WOLFRAM NOTEBOOK

Orthonormal Scales in a Nyquist Diagram

​
A: R/C equivalent circuit for a
Tafelian reaction
B: Randles equivalent circuit for a
redox reaction
unit length ratio
u
Im
/
u
Re
1.5
Orthonormal scales should be used for Nyquist impedance plots. The length
u
Im
from 0 to 1 along the imaginary axis should be equal to the length
u
Re
from 0 to 1 along the real axis. Otherwise, semicircle graphs are not semicircles and it becomes difficult to measure angles. This Demonstration presents two examples: the impedance for a Tafelian redox system and the Randles circuit with Warburg impedance. Orthonormal and non-orthonormal plots are compared (blue curves and scale: non-orthonormal scale; orange curves and scale: orthonormal scale).

Details

This Demonstration uses an orthonormal representation for the impedance of electrochemical systems. Two examples are dealt with, A and B.
A. equivalent circuit for a Tafelian electrochemical system with:
Z=
R
ct
/(1+
R
ct
C
dl
jω)
,
j=
-1
where
ω
is the angular frequency,
R
ct
is the charge transfer resistance and
C
dl
is the interfacial double-layer capacitance.
B. Randles circuit for the electrochemical (E) reaction occurring at the interface with a quiescent solution:
Z
f
=
R
ct
+σ
jω
and
Z=
R
Ω
+
Z
f
/(1+
Z
f
C
dl
jω)​
where
σ
is the Warburg parameter.

References

[1] J.-P. Diard, B. Le Gorrec and C. Montella, Cinétique electrochimique, Paris: Hermann, 1996.
[2] C. Montella, J.-P. Diard and B. Le Gorrec, Exercices de cinétique electrochimique, II Méthode d'impédance, Paris: Hermann, 2005.
[3] M. E. Orazem and B. Tribollet, Electrochemical Impedance Spectroscopy, Hoboken, NJ: John Wiley & Sons, 2008.

External Links

Permanent Citation

Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.