Application of Impedance Spectroscopy to Electrochemical Instabilities

Abstract

Electrochemical impedance spectroscopy (EIS), a well-established technique in classical electrochemistry [1], can also be very useful for the analysis of stability of electrochemical systems, including diagnosis of selected bifurcations. Impedance spectra of such dynamical systems allow also classify electrochemical oscillators into respective types. In fact, due to linearization involved in the concept of impedance, this way of the stability analysis of electric (electrochemical) circuits is a specific variant of linear stability analysis described in Sect. 1.3.In this section a short presentation of the principle of impedance measurements is described, in order to make the reader familiar with the notation used further in this chapter. The basis for this summary will be typical (Randles-type) equivalent circuit from Fig. 2.6, in which Z f will henceforth mean generally the ac impedance, measured for ac frequency f [Hz] (or angular frequency o ¼ 2pf [rad s À1 ]). The idea of such equivalent circuits, coming from the seminal work of Randles [2], was concordant with the experimental equipment used in early times of impedance measurements. It involved the ac bridge, in which one branch contained the experimental system, the impedance characteristics of which had to be balanced, in the other branch, by the impedance of the electric (equivalent) circuit, possibly closely reflecting the properties of the experimental one.Typically the electrochemical cell is first brought into steady-state, or at least quasi-steady-state (E ss , I ss ) which is further perturbed with the externally applied small amplitude, sinusoidal ac voltage (typically) or ac current. As a consequence, the electrode potential E and the current I will oscillate around their steady-state values with the same frequency o, but in general case exhibiting (frequency dependent) phase difference. In general notation one can denote the phase shifts for both the electrode potential and the current as ' 1 and ' 2 , respectively, and then:M. Orlik, Self-Organization in Electrochemical Systems I, Monographs in Electrochemistry,

Direct Liquid Fuel Cells—The Influence of Temperature and Dynamic Instabilities

“…In other words, there is a negative differential resistance (NDR) region. There is a range of work on the origin of bistability and oscillatory kinetics, ,,,, but here, we will restrict ourselves to practical concepts, such as the use of the electrochemical impedance spectroscopy (EIS) technique ,,,,,, to locate in which region of the j – E curve transitions from a stationary to an oscillatory state can occur. This will help us understand why methanol and formic acid have robust potential oscillations that remain until 60 and 70 °C, respectively, while ethanol has its dynamics restricted to a small current window, and DME did not exhibit oscillatory kinetics.…”

“…It is worth noting that an EIS spectrum covering a wide range of frequencies must be capable of linearization throughout its domain and for that, it must be stable. Linearity is guaranteed using AC disturbances of small amplitudes and by asymptotic stability, and the latter is the return to the initial steady state when the external stimulus is removed. , Thus, when dealing with nonlinear and unstable systems, such as the electro-oxidation of some organic molecules, the EIS analyses must be carried out under conditions in which the steady state is maintained over time. It is noted that the polarization curves for fuel cells evaluated here (Figures , , , and ) are stable under potentiostatic control: for each potential, there is only one associated current value.…”

“…It is noted that the polarization curves for fuel cells evaluated here (Figures , , , and ) are stable under potentiostatic control: for each potential, there is only one associated current value. In fact, it is known from previous studies that the electro-oxidation of most small organic molecules is classified as hidden N-shaped negative differential resistance (HN-NDR) oscillators. ,,,,,,,, Basically, this class of electrochemical oscillators is characterized by an N-shaped j – E curve that is partially hidden at low potentials because of adsorbates that inhibit the reaction to continue. ,,, In other words, a fast reaction step that otherwise could occur freely is masked/hidden under DC conditions by a slow step that forms a strongly adsorbed intermediate, a catalytic poison. These systems show current and potential oscillations.…”

“…The second is known as saddle-node bifurcation and occurs when Z = 0 for ω → 0. The latter is associated with bistability/hysteresis. , …”

Nonlinear Behavior of Nickel Dissolution in Sulfuric Acid in a Cathode-Anode Cell Configuration: Effect of Cathode Area

“…Nonlinear phenomena (e.g., bistability, oscillations, and pattern formation) in electrochemical systems are often studied in the traditional three-electrode configuration utilizing the working, reference, and counter electrodes. [1][2][3][4] Reactions of interest take place on the surface of the working electrode, whose potential is set with a potentiostat with respect to a reference electrode. The use of potentiostat, along with proper cell design, allows minimizing interferences from the processes at the counter electrode.…”