Faradaic and diffusion control

This method requires a VoltaLab 40 or a VoltaLab 80

Files:
Dynamic EIS.(Impedance).EXP
Dynamic EIS.(Impedance) 000_01Z.CRV

Abstract

The principle is to measure the impedance at fixed potential during a frequency scan. Electrochemical Impedance Spectroscopy is useful to study the kinetics at the interfaces and to distinguish between the various mechanisms which regulate the charge transfer. Here, we examine a heterogeneous charge transfer going with a linear diffusion process. In such a case, the resulting Nyquist diagram shows two distinct

Parts[1]:

1) Kinetic control : The semi-circle at high frequencies corresponds to the faradic charge-transfer behaviour. The polarisation resistance is equal to the intercept segment of the semi-circle with the real impedance axis.

2) Mass transfer control: The straight line at low frequencies corresponds to the linear diffusion process of oxidised and reduced species and is described as the "Warburg" impedance. The slope of this line gives information about the type of diffusion.

Sample

Solution : Redox buffer type BS870, diluted 10 times in phosphate buffer type PH7-6B {Potassium Hexacyanoferrate III (Ferricyanide) plus Potassium Hexacyanofferate II (Ferrocyanide) at 10E-2 mol/l in phosphate buffer, pH 7.00}.

WORK Static platinum disc electrode
Area = 0.196 ±0.01 cm² (Diameter = 5.0±0.05 mm)
REF Calomel electrode type XR100
AUX Platinum wire type XM100
CP06 cell at room temperature (22°C) fitted with a nitrogen bubbler, in order to remove dissolved oxygen. The bubbling is stopped during the experiment.

Settings - Experimental

The impedance data are collected at OCP from 10 KHz down to 0.1 Hz with an AC sine wave amplitude of 10 mV and 20 frequencies per decade.

Curve examination

Display : Type = Nyquist Z

1) Kinetic control: The semi circle at high frequencies corresponds to the faradic charge-transfer behaviour. The polarisation resistance is equal to the intercept segment of the semi circle with the real impedance axis.

Circular regression ( with R1R2C fitting) **** Display Type = Nyquist Z

Point1 : 0
Point2 : 38
Centre, X: 28.54 ohm.cm²
Centre, Y: -2.44 ohm.cm²
Diameter: 21.75 ohm.cm²
Coefficient: 1
Depletion angle: -6.44 °
X min: 17.936 ohm.cm²
X max.: 39.137 ohm.cm²
R1: 17.936 ohm.cm² (Corresponds to the "cell-electrolyte resistance")
R2: 21.200 ohm.cm² (Corresponds to the "polarisation resistance")
C: 16.815 µF/cm² (Corresponds to the "double layer capacity")

2) Mass transfer control
The straight line at low frequencies, corresponds to the linear diffusion process of oxidised and reduced species and is described as the "Warburg" impedance. The slope of this line gives information about the type of diffusion.

Linear regression **** Display Type = Nyquist Z

X min.: 45.27
X max.: 58.62
Mode: y=f(x)
Correlation coefficient: 0.999788
y(ohm.cm²) = 0.912*x(ohm.cm²) -33.672
x(y=0) = 36.9564

**** Slope = 0.912
If the thickness of the diffusion layer is "infinite" and the electrode surface is flat, the angle of the Warburg line with the real axis is expected to be very close to 45°. This angle corresponds to a slope equal to 1 [1].

**** x(y=0) = 36.9564
In the case of a reversible reaction, the extrapolated real component of the Warburg line (x(y=0)) is directly connected to the diffusion coefficients and Kinetic constants of the redox species [1].

Conclusion

The Nyquist display is in accordance with the theory.

[1] C.M.A. Brett and A.M.O. Brett "ELECTROCHEMISTRY" p 224 and next - Oxford Science Publ. , 1993.