R T}{An^2F^2\sqrt2}}{\left(\frac{1}{C_\mathrm{O}^b\sqrt{D_\mathrm{O}}}+{\frac{1}{C_\mathrm{R}^b\sqrt{D_\mathrm{R}}}}\right)}=\frac{R T}{An^2F^2\Theta C\sqrt{2D}} }[/math]
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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