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

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.     

Current-potential curves with an EE mechanism

The dc polarographic response for the EE mechanism both in the expanding plane electrode and in the expanding sphere electrode is examined. Explicit equations for the current-potential curves when all species are initially added to the solution and without using the steady-state approximation have been derived. The situation obtained in some particular cases (reversible steps, one reversible and the other irreversible, totally irreversible steps and well-separated steps) is also discussed.     

Reduction of complexes in unbuffered solutions a unified treatment of the reduction of complexes at a stationary planar electrode or at an expanding mercury electrode

A general treatment is given of an electrode reaction connected with complexation at low ligand concentrations in unbuffered media. The reduction of the simple or complex metal ions occurs at an electrode expanding in accord with some power law; the stationary (solid or mercury) electrode and the dropping mercury electrode are special cases. The ligand is added to the solution as a j-protic acid. Linear semi-infinite diffusion is regarded as the sole mode of transport of all dissolved substances.The solution found, being of a very wide generality, was applied to the case of a potentiostatic regime of electrolysis on a dropping mercury electrode, as well as to the case of a galvanostatic regime on a stationary electrode. The voltammetric relationships obtained embrace all known equations of polarographic and chronopotentiometric reduction of simple and complex metal ions.The theoretical polarographic I—E curves in buffered and unbuffered solutions are presented graphically and compared. Apparently, the changes in the surface proton concentration cause a stretching of the wave.     

Pulse polarography: Part VII. Theoretical relationships for electrode processes with an ECE mechanism

A theoretical study of the pulse polarographic response for the instantaneous limiting current with an ECE mechanism is presented. Thus, equations for the current have been derived under the following conditions: (a) Both the expanding plane electrode and the expanding sphere electrode models have been accounted. (b) The steady-state approximation was not used. (c) All species are initially present in the solution. With these conditions we have: (a) proposed a method for the calculation of the rate constant values through measurements of instantaneous limiting currents; (b) shown that the interval of the rate constant values that can be determined is about 10³ times larger than in dc polarography; (c) checked the validity of the steady-state approximation.     

Unified treatment of the potentiostatic reduction on an expanding mercury electrode of complexes at any concentration ratio of reacting species

The article describes a general treatment of voltammetry of equilibrium complexation reactions at an electrode expanding in accord with any power law, the stationary electrode and the dropping mercury electrode being special cases. Reversible, irreversible and quasireversible electrode reactions are embraced by the treatment. A general expression for the current—voltage characteristic was derived, which was applied to the case of the polarographic reduction of complex ion, where either the simple or complex ion is electrochemically active. An equation accounting for the surface concentration of all reacting species is derived, the solution of which under appropriate conditions gives the equations of Lingane, Matsuda and Ayabe, etc. Correlations of potential, current and wave shape with complexing agent concentration are presented and discussed. A criterion for the splitting of the polarographic wave in the absence of excess of the complexing agent is proposed. Experimental results of several papers are discussed in the light of these criteria and a satisfactory agreement between the results and the predictions is established.     

On the kinetics of the inhibition of electrochemical homogeneous catalytic processes: Theory of the pulse-polarography and its application to the Fe-catalysed chlorite reduction,in the presence of EDTA acting as deactivator

A theory is developed for catalytic homogeneous processes inhibited by a bulk deactivation reaction in the case of a plane stationary electrode. The time-dependent diffusion equations, corrected for the kinetic terms, have been solved exactly using the Laplace transformation. The final equations have been successfully verified by studying the deactivation effect of EDTA on the reduction of chlorite ions, catalysed by the ferrate-ferrite couple.     

Application of the superposition principle to the study of a charge transfer reaction in cyclic chronopotentiometry. Part II

The general analytical expressions corresponding to the response obtained for a charge transfer process in cyclic chronopotentiometry are presented. The different geometries considered for the mass transport operator are planar, tubular and spherical. In the case of spherical electrodes (such as the dropping mercury electrode and the static mercury dropping electrode), we have analyzed the following two cases: solution soluble product and electrode soluble product or amalgamation. The solutions deduced here are independent of the method used in solving the differential equations system since we have applied the superposition principle for which we have only used the properties of the linear operators.     

Effect of ion solvation on the diffuse layer structure in mixed electrolytes

A “solvionic” model of a multicomponent electrochemical system (mixed electrolyte) is considered. An ion in the solution is considered as a point charge rigidly fixed inside its solvation shell. The corresponding equations for the diffuse layer on an ideally polarizable electrode are derived, and an effective method of their numerical solution is formulated. The calculations are performed in order to follow the changes in the diffuse layer structure with variations in the electrode charge and electrolyte composition. Far from the zerocharge potential of solution, the dependences of distributions of solution components over the diffuse layer on the electrode charge radically differ from those within the classic Gouy-Chapman theory. Analytical equations (asymptotics at large electrode charges) for concentrations of solvated ions in the plane of their maximum approach and for their “surface excesses” (diffuse adsorption) are determined. Results of numerical calculations for a 0.2 M LiCl + 0.05 M BaCl₂ solution are plotted.     

Determination of the Diffusion Coefficient for SDS Micelle with Different Shape and the Effects of Ethanol by Cyclic Voltammetry Without Probes

Micelle diffusion coefficient of SDS with different micelle shape in aqueous and water-ethanol solutions are determined by cyclic voltammetry without any probe. The diffusion coefficient decreases with as increasing SDS concentration. The first critical micellar concentration is 8.0xl0³, mol 1¹.corresponding to the transformation from premicelle to spherical micelle. The second critical micellar concentration is 5.60x10²and corresponding to transformation from spherical micelle to rod-like micelle. The less the weight ratio of SDS to ethanol is, the larger the diffusion coefficient is. The influence of added water to the micelle solution is almost the same for SDS-ethanol-HaO system with different micelle shape. Mechanism of electrochemical reaction for SDS at platinum electrode is discussed as well.     

The Diffusion Coefficient of Molecular Oxygen in Macroporous Sulfocationite

An electrochemical method for experimentally estimating the diffusion flux of molecular oxygen through a spherical porous medium by taking chronoamperograms with an electrode of a special design was suggested. The corresponding mathematical apparatus based on numerically solving the molecular diffusion equation in spherical coordinates was developed, which enabled the diffusion coefficient and medium porosity to be determined from the experimental data. The method was tested by applying it to the system KU-23 15/100 macroporous sulfocationite—aqueous solution of molecular oxygen.     

Theoretical analysis of catalytic current-potential curves: Part I. First-order regeneration mechanisms at different electrolysis regimes

The article describes a general treatment of the catalytic reaction mechanism at an electrode expanding in accord with any power law, the stationary electrode and the dropping mercury electrode being special cases. Reversible, irreversible and quasi-reversible electrode reactions are embraced by the treatment. A general expression for the current-voltage characteristic was derived, which was applied to different electrolysis regimes. The cases when the regeneration reaction will influence the catalytic wave characteristics are also discussed.     

Surface modification of spherical nickel hydroxide for nickel electrodes

Electroless cobalt plating on spherical nickel hydroxide is tested in order to improve the conductivity of Ni(OH)₂ and the capacity of the electrode. The factors affecting the process of electroless cobalt plating are cobalt solution, temperature and pH, etc. The effects have been examined and the optimum process parameters have been obtained. The nickel hydroxide electrode which is made by nickel hydroxide deposited cobalt has excellent performance, the results showing that electroless cobalt plating on the surface of spherical nickel hydroxide particles is an effective method for modifying electrodes.     

The applicability of the superposition principle in differential pulse polarography

It is shown theoretically that the superposition principle is applicable to pulse voltammetry if the electrochemical system can be separated into a potential-dependent nonlinear part and a linear part. For systems not complicated by adsorption or electrode kinetics, the applicability of the principle depends on diffusion coefficients, electrode and cell geometry. For plane semi-infinite diffusion, applicability is expected; this is generally not the case for spherical electrodes or bounded regions (film electrode or thinlayer cell). The implications of the theory on differential pulse polarography are discussed and an experimental study on the applicability for iron(III), cadmium(II) and lead(II) is presented.     

Evaluation of differential pulse anodic-stripping voltammetry at a stationary mercury-film electrode with stirred solution

Differential pulse anodic-stripping voltammetry at a stationary mercury-film electrode with the solution stirred during the deposition step has been investigated. The sensitivity achieved by using such a simple set-up is similar to that obtained with a mercury-film rotating disk electrode. The effects of various experimental parameters on the peak current are described. Lead and cadmium were used as test systems, and gave detection limits of around 1 x 10(-10)M with 5-min deposition times.     

Amperometric titration of mercury with a stationary platinum electrode in stirred solutions

Amperometric titration of mercury (in the range of 0-4 to 3.5 mg) has been carried out with 2-mercaptobenzoxazole with a stationary electrode in stirred solution in a sodium acetate-acetic acid medium.     

Pulse polarography: Part V. on the theory for the kinetic currents with an ece mechanism

We have derived an equation for the instantaneous limiting current in pulse polarography with an ECE mechanism. That equation has been derived for the expanding sphere electrode model (and also for the expanding plane electrode model) with the condition (k₁+k₂)>>1, k₁ and k₂ being the rate constants of the chemical reaction. We show that by an adequate choice of the time of application of the potential and time of the drop growth prior to potential application, it is possible — if the equilibrium constant for chemical reaction is known — to widen the interval of values for k₁ and k₂ that may be determined using this technique. At the same time, we also show that if the electrode sphericity is not taken into account, the values obtained for k₁ and k₂ are always lower than the real ones.     

Demodulation of a sinusoidal signal by a reversible electrode and its application to polarography

A theoretical analysis of the “faradaic demodulation signal” caused by the non-linearity of the faradaic admittance is given for a plane, stationary electrode with a single step electrode process. It is assumed that mass transfer of the substances involved occurs by diffusion only. The theoretical conclusions are tested and confirmed by polarographic measurements with a dropping mercury electrode (DME).     

Calculation of effective diffusion coefficient in a colloidal crystal by the finite-element method

The work is devoted to the calculation of effective diffusion coefficient of ions from the bulk solution to the electrode through a mask and the calculation of the distribution of the limiting current density over the electrode surface. A colloidal crystal, which is formed by orderly arranged monodispersed spherical particles, serves as a mask. It is shown that the diffusion of electroactive ions in the pores between spherical particles can be simulated by unit cells with rhombic, rectangular, or triangular cross-section. In the latter case, the cell side surface has no periodical boundaries. This simplifies significantly the numerical solution of the Laplace??s equation by the finite-element method. The effective diffusion coefficient in the bulk colloidal crystal is calculated at various values of its porosity. The calculated results agree well with the literature data. It is found that, for close-packed spherical particles, the relative effective diffusion coefficient in the bulk colloidal crystal is 0.16. The thicknesses of transient zones adjacent to the electrode surface and outer boundary of colloidal crystal and the effective diffusion coefficients for these zones are determined. The dependence of effective diffusion coefficient on the number of spherical particle layers in the colloidal crystal is obtained. The distribution of the limiting current density over the electrode surface is analyzed at various numbers of particle layers.     

Morphology dependent electrocatalytic activity of Au nanoparticles

The electrocatalytic activity of spherical shape Au particles chemically grown on a sol–gel derived 3D silicate network modified conducting surface has been studied using ascorbate as a model. The nanostructured Au particles show morphology dependent electrocatalytic activity towards ascorbate. Unusual voltammetric behavior for ascorbate has been observed. Unlike the polycrystalline Au electrode, the nanostructured electrode shows two well defined voltammetric peaks for ascorbate at 0 and 0.3 V in neutral and alkaline pHs. These voltammetric peaks are assigned for the oxidation of ascorbate to dehydroascorbate (DHA) and the further oxidation of 2,3-diketogluonic acid (DKG), the hydrolyzed product of DHA. The voltammetric peak corresponding to the oxidation of DKG is very sensitive to the supporting electrolyte anions and solution pH. Voltammetric behavior of DHA has been investigated to support the oxidation pathway of ascorbate on the nanostructured electrode. Surface morphology of the particle controls the electrocatalytic activity.     

Interaction between a stationary mercury electrode and a hydrogen bubble in an aqueous sodium dodecyl sulphate solution

The stability and rupture of thin liquid films formed from an aqueous solution of Na₂SO₄ (0.05 mol dm⁻³) in the presence of 5 × 10⁻⁵ mol dm⁻³ sodium dodecyl sulphate between a stationary mercury electrode and a hydrogen bubble has been investigated as a function of electrode potential. The electrostatic component of disjoining pressure has been calculated using the results of capacity measurement for the mercury-solution interface. Special attention has been paid to films formed on positively charged mercury surfaces. In this case, despite the positive electrode polarization, the outer Helmholtz plane potential is found to be negative due to the high surface activity of the dodecyl sulphate anion. The van der Waals component of disjoining pressure has been calculated on the basis of a double sheath model of the two interacting surfaces, taking into consideration the orientation of the adsorbed surfactant layers at the interfaces. Calculations of the total disjoining pressure can explain film stability at negative mercury potentials, but do not explain film rupture when the polarization of the mercury is positive. The existence of a hydrophobic attractive interaction is postulated in the latter case.