Kramers-Kronig Transforms as Validation of Electrochemical Immittance Data Near Discontinuity

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Abstract
Immittance data was recorded for copper rotating disk in concentrated copper sulphate/sulphuric acid electrolyte, and its evolution under potential control (PC) was analyzed starting from the active state at rest potential, through active/passive transition up to the stable passivity. In the potential range corresponding to the passivity under PC, the transition was observed from the nonminimum phase (nmp)-type of immittance to the minimum phase (mp) one which corresponded to Hopf bifurcation under current control. This transition was manifested by a resonance-like peak on the amplitude characteristic and the phase change from apparently discontinuous as displayed in [−180°, +180°] range (nonminimum) to the continuous (minimum) one. In complex coordinates this was featured by scattered impedance points. Validation by Kramers-Kronig (KK) transformation of nmp-type immittance data failed for impedance representation used in transformation but was successful for admittance representation as the latter was the form actually recorded under PC. This finding validates both nmp and mp immittance data in agreement with earlier suggestions of other authors. [See, Gabrielli et al. , in Electrochemical Impedance: Analysis and Interpretation, p. 140, ASTM, Philadelphia, PA (1993).] Transition from mnp to mp type of electrode dynamics can be attributed to appearance of conduction channels representing local depassivation of the electrode. © 2003 The Electrochemical Society. All rights reserved.