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The cyclic voltammetry response of partially blocked electrodes is modeled using finite difference simulations and a method presented for determining currents at electrode surfaces which have a well-defined geometric blocking pattern. Peak current and peak separation data are presented for six decades of scan rates, blocking coverage values between 0.1 and 0.9 and between the limits of reversible and irreversible electrochemistry. The validity of the simulation approach employed is verified by data obtained experimentally from purpose-built partially blocked gold film electrodes, with either a cubic or hexagonal geometric array of electroinactive disks uniformly distributed on the electrode surface. Comparison of theory with experiment suggests that the modeling of hexagonally distributed blocking systems is superior to that of the cubically arranged ones.

Investigations at microring electrodes are limited by the lack of equations that describe short and long time behavior at rings of all thicknesses. In this paper, a robust finite difference numerical method is presented for the simulation of electrochemical processes at microring electrodes of intermediate thickness. The method relies on a careful meshing strategy to minimize electrode flux errors. The accuracy of the method is first tested by comparison with a well-established reversible steady-state analytical equation. The meshes obtained through this process are reused to produce current results for chronoamperometry and linear-sweep voltammetry. In the case of chronoamperometry, simulated currents show less than ±1.5% difference compared to integral-equation methods. In the case of linear-sweep voltammetry, currents are recorded across nine decades of dimensionless scan rate. Both the dimensionless peak current and voltage at half-peak height are compared with other known methods and shown to be either comparable to or better than alternative results. In the case of the voltage at half-peak height, results are confirmed by simulations at the microdisk electrode.

Acoustic cavitation considerably enhances the mass transport toward a surface. When suitably fast electrochemical equipment is used, periodic peak currents can be observed. Previous observations attributed these peaks to diffusion inside a thin liquid layer present between the electrode and the bubble (Maisonhaute, E.; White, P.C; Compton, R. G. J. Phys. Chem. B 2001, 105, 12087−12091). This paper provides a semiquantitative model for explaining the bubble behavior, leading to an estimation of the diffusion layer thickness as well as the time during which the bubble “discovers” the electrode. Layer thicknesses ranging from 25 nm for very high acoustic pressures up to ca. 60 nm for smaller ones are found. Collapse velocities are estimated to be more than hundreds meters per second. Moreover, between two collapses, a slow bubble movement apart from the surface is evidenced. The force balance responsible for the collapse is reexamined and the viscosity constraint found to be an important parameter in explaining the global behavior.

The halogen exchange reaction of 2,4-dichloronitrobenzene with potassium fluoride in dimethylformamide containing tetrabutylammonium salts has been studied employing an electrochemical detection methodology based upon the use of square wave voltammetry to follow the loss of reactant and the formation of the product and intermediates. The results obtained show that the kinetics of loss of parent material behave on one hand as a dissolution-rate-controlled process and on the other as a homogeneous chemical process. Initially homogeneous reaction dominates the observed kinetics as the presaturated solution is stripped of fluoride ion; at longer time, the observed kinetics are controlled by the rate of KF dissolution. Modeling the system using a fully implicit finite difference method with Richtmyer modification (FIRM algorithm) yielded a mean value for the homogeneous rate constant for the formation of 2,4-dinitrofluorobenzene by reaction of 2,4-dichloronitrobenzene with fluoride ion in DMF at 85 °C of 640 ± 250 mol^-1 cm³ s^-1 and a mean value for the saturation concentration of fluoride ion of (6.5 ± 0.5) × 10^-6 mol cm^-3. Ultrasound was found not to significantly enhance the rate of the reaction in the intensity range studied. Furthermore, the utility of microelectrodes for obtaining simple quantifiable voltammetric responses from compounds of which the macroelectrode responses are complicated by chemical followup steps is demonstrated. Ultrasonically induced mixing has been shown to facilitate reproducible microelectrode responses in intrinsically heterogeneous systems.

A numerical method is illustrated for the modeling of an important electrocatalytic reaction at the rotating disk electrode (RDE). This reaction, labeled EC2XE, occurs via the following route:  A − 2e^- &rlhar2; B, B + X → B−X (k2), B−X − 2e^- &rlhar2; [B−X]²⁺. The numerical method is based on a finite difference formulation of coupled mass transport and kinetic equations and makes use of a Hale coordinate transformation. Iterative solutions are performed using a Gauss−Newton scheme to solve the nonlinear differential equations. Numerical solutions are calculated to generate working surfaces in the effective number of electrons transferred, Neff. Cyclic voltammetry is reported in hydrostatic conditions with a 4-acetamidophenol (paracetamol)/cysteine system, which is shown to proceed via the EC2XE reaction pathway. The resulting data is modeled using the commercial package DIGISIM, and a result of k2 = 1.25 ± 0.25 × 10⁷ mol^-1 cm³ s^-1 is obtained. RDE studies of the same system using steady-state linear sweep hydrodynamic voltammetry is next performed to collect limiting current data at rotation speeds of 2, 4, 8, 16, and 25 Hz. Working surface interpolation of the resulting data results in a mean value of 1.6 ± 0.35 × 10⁷ mol^-1 cm³ s^-1 for the rate constant k2.

The electro-reduction of carbon dioxide is studied by linear sweep and cyclic voltammetry in DMSO electrolyte solutions and at polycrystalline gold microdisk electrodes. An electrode reaction pathway is suggested. Numerical simulation of the reaction mechanism gives current | potential waveshapes in excellent agreement with those observed experimentally. Kinetic parameters for the reduction process are deduced from this waveshape approach, and the charge-transfer coefficient is found to be approximately 0.43 ± 0.05.

A numerical method is used to characterize the steady-state voltammetry at microdisk electrodes of a new electrocatalytic reaction. This reaction, which occurs for the oxidation of N,N-dimethylphenylenediamine (DMPD, A) in the presence of H2S (X) is believed to proceed via the following route:  A − 2e^- &rlarr2; B, B + X → B&sbd;X (k2), B−X − 2e^- &rlarr2; [B&sbd;X]²⁺. Due to the presence of a reagent restricted homogeneous kinetic step, the reaction is labeled EC2XE. The numerical method for simulating this reaction scheme is based on the finite-difference formulation of coupled mass transport and kinetic equations in oblate spherical coordinates. The method is illustrated for not only the EC2XE but also the EC‘ reaction and is applicable to the simulation of steady-state limiting currents at microdisk electrodes. Iterative solutions are calculated using a Gauss−Newton scheme to overcome nonlinear homogeneous kinetic terms. The spatial convergence of the simulation for both reactions is investigated by considering the form of the concentration function describing the species. Via the comparison of working surfaces generated from simulated results, measuring the steady-state limiting current is shown to be insensitive to the resolution of EC‘, ECE, and EC2XE reactions. Experimental steady-state limiting current data is reported for the DMPD/H2S system at microelectrodes of 7.3, 19.5, and 25.0 μm diameter to verify the theory behind the EC2XE reaction. These results are shown to closely fit experimental data using a working surface interpolation method. Specifically, this method correctly predicts the variation of the steady-state limiting current with the concentration of H2S for a 19.5 μm diameter microelectrode to a relative standard deviation of 1.9%. Similar analysis for the 7.3 and 25.0 μm electrodes results in a mean value of 1.4 × 10⁷ mol^-1 cm³ s^-1 for the rate constant k2 in the DMPD/H2S system.

A general approach is developed for the numerical simulation of square wave voltammetry (SWV) at hemispherical electrodes based on the backward implicit method. The latter is applied to the modeling of electrochemically reversible, irreversible and quasi-reversible redox couples. Data from the simulations are analyzed by comparing voltammograms for different hemispherical electrode radii with those for diffusion at uniformly accessible planar electrodes for a range of electrochemical rate constants so as to evaluate the qualitative effects of transport regime on the observed voltammetry. Experimental data are presented for the oxidation of 4-chloronitrobenzene in dimethylformamide solution at two disk electrodes of radii 250 and 12.5 μm. The peak current is recorded over a range of square wave frequencies and compared to results calculated from simulation of both planar and hemispherical electrodes.

A general approach is developed for the numerical simulation of square wave voltammetry (SWV) at uniformly accessible electrodes, based on the backward implicit method. Appropriate transformations of both the spatial coordinate normal to the electrode surface and of the time variable are developed and are shown to lead to efficient and accurate simulations. The method is applied to the modeling of electrochemically reversible processes, and the results predicting the variation of peak height, width at half-height, and the area as a function of square wave frequency and amplitude are shown to be in excellent agreement with the previously derived full analytical theory. Approximate expressions for these quantities are assessed and shown to have limited value. A superior approximation is developed for the case of the peak width at half-height.