Chemistry:Warburg coefficient

Short description: Diffusion coefficient of ions in solution

The Warburg coefficient (or Warburg constant; denoted A_W or σ) is the diffusion coefficient of ions in solution, associated to the Warburg element, Z_W. The Warburg coefficient has units of $\mathrm{\Omega }/\sqrt{\text{seconds}}=\mathrm{\Omega }(s^{-1/2})$

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:

$$A_W=\frac{RT}{A{n}^2{F}^2\sqrt{2}}(\frac{1}{C_{\mathrm{O}}^b\sqrt{D_{\mathrm{O}}}}+\frac{1}{C_{\mathrm{R}}^b\sqrt{D_{\mathrm{R}}}})=\frac{RT}{A{n}^2{F}^2\mathrm{\Theta }C\sqrt{2D}}$$

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;
• Θ denotes the fraction of the O and R 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

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