John A. Alden

Hydrodynamic voltammetry with channel microband electrodes: axial diffusion effects

The strongly implicit procedure is used to simulate the response of channel electrodes under conditions where diffusional effects in the direction (axis) of solution flow are significant. The cases of flow rate dependence of the steady-state transport limited current, potential step transients and ECE processes are considered and the conditions identified under which axial diffusion effects are considerable.

Diffusional mass transport to microband electrodes of practical geometries : a simulation study using the strongly implicit procedure

Abstract The strongly implicit procedure is used to model the diffusion-only chronoamperometric responses of microband electrode geometries which deviate from the ideal. Specifically, attention is focused on four electrode shapes: elevated microband electrodes (with conducting supporting sides), recessed microband electrodes (with insulating pit walls), platform electrodes (with insulating supporting sides) and, for the purposes of comparison, a hypothetical line electrode without any support which permits diffusional mass transport to both sides of the infinitesimally thin electrode. In all cases the short time transient is found to be described by simple analytical expressions in which the contributions from linear diffusion over the electrode area(s) and non-linear diffusion to the electrode perimeters are clearly distinguishable.

A comparison of finite difference algorithms for the simulation of microband electrode problems with and without convective flow

Various microband electrode problems are simulated using finite difference methods. These are (i) the chronoamperometric transient obtained under diffusion-only conditions, and (ii) the steady-state and (iii) the transient responses observed when the microband electrode is located in a convective flow. Three separate algorithms are employed to solve the problems, namely the strongly implicit procedure (SIP), the alternating direction implicit (ADI) method and the backwards implicit (BI) method. The different approaches are compared and contrasted in terms of their relative efficiencies. Optimal simulation approaches to the solution of microband electrode problems are identified.

The multigrid method, mgd1: an efficient and stable approach to electrochemical modelling. the simulation of double electrode problems

The application of the multigrid method MGD1 for the efficient and stable simulation of electrochemical transport problems is described. The approach is illustrated by its application to the simulation of double electrode problems, thought not to be readily tractable by other approaches. In particular the reverse collection efficiency is successfully simulated in addition to the modelling of conventional double electrode problems. In the reverse case, material generated on a downstream electrode in a double channel electrode system diffuses upstream against the direction of the convective flow to a detector electrode, whereas conventionally the generator electrode is located upstream. The dependence of the collection efficiency (defined as the ratio of the detector to generator electrode current) on the cell geometry and solution flow rate is established and reported.

Hydrodynamic voltammetry with channel microband electrodes: the simulation of voltammetric waveshapes

Abstract The strongly implicit procedure and the multigrid method MOD1 are used to simulate the steady-state current-voltage response of channel electrodes, including under conditions where diffusional effects in the direction of flow are significant. Reversible, quasi-reversible and irreversible heterogeneous kinetics are all considered.

Perspectives in Modern Voltammetry: Basic Concepts and Mechanistic Analysis

Publisher Summary Voltammetric techniques have become popular since the 1940s when instrumentation required to conduct such experiments became readily available. Voltammetric techniques considered in this chapter involve monitoring the current when a time-dependent potential is applied to an electrochemical cell. The measured current results from frequently complex combinations of heterogeneous (in which an electron is transferred at the solutionelectrode interface) and homogeneous processes (which occur in the solution phase). The early studies invariably used a linear sweep DC technique. In the last 50 years, a wide range of techniques of interest have emerged. This chapter describes a range of voltammetric techniques based on the use of inherently simple DC waveforms (linear, cyclic or staircase). The description of the techniques begins at a level that presupposes only limited prior knowledge and is suitable for those unfamiliar with the application of voltammetric techniques for the elucidation of electrode reaction mechanisms. The chapter also focuses on typical solution phase reaction mechanisms encountered in organic and organometallic electrochemistry.

The electrochemical oxidation of cobalt tris(dithiocarbamates) and tris(diselenocarbamates) in acetonitrile; a combined spectroscopic and voltammetric study

Abstract The electrochemical oxidation of cobalt(III) dithiocarbamates and diselenocarbamates (CoL 3 ) in acetonitrile+0.1 M Bu 4 NPF 6 is shown to occur via the mechanism: (E) CoL 3 ↔[CoL 3 ] + +e − ; (C 2 ) 2[CoL 3 ] + →[Co 2 L 5 ] + +oxidized ligand; (C) [Co 2 L 5 ] + +2CH 3 CN→CoL 3 +[CoL 2 (CH 3 CN) 2 ] + . A combination of electrochemical, electrospray mass spectrometry, and 59 Co/ 77 Se NMR experiments confirms that the binuclear species, [Co 2 L 5 ] + , reacts with acetonitrile forming CoL 3 and [CoL 2 (CH 3 CN) 2 ] + . At the electrode surface, CoL 3 species generated by this reaction may then be reoxidised resulting in an enhanced peak or limiting current. Consequently, the oxidation of CoL 3 in acetonitrile represents an overall EC 2 C mechanism. The data obtained from cyclic voltammetry at Pt disc electrodes and steady-state hydrodynamic voltammetry at platinum channel electrodes for oxidation of CoL 3 were modelled according to this EC 2 C scheme using the commercial DigiSim electrochemical simulation package and the backwards implicit finite difference technique, respectively. Good fits between experiment and simulation were obtained using the same kinetic parameters for both methods. The calculated dimerisation rate constant (C 2 step) is similar to the value obtained in dichloromethane, which is uncomplicated by reaction of [Co 2 L 5 ] + with the solvent. It was observed that if either voltammetric technique was used in isolation, a wider range of combinations of kinetic parameters could be utilised in order to obtain satisfactory fits between experiment and theory.

Channel electrode voltammetry and reversible electro-dimerisation processes. The reduction of the methyl viologen di-cation in aqueous solution

Abstract Theory is developed to account for the variation of the voltammetric half-wave potential with the rate of mass transport at a channel electrode for the case where an electrochemically reversible electron transfer is followed by the (partially) chemically reversible dimerisation of the electrode product. A working surface is presented which allows the analysis of experimental data and it is shown that when the homogeneous dimerisation kinetics are sufficiently rapid the half-wave potential becomes independent of the rate of mass transport but is shifted from the true formal potential. Experiments are reported on the reduction of the methyl viologen di-cation in aqueous solution. The resulting mono-cation is believed to undergo a reversible dimerisation forming a π-dimer, and the possibility of further aggregation is investigated. Measurements of the half-wave potential as a function of solution flow-rate and concentration are consistent with dimer formation and permit the inference of a value of −0.703 ± 0.003V (vs. SCE) for the one-electron reduction of the di-cation.

Theory of ECE processes at hemicylinder and band microelectrodes

Numerical simulations are used to predict the chronoamperometric current transients resulting from an ECE process at both hemicylinder and band microelectrodes. Working curves are presented to permit the analysis of experimental data. It is demonstrated that the long-time behaviour at a band of width w and length xe is identical with the current at a hemicylinder of width w and radius a = xc4, as has previously been shown to be the case for electrode processes involving simple electron transfer in the absence of coupled homogeneous kinetics.

Impedance voltammetry of electro-dimerization mechanisms: Application to the reduction of the methyl viologen di-cation at mercury electrodes and aqueous solutions

Abstract The faradaic impedance for an electrode mechanism with a reversible homogeneous dimerization reaction following the electron transfer step is derived. The chemical reaction shows up in the frequency dependence of the faradaic impedance and admittance in a similar way as deduced by Sluyters-Rehbach and Sluyters (J. Electroanal. Chem. 23 (1989) 457; J. Electroanal. Chem. 26 (1990) 237) for a homogeneous first-order chemical reaction. Two limiting cases can be distinguished in which the general expression reduces to the simpler Randles or pseudo-Randles expression. Under those conditions, the presence of the dimerization reaction can be inferred from the potential dependence of the impedance parameters. The theory is applied to the reduction of the methyl viologen di-cation at mercury electrodes in aqueous solution. The rate and the equilibrium constants for the dimerization reaction and the standard potential for the electron transfer step are obtained from the Warburg coefficient, while the potential dependence of the irreversibility coefficient allows the calculation of the standard rate constant and the transfer coefficient for the electron transfer step.