Koichi Aoki

Quantitative analysis of reversible diffusion-controlled currents of redox soluble species at interdigitated array electrodes under steady-state conditions

Abstract Equations for diffusion-controlled currents at interdigitated array electrodes (IDA) were derived analytically for the reversible redox reactions of soluble species under steady-state conditions. The two-dimensional diffusion equation was solved by the Schwarz-Christoffel transformation. Current and concentration distributions were obtained. The total current was expressed by the ratios of the two complete elliptic functions and the geometric widths of the anode, the cathode and the gap. The current at each microband electrode of the IDA depended on the ratios of the three widths rather than the absolute values of the widths. Platinum IDAs were fabricated by photolithography on silicon wafers. The widths of the microband electrodes were 3–10 μm while those of the gap were 2–5 μm. Voltammograms of ferrocene were measured with a dual potentiostat under steady-state conditions. The collection efficiency was ca. 95%. The limiting current agreed with the theoretical prediction.

Linear sweep voltammetry at very small stationary disk electrodes

An expression for linear sweep voltammograms at very small stationary disk electrodes is presented. From numerical calculations theoretical voltammograms are obtained for various values of the dimensionless parameter, p = (nFa2v/RTD)12, where a is the radius of the electrode, v the potential sweep rate and D the diffusion coefficient. The maximum current and the half-maximum potential are evaluated from the voltammograms as functions of p and are expressed by approximate equations with high precision. In order to examine the validity of the equations, an experimental study was made at platinum small disk electrodes (a = 0.025 to 0.10 mm). The experimental voltammograms were in good agreement with the ones theoretically predicted for various values of the sweep rates and for several different radii of the electrodes.

Voltammetry at microcylinder electrodes: Part I. Linear sweep voltammetry

Abstract An expression for reversible linear sweep voltammograms at stationary microcylinder electrodes is presented. From numerical calculations theoretical voltammograms are obtained for various values of the dimensionless parameter, p=(nFa2v/RTD) 1 2 , where a is the radius of the electrode, v the potential sweep rate and D the diffusion coefficient. The peak current and the peak potential are evaluated from the voltammograms as functions of p and are expressed by approximate equations with high precision. In order to examine the validity of the equations, an experimental study was made at platinum wire micro-electrodes (a=10−10) μm). The experimental voltammograms were in good agreement with the ones predicted theoretically for various values of the sweep rates and for several different radii of the electrodes.

Theory of stationary current-potential curves at microdisk electrodes for quasi-reversible and totally irreversible electrode reactions

Abstract An analytical equation for stationary current-potential curves at microdisk electrodes was derived by the Wiener-Hopf method when the electrode reaction is quasi-reversible and totally irreversible. The current-potential curve is a function of the kinetic parameter, , where and are the forward and backward reaction rate constants, respectively; a is the radius of the electrode and D is the diffusion coefficient. The equation consisted of a set of simultaneous equations and was solved numerically. A technique of evaluating the kinetic parameters from experimental current-potential curves is presented which is similar to the method of a polarographic log-plot. The theoretical current-potential curves were compared with that at a hemispherical electrode.

Time-dependence of diffusion-controlled currents of a soluble redox couple at interdigitated microarray electrodes

Abstract Chronoamperometric curves for a soluble redox couple at the interdigitated array electrode (IDA) were computed by the time-dependent finite element method for various combinations of electrode geometry. In the simulated system involving the reduced species, a positive potential was applied to one pair of the IDA and the potential was stepped simultaneously negatively to the other electrode of the pair. The anodic current at first decayed following Cottrellian behavior, was then subjected to the edge effect, influenced by electrolysis at the neighboring electrodes and finally approached a steady-state value. The cathodic current began to flow with a lapse, which corresponded to the time of travel for the oxidized species from the anode to the cathode. The cathodic transient curve was characterized by the time at half of the steady-state current. The time was related directly to the square of the effective electrode gap. Six kinds of platinum IDAs, each microband electrode being 3–10 μm, were constructed by photolithography. The observed transient curves were in agreement with the computed ones.

Voltammetry at microcylinder electrodes: Part II. Chronoamperometry

An approximate expression for chronoamperometric curves at stationary microcylinder electrodes is derived in the following form: ia/nFc*D = 1/πθ + 0.422 - 0.0675 log(θ)±0.0058{log(θ)-1.47}2 with θ = Dt/a2, where i is the current density, a the radius of the electrode, c* the bulk concentration, D the diffusion coefficient and ± denotes + for log(θ) ⩾ 1.47 and − for log(θ) <1.47. This equation holds for 0 < θ ⩽ 106 within 1% error. In order to examine the validity of the equation, experimental studies were carried out on carbon fiber (a = 4.2 μm) and platinum wire (a = 10–100 μm) microelectrodes. The chronoamperometric curves measured at times ranging from 40 ms to 8 s were in good agreement with the ones theoretically predicted for several different radii of the electrodes.

Electrode kinetics of surfactant polypyridine osmium and ruthenium complexes confined to tin oxide electrodes in a monomolecular layer by the Langmuir-Blodgett method

Abstract Lavirons theoretical treatment of cyclic voltammograms for redox species confined to the electrode surface was modified so as to clarify the experimentally accessible physical quantities. The resulting equations were applied to the analysis of the redox-electrode reactions in acidic media of surfactant polypyridine osmium and ruthenium complexes, M(I:/III)(ndbpy), where M = Os or Ru, bpy = 2,2′-bipyridine and ndbpy = 4,4′-dinonadecyl-2,2′-bipyridine, confined to the surface of SnO 2 electrodes in a monomolecular layer by the Langmuir—6Blodgett method. The deviations of the experimental voltammograms from an ideal “surface wave” could be interpreted by taking into account the interactions among the adsorbed reactants.

Square wave voltammetry at small disk electrodes: Theory and experiment

Abstract An equation is derived for the current response of a reversible electron transfer reaction for square wave voltammetry at an embedded disk electrode. Peak shape and position are invariant to the dimensionless parameter D τ/ r 2 where D is the diffusion coefficient, τ the square wave period, and r the radius of the disk, whereas peak current density increases without limit with increasing D τ/ r 2 . A simple empirical equation predicts the peak current for any value of D τ/ r 2 for square wave amplitude 50/ n mV and step height 10/ n mV. Experimental results for oxidation of ferrocyanide at small platinum electrodes agree well with the theory and demonstrate the practical utility of the experiment.

Chronoamperometric response to potentiostatic doping at polypyrrole-coated microdisk electrodes

Abstract Chronoamperometric oxidation curves at conducting polymer electrodes were obtained theoretically on the basis of the concept of propagation for a conductive domain of the polymer. The theory predicted the appearance of a peak and an exponential decay. The time at the peak was proportional to the thickness of the film. Chronoamperometric doping curves of polypyrrole were measured at a polypyrrole-coated microdisk electrode for various thicknesses of the film. The curve exhibited a peaked wave rather than a monotonic decay. The peak height increased linearly with the stepped potential. The peaked wave included mainly the capacitive current and partly the faradaic current for oxidation of the polypyrrole. The Chronoamperometric curve after the peak decayed exponentially with time. The peak time was proportional to the thickness of the film, and the logarithmic peak time varied linearly with the potential. These variations are explained by the propagation theory.

Derivation of an approximate equation for chronoamperometric curves at microband electrodes and its experimental verification

Abstract An approximate equation for chronoamperometric curves at a microband electrode is presented by taking into account a functional form derived from the rigorous analytical equations obtained previously. It is simple and accurate enough to facilitate simulating experimental chronoamperometric curves. In order to examine the validity of the approximate equation, chronoamperometric experiments were carried out using platinum microband electrodes 0.02–0.2 mm in width. Currents at long times showed a quasi-steady state, which was almost independent of the electrode width. The dimensionless time θ (=Dt/w2) was evaluated from the measured current-time curves with the help of the approximate equation on the assumption that the diffusion coefficient D is unknown; t is the electrolysis time and w is the width of the electrode. The values of θ thus obtained were proportional to both t and w−2, indicating that the approximate equation is correct.