Significance of Nonsteady-State A-C and D-C Measurements in Electrochemical Adsorption Kinetics

Abstract

Information obtainable from nonsteady-state electrochemical studies is examined with particular reference to the determination and significance of capacitance associated with adsorbed intermediates in consecutive reactions. The frequency dependence of the capacity in a-c measurements is related to the rise-time dependence in d-c charging transients and the concept of an equivalent frequency in d-c measurements is proposed. The nonsteady-state kinetics for a galvanostatic charging process is examined for a reaction sequence involving adsorbed intermediates, and it is shown how the capacitance behavior depends on the charging current density. Applications to the triangular voltage sweep method are made, and it is shown that for this case where neither steady-current nor steady-state kinetics apply, care must be exercised in interpretation of results derived from this method. The nonsteady-state kinetics for this case are derived and the dependence of the capacity on sweeprate is deduced. The differential galvanostatic method leads to results which can be much more explicitly analyzed in a rigorous kinetic manner, for irreversible charging processes. Applications to experimental results which support the treatment given are discussed.The adsorption pseudocapacitance (1) arising in certain electrochemical reactions, where an initial discharge step is at quasi-equilibrium when followed by a rate-determining step, may be defined aswhere 0 is the fractional surface coverage by intermediates formed by the discharge of an ionic species, V is the metal-solution potential difference, and k is a proportionality constant, representing the Faradaic charge which has to cross the metal-solution interface for a complete monolayer of discharged species (e.g., adsorbed radicals, metal adions) to be formed on unit real surface area of the electrode.Experimental methods for determining the adsorption pseudocapacitance have been reviewed recently (2-4) and the form of the C --V relationship has been derived, assuming that the electrode system obeys an ideal Langmuir isotherm (5, 6) and for the more general and experimentally applicable case when the variation of the heat of adsorption with coverage (Temkin type of isotherm) is also taken into account (1, 7). Cases for which the assumption of quasi-equilibrium in the initial ion discharge step cannot be made have also been considered (7,8).The capacitance at the metal-solution interface can be obtained from a-c impedance determinations by a compensating bridge method or from phase angle measurements. The electrode is first polarized to a steady-state by applying a constant current or potential, and its impedance with respect to a small a-c signal is measured and resolved into its capacitative and resistive components. The amplitude of the a-c signal is maintained very low so that the steady current condition at the electrode is not significantly disturbed. The capacitance measured by the method is usually found to depend on the frequency and at any frequency it is the sum of the ionic ...

The Mechanism of Electrochemical Oxidation of Organic Fuels

“…39 Conway has recently commented on the significance of measurements by the triangular-voltage-sweep method applied to adsorption reactions, 168 and this has been subsequently expanded. 169 The derived equations indicate a complex variation of the capacity with sweep rate, involving several terms in dV jdt, and the adsorption pseudocapacities measured at significant sweep rates are then difficult to interpret. Conway concluded: "The steady, slow, point-by-point potentiostatic examination of a current potential relationship is to be preferred for evaluating kinetic behavior, and the direct differential galvanostatic method is to be preferred for dealing quantitatively with charging processes, since the current density is kept constant and is measured, and the resulting equations for the variation of the fractional coverage and the adsorption pseudocapacity with time and potential are much simpler."…”

“…In most of these investigations kinetic parameters have not been clearly determined nor have reaction mechanisms been established. The polarographic oxidation of a number of compounds at solid electrodes, or simply cyclic voltametry, was reported by Pysh and Yang 292 and by Suantoni et al 293 The electrochemical processes involved in the quinonehydroquinone redox couple have recently been examined by Bagotzky et al 294 In acid solutions the rate determining step was found to be (167) followed by QHad + H+ ¢ QHiad (168) and QHiad + e¢QH2 (169) In alkaline solution a similar mechanism was proposed, namely, A discussion of the nature of electronic interactions between the metal surface and adsorbed molecules requires the consideration of several factors: the magnitude of the electronic work function, the number of unfilled electron levels in the 3d, 4d and 5d bands, the structure of adsorbing crystal planes, the electron affinity of the adsorbing species, the asymmetry of the electron configuration of the adsorbed species, the presence of unpaired electrons and n electrons, the effects due to steric hindrance, and the various bond energies in the adsorbing species. The first three are characteristics of the metal surface.…”

Electrode Kinetic Aspects of the Kolbe Reaction

“…Effect of ¿cath on the C-V Profiles The effect of ¿oath (¿.e., cathodic current density used in the reduction transient) on Cmax (¿.e., the capacity maximum) and Vcmax may also be of some value in the identification of an adsorbed species. Thus, it can be shown theoretically (29) that for an irreversibly adsorbed electroactive species, an increase in ¿cath used in the cathodic transient should shift Cmax to higher values and Fcmax to more cathodic potentials. This effect arises because the capacity measured during a constant current charging process is not the "equilibrium capacity", i.e., it is not the value of capacity that will correspond to the value extrapolated to zero ac frequency if the capacity measurements were made by an ac method, e.g., as in the work of Dolin and Ershler (44).…”

“…The kinetic interpretation of the results obtained are discussed below (section V.A.2.b). which the various capacity maxima, Cmax (i.e., peaks in the differentiated potential decay, cathodic reduction profiles, or potentiodynamic profiles) appear; (d) general shape of capacity-potential profiles which under favorable circumstances can be indicative of the nature of adsorbed intermediates; (e) departures from equilibrium behavior induced in the capacity-potential profiles by applied "perturbations" (i.e., the dependence of the position and shape of the capacity profile on the reduction current in cathodic transient curves and on scan rate in the potentiodynamic profiles) (29) interpreted in some cases as diagnostic of the nature of the surface species involved in the Kolbe reaction ( 162).…”

Capacitance Studies of Passive Iron in Neutral Solutions by the Potentiostalic Pulse Method

“…In principle it is equivalent to the galvanostatic pulse method. The charge can be passed at a high initial c. d., which, according to Conway et al [16], corresponds to a high frequency in the a. c. method. In accuracy and reproducibility the potentiostatic pulse method is better than the galvanostatic pulse method and in most cases it is comparable to the a. c. method.…”