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UNUSUAL ELECTROCHEMICAL IMMITTANCE SPECTRA WITH NEGATIVE RESISTANCE AND THEIR VALIDATION

UNUSUAL ELECTROCHEMICAL IMMITTANCE SPECTRA WITH NEGATIVE RESISTANCE AND THEIR VALIDATION BY KRAMERS-KRONIG TRANSFORMATION. Andrzej Sadkowski - Institute of Physical Chemistry of the Polish A cademy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, PL ansad@ichf.edu.pl.

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UNUSUAL ELECTROCHEMICAL IMMITTANCE SPECTRA WITH NEGATIVE RESISTANCE AND THEIR VALIDATION

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  1. UNUSUAL ELECTROCHEMICAL IMMITTANCE SPECTRA WITH NEGATIVE RESISTANCE AND THEIR VALIDATION BY KRAMERS-KRONIG TRANSFORMATION Andrzej Sadkowski - Institute of Physical Chemistry of the Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, PL ansad@ichf.edu.pl

  2. Local depassivation by creation of stable centres of active dissolution on the passiveelectrode is a crucial step for local processes including spatial pattern formation and various forms of localized corrosion, one of the most harmful forms of corrosion damage. The forewarning, much in advance of this to happen, is essential for effective control.

  3. Useful may be non-minimum-phase characteristics of electrodes subject to local depassivation. This feature is related to stability (metastability) of electrodes. (to reference the title of this Symposium!) Non-minimum phase electrodes show negativeresistance („hidden” sometimes) in electrochemical impedance spectra (EIS).

  4. This is demonstrated in the simplest case of 2nd order system: And modelled by electrical equivalent circuit: R0 R2 R1 C0 C1 R1, R2 ,C1 > 0 lub < 0. z1, z2 – zeros; p1, p2 - poles

  5. In general case: (m = n  n+1) zi - zeros, pi - poles, Z - hf limit In case of „bounded” or limited diffusion – approximation is possible: F. Berthier et al. Electrochimica Acta 44 (1999) 2397; J. Electroanal. Chem. 502 (2001) 126.

  6. Z(iω) – impedance = EAC / IAC z1, z2, p1, p2 <0 - minimum-phase (mp) system, stable unconditionally(under currentor voltage control, with any additional resistance added in series or in parallel). -90o < phase angle of mp (ArcTg(Im(Z)/Re(Z)) < 90o Non minimum-phase (nmp_ – when at least one of (zi, pi ) > 0 phase angle of nmp – any value !

  7. mp – equivalent to „passive” electrical circuits with R, L, C > 0 Always stable!

  8. nmp – includes negative resistance:Ri < 0 (sometimes „hidden”) stability limited ! here Rdc = R1+R2 < 0 („explicite” negative resistance)

  9. Fe armco, borate buffer, active-passive transition range. „Explicit” negstive resistance represents negative slope of steady state polarisation curve.

  10. Nmp: here: „hidden” negative resistance, seen only at certain frequencies. This is the case most interesting for us ! Stability under control of the voltage i.e. source with very small output resistance. Instability under control of the current i.e. source with very high output resistance.

  11. Copper passivation in sulphates: 0.15 M CuSO4+ 5M H2SO4 RDE: 994 rpm, 99.4 rpm, T=298 K E= 20, 30, 40, 50, 60 mV  110, 140, 150, 170, 175 mV Negative resistance. ++ Rs – loss of stability under potential control due to Z0

  12. E=400 mV/Cu before and after anodic (E=500 mV) polarisation. „hidden” negative impedance = nmp system (black) changes to stable unconditionally (mp – red) system as a result of local depasivation.

  13. The same plots:

  14. Impedance recorded almost exactly at the point of discontinuity. Hopf bifurcation under current (galvanostatic) control.

  15. All the more often reported are similar results: Electrochimica Acta 47 (2001) 501–508 „On the origin of oscillations in the electrocatalytic oxidation ofHCOOH on a Pt electrode modified by Bi deposition”. Jaeyoung Lee *, Peter Strasser, Markus Eiswirth, Gerhard Ertl

  16. Oscillatory Peroxodisulfate Reduction on Pt and Au Electrodes under High Ionic StrengthConditions, Caused by the Catalytic Effect of Adsorbed OH. Shuji Nakanishi, Sho-ichiro Sakai, Michiru Hatou, Yoshiharu Mukouyama, andYoshihiro Nakato*J. Phys. Chem. B 2002, 106, 2287-2293 

  17. M. Bojinov – A model of the anodic oxidation of metals in concentrated solutions. J. Electroanal. Chem. 405 (1996) 15

  18. Electrochimica Acta 47 (2002) 2297_/2301 Electrochemical oscillations in the methanol oxidation on Pt Jaeyoung Lee *, Christian Eickes, Markus Eiswirth, Gerhard Ertl

  19. Mechanism of discontinuity (switching circles from left to right half-planes, Hopf bifurcation under GC): appearence of local conduction channels, active centers on passive surface: Gp – local conduction channel. (local active center). Gp = (0, 0.9, 1.0, 1.1, 1.2) * Gh

  20. Calculated Voltage-step (left) and current-step (right column) responsesfor nmp electrode with local depassivationrepresented by parallel conductance Gp = 1/Rp = x * Gh x = 0 x = 0.9 x = 1.1 x = 1.4

  21. Some authors still deny validity of such data based on their failing to comply with Kramers-Kronig transformation (KKT). Imaginary part reconstructed from real part of the spectrum: Real part reconstructed from imaginary part of the spectrum:

  22. This rebuttal is evidently erroneous: In case of nmp-type electrodes KKT fails for impedance data but is successful for admittance representation of data. Under voltage control it is admittance which is measured is and it should be KK tested.

  23. Failing of the KKT for data transformed as impedance. (lines– experimental data, dots KKT data) The same data KK transformed in admittance representation and back-calculated to impedance. (lines– experimental data, dots KKT data) Good agreement !

  24. To be quite honest: the agreement is good at peaks. Much worse close to zero. Errors of integration! KRAMERS-KRONIG TRANSFORMS AS VALIDATION OF ELECTROCHEMICAL IMMITTANCE DATA NEAR DISCONTINUITY A. Sadkowski1*, M. Dolata, J.-P. Diard Journal of Electrochemical Society, in press (MS03.02.062)

  25. Financial support by Research Grant No 7T08C 012 20 of the State Committee for Scientific Research is gratefully acknowledged.

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