Frequency of negative differential resistance electrochemical oscillators: theory and experiments

Abstract

An approximate formula for the frequency of oscillations is theoretically derived for skeleton models for electrochemical systems exhibiting negative differential resistance (NDR) under conditions close to supercritical Hopf bifurcation points. The theoretically predicted omega infinity (k/R)1/2 relationship (where R is the series resistance of the cell and k is the rate constant of the charge transfer process) was confirmed in experiments with copper and nickel electrodissolution. The experimentally observed Arrhenius-type dependence of frequency on temperature can also be explained with the frequency equation. The experimental validity of the frequency equation indicates that 'apparent' rate constants can be extracted from frequency measurements of electrochemical oscillations; such method can aid future modeling of complex responses of electrochemical cells.

Experimental Assessment of the Sensitiveness of an Electrochemical Oscillator towards Chemical Perturbations

“…The reaction of those molecules can thus be thought as one of the simplest yet very interesting experimental systems. Of late, Kiss and co-workers [21]–[22], [23], [24] have discussed the role of temperature and some electrical properties on the oscillation features. For a NDR oscillator, which typically oscillates under potentiostatic control, the authors found theoretically and experimentally that the frequency of oscillations is directly related to the square root of the velocity of charge transfer [21].…”

“…Of late, Kiss and co-workers [21]–[22], [23], [24] have discussed the role of temperature and some electrical properties on the oscillation features. For a NDR oscillator, which typically oscillates under potentiostatic control, the authors found theoretically and experimentally that the frequency of oscillations is directly related to the square root of the velocity of charge transfer [21]. On the other hand however, for HN-NDR oscillators in which the full activity of the catalyst is inhibited by a poisoning process it was found that the frequency was directly proportional to the square root of the velocity of poisoning [22].…”

Electrochemical oscillations of nickel electrodissolution in an epoxy-based microchip flow cell

“…[1] In such configurations the effects of physical parameters (series resistance, rotation rate and size of the working electrode) on oscillation properties can be quantitatively described with nonlinear analysis of predictive skeleton models for NDR type of electrochemical systems. [5-8] For example, it was shown that appearance of oscillatory instabilities with large rotation rates [7, 9-11] and large electrode sizes [7, 12] can be quantitatively contributed to the presence of a minimal ohmic (IR) drop requirement[7, 13] : large electrodes with ohmic drops that surpassed the critical IR drop exhibited oscillations while small electrodes with small IR drops retained their stable stationary states. (Note that there could also exist a maximum IR drop above which oscillations cease to exist[2, 3].…”

Bursting Oscillations in Shimizu‐Morioka System with Slow‐Varying Periodic Excitation

“…Wang et al [19] examined the synchronization of bursting through the introduction of finite delays. Kiss et al [20] studied the bursting oscillations in electrochemical systems caused by changes in the geometrical structure. Li et al [21] examined the mechanism of bursting oscillations in a nonsmooth generalized Chua's circuit with two time scales.…”