Abstract
The high-frequency region of the impedance diagram of an electrochemical cell can be deformed by the inductance of the wiring and/or by the intrinsic inductance of the measuring cell. This effect can be noticeable even in the middle frequency range in the case of low impedance systems such as electrochemical power sources. A theoretical analysis of the errors due to inductance effects is presented here, on the basis of which the admissible limiting measuring frequency can be evaluated. Topology deformations due to the effect of inductance in the case of a single-step electrochemical reaction are studied by the simulation approach. It is shown that an inductance can not only change the actual values of the parameters (electrolytic resistance, double layer capacitance, reaction resistance), but can also substantially alter the shape of the impedance diagram, this leading to erroneous structure interpretations. The effect of the size and surface area of the electrode on its intrinsic inductance is also evaluated.
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Abbreviations
- A :
-
linear dimension of the surface area confined by the circuit (cm)
- C D :
-
double layer capacitance (F)
- C M :
-
measured capacitance
- d :
-
diameter of the mean effective current line (mm)
- f max :
-
limiting (maximum) frequency of measurement (Hz)
- K 1,K 2 :
-
shape coefficients with values of 2π×10−9 and 0.7 for a circle, and 8×10−9 and 2 for a square (dimensionless)
- L :
-
intrinsic inductance of the electrochemical cell assumed as an additive element (H)
- R E :
-
electrolyte resistance (Ω)
- R M :
-
measured resistance (Ω)
- R P :
-
reaction resistance (Ω)
- r 0 :
-
specific resistance (Ω cm)
- S :
-
electrode surface area (cm2)
- T c :
-
time constant (s)
- Z :
-
impedance (Ω)
- Z lm :
-
imaginary component of the impedance without accounting for the influence of inductance (Ω)
- Z′ lm :
-
imaginary component of the impedance accounting for the influence of the additive inductance (Ω)
- β:
-
shape coefficient; β=1 for a square and β=π1/2/2 for circle (dimensionless)
- εL :
-
relative complex error due to the influence of inductance (dimensionless)
- ε AL :
-
relative amplitude error due to inductance (%)
- ε Lϕ :
-
relative phase error due to inductance (%)
- ϱ:
-
ratio between the effective inductance time constant and the capacitive time constant (dimensionless)
- ω:
-
angular frequency (s−1)
- ωR :
-
characteristic frequency at which the inductive and capactive parts of the imaginary component of impedance are equal (s−1)
References
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Z. Stoynov, 28th ISE Meeting, Extended Abstracts, Varna (1977) p. 148.
Z. Stoynov and B. Savova-Stoynov,J. Electroanal. Chem. 209 (1986) 11.
G. Staikov, P. D. Yankulov, B. S. Savova-Stoynov and Z. B. Stoynov,J. Appl. Electrochem. 15 (1985) 895.
Z. Stoynov and B. Savova-Stoynov,J. Electroanal. Chem. 170 (1984) 63.
‘Elektrotekhnicheskii Spravochnik’, Vol. 1, Gosenergoizdat, Moscow (1955).
H. Göhr, M. Mirink and C. A. Schiller,J. Electroanal. Chem. 180 (1984) 273.
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Savova-Stoynov, B., Stoynov, Z.B. Analysis of the inductance influence on the measured electrochemical impedance. J Appl Electrochem 17, 1150–1158 (1987). https://doi.org/10.1007/BF01023598
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DOI: https://doi.org/10.1007/BF01023598