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Popular topics · Modelling and fitting (ZFit, ZSim)

Which equivalent circuit models the low-frequency inductive arc in acidic corrosion? (ZSim and ZFit)

Two-step reactions (iron dissolution in acidic medium, Volmer-Heyrovský proton reduction) show a capacitive or inductive low-frequency arc depending on potential. The indistinguishability of the C1/R1/(R2 + L2) and C1/(R1 + C2/R2) circuits.

Key points

  • In the Volmer-Heyrovský reaction the low-frequency arc of the impedance diagram changes from inductive to capacitive (or the reverse) as the electrode potential changes.
  • The C1/R1/(R2 + L2) circuit produces a low-frequency inductive arc; the same data are fitted perfectly with C1/(R1 + C2/R2) by forcing R2 and C2 negative.
  • Conversely, a capacitive arc simulated with C1/(R1 + C2/R2) is fitted with C1/R1/(R2 + L2) taking R2 and L2 negative.
  • The two circuits are indistinguishable: they give the same impedance and the choice rests on physical interpretation. A negative adsorption resistance or capacitance arises from the kinetics of the adsorption step.
  • In ZFit the sign of a parameter can be forced with the 'sign' box; because initial values are searched randomly, several attempts may be needed.
  • The most common case is the unpolarised system, i.e. natural corrosion in acidic medium. The rest of the series covers why circle fitting is wrong, detecting inductive behaviour, high-frequency inductance, circuit choice, distinguishability and identifiability.

Figures

Volmer-Heyrovský reaction: along the steady-state i-E curve the low-frequency arc turns from capacitive to inductive as potential changes.
Figure 1. Volmer-Heyrovský reaction: along the steady-state i-E curve the low-frequency arc turns from capacitive to inductive as potential changes.
ZSim simulation of a low-frequency inductive arc from the C1/R1/(L2 + R2) circuit.
Figure 2. ZSim simulation of a low-frequency inductive arc from the C1/R1/(L2 + R2) circuit.
The same inductive data are fitted perfectly with C1/(R1 + C2/R2) by forcing R2 and C2 negative.
Figure 3. The same inductive data are fitted perfectly with C1/(R1 + C2/R2) by forcing R2 and C2 negative.
Low-frequency capacitive arc from the C1/(R1 + C2/R2) circuit simulated with ZSim.
Figure 4. Low-frequency capacitive arc from the C1/(R1 + C2/R2) circuit simulated with ZSim.
Capacitive data are fitted with C1/R1/(L2 + R2) taking R2 and L2 negative: the two circuits are indistinguishable.
Figure 5. Capacitive data are fitted with C1/R1/(L2 + R2) taking R2 and L2 negative: the two circuits are indistinguishable.
Summary: Volmer-Heyrovský diagrams and the two corresponding equivalent circuits, by sign (R2, L2 > 0 or R2, C2 < 0).
Figure 6. Summary: Volmer-Heyrovský diagrams and the two corresponding equivalent circuits, by sign (R2, L2 > 0 or R2, C2 < 0).

Images: Bio-Logic Science Instruments; taken from the source article.

Related application notes

Related curriculum module: Electrochemical Impedance Spectroscopy (EIS)

Related products:EC-Lab®SP-200SP-300
Source: Bio-Logic Learning Center, “ZSim and ZFit as learning tools. Part I – Acidic corrosion” · Source updated: November 18, 2024
Copyright of the images and the original text belongs to Bio-Logic SAS.

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