K. Holub

Voltammetry of metal complex systems with different diffusion coefficients of the species involved. I. Analytical approaches to the limiting current.

Abstract An exact solution is derived for the limiting current of a metal complex system for which the diffusion coefficients of the free and complexed metal are different. The solution is formulated in the Laplace domain and holds for a stationary planar electrode under conditions of an excess of ligand. It is valid for any set of values of the association/dissociation rate constants, which includes any value for the stability constant of the complex. In combination with a suitable inverse transformation method, highly interesting results are obtained for the current transients. The exactness of the treatment has been verified in various ways. For a number of limiting cases, fully analytical expressions in the time domain are derived. Important features appear, among them a generalized lability criterion for metal complex systems.

Facilitated ion transfer across the water/nitrobenzene interface Theory for single-scan voltammetry applied to a reversible system☆

The transfer of the metal cation across the interface between two immiscible electrolyte solutions facilitated by complex formation with a ligand at the interface was investigated both theoretically and experimentally. The theory of single-scan voltammetry was derived which enables the complex stoichiometry (1:1, 1:2 or 1:3. cation to ligand) to be determined as well as the thermodynamic and transport parameters of the facilitated charge transfer controlled by the diffusion of the ligand. Application of the theoretical results was illustrated for the transfer of Li+ and Cd2+ ions across the water/nitrobenzene interface facilitated by complexation with the neutral macrocyclic polyether diamine.

Influence of reactant adsorption on limiting currents in normal pulse polarography: Part II. Theory for the stationary, spherical electrode

Abstract The basic analytical theory for NPP limiting currents affected by reactant adsorption is extended to the case of a spherical electrode. Explicit expressions for the current are derived for the two limiting cases of a linear adsorption isotherm and full coverage before pulse application respectively. The enhanced mass transport towards the spherical electrode always leads to a lower degree of adsorptive depletion as compared with the planar case. The correspondingly higher surface concentration gives rise to increased pulse currents and this is the main effect of sphericity on the depressed NPP signal. It is clearly reflected by the dependencies of the current on the pulse duration and the drop time.

The double layer at the interface between two immiscible electrolyte solutions: Part III. Capacitance of the water/1,2-dichloroethane interface

Abstract From ac impedance and galvanostatic pulse measurements the capacitance of the interface between solutions of LiCl in water and tetrabutylammonium tetraphenylborate in 1,2-dichloroethane has been evaluated at various electrolyte concentrations. The experimental data have been interpreted on the basis of the modified Verwey-Niessen model, according to which a layer of oriented solvent molecules (inner layer) separates two space charge regions (diffuse double layer). As for the water/nitrobenzene interface, the interfacial potential difference is spread mainly within the diffuse double layer. In the sequence nitrobenzene

Influence of reactant adsorption on limiting currents in normal pulse polarography. Part. IV. Theory for the expanding drop electrode

Abstract The analytical theory for NPP limiting currents affected by reactant adsorption is extended to the case of the expanding drop electrode. Explicit expressions for the current I 1 are derived after a suitable choice of the independent variables and expansion of the surface concentration functions into power series. Two limiting cases are considered i.e. a linear adsorption isotherm and full coverage before pulse application. The dependences of I 1 on drop time, pulse duration and reactant concentration are discussed in some detail. Qualitatively, the dependence of I 1 on pulse duration is analogous to what was found for the stationary planar electrode. The agreement with literature data obtained from digital simulation is good.

The analog method for solution of problems involving diffusion to the electrode: I. Diffusion to a sphere with langmuirian adsorption solved by analog method

Abstract The RC network commonly used as a model of diffusion is studied and its utilization as a new functional element for analog computation with transfer function s 1 2 is shown. This functional element makes it possible to obtain analog solutions of many diffusion problems in electrochemistry. The diffusion to a sphere with Langmuirian adsorption was solved as an example of the versatility of this functional analog element.

Regeneration of a substance undergoing an electrode reaction by disproportionation at a rotating electrode: I. Theory

Abstract The relation between J—the relative increment of the current i corresponding to the electrode process on a rotating disc electrode with regeneraton of the substance by the disproportionation over the current io, corresponding to the electrode process without disproportionation reaction—and the rate constant k of the disproportionation reaction has been calculated. The relation is given in Table 1 for values of ϰ = (2ka*/(0.51 2 5 ω)) (ν/D) 1 3 ⩽ 50. The approximate analytical expression ϰ = 1.809 (1 + J)2/(1 − J)3, first derived in another way by Ulstrup4 is valid with good accuracy for ϰ ≧ 50 (or J ≧ 0.56). Estimates of the relative error of k due to the error in the measurement of J is discussed. It is shown that the value of J used for the determination of the rate constant k of the disproportionation reaction should be far enough from 0 and also far enough from 1.

The analog method for solution of problems involving diffusion to the electrode: II. Kinetics of adsorption controlled by diffusion to the plane, spherical, and dropping electrodes for an arbitrary adsorption isotherm

Summary Kinetics of adsorption controlled by diffusion can be solved on an analog computer with the functional element s 1/2 +constant, previously proposed 1 . The method covers the plane, spherical, and dropping electrodes and any kind of adsorption isotherm. The general formulation for these cases has been given. Examples of solution for the Frumkin isotherm (plane and spherical electrodes) and for the linear isotherm (dropping electrode) are shown.

Influence of reactant adsorption on limiting currents in normal pulse polarography: Part V. Theory for non-linear adsorption

Abstract The analytical theory for adsorption-influenced limiting currents in normal pulse polarography is extended to conditions where the adsorption isotherm is non-linear. The case of Langmuirian adsorption at a stationary planar electrode is treated in detail, using the Reinmuth series for the dependence of surface coverage on time, and it is explained how the measured currents are affected by the isotherm parameters. The approach to Langmuirian adsorption at stationary spherical and expanding plane electrodes is briefly indicated. Finally it is pointed out how the problem can be solved for an arbitrary type of isotherm.

Study of first order chemical reaction following charge transfer using the double potential-step chronocoulometric method: I. Theory

Abstract Modification of the double potential-step chronocoulometric method is proposed. The modification consists in measuring up to the constant value of the charge which passes through the electrode during the second step. This leads to simplification of the theory advanced for the chemical reaction following the charge transfer. An analytical relation between the product kt1 (the rate constant k multiplied by the during the first and the second step was obtained. It was estimated that the method enables the determination of the rate constant k in the range of six decades. The relative error of the rate constant k is also estimated.