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Electrochemical simulation is used to validate the geometry of commercially manufactured interdigitated array electrodes intended for use in generator–collector experiments, consisting of two interlocked arrays of band electrodes. A working surface is generated showing peak current as a function of scan rate and the inter electrode distance when cyclic voltammetry is performed at a single array of band electrodes. This working curve is then used to establish accurate electrode widths and inter-electrode distances of an interdigitated band array using a fully supported aqueous solution of ruthenium hexamine trichloride as a test system by running voltammetry at one of the two arrays at a time. Both arrays are then used at the same time to perform cyclic voltammetry to validate the established electrode geometries of 9.9 and 10.7 μ m for the electrode widths in the two arrays, and 10.5 μ m for the distance between adjacent electrodes. Cyclic voltammetry in generator–collector mode is then carried out, and these parameters used to successfully simulate the experimental data. The level of precision determined is essential for the quantitative interpretation of generator–collector measurements using interdigitated electrodes.

Recent progress in the theory and practice of voltammetry is surveyed and evaluated. The transformation over the last decade of the level of modelling and simulation of experiments has realised major advances such that electrochemical techniques can be fully developed and applied to real chemical problems of distinct complexity. This review focuses on the topic areas of: multistep electrochemical processes, voltammetry in ionic liquids, the development and interpretation of theories of electron transfer (Butler-Volmer and Marcus-Hush), advances in voltammetric pulse techniques, stochastic random walk models of diffusion, the influence of migration under conditions of low support, voltammetry at rough and porous electrodes, and nanoparticle electrochemistry. The review of the latter field encompasses both the study of nanoparticle-modified electrodes, including stripping voltammetry and the new technique of 'nano-impacts'.

Asymmetric Marcus–Hush (AMH) theory is applied for the first time in ionic solvents to model the voltammetric reduction of oxygen in 1-butyl-1-methylpyrrolidinium bis-(trifluoromethylsulfonyl)-imide and of 2-nitrotoluene (2-NT), nitrocyclopentane (NCP), and 1-nitro-butane (BuN) in trihexyltetradecylphosphonium tris(pentafluoroethyl)trifluorophosphate on a gold microdisc electrode. An asymmetry parameter, γ, was estimated for all systems as −0.4 for the reduction of oxygen and −0.05, 0.25, and 0 ± 0.05 for the reductions of 2-NT, NCP, and BuN, respectively, which suggests equal force constants of reactants and products in the case of 2-NT and BuN and unequal force constants for oxygen and NCP where the force constants of the oxidized species are greater than the reduced species in the case of oxygen and less than the reduced species in the case of NCP. Previously measured values for α, the Butler–Volmer transfer coefficient, reflect this in each case. Where appreciable asymmetry occurs, AMH theory was seen...

The voltammetry for the reduction of 2-nitrotoluene at a gold microdisk electrode is reported in two ionic liquids: trihexyltetradecylphosphonium tris(pentafluoroethyl)trifluorophosphate ([P14,6,6,6][FAP]) and 1-ethyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([Emim][NTf2]). The reduction of nitrocyclopentane (NCP) and 1-nitrobutane (BuN) was investigated using voltammetry at a gold microdisk electrode in the ionic liquid [P14,6,6,6][FAP]. Simulated voltammograms, generated through the use of Butler–Volmer theory and symmetric Marcus–Hush theory, were compared to experimental data, with both theories parametrizing the data similarly well. An experimental value for the Marcusian parameter, λ, was also determined in all cases. For the reduction of 2-nitrotoluene, this was 0.5 ± 0.1 eV in both solvents, while for NCP and BuN in [P14,6,6,6][FAP], it was 2 ± 0.1 and 5 ± 0.1 eV, respectively. This is attributed to the localization of charge on the nitro group and the primary nitro alkyl’s increase...

Microelectrode voltammetry is used to study the electrochemical reduction of dioxygen, O2, in the room-temperature ionic liquid trihexyl(tetradecyl)phosphonium trifluorotris(pentafluoroethyl)phosphate [P6,6,6,14][FAP]. The nature of the unusual voltammetric waves is quantitatively modeled via digital simulation with the aim of clarifying apparent inconsistencies in the literature. The reduction is shown to proceed via a two-electron reaction and involve the likely capture of a proton from the solvent system. The oxidative voltammetric signals seen at fast scan rates are interpreted as resulting from the reoxidation of HO2•–. In the presence of large amounts of dissolved carbon dioxide the reductive currents decrease by a factor of ca. two, consistent with the trapping of the superoxide radical, O2•–, intermediate in the two-electron reduction process.

The amperometric detection of oxygen under moist (humid) conditions via Clark cell type devices using Room Temperature Ionic Liquids (RTILs) as electrochemical solvents can be complicated, because the number of electrons transferred in the electrode reaction varies between one and two as a function of the humidity. The problem is avoided through the use of phosphonium cation based ionic liquids in which the alkyl group of the phosphonium cation has acidic protons which are rapidly abstracted by superoxide ions. Thus the reduction of O2 is to be trapped at the one electron level on the micro-electrode voltammetric timescale, allowing the amperometric detection of oxygen under humid conditions to be quantitatively viable. © 2014 Elsevier B.V.

The influence of near wall hindered diffusion of nanoparticles on anodic particle coulometry (APC) is investigated. In an APC experiment, an electrode in a solution of nanoparticles is subject to a potential step from a value where no oxidation of nanoparticles occurs, to one where oxidative dissolution of nanoparticles is transport controlled. Nanoparticle-electrode impacts are then observed as spikes in the measured current. The area under these spikes corresponds to the charge transferred during the nanoparticle oxidation. A computational model is developed to simulate APC experiments, including the effect of near wall hindered diffusion. It is shown that this new, more complete picture is able to successfully simulate the experimental APC of nickel nanoparticles. It is also shown that a detailed, quantum mechanical tunnelling model is not required to describe the destructive oxidation of nanoparticles; an alternative simple impact model can successfully simulate experimental data. © 2013 Elsevier B.V. All rights reserved.

Theory is developed for the rate of irreversible adsorption of nanoparticles from solution onto an electrode surface, including the effects of hindered diffusion of large nanoparticles. The effect of nanoparticle size on adsorption processes is studied, and found to be significant for large particles, where the nanoparticle radius to electrode radius ratio is larger than 1 × 10-3. The extent of adsorption in a typical electrochemical nanoparticle experiment at a 5 μm radius hemispherical electrode is studied for different adsorption rate constants, along with the effect this has on concentration of nanoparticles in the vicinity of the electrode and the frequency of impacts of nanoparticles on the electrode. For fast adsorption rate constants, significant and long lasting (in extreme cases greater than 4 h) concentration gradients can form, necessitating careful experimental practice.© 2013 Elsevier B.V. All rights reserved.

This thesis is concerned with the simulation of various electrochemical experiments and its application to electroanalysis. Chapter 1 outlines the fundamental principles of electrochemistry which are of importance for the reading of this thesis. Chapter 2 then outlines the methods used in the numerical simulation of electrochemical experiments. Chapters 3 and 4 are concerned with the electrochemistry of nanoparticles, and how this is affected by the presence of near wall hindered diffusion. In Chapter 3, a computational model to simulate anodic particle coulometry of nanoparticles in the presence of hindered diffusion is developed, and the effect of this hindered diffusion investigated. The model is then applied to simulate experimental data. Chapter 4 looks at the effect of hindered diffusion on the adsorption of nanoparticles on electrode surfaces, and investigates the effects of this adsorption on electrochemical experiments with nanoparticles generally. Chapters 5, 6 and 7 are concerned with band electrodes in isolation, in a pair and in an array respectively. In Chapter 5, a model to simulate double potential step chronoamperometry at an individual band electrode is developed, and used to successfully simulate experimental data. Chapter 6 looks at dual band electrodes used in generator-collector mode, and how this can be used to simultaneously measure the concentration of two species in solution. Chapter 7 looks at interdigitated arrays of band and ring electrodes in generator-collector mode, and develops a model to simulate cyclic voltammetry in both cases, as well as investigating under what conditions interdigitated ring arrays may be modelled as interdigitated band arrays. Chapter 8 develops a model to simulate chronoamperometry and cyclic voltammetry at porous electrodes, and investigates the consequences for electroanalysis of having a porous layer. Finally, Chapter 9 investigates the Marcus-Hush theory of electron transfer kinetics, and looks at the effect of the kinetically limited currents resulting from this theory to the equivalence relation between microdisc electrodes and sphere-on-a-surface electrodes.

A general, simple, analytical expression for the steady state voltammetric response at electrodes of three different geometries is developed. These geometries have both uniform (isolated microsphere) and nonuniform (microdisc and microsphere supported on an electroinactive surface) accessibility. The expression is applicable over the full range of electrochemical reversibility and for any initial concentrations of both species in the redox couple of interest. By making the assumption that, in all cases, the concentration of each species across the electrode surface is constant (representing an average of the true concentration profile), an equation describing the steady state voltammetric wave is deduced. Although approximate, the developed equation has a high degree of accuracy when compared to simulated results. This method, based on sound physical principles, is open to extension to other geometries and represents an advantage of previous solutions largely restricted to microdiscs. © 2013 American Chemical Society.

Two flat gold electrodes are placed vis-a-vis with an epoxy spacer layer that is etched out to give a ca. 100 μm-deep electrochemically active trench. A water-insoluble oil phase, here the redox system N,N-diethyl-N'N'-didodecyl-phenylenediamine (DDPD) in 4-(3-phenylpropyl)-pyridine (PPP), is immobilized into the trench to allow anion transfer upon oxidation of DDPD (oil) to DDP⁺ (oil). In "mono-potentiostatic mode" quantitative transfer/expulsion of anions into the trench oil phase occurs. However, in "bi-potentiostatic mode" feedback currents dominated by rapid plate-to-plate diffusion normal to the electrode surfaces are observed. Comparison of "normal" diffusion and "lateral" diffusion shows that the rate of diffusion-migration charge transport across the oil film is anion hydrophobicity dependent.

Square wave voltammetry (SWV) and differential multipulse voltammetry (DMPV) in weakly supported media are investigated. The numerical simulation procedures reported in literature (Streeter et al., J. Phys. Chem. C 112 (2008) 13716-13728; Limon-Petersen et al., J. Phys. Chem. C 114 (2010) 2227-2236) for electrochemical experiments in low conductivity solutions is applied with success. From this theory, the influence of the concentration of supporting electrolyte on the voltammograms is discussed for different redox couples and at electrodes of different size. The variation of the peak current and peak potential due to migration and ohmic drop effects are reported. The theory is applied to the experimental study of the one-electron reduction processes of cobaltocenium and cobalt (III) sepulchrate at mercury hemispherical electrodes of 25 μm radius. The kinetic parameters and formal potential are obtained in a wide range of support ratio from the SWV and DMPV voltammograms. Possible changes of the kinetic and thermodynamic properties of the electrode reactions are analyzed as a function of the level of support. © 2012 Elsevier B.V. All rights reserved.

Pairing effect: Varying the concentration of support electrolyte in the electrochemical EC 2 reduction of 2,6-diphenylpyrylium reveals the presence of ion pairing between the electroactive species and BF 4-. Experiment and theory are shown to be in good agreement only if ion pairing is included in the simulations. This previously unanticipated effect is only observable if voltammetry is performed under conditions of weak support. Copyright © 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim.

The electrochemical oxidation of catechol and dopamine has been studied at a platinum micro-electrode (10 μ m diameter) in two room temperature ionic liquids (RTILs): 1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C2mim][NTf2]) and 1-Butyl-3-methylimidazolium tetrafluoroborate ([C4mim][BF4]). For catechol in [C2mim][NTf2], an electrochemically quasi-reversible oxidation peak was observed at 1.1 V vs. Pt with a back peak at 0.4 V vs. Pt. This is assigned to the two-electron oxidation of catechol to doubly protonated o-benzoquinone. Double-step chronoamperometry gave a diffusion coefficient for the catechol and the oxidised species which is 3.8 × 10 - 11 m 2 s - 1 for both. For catechol in [C4mim][BF4], a two-electron oxidation wave was observed at 1.0 V vs. Pt with no back peak. Another peak at less positive potential was also observed at 0.6 V vs. Pt in [C4mim][BF4] but not in [C2mim][NTf2] which is assigned to the adsorption of electrochemically formed neutral o-benzoquinone on the platinum electrode. The oxidised protonated o-benzoquinone is suggested to be deprotonated by the [ BF 4 ] - anion, but not by the [ NTf 2 ] - anion: hence adsorption of the neutral species at the platinum electrode, not the charged species. For dopamine in both RTILs, two chemically irreversible oxidation peaks were observed at 0.75 V and 1.1 V vs. Pt, and assigned to the oxidation of dopamine to the corresponding semi-quinone and the quinone. Potential-step chronoamperometry was carried out on the oxidation waves of dopamine in [C2mim][NTf2] and the diffusion coefficient of species in solution was calculated to be 6.85 × 10 - 12 m 2 s - 1 and confirmed that the waves corresponded to one and two electron processes. A third wave was observed at 1.8 V vs. Pt which is attributed to the oxidation of the amine group to a radical cation with likely subsequent follow up chemistry. In [C4mim][BF4] a peak at less positive potential was observed for dopamine, similar to catechol which is assigned to the adsorption of the neutral quinone species on the platinum electrode formed by the reaction of the removal of protons from the oxidised dopamine with the [ BF 4 ] - anion.

The voltammetry of N,N-dimethyl-p-phenylenediamine, DMPD, in the room temperature ionic liquid (RTIL) 1-butyl-3-methylimidazolium tetrafluoroborate, [C4mim][BF4] is studied by means of microdisc voltammetry over a wide range of voltage scan rates incorporating the transition from linear to convergent diffusion. Two voltammetric waves were recorded corresponding to the formation of the radical cation DMPD+ and dication DMPD 2+; both are stable on the voltammetric time scale. Double potential step chronoamperometry was used to measure the diffusion coefficients of DMPD and DMPD+. These values, in conjunction with simulations of the cyclic voltammetry, permit the inference of the equilibrium constant and kinetics for the comproportionation of DMPD and DMPD2+ forming DMPD+ to be studied. © 2009 American Chemical Society.

The voltammetry for the reduction of oxygen at a microdisc electrode is reported in two room temperature ionic liquids: 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl) imide ([Bmpyrr][NTf2]) and trihexyltetradecylphosphonium bis(trifluoromethylsulfonyl) imide ([P 14,6,6,6][NTf2]) at 298 K. Simulated voltammograms using Butler-Volmer theory and Symmetric Marcus-Hush (SMH) theory were compared with experimental data. Butler-Volmer theory consistently provided experimental parameters with a higher level of certainty than SMH theory. A value of solvent reorganisation energy for oxygen reduction in ionic liquids was inferred for the first time as 0.4-0.5 eV, which is attributable to inner-sphere reorganisation with a negligible contribution from solvent reorganisation. The developed Butler-Volmer and Symmetric Marcus-Hush programs are also used to theoretically study the possibility of kinetically limited steady state currents, and to establish an approximate equivalence relationship between microdisc electrodes and spherical electrodes resting on a surface for steady state voltammetry for both Butler-Volmer and Symmetric Marcus-Hush theory. © 2014 Elsevier B.V. All rights reserved.

Two types of generator–collector electrode systems, (i) a gold–gold interdigitated microband array and (ii) a gold–gold dual-plate microtrench, are compared for nitrobenzene electroanalysis in aerated aqueous 0.1 M NaOH. The complexity of the nitrobenzene reduction in conjunction with the presence of ambient levels of oxygen in the analysis solution provide a challenging problem in which feedback-amplified generator–collector steady state currents provide the analytical signal. In contrast to the more openly accessible geometry of the interdigitated array electrode, where the voltammetric response for nitrobenzene is less well-defined and signals drift, the voltammetric response for the cavity-like microtrench electrode is stable and readily detectable at 1 μM level. Both types of electrode show oxygen-enhanced low concentration collector current responses due to additional feedback via reaction intermediates. The observations are rationalised in terms of a “cavity transport coefficient” which is beneficial in the dual-plate microtrench, where oxygen interference effects are suppressed and the analytical signal is amplified and stabilised.

Theory is presented to simulate both chronoamperometry and cyclic voltammetry at porous electrodes fabricated by means of electro-deposition around spherical templates. A theoretical method to extract heterogeneous rate constants for quasireversible and irreversible systems is proposed by the approximation of decoupling of the diffusion within the porous electrode and of bulk diffusion to the electrode surface.

A generator-collector "nano-litre cavity" based on two opposed platinum-coated gold film electrodes with 19 μm gap and either 38 μm or 83 μm depth is employed for the titration of protons and/or hydrogen. Diffusional feedback currents between generator and collector electrode in a platinum-platinum dual-plate sensor configuration provide a sensitive analytical tool for cycleable redox systems, here, the proton/hydrogen redox system in the presence of oxygen. Experimental data are compared with the theoretical expression proposed by Hubbard and Peters (A.T. Hubbard, D.G. Peters, Critical Reviews in Analytical Chemistry, 1973, 3, 201-242) suggesting a dominating transport effect of "slow diffusers". Good agreement is observed even at relatively high proton concentrations where hydrogen bubble nucleation within the micro-trench starts to occur. Low concentration measurements are strongly affected by oxygen reduction locally consuming/depleting protons. Catalytic activity of the platinum deposit is crucial for maximising the current output. © 2014 Published by Elsevier Ltd. All rights reserved.

We computationally investigate the chronoamperometric current response of spherical and cubic particles on a supporting insulating surface. By using the method of finite differences and random walk simulations, we can show that both systems exhibit identical responses on all time scales if their exposed surface areas are equal. This result enables a simple and computationally efficient method to treat certain spherical geometries in random walk based noise investigations.

Generator-collector electrode systems are based on two independent working electrodes with overlapping diffusion fields where chemically reversible redox processes (oxidation and reduction) are coupled to give amplified current signals. A generator-collector trench electrode system prepared from two tin-doped indium oxide (ITO) electrodes placed vis-à-vis with a 22 μm inter-electrode gap is employed here as a sensor in aqueous media. The reversible 2-electron anthraquinone-2-sulfonate redox system is demonstrated to give well-defined collector responses even in the presence of oxygen due to the irreversible nature of the oxygen reduction. For the oxidation of dopamine on ITO, novel "Piranha-activation" effects are observed and chemically reversible generator-collector feedback conditions are achieved at pH 7, by selecting a more negative collector potential, again eliminating possible oxygen interference. Finally, dopamine oxidation in the presence of ascorbate is demonstrated with the irreversible oxidation of ascorbate at the "mouth" of the trench electrode and chemically reversible oxidation of dopamine in the trench "interior". This spatial separation of chemically reversible and irreversible processes within and outside the trench is discussed as a potential in situ microscale sensing and separation tool.

We present a simple and general theoretical model which accounts fully for the influence of an electrode modifying non-electroactive layer on the voltammetric response of a diffusional redox probe. The layer is solely considered to alter the solubilities and diffusion coefficients of the electroactive species within the thin layer on the electrode surface. On this basis it is demonstrated how, first, the apparent electrochemical rate constant can deviate significantly from that measured at an unmodified electrode. Second, depending on the conditions within the layer the modification of the electrode may lead to either apparent 'negative' or 'positive' electrocatalytic effects without the true standard electrochemical rate constant for the electron transfer at the electrode surface being altered. Having presented the theoretical model three experimental cases are investigated, specifically, the reductions of ruthenium(III) hexaamine, oxygen and boric acid on a gold macro electrode with and without a multi-layer organic capped nanoparticle film. In the latter case of the reduction of boric acid the voltammetric reduction is found to be enhanced by the presence of the organic layer. This result is interpreted as being due to an increase in the solubility of the analyte within the non-electroactive layer and not due to an alteration of the standard electrochemical rate constant.

A computational model for the simulation of a double band collector-generator experiment is applied to the situation where two electrochemical reactions occur concurrently. It is shown that chronoamperometric measurements can be used to take advantage of differences in diffusion coefficients to measure the concentrations of both electroactive species simultaneously, by measuring the time at which the collection efficiency reaches a specific value. The separation of the electrodes is shown to not affect the sensitivity of the method (in terms of percentage changes in the measured time to reach the specified collection efficiency), but wider gaps can provide a greater range of (larger) absolute values of this characteristic time. It is also shown that measuring the time taken to reach smaller collection efficiencies can allow for the detection of smaller amounts of whichever species diffuses faster. The case of a system containing both ascorbic acid and opamine in water is used to exemplify the method, and it is shown that mole fractions of ascorbic acid between 0.055 and 0.96 can, in principle, be accurately measured., Comment: 34 pages, 8 figures

The oxidation of potassium ferrocyanide, K4Fe (CN)6, in aqueous solution under fully supported conditions is carried out at interdigitated band and ring electrode arrays, and compared to theoretical models developed to simulate the processes. Simulated data is found to fit well with experimental results using literature values of diffusion coefficients for Fe ( CN ) 6 4 - and Fe ( CN ) 6 3 - . The theoretical models are used to compare responses from interdigitated band and ring arrays, and the size of ring array required to approximate the response to a linear band array is investigated. An equation is developed for the radius of ring required for a pair of electrodes in a ring array to give a result with 5% of a pair of electrodes in a band array. This equation is found to be independent of the scan rate used over six orders of magnitude.

Gold-gold double-hemisphere junction electrodes with an inter-electrode gap of typically 1μm are employed for generator-collector square wave voltammetry. Electrochemical data are recorded as a function of both generator and collector potential to give three-dimensional response "maps". At sufficiently low frequencies, close-to-steady-state conditions for the collector response are achieved and peak responses complementary to those for the generator electrode are recorded. Due to localised interelectrode gap diffusion (fast) as opposed to peripheral diffusion (slow), information about reaction products and intermediates can be obtained. Local pH gradient effects provide additional "fingerprint" information beneficial for future application in analytical detection. © 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim.

The variation of supporting electrolyte concentration so that the relative contribution of migration and diffusion to transport is altered has been shown to be mechanistically revealing in some cases. We consider the following ECE/DISP1 mechanism, in which the chemical step, B ⇌ C, is an isomerisation: A + e - ⇌ B B ⇌ C B + C ⇌ A + P C + e - ⇌ P This system is studied by simulating voltammetric responses at a hemispherical microelectrode over a range of scan rates and support ratios. A wide range of rate constants for the intermediate chemical step are investigated. It is found that, for a certain range of rate constants, significant variations become apparent in the responses of the two mechanisms. In particular it is found that for intermediate values of the rate constant of the chemical step, the reductive current produced from an ECE mechanism is reduced relative to that of DISP1 as the support ratio is lowered.

The reduction of 2-nitrobromobenzene in acetonitrile has been studied in the presence and near absence of supporting electrolyte at a mercury hemispherical microelectrode. In the presence of a high concentration of tetra-n-butylammonium perchlorate, voltammetric studies over a wide range of voltage scan rates spanning the transition from convergent to linear diffusion confirms the reduction mechanism as DISP1, rather than ECE, as previously thought by the majority of earlier studies. A rate constant of approximately 23 s-1 at 298 K was inferred for the loss of bromide ion from the 2-nitrobromobenzene radical anion. In the presence of weak support, with concentration ratios of electrolyte to reactant of 5 and 0.5, the Nernst-Planck-Poisson system of equations were used to model the coupled diffusion-migration-reaction. It was found the both the mechanism of reaction and the derived homogeneous kinetics were unchanged in the near absence of supporting electrolyte. © 2011 Elsevier B.V. All rights reserved.

A variety of generator-collector systems are reviewed, from the original rotating ring-disc electrodes developed in the 1950s, to very recent developments using new geometries and microelectrodes. An overview of both theoretical and experimental aspects are given, and the power of these double electrode systems in analytical electrochemistry is illustrated with a range of applications.