Hydrodynamic voltammetry at channel electrodes: Part III. Theory of kinetic currents

A theory of kinetic currents at a channel electrode is developed without any assumption on the magnitude of the rate constant of the preceding chemical reaction. An approximate equation with reasonable accuracy which relates the limiting current to the rate constant, flow velocity and the electrode geometries, is presented. The validity of the equation derived from the concept of the thin reaction layer is also discussed.     

Hydrodynamic voltammetry at channel electrodes: Part II. Theory of first-order kinetic collection efficiencies

The theory of first-order kinetic collection efficiencies at the double channel electrode is developed for the following two schemes: (I) A±n₁e→B (at the generator electrode), B→^kP (in solution), B±n₂e→Y (at the detector electrode), (II) A±n₁e→B, B→^kA, B±n₂e→Y. The exact expressions for the kinetic collection efficiencies are obtained as ascending and asymptotic series with respect to the kinetic parameter. Further, approximate formulae in exponential forms are given, which hold within an error of about 2% for conventional electrode geometry. Finally, the validity of the approximate procedure, which has been used previously to obtain the kinetic collection efficiencies for fast homogeneous reactions, is discussed in comparison with the present theory.     

An e.m.s. study of the cathodic H/D separation factor at gold electrodes in sulfuric acid

The cathodic H/D separation factor (S_D) at gold electrodes was studied with respect to its dependence on overpotential, time of electrolysis, and deuterium enrichment. All experiments were performed in sulfuric acid and under potentiostatic control. The evolved gas was on-line transferred through a porous hydrophobic electrode into a mass spectrometer there being analyzed directly. The results showed no influence of the applied overpotential between ?100 and ?600 mV RHE on the separation factor, which has a value of 5.3±0.2. A time dependence of S_D could not be noticed within 11 h of experiment. Between 0.5 and 4.7% deuterium enrichment the average separation factor remained constant with 5.2±0.4.     

Ellipsometry of DNA adsorbed at mercury electrodes: A preliminary study

The adsorption of DNA at a mercury electrode can be detected ellipsometrically. Native DNA is probably more weakly absorbed at positive charges than at negative charges. Denatured DNA is more strongly adsorbed in the reduced form than in the protonated form and is desorbed at large negative charges. Adsorption of both forms is characterized by small negative values of δΔ/δ. It is suggested that these results should be interpreted in terms of an anisotropic film.     

Interfacial electrochemistry of cytochrome c at tin oxide,indium oxide,gold, and platinum electrodes

Cyclic voltammetry has been used to study the heterogeneous electron transfer kinetics of horse heart cytochrome c in pH 7 tris/cacodylate media at several electrode surfaces. Reversible voltammetric responses (formal heterogeneous electron transfer rate constant>10^?2 cm/s) were observed at bare gold electrodes and at tin-doped indium oxide semiconductor electrodes for certain experimental conditions. Quasireversible voltammetric responses were more typically observed at fluorine-doped tin oxide semiconductor electrodes, bare platinum electrodes, and at the indium oxide electrodes. Reaction rates at bare metal electrodes were strongly dependent on pretreatment procedures and experimental protocol. Reaction rates at metal oxide electrodes were strongly dependent on solution conditions, pretreatment procedures, and on the hydration state of the electrode surface. A general mechanistic scheme involving both interfacial electrostatic and chemical interactions is proposed for cytochrome c electrode reactions. The asymmetric distribution of surface charges on cytochrome c appears to play a dominant role in controlling electron transfer rates by its interaction with the electric field at the electrode surface. Electron transfer distances are also considered, and it is concluded that electron transfer between an electrode surface and the exposed heme edge of properly oriented cytochrome c molecules involves maximum distances of ca. 0.6–0.9 nm.     

Voltammetry at partially covered electrodes: Part I. Chronopotentiometry and chronoamperometry at model electrodes

Equations for chronopotentiometry and chronoamperometry at partially covered electrodes have been derived using a model of hexagonal array of cylidrical spaces terminated, at the electrode surface, by concentric active and inactive regions. The boundary value problem was shown to be analogous to that for a charge transfer preceded by a chemical reaction. Experiments with the reduction of ferricyanide on gold model electrodes partially covered with photoresist layer showed excellent agreement with the theory. Application of the equations to estimation of coverage and size of active sites distributed on a electrode surface is discussed.     

Hydrodynamic voltammetry at channel electrodes: Part VII. Current transients at double channel electrodes

Expressions for the transient current at the downstream electrode in response to galvanostatic electrolysis at the upstream electrode in the channel flow cell were derived by applying double Laplace transformation when the electrode reaction at the upstream electrode is kinetically controlled. The ratio of the transient current to the steady state current or the transient collection efficiency was calculated as a function of electrode geometry and θ

, where U_m is the mean flow velocity in the channel cell, D the diffusion coefficient of the electroactive species, b the half height of the channel, x₁ the length of the upstream electrode and t the time elapsed since the beginning of the galvanostatic electrolysis at the upstream electrode. Curves for the transient collection efficiency can be applied to evaluating the amount of adsorption at the upstream electrode when metal at the electrode is anodically dissolved in solution. Digital simulation was carried out. Transient curves, obtained analytically, were in good agreement with those evaluated from the digital simulation. In order to allow one to draw transient curves readily, we derived a simple approximate equation.     

Chronoamperometric current at finite disk electrodes

The chronoamperometric current at a stationary finite disk electrode is studied using both analytical and digital simulation techniques. The exact long-time expansion of the current is obtained and its short-time behavior is considered. Digital simulation of the current using an explicit hopscotch algorithm is presented. In contrast to the usual explicit difference method, the ‘hopscotch’ algorithm is unconditionally stable, and thus, it is particularly suited for studying electrochemical problems at intermediate and long times. A simple analytic expressions for the current, which is accurate to 0.6% for all times, is presented.     

Chronopotentiometry at very small stationary disk electrodes

Expressions for chronopotentiometry at very small stationary disk electrodes are presented. The transition time, τ, is expressed as a function of I_ss/I, where I is the applied current and I_ss is the steady-state diffusion current for the disk electrode given by I_ss/I=4nFc*_RDa, (where n is the number of electrons transferred, a the radius of the electrode, D the diffusion coefficient and c*_R the bulk concentration). When values of I_ss/I are small, the transition time constant,

, depends linearly on I_ss/I and gives the intercept of the Sand equation. When I_ss/I approaches unity, the transition time increases rapidly and diverges to infinity at I_ss/I=1. If I_ss/I exceeds unity, the transition does not occur and the electrode potential approaches a steady-state value corresponding to I. An approximate equation for the transition time is presented, from which one can evaluate the diffusion coefficient. Equations for the potential-time curve and the quarter-wave potential are also obtained. The equations were tested experimentally using platinum small disk electrodes (a=0.025–0.10 mm). The transition times obtained experimentally were in good agreement with these predicted theoretically for various values of the applied current, for several different radii of the electrodes.     

The electrooxidation of methanol and related compounds at ruthenium dioxide-coated electrodes

The underlying metal was observed to corrode when a ruthenium dioxide-coated titanium electrode was anodized in an aqueous methanol solution. With a similarly coated platinum electrode peaks were observed on the voltammogram below 1.0 V which were attributed to methanol oxidation on the underlying metal. This effect was more pronounced when the electrode was subjected during cycling to potentials close to 0 V. Rapid oxidation of methanol on RuO₂ was observed at potentials above 1.0 V, the rate at a given potential increasing in an approximately linear manner with increasing alcohol concentration. The rate of reaction also increased with increasing temperature and increasing surface roughness. Tafel slope values were rather high (>100 mV decade^?1) and a mechanism involving anodically generated species such as OH_ads was proposed to account for these results. The variation of activity with pH was similar to that reported earlier for oxygen evolution at these anodes and this was again explained in terms of partial deactivation of the surface due to a combination of proton loss and phosphate ion adsorption at intermediate pH values. The release of carbon dioxide from aqueous solutions of higher alcohols at 25°C confirmed the high oxidizing power of RuO₂ anodes.     

On the mechanism of hydrogen evolution at GaAs electrodes

The hydrogen evolution reaction at n- and p-GaAs electrodes has been reinvestigated. As in the case of metal electrodes, hydrogen evolution can occur in two ways: at ?0.5 V (SCE) hydronium ions are reduced, at ?1.25 V (SCE) reduction of water molecules takes place. It is confirmed that in both cases conduction band electrons are responsible for the two reduction steps, forming adsorbed hydrogen atoms in the first and hydrogen molecules in the second step. Hole injection can occur only to a negligible extent, although it appears energetically feasible.     

Faradaic electrochemistry at microcylinder,band, and tubular band electrodes

Current-time relationships of faradaic processes at microcylinder, band, and tubular band electrodes have been evaluated. Microcylinder electrodes were fabricated from platinum wires (5 μm radius) sealed in glass capillaries. Band and tubular electrodes were constructed with platinum sheets (～ 20 μm width) or thin pieces of graphite (～ 5 μm width) sealed between insulating mateials. The temporal response of the current at a microcylinder electrode for the reduction of ferricyanide in aqueous potassium chloride solutions is in excellent agreement with that predicted by equations derived for heat flux to a cylinder. An estimation of the magnitude and temporal properties of the measured current at a band electrode can be obtained when a hemicylinder geometry is assumed. The current respone is identical at band and tubular band electrodes even for the smallest tubular radius investigated, 0.54 mm. Cyclic voltammograms at electrodes of all three geometries show significant contributions from radial diffusion at slow scan rates (< 20 mV s^?1). The current at a graphite tubular band electrode was found to be independent of flow of solution through the electrode at flow rates up to 3 ml min^?1.     

Voltammetry at microcylinder electrodes: Part III. Chronopotentiometry

Expressions for chronopotentiometry at stationary microcylinder electrodes are presented. The transition time, τ, is expressed as a function of a single parameter λ ( = nFc^*_RD / ia, where a is the radius of the electrode, D is the diffusion coefficient, i is the current density, n is the number of transferred electrons, F is the Faraday constant and c^*_R is the bulk concentration. When the values of λ are small, the transition-time constant, i√τ / c^*_R, depends linearly on λ, with the intercept predicted from the Sand equation. Conversely, when values of λ increase, the transition time also increases exponentially. Therefore transition necessarily occurs no matter how small a current flows. An approximate equation for the transition time is presented, from which one can evaluate the diffusion coefficient. Equations for the potential-time curve and the quarter-wave potential are also obtained. The equations were tested experimentally using carbon fiber electrodes (a = 4.1 μ m) and platinum wire electrodes (a = 10-100μ m). The transition times obtained experimentally were in good agreement with those predicted theoretically for various values of the applied current, for several different radii of the electrodes.     

Voltammetric behavior of tertiary butyl bromide at mercury electrodes in dimethylformamide

Polarograms for t-butyl bromide in dimethylformamide containing tetramethylammonium perchlorate exhibit two waves which signal stepwise reduction of the starting material to the t-butyl radical and the t-butyl carbanion. Cyclic voltammograms obtained with a hanging mercury drop and at a scan rate of 50 mV s^?1 confirm that the alkyl bromide undergoes stepwise reduction; but the height of the second peak is abnormally small, indicating that t-butyl radicals engage in combination and disproportionation. At a faster scan rate (500 mV s^?1), the first wave nearly merges with the second wave. At all scan rates, two pairs of anodic-cathodic waves, associated with reversible bromide-assisted oxidation of mercury, appear at positive potentials. In addition, another set of anodic-cathodic waves is seen if the potential is scanned rapidly to a value at which the t-butyl carbanion is generated; this set of waves might be related to the formation of trimethylammonium methylide (produced when the tetramethylammonium cation donates a proton to the t-butyl carbanion). Although this latter set of waves is eliminated by addition of a proton donor (diethyl malonate) to the system, the anion of diethyl malonate is itself involved in the appearance of yet another pair of anodic-cathodic waves.     

The effect of pH on some outer-sphere electrode reactions at carbon electrodes

The apparent heterogeneous rate constant, k°_app, for three couples known to undergo outer-sphere electron transfer reactions has been investigated at carbon, gold, and platinum electrodes as a function of solution pH. The rates are found to be pH dependent at two different types of glassy carbon and at carbon paste but not at metallic electrodes. The rate is found to decrease with increasing pH for Fe(CN)^{$\text{3?}\text{4?}$}₆ and IrCl^{$\text{2?}\text{3?}$}₆, and the opposite effect is observed for the Ru(NH₃)^{$\text{3+}\text{2+}$}₆ couple. For the three compounds examined, the magnitude of the pH dependent rate changes can be associated with a change in the magnitude of the potential of the reaction layer induced by a change in surface charge of ～ 2 × 10^?7 C cm^?2. The pH dependence of the observed rate constant at glassy carbon can be attenuated by heat treatment, chemical reduction, or esterification of the surface. This behaviour is consistent with the theory that the pH dependence of k°_app arises from the presence of functional groups on the carbon surface.     

A study of isomeric retinal triplets by low temperature spectroscopic and kinetic flash photolysis

Spectroscopic and kinetic data of triplets of all-trans retinal and several of the cis isomers obtained with frozen samples at liquid nitrogen temperature are reported. They are believed due to unisomerized triplets of the corresponding ground state isomers. Interestingly, decay of transients from 7-cis-retinal was found to be wavelength dependent.     

Transport and kinetics at microheterogeneous electrodes: Part III. Application to the photoelectrochemical decomposition of water

The transport and kinetics in a system involving two sets of microheterogeneous electrodes, which are designed to use solar radiation to split water into H₂ and O₂, are described. A reaction scheme involving fourteen different processes is considered. The conditions for an efficient system are derived. It is shown that the main problems are electrode selectivity and the loss of H₂ and O₂ by back reactions.     

Diffusion current at microdisk electrodes—application to accurate measurement of diffusion coefficients

Stationary electrodes (platinum and glassy carbon) were used for accurate measurement of diffusion coefficients. The theoretical diffusion current-time profile was calculated by digital simulation, by means of which the diffusion coefficient and the product of the charge number of electrode reaction n and the reactant concentration c^o were determined simultaneously from a single chronoamperogram. The feasibility of the method was demonstrated by measuring the diffusion coefficients of Tl(I) ions. When the nc^o value agreed with the corresponding known value, the diffusion coefficients were in good agreement with the standard values determined by the thin-walled hanging mercury drop electrode method. The diffusion coefficient of hexacyanoferrate(III) ions in 1 mol dm^?3 KCl at, 25°C was also determined.     

The kinetic study of isothermal solid state decompositions: a combined numerical and experimental approach

This paper identifies and makes quantitative allowance for experimental errors in isothermal weight change data. For experiments which involve a purge gas to remove decomposition products, attention is directed to errors due to variations in the gas flow rate and the need to heat the sample initially to the temperature of study. For experiments carried out at reduced pressure, importance is also attached to the undesirable influence of draughting, buoyancy, pressure and conventional effects. An experimental procedure which minimises the errors due to some of these factors is discussed. The paper also examines how the non-linear least squares method employed to analyse the kinetic data may be extended to allow for error produced by the initial temperature change. This extended method is used to analyse weight change data which are consistent with a contracting-interface mechanism, and the results clearly demonstrate the improved accuracy of the kinetic parameter estimates.