The galvanostatic double-pulse method in the study of the kinetics of stepwise electrode processes involving the adsorption of intermediates

Abstract

The kinetics of the overall electrode reaction Me 0−3 e − = Me 3+ proceeding through three consecutive charge-transfer steps involving the intermediate ions Me + and Me 2+ adsorbing on the electrode according to the Langmuir. Temkin and Frumkin isotherms under transient single- and double-pulse galvanostatic conditions, have been analysed. The curves of η− t, θ 1− t, θ 2− t have been calculated by computer for different ratios of the exchange current densities of the charge transfer steps and different adsorption isotherms, taking account of the absence of interaction, repulsion and attraction between the intermediates adsorbed. The general equation for the stationary polarization curve of the three-step electrode process with two steps of adsorption of intermediates obeying the Langmuir and Temkin isothersm, has been derived and analyzed. It is shown that when the equilibrium surface coverage with Me + (Me 2+) ions, θ 1° (θ 2°), exceeds a certain critical value, θ 1cr° (θ 2cr°), determined by the ratio of the kinetic parameters of the partial charge transfer steps, the anode (cathode) stationary polarization curve has no linear region corresponding to the limiting step of the first electron transfer, as demanded by the classical theory of stepwise processes without adsorption of intermediates. In this case, the evaluation of the kinetic parameters of the fast first step from stationary polarization data and the data obtained by the galyanostatic single-pulse method is impossible. It is shown that when the equilibrium coverage of the electrode surface with Me + ions exceeds a certain critical value, θ 1cr°, kinetic parameters of the fastest step, Me 0 − e − = Me + ads, can be determined by the double-pulse method; the standard value of the rate constant of this step should not exceed 180 s −1 (direct mechanism of insertion of adatoms into the metal lattice, assuming that surface concentrations of adatoms and ad-ions in k s calculations are expressed as mol/cm 2). On the basis of the theory worked out, the galvanostatic double-pulse method (GDP) is used for studying the kinetics of the overall electrode process Bi 0(solid) − 3 e − = Bi 3+ The GDP study is carried out on a polycrystalline Bi electrode in solutions containing 10 −3 −10 −1 M Bi and 2 M perchloric acid at 25°C. It is shown that the overall electrode reaction proceeds through three partial steps of charge transfer involving the adsorption of intermediates: Bi 0(solid) − e − = Bi + ads (a) Bi + ads − e − = Bi + ads (b) Bi 2+ ads − e − = Bi 3+ (c) The kinetic parameters of the partial charge transfer steps (b) and (C) are found to be i 02 = 8.9 × 10 −6 A/cm 2; i 03 = 8.9 × 10 −5 A/cm 2 at [Bi 3+] = 10 −3 M; β 2 = α 3 ≅ 0.5. The equilibrium surface coverage with Bi + ads exceeds a critical value (θ 1° > θ 1cr°). In this case, in conformity with the theory developed, it is impossible to study the kinetics of the fastest step (a) of Bi + ion transfer using stationary polarization curves. The analysis of transient η− t curves for an extremely short period of time (2–8 μs) after the beginning of the polarization yields detailed information on the kinetics of the fastest step (a) ( i 01 = 4.1 × 10 −3 A/cm 2 at [Bi 3+] = 10 −3 M; α 1 = β 1 = 0.5 ± 0.01). It is shown that the kinetics of step (a) obeys the Butler-Volmer-Frumkin theory of slow charge transfer quantitatively. The adsorption of Bi + intermediate is shown to proceed on the energetically inhomogeneous surface of solid bismuth electrode and to obey the Temkin isotherm with a high parameter of inhomogeneity.