J.H. Sluyters

The theory of chronoamperometry for the investigation of electrocrystallization : Mathematical description and analysis in the case of diffusion-controlled growth

A critical study is made of the mathematics needed to describe the current response towards a potential step perturbation of an electrode at which phase formation takes place by the process of nucleation and diffusion-controlled hemispherical growth. As a result, an expression for the current-time transient is derived which is more general than the expressions for the limiting cases used hitherto. Procedures are discussed for fitting experimental data to this new expression in order to obtain the number density of nucleation sites and the nucleation rate constant. The theory is extended to cases where overlap of growing nuclei has to be accounted for, resulting in a new expression as well. From a comparison with existing theories it is concluded that the present derivation, and its result, although also not rigorous, is to be preferred because it is unique in extrapolating to both short-time and long-time limiting behaviour exactly.

On the impedance of galvanic cells

Summary A critical discussion is presented of some important theories for the electrode impedance in the case that the electroactive species are specifically adsorbed at the electrode-solution interface. It is argued that the equations given by Reinmuth are the most satisfactory so far available for reversible systems. These equations are based on the idea of coupling between faradaic and double-layer charging processes, asintroduced by Delahay . A derivation of the equations is presented in an Appendix. Procedures are proposed for analysing impedance data according to the equations of Reinmuth . Three cases must be considered, viz. , no, weak, and strong reactant adsorption. Experimental results are given for the Pb 2+ /Pb(Hg) electrode system in M KNO 3 −KCl mixtures. It is shown that the adsorption of lead at the interface increases with KCl concentration, as can be concluded from the increasing enhancement of the “double-layer capacitance”. The proposed procedures for analysing impedance data are shown to be applicable. Some arguments are presented to show that the neutral PbCl 2 species is adsorbed at the interface.

The mechanism of the reduction of Zn(II) from NaClO4 base electrolyte solutions at the DME

Abstract The reduction of Zn(II) has been studied by means of the faradaic impedance method in wide potential and frequency ranges and at varied water activity. The results obtained could be quantitatively explained on the assumption of a mechanism including at least the following consecutive steps: 1. (1) fast partial dehydration of the electroactive species; 2. (2) fast transport from the solution into the double layer; 3. (3) slow transfer of the first electron; 4. (4) a fast second partial dehydration step; 5. (5) slow transfer of the second electron. The hydration number of the Zn2+ ions in the solution was obtained from the shift of E 1 2 r and Eox with water activity, and was found to agree fairly well with the results obtained from the kinetic study.

On the selection of the most probable mechanism of the Cd(II) reduction at mercury from 1 M KF solution

Abstract A faradaic impedance study has been made of the reduction of Cd(II) ions from a 1 M KF base electrolyte at the DME. It could be shown that only the Cd(II) present in the solution and the end product, viz. Cd(Hg), are the diffusing particles and that intermediates are present only at the interface. From the analysis of the impedance dat it followed that at the interface the Cd(II) species is first subject to a heterogeneous chemical transfer and there-after is reduced according to two discrete one-electron transfers, both obeying the Butler-Volmer equation. The kinetic parameters of the steps are reported. A number of other conceivable mechanisms were considered, but fortunately they all either could be definitely ruled out or were found to be less acceptable.

On the impedance of galvanic cells: XXII. Determination of the parameters of the double-layer impedance from the electrode impedance and the electrocapillary curve in the case of specific

Abstract The electrode impedance in the case of specific adsorption of the electroactive species is discussed, critically applying the charge separation model of delahay . Comparison with experiments performed with the In 3+ /In(Hg) couple in 1 M KCNS, comprising impedance, chronopotentiometric and surface-tension measurements, is given. An improved theory of the relation between surface tension and double-layer parameters is presented, leading to a better agreement with experiment. Consistent values are obtained for the surface excess of In 3+ . It is shown that the linear relation between the value of the double-layer capacity and Tl + concentration that has been found earlier at low concentrations, also holds for concentrations up to 2 m M . The consequences of the application of a modified treatment given by reinmuth , are discussed.

On the impedance of galvanic cells: XVIII. The potential dependence of the faradaic impedance in the case of an irreversible electrode reaction, and its application to A.C. polarography

A theoretical treatment for the potential dependence of the faradaic impedance, in the case that the electrode reaction behaves irreversibly with respect to the direct current, using the steady-state concept, is presented. An analysis of the expressions obtained in the complex impedance plane is given and a method is described to measure even a very small rate constant, ksh. The consequences for a.c. polarography are discussed. It has been found that even very irreversible electrode reactions exhibit substantial peaks in an a.c. polarogram. If only the oxidized form of the reactant is present, one peak appears even for very small ksh-values. For decreasing ksh, the peak height decreases to a limiting value, independent of ksh andsufficiently large to be detectable in an a.c. polarogram. If both the oxidized and reduced form are present, two peaks occur for irreversible systems, the peak heights again being independent of the ksh-value.

A high-precision network analyzer system for the measurement of the electrode impedance of both stationary and non-stationary electrode, with special attention to the dropping mercury electrode

A largely automatic instrument for the measurement of the admittance of a galvanic cell is described. During a measurement the frequency of the alternating voltage and the dc voltage are scanned stepwise in a programmed sequence. A high precision has been obtained by applying a programmed correction procedure and an automatic correction for short-term drift. The performance of the instrument is demonstrated on a dummy cell, a cell with supporting electrolyte only and on the determination of the kinetic parameters of the fast Cd(II) ion reduction on the DME in 1 M KCl.

On the impedance of galvanic cells: XXIV. The impedance of the In3+/In(Hg) electrode reaction in KSCN and KCl solution

Summary The In3+/In(Hg) system in KSCN and KCl solutions has been investigated using both d.c. and a.c. measurements. The experimental data are analysed and interpreted according to theoretical equations presented recently. It is shown that the specific adsorption of indium from 1 M KSCN follows a linear adsorption isotherm up to 0.4 mM. No specific adsorption of indium can be detected from KCl solutions. The electrode reaction in 1 M KCl is not complelely reversible: ksh=(6±2)·10−2 cm/sec at the standard potential, supporting the hypothesis that adsorption of reactants renders an electrode reaction reversible. Also, the minima in the In3+ limiting current have been studied. It appears that the faradaic impedance is negative at the potentials of the minimum. The phenomena are explained qualitatively with equations based on a potential-dependent ksh. Some arguments are presented for this potential-dependency; it is proposed that ksh depends exponentially on the specifically adsorbed charge, q1, of the anions of the supporting electrolyte. The exponential dependence of ksh on q1 was verified for 0.4 mM In3+ in 1 M KCl at potentials near the half-wave potential.

Electrode kinetics and double-layer structure: II. The potential-dependence of the kinetic parameters of the Zn2+/Zn(Hg) electrode reaction

Summary The impedance of the Zn2+/Zn(Hg) electrode in 1 M KI, KBr, KCl and NaClO4 solutions has been measured as a function of potential, using an externally polarised dropping mercury electrode. The potential-dependence of the faradaic impedance has been carefully analysed. It is shown that, in general, both the apparent rate constant and the apparent transfer coefficient are potential-dependent. In the cathodic potential region (−1.05 to −1.35 V vs. SCE) the results are in accordance with a constant value, β=0.19±0.02 for the “true” cathodic transfer coefficient and a potential-dependent rate constant which increases if the amount of specifically adsorbed anions increases. In the anodic potential region (−0.90 to −0.95 V vs. SCE) a significantly different transfer coefficient is found, β=0.60±0.03, which indicates that the mechanism of the electrode reaction depends on the d.c. potential. It is suggested that the interpretation of kinetic parameters and the testing of simple theories with such systems should be approached with caution.

On the impedance of galvanic cells: XXI. Analysis of the electrode impedance in the case of a non-reversible electrode reaction with specific adsorption of the electroactive species; appl

Abstract The impedance of the Pb2+/Pb(Hg) electrode has been measured in order to demonstrate the effect of specific adsorption of the electroactive species. The simple randles circuit is not in accordance with the experimental facts and therefore an attempt has been made to interpret them in terms of the theory of S enda A nd D elahay , or D elahay s new charge separation, model. The procedure for evaluating the parameters is fully outlined. It is found that the experimental data fit both models.