Theory of square-wave voltammetry of two-step electrode reaction with kinetically stabilized intermediate

Square-wave voltammograms of quasireversible EE mechanism with thermodynamically unstable intermediate may consist either of a single peak, or of two peaks if the second electron transfer appears quasireversible at the lowest frequency and irreversible at the highest frequency. The development of the second peak depends on the critical dimensionless kinetic parameter which was calculated in this paper. This parameter can be used for the estimation of standard rate constant of the second electrode reaction.     

Square-wave voltammetry of quasi-reversible electrode processes with coupled homogeneous chemical reactions

The electrochemical behaviour of systems complicated by electrode kinetic and quasi-reversible preceding or following homogeneous chemical reactions under square-wave voltammetry (SWV) conditions is analysed theoretically. The results are discussed in detail, considering the influence of rate and equilibrium constants, together with experimentally controlled parameters such as f and E_sw. Both kinetic stages act synergistically for the case of a CE mechanism, but the EC reaction scheme exhibits more complex behaviour, especially for reversible and quasi-reversible electrochemical reactions, which present a minimum response of current for the quasi-reversible chemical reactions. These curves are characteristic for each system, providing not only the bases for their distinction but also for the extraction of kinetic and thermodynamic information.     

Theoretical and experimental study of the catalytic hydrogen evolution reaction in the presence of an adsorbed catalyst by means of square-wave voltammetry

Surface catalytic electrode mechanism based on the hydrogen evolution reaction is analyzed both theoretically and experimentally under conditions of square-wave voltammetry (SWV). The electrode mechanism involves preceding chemical reaction in which the adsorbed catalyst (Cat_(ads)) is undergoing protonation at the electrode surface, i.e., ${\mathrm{Cat}}_{(\mathrm{ads})}+{\mathrm{H}}_{(\mathrm{aq})}^{+}?{\mathrm{CatH}}_{(\mathrm{ads})}^{+}$. The protonated form of the catalyst $({\mathrm{CatH}}_{(\mathrm{ads})}^{+})$ is irreversibly reduced yielding the initial form of the catalyst and atomic hydrogen, i.e., ${\mathrm{CatH}}_{(\mathrm{ads})}^{+}+\mathrm{e}\to {\mathrm{Cat}}_{(\mathrm{ads})}+{\mathrm{H}}_{(\mathrm{aq})}$. The concentration of protons is assumed to be constant in the course of the voltammetric experiment due to the buffered solution, whereas the current is controlled by the variation of the surface concentration of both unprotonated and protonated forms of the catalyst. The overall voltammetric behavior of the system is a specific combination of a simple surface irreversible electrode reaction, surface catalytic reaction and surface reaction preceded by a chemical reaction (CE mechanism). The effect of the thermodynamics and kinetics of the preceding chemical reaction, as well as the kinetics of the irreversible electrode reaction, to the SW voltammetric response is examined in detail. The overall catalytic effect is predominantly controlled by the ratio of the protonation rate constant and the time window of the voltammetric experiment that is represented by the frequency of the potential modulation. Theoretical predictions are illustrated by experiments with the hydrogen evolution reaction at the hanging mercury drop electrode catalyzed by adsorbed famotidine.     

EC mechanism of an adsorbed redox couple. Volume vs surface chemical reaction

A theoretical model of a complex electrode mechanism coupled by adsorption of the redox couple and followed by two different types of irreversible chemical reactions is developed:

$\text{Ox}{}_{\mathrm{<mtext>(</mtext><mtext>ads</mtext><mtext>)</mtext>}}\text{+n}\text{e}{}^{\mathrm{?}}\text{?}\text{Red}{}_{\mathrm{<mtext>(</mtext><mtext>ads</mtext><mtext>)</mtext>}}\text{→}\text{k}{}_{\mathrm{<mtext>s</mtext>}}\text{P}\text{?}\text{?}\text{(}\text{Ox}{}_{\mathrm{<mtext>(</mtext><mtext>aq</mtext><mtext>)</mtext>}}\text{)}{}_{\mathrm{x=0}}\text{+n}\text{e}{}^{\mathrm{?}}\text{?}\text{(}\text{Red}{}_{\mathrm{<mtext>(</mtext><mtext>aq</mtext><mtext>)</mtext>}}\text{)}{}_{\mathrm{x=0}}\text{→}\text{k}{}_{\mathrm{<mtext>v</mtext>}}\text{P}$

The theoretical consideration for this specific type of EC mechanism comprises all relevant phenomena such as diffusion mass transport, adsorption equilibria and kinetics of the following irreversible chemical reactions. The adsorbed electroactive product Red_(ads) decays to the final inactive product P through a chemical reaction occurring exclusively on the electrode surface. It is designated as a surface chemical reaction associated by the rate constant k_s, whereas the dissolved Red_(aq) form transforms independently via a volume chemical reaction taking place in the solution layer adjacent to the electrode surface and is characterized by the rate constant k_v. Adsorptions of both species of the redox couple are assumed to obey a linear adsorption isotherm law. The solutions obtained with the aid of Laplace transforms for the surface concentrations for both oxidized and reduced species are presented as integral equations, thus they are valid for any chronoamperometric technique. The numerical solution is adopted for square-wave voltammetry and both reversible and quasireversible cases were studied. Special attention is paid to revealing discrepancies between the surface and volume chemical reactions. It has been demonstrated that for a reversible case the influence of both chemical reactions is rather similar disabling a simple distinguishing of the reaction type. For the quasireversible case, clear and simple criteria for distinguishing the type of chemical reaction can be established utilizing the properties of split SW peaks and a quasireversible maximum.     

Simulation of square-wave voltammetry at a channel electrode: E,EC and ECE processes

A simulation is developed for square-wave voltammetry occurring at a channel electrode. The technique is based on the space marching variation of the backward implicit method and facilitates the study of E, EC and ECE mechanistic schemes. Further, the investigation of the effects of the rate of mass transport on the three key voltammetric properties — peak current, peak position and peak width at half-height — is possible and the results are compared with previously published work where a stagnant Nernstian diffusion layer was used as a general approximation to all hydrodynamic electrodes.     

The kinetics of neutral methyl viologen in acidic H2O+DMF mixed solutions studied by cyclic voltammetry

The chemistry of the two-electron reduction product of viologen (1,1′-dialkyl-4,4′-bipyridinium, V²⁺) neutral species, is important in understanding the electrochemical behavior of viologens and their utilization. The kinetics for the reactions of neutral methyl viologen (V⁰) in the presence of H⁺ (from HCl), CH₃COOH (pK_a=4.75), ClCH₂CH₂COOH (pK_a=4.00), HCOOH (pK_a=3.75) in aqueous media was examined by cyclic voltammetry according to the EEC_i mechanism. To avoid the electrodeposition of V⁰, we used a 9:1 (v/v%) H₂O+DMF mixture as the solvent medium. To evaluate the rate constants for the chemical reaction followed by the second electron transfer step of V²⁺, the ratio of the anodic and cathodic peak current (I_pa2/I_pc2) corresponding to V⁰–e^??V⁺ was plotted against log τ, where τ is the time between E_1/2 and the switching potential, at various scan rates of 0.02–3.5 V s^?1. The chemical reaction was found to be a parallel reaction consisting of H⁺-catalyzed and general-acid (HA) catalyzed reactions. The second-order rate constants are determined as k_H⁺=3.5×10³ M^?1 s^?1, k_CH3COOH=5.7 M^?1 s^?1, k_HCOOH=4.6×10¹ M^?1 s^?1, and k_ClCH2CH2COOH=3.2×10¹ M^?1 s^?1 using the Nicholson–Shain method and k_H2O was estimated as <3×10^?6 M^?1 s^?1. The CVs were digitally simulated under the assumption of a two-step reaction of V⁰ following the two-step electrode reactions of V²⁺ to V⁰. The simulated CVs show good agreement with those obtained experimentally, when the first-step reaction of V⁰ is a relatively fast reversible reaction and the second-step reaction is a slow irreversible one. Based on these results, we propose that V⁰ is in pseudo-equilibrium with H⁺ or HA to produce VH⁺ which undergoes a reaction with H₂O.     

Dynamic aspects of metal speciation by competitive ligand exchange–adsorptive stripping voltammetry (CLE–AdSV)

Competitive ligand exchange–adsorptive stripping voltammetry (CLE–AdSV) measures speciation of a metal M via a bulk exchange reaction with an adsorptive ligand L_ad followed by electrochemical detection of the adsorbed metal complex. Thermodynamic aspects of the detection window of the technique are well understood. Here, we analyse the kinetic aspects including those involved with the adsorptive accumulation step.The upper border of the kinetic detection window is defined by the requirement of equilibration before accumulation of the complex ML_ad at the electrode surface. Analysis of the exchange step demonstrates that complexes with sample ligands that remain unaffected by the exchange step are generally nonlabile and do not contribute to the AdSV signal. Any residual free metal, however, does contribute to the accumulation process, but this contribution will be negligible in the usual situation of a sufficiently strong complex ML_ad and an excess of L_ad over M. The adsorption of the surface-active complex ML_ad is of a transient nature in the initial stage of the accumulation period, before the diffusive adsorption process approaches a steady-state nature.     

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

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.     

Uncovering the influence of antioxidants on polyphenol oxidation in wines using an electrochemical method: Cyclic voltammetry

The influence of sulfur dioxide, glutathione and ascorbic acid on the cyclic voltammograms of four representative wine polyphenols (catechin, caffeic acid, rutin and quercetin) and five different wines was investigated using a glassy carbon electrode in a model wine solution. Sulfur dioxide increased the anodic current and decreased the cathodic current for all four polyphenols and all wines, pointing to a rapid interaction of SO₂ with the oxidized polyphenol quinones. A similar trend was seen for glutathione, except that in the case of quercetin, addition of glutathione led to the formation of a second set of voltammetric peaks, corresponding to redox activity of a glutathione derivative. However, ascorbic acid produced no additional effect on the cyclic voltammograms of wine polyphenols and wines, beyond that expected for a simple sum of the polyphenol and ascorbic acid responses, with the exception that adsorption of quercetin and rutin on the carbon electrode caused a shift in the ascorbic acid oxidation peak to more positive potentials.     

A comparison of sinusoidal,square wave,sawtooth, and staircase forms of transient ramped voltammetry when a reversible process is analysed in the frequency domain

Sawtooth and squarewave forms of transient voltammetry have been simulated in order that a detailed comparison with results previously undertaken on sinusoidal and square wave forms of voltammetry could be made in the frequency domain. All theoretical calculations were performed for a reversible process, assuming a linear dc ramped potential is present, and using numerical simulations which were analysed using the fast Fourier transform method. On the basis of this study, the conclusion is reached that transient voltammetric methods, where a periodic signal is superimposed onto a dc potential, are part of a family of techniques having essentially common characteristics, which can all be analysed in a unified theoretical framework, in contrast to current practice of treating them in inherently different manners. The subtle differences that arise are related to the non-linear effects encountered when large amplitudes of the periodic waveform are superimposed onto the dc potential. Experimental data on the oxidation of ferrocene in acetonitrile support the fidelity of the simulations of sawtooth voltammetry.     

The effect of acetate concentration,solution pH and conductivity on the anodic stripping voltammetry of lead and cadmium ions at in situ bismuth-plated carbon microelectrodes

The use of carbon microdisc electrode substrates allowed Pb(II) and Cd(II) anodic stripping voltammetry at in situ plated bismuth films to be studied in an extended acetate buffer/electrolyte concentration range that includes very low or zero acetate levels. The change of the Pb and Cd Square Wave Anodic Stripping Voltammetry (SWASV) peak height with acetate concentration, pH and conductivity has been studied systematically. It was found that the stripping peak signal is considerably enhanced in the absence of added acetate or in acidic solutions. This behaviour has been attributed to the extent of metal ion complexation at different levels of free acetate ions that are present at different buffer concentrations or pH values. Recording both the forward and the reverse voltammograms of each SWASV curve, the signal variation could be attributed to changes in the metal ion deposition rate (as its complexation state is varied) both during the preconcentration step and the reverse pulse of the SWASV potential sequence.     

The theory of square wave voltammetry at uniformly accessible hydrodynamic electrodes

An integral equation approach which allows the ready simulation of square wave voltammetry for electrochemically reversible, quasi-reversible and irreversible processes is developed for the case where transport to the electrode occurs across a uniform diffusion layer of finite thickness.     

Direct simultaneous determination of dihydroxybenzene isomers at C-nanotube-modified electrodes by derivative voltammetry

The voltammetric behavior of dihydroxybenzene isomers was studied with glassy carbon electrodes modified with multi-wall carbon nanotubes. In 0.1 mol L^?1 HAc + NaAc buffer solution (pH 5.5), the modified electrode showed a good electrocatalytic response towards dihydroxybenzenes. The peak currents increased significantly and their oxidation potentials shifted negatively. Through a derivative technique, the three oxidation peaks of dihydroxybenzene isomers can be separated, thus the method can be applied to direct simultaneous determination without previous separation. The linear calibration ranges were 2 × 10^?6–1 × 10^?4 mol L^?1 for hydroquinone and catechol, respectively, and 5 × 10^?6 to 8 × 10^?5 mol L^?1 for resorcinol, with detection limits of 6 × 10^?7, 6 × 10^?7 and 1 × 10^?6 mol L^?1, respectively. This method has been applied to the direct determination of dihydroxybenzene isomers in artificial wastewater, and the recovery was from 92% to 104%.     

Numerical determination of extended semi integrals and semi differentials by using spline cubic functions. Applications to an EE reversible mechanism in cyclic voltammetry

In this work, we propose a new general method based on the use of cubic spline functions, suitable for the numerical determination of extended semi integrals and semi differentials. The procedure combines these interpolation functions with different numerical integration and differentiation standard methods, including commercial software. The method has been applied to the electrochemical reduction of the meso-tetra(4-N-methylpyridyl)porphyrin in acidic aqueous solution, where this compound exhibits a two-electron wave in cyclic voltammetry. In this work, we determine the semi differential of the current and demonstrate that the signals obtained correspond to an EE process, where both electrochemical steps are reversible and their formal potentials are very close.     

Determination of trace vanadium(V) by adsorptive anodic stripping voltammetry on an acetylene black paste electrode in the presence of alizarin violet

A sensitive and simplified voltammetric method is developed for the determination of trace amounts of vanadium(V) by adsorptive anodic stripping voltammetry using an acetylene black (AB) paste electrode. The method is based on the preconcentration of the V(V)–alizarin violet (AV) complex at open circuit while stirring the solution for 90 s in 0.15 mol dm⁻³ hexamethylenetetraamine–hydrochloric acid buffer (pH 4.4), the adsorbed complex is then oxidized, producing a response with a peak potential of 564 mV when scanning linearly from 0 to 1000 mV. For voltammetric determination of V(V), the parameters influencing the peak current have been optimized. Under the selected conditions, the peak current and concentration of V(V) accorded with linear relationship in the range of 8.0 × 10⁻¹⁰ mol dm⁻³–1.0 × 10⁻⁷ mol dm⁻³ (c_AV = 2.0 × 10⁻⁶ mol dm⁻³) and 1.0 × 10⁻⁷ mol dm⁻³–8.0 × 10⁻⁶ mol dm⁻³ (c_AV = 2.0 × 10⁻⁵ mol dm⁻³), the detection limit (three times signal to noise) was estimated to be 6.0 × 10⁻¹⁰ mol dm⁻³ for 90 s accumulation. The relative standard deviation (RSD) is 1.9% and 2.3% for V(V) concentrations of 1.0 × 10⁻⁷ mol dm⁻³ and 1.0 × 10⁻⁸ mol dm⁻³ respectively. Finally, this proposed method was successfully applied to the determination of V(V) in natural water samples.     

Conducting films obtained by electro-oxidation of p-aminodiphenylamine (ADPA) in the presence of aniline in buffer aqueous solution at pH 5

The electrochemical oxidation of aniline and p-aminodiphenylamine (ADPA) was carried out in a phosphate buffer solution at pH 5. Cyclic voltammetry and “in situ” FTIR spectroscopy were combined to study the redox behavior of the oxidation products. When ADPA is oxidized in the presence of aniline, two redox processes are observed. One of these redox processes is related to a soluble species, while the other pertains to a species attached to the electrode surface. Only those films synthesized from ADPA oxidation in the presence of aniline are electroactive in this buffered medium. No evidence pointing to the occurrence of autocatalytic polymerization exists under the experimental conditions employed.     

Catalysis by immobilized redox enzymes. Diagnosis of inactivation and reactivation effects through odd cyclic voltammetric responses

Odd cyclic voltammetric responses, with an inverted peak appearing on the reverse scan, have been recently reported for the catalysis of immobilized enzymes involved in a direct electron transfer at the electrode surface and implicated in a chemical inactivation/redox reactivation mechanism. In this work, it is shown that this twisted reverse trace behavior can be related rigorously and quantitatively to such a reaction scheme by means of a minimal number of dimensionless parameters. As a prelude, the requirements for ‘pure catalytic’ conditions to be achieved are established quantitatively. It is also shown that simple irreversible or reversible inactivation does not entail the appearance of twisted reverse traces. The quantitative analysis of the inactivation/reactivation mechanism does not lead to a closed form expression of the current responses, but rather requires the numerical resolution of the pertinent differential equations. This approach may be readily extended to virtually any kind of mechanism, including more complex reactions schemes, distance-dependent electron transfer kinetics, the use of immobilized or free-moving redox cosubstrates, consideration of substrate mass transport limitations, etc.     

Investigation of LiMn2O4 cathodes for use in rechargeable lithium batteries by linear sweep voltammetry: Part I. Theoretical study

Linear sweep voltammetry (LSV) is a well-known tool for electrochemical investigations. Different aspects on the use of LSV in the study of an intercalation electrode in the rechargeable lithium battery system have been studied. Mathematical models were used to simulate voltammetry responses for an intercalation material influenced by solid phase diffusion, charge transfer and IR-drop. It was shown how the peak potential and the peak current density vary with sweep rate for different rate determining processes. The simulations show that finite and semi-infinite diffusion is relatively easy to distinguish and also, these two processes behave differently from processes influenced by charge transfer and an external IR-drop. However, the separation of charge transfer and IR-drop is difficult. The use of the convolution sweep voltammetry method was also investigated. It was found that finite diffusion and a non-zero initial concentration limit the applicability in these systems.     

Electrodeposition and stripping analysis of bismuth selenide thin films using combined electrochemical quartz crystal microgravimetry and stripping voltammetry

Combined stripping voltammetry and electrochemical quartz crystal microgravimetry were employed for the compositional analysis of electrodeposited bismuth selenide (Bi–Se) thin films. Electrodeposited films contain free Bi and free Se in addition to the targeted Bi₂Se₃ compound and the amount of these “impurity” phases depends on the electrodeposition variables. Thus the free Se content was determined using the reduction peak of Se to Se²⁻ obtained during the cathodic scan of films in 0.1 M Na₂SO₄ blank electrolyte. The Se content obtained during the cathodic stripping of Bi₂Se₃ to Bi + Se²⁻ was used for the determination of Bi₂Se₃ content using the assumption of 2:3 compound stoichiometry. Finally, the total Bi content was obtained from the anodic scan and the free Bi content was calculated from the difference between total Bi and the Bi present in Bi₂Se₃. The compositional assays thus obtained from the combined use of stripping voltammetry and EQCM are presented as a function of electrodeposition potential and electrolyte composition. The Bi₂Se₃ content decreased as the deposition potential was decreased (made more negative) and was highest when the electrolyte contained the same molar ratio of Bi³⁺ and Se⁴⁺ species. Unlike the Bi₂Te₃ previously studied by us, electrodeposition of Bi₂Se₃ was not efficient at potentials more negative than −0.5 V because of Se stripping and hydrogen evolution.