Quasireversible Maximum Research Articles

Theoretical and experimental study of the surface redox reaction involving interactions between the adsorbed particles under conditions of square-wave voltammetry

A surface redox reaction of a strongly adsorbed redox couple involving interactions between the adsorbed particles was analyzed theoretically under conditions of square-wave voltammetry (SWV). If uniform interactions act between the adsorbed particles, the effect of interaction forces is represented through the product of the relative surface coverage and Frumkin interaction parameter Θa. The kinetics of the redox reaction in the presence of uniform interactions are a function of the apparent rate constant defined as k s,app.= k s exp(−2 aΘ), where k s is a real standard rate constant. The apparent reversibility of the redox reaction is determined solely by a dimensionless kinetic parameter defined as the ratio of the apparent rate constant and the signal frequency, ω= k s,app/ f. This dimensionless kinetic parameter unifies the effects of both the interaction forces and the charge transfer rate. The height of the dimensionless response depends parabolically on the kinetic parameter ω, as a consequence of the phenomenon known as a ‘quasireversible maximum’. Based on this peculiarity, a method for estimating the real standard rate constant k s and Frumkin interaction parameter a is proposed. The theoretical results are compared qualitatively with the experimental SW voltammograms of probucole.

Surface Catalytic Mechanism in Square-Wave Voltammetry

A pseudo-first-order catalytic mechanism in which both reactant and product of the redox reaction are strongly immobilized on the electrode surface is theoretically analyzed under conditions of square-wave voltammetry (SWV). A mathematical procedure is developed for diffusionless conditions. The relationships between the properties of the voltammetric response and both the kinetic parameters of the redox reaction and the parameters of the excitement signal are studied. The phenomenon of the quasireversible maximum is discussed. The theoretical results are confirmed with the experiments of azobenzene performed in a presence of hydrogen peroxide. In acetate buffer with pH 4.2 the standard rate constant of charge transfer of azobenzene is ks = 12 s−1 and the catalytic rate constant in the presence of hydrogen peroxide is kc = 2.24×104 s−1 mol−1 L.

Ohmic drop effects in square-wave voltammetry

The ohmic drop effects in square-wave voltammetry (SWV) are studied theoretically. Three different electrode mechanisms are considered: (i) simple redox reaction of a dissolved redox couple, (ii) redox reaction with adsorption of the reactant and (iii) surface redox reaction of a strongly immobilized redox couple. The ohmic drop effect is represented through the complex dimensionless resistance parameter defined as ρ=(nF)2S(cOx)0(Df)1/2RΩ(RT)−1 for (i) and (ii) and ρs=(nF)2SΓ0RΩf(RT)−1 for (iii). The relationships between the properties of the SWV response and the resistance parameters are investigated thoroughly. An attempt is made to establish criteria for distinguishing the kinetic from the ohmic drop phenomena. The influence of the ohmic drop on the quasi-reversible maximum in the case of adsorption-complicated redox reactions (ii) and (iii) is analyzed. The error that can be involved in the estimation of the standard rate constant using the quasi-reversible maximum in the presence of ohmic drop is evaluated in the case of the surface redox reaction (iii).

Characterization of the Redox reaction of V(V) in Ammonia Buffers with Square-Wave Voltammetry

The redox reaction of V(V) in ammonia buffer solution of pH = 8.60 was studied by means of square-wave (SWV) and cyclic (CV) voltammetry. The redox reaction studied exhibits properties of a surface redox process in which both reactant and product of the redox reaction are immobilized to the electrode surface. A mathematical model for the electrode mechanism proposed was developed under conditions of square-wave voltammetry. In agreement with the theoretical findings, the phenomena of split SW peaks and quasireversible maximum are demonstrated experimentally. These unique features of the SWV response of a surface redox reaction are utilized for characterization of the redox process of V(V) in ammonia buffer. The following values of the kinetic parameters of the investigated redox reaction were estimated: standard rate constant &s = 120 ± 10 s1 and electron transfer coefficient a = 0.4 ± 0.05. The formal potential of the redox couple V(V)/V(IV) in ammonia buffer with pH = 8.6 is E° = -0.56 V vs. Ag/AgCl (sat. KC1).

Square-wave voltammetry of 5-fluorouracil

The redox reaction of 5-fluorouracil (FU) at a hanging mercury drop electrode (HMDE) is studied by means of square-wave voltammetry (SWV). It is demonstrated that the redox reaction proceeds according to the scheme: L2�(aq)vL2�(ads)� Hg(l)vHgL(s)�2e�, which involves both chemisorption of FU on the electrode surface and creation of a sparingly soluble compound with the electrode material. The overall response exhibits properties of a surface process in which both the reactant and the product of the redox reaction are immobilized on the electrode surface. The square-wave voltammetric response of FU possesses features typical of surface confined processes such as ‘split SW peaks’ and a ‘quasi-reversible maximum’. The proposed electrode mechanism is studied theoretically. The numerically calculated response under conditions of SWV is in qualitative agreement with the experimental data. Comparing the theoretical and the experimental data, the kinetic parameters of the redox reaction investigated are estimated. The standard rate constant appears to be within the interval 545ks:s�15108, the adsorption constant is K�10 cm�1, and the transfer coefficient is a�0.5490.01. The effect of the Cu(II) ions on the adsorptive SWV response of FU is discussed from an analytical point of view. It is demonstrated that SWV is a particularly appealing technique, which enables determination of FU at an ultra-trace concentration level. A linear calibration plot was established at 10�11 mol l�1 concentration level with a correlation coefficient of R2�0.992. The detection limit is 7.7�10�12 mol l�1. The reproducibility of the results in terms of the relative standard deviation ranges from 0.9 to 3.2%

Quasireversible Maximum in Cathodic Stripping Square-Wave Voltammetry

Square-wave voltammetry of the cathodic stripping processes exhibits maximum response for a quasireversible redox reaction. This phenomenon, known as a “quasireversible maximum” is explored for kinetic measurements of this class of redox reactions. The apparent reversibility of a redox reaction, together with the position of the quasireversible maximum, depend on the single complex kinetic parameter K, which is defined through the standard rate constant, diffusion coefficient of the ligand and frequency of the SW signal. Critical values of the kinetic parameter Kmax are theoretically calculated for different values of the transfer coefficient α and amplitudes of the signal. If the frequency which corresponds to the quasireversible maximum is experimentally obtained, the standard rate constant of the investigated redox reaction could be estimated. Standard rate constant can be defined either in units cm s–1, which is the same as for a redox reaction of a dissolved redox couple, or only in s–1, which is typical for a redox reaction of an adsorbed redox couple. This feature shows that cathodic stripping redox reactions are an important class of redox reactions which can be regarded as an intermediate form between the redox processes of adsorbed and dissolved redox couple.

Redox Kinetics Measurements of Probucole Using Square-Wave Voltammetry

Probucole is both electroactive and a surface-active compound. It undergoes fast and chemically reversible reduction at a HMD electrode in either 0.1 mol dm–3 KClO4 or 1 mol dm–3 KNO3. Both probucole and its electrode reduction product are strongly adsorbed to the electrode surface and the overall electrode mechanism exhibits characteristic properties of a surface redox reaction. The kinetics of the surface redox reaction of probucole is measured by means of square-wave voltammetry. The kinetic parameters of the redox reaction of probucole were estimated applying the methods of a split SW peak and a quasireversible maximum. In 1 mol dm–3 KNO3, the standard rate constant is ks=1400 ±30 s–1 and the cathodic transfer coefficient is α=0.55 ±0.02.

Redox Kinetics Measurements of Probucole Using Square-Wave Voltammetry

Probucole is both electroactive and a surface-active compound. It undergoes fast and chemically reversible reduction at a HMD electrode in either 0.1 mol dm–3 KClO4 or 1 mol dm–3 KNO3. Both probucole and its electrode reduction product are strongly adsorbed to the electrode surface and the overall electrode mechanism exhibits characteristic properties of a surface redox reaction. The kinetics of the surface redox reaction of probucole is measured by means of square-wave voltammetry. The kinetic parameters of the redox reaction of probucole were estimated applying the methods of a split SW peak and a quasireversible maximum. In 1 mol dm–3 KNO3, the standard rate constant is ks=1400 ±30 s–1 and the cathodic transfer coefficient is α=0.55 ±0.02.

Using the Pulsed Nature of Staircase Cyclic Voltammetry To Determine Interfacial Electron-Transfer Rates of Adsorbed Species

Staircase cyclic voltammetry (SCV) is the digital counterpart of analog cyclic voltammetry (CV). However, when the redox-active species is adsorbed at the electrode surface, the voltammetric peak shapes (width, height, area, and to a lesser extent the reduction potentials) obtained with SCV can be very different from those of CV, even when small potential steps are used. Like analog CV, SCV provides a straightforward method to estimate and subtract the background and charging currents from the desired Faradaic current, while the pulsed nature of SCV provides the time-dependent decay of the Faradaic current, similar to chronoamperometry. Thus, electron-transfer rate constants can be directly measured as a function of applied potential, and no a priori model is required. An SCV equivalent of the square wave "quasi-reversible maximum" of observed peak height versus sampling moment and step size is predicted. The SCV response can only become independent of potential step size and similar to CV at high scan rates (ν > 10 k(0)E(step)), if the current is sampled at half the step interval. The applicability of SCV to studies of redox centers in proteins is illustrated for the two-electron oxidation/reduction of yeast cytochrome c peroxidase, adsorbed at a pyrolytic graphite edge-plane electrode.

A Cathodic Stripping Square-Wave Voltammetry of a Second-Order Redox Reaction and Its Application to the Mercury-Cysteine System

A model of cathodic stripping square-wave voltammetry of a second-order redox reaction is developed. Both reversible and quasireversible redox reactions are considered. The relationships between the properties of SWV response and both parameters of the redox reaction and the SWV excitation signal are analyzed. The effect of the concentration of the reacting ligand on the SW voltammograms is discussed. The phenomenon of a quasireversible maximum is demonstrated. Numerical simulations are compared qualitatively with the cathodic stripping square-wave voltammetric response of cysteine.

Square‐wave voltammetry of 4,4′‐diisopropyl‐2,2′‐bithiazoline and its complex with copper(II)

Abstract(4S)‐4′‐diisopropyl‐2,2′‐bithiazoline (DPT) is an electroactive organic chiral compound giving two reduction responses in square‐wave voltammograms at potentials about −0.2 and −0.4 V by forming a complex with mercury which deposits at the electrode surface. By the addition of copper(II) ion to the solution of DPT a third peak appears between them at about −0.3 V, which corresponds to the reduction of adsorbed Cu‐DPT complex. Optimal pH for the investigation of those redox processes was found to be 2.8. By square‐wave voltammetric measurements it was interpreted that these redox reactions were quasireversible with immobilized reactants. By plotting ip/f vs. frequency a quasireversible maximum was obtained, and the apparent standard reaction rate constants were calculated: log (ks)DPT=(0.91 ± 0.9) and 1 < ks < 65S−1, log (ks)CuDPT= (0.35 ± 0.9) and 0.3 < ks < 18 S−1 in 0.55 M NaCl.

A peak current – scan rate relationship in staircase voltammetry of a surface redox reaction

AbstractStaircase voltammetry of surface redox reactions is characterized by a “quasireversible maximum”. The relationship between peak currents and scan rates is not linear, except for totally irreversible reactions, and the response may entirely vanish if the reaction is fast and reversible. For surface redox rections, the equivalence of staircase and linear sweep voltammetries can not he obtained by the variation of the current sampling fraction.

Redox kinetics in cathodic stripping square‐wave voltammetry

AbstractSeveral redox systems with reactants which are immobilized at the electrode surface (EuSal complex, SeIV and SeIV in the presence of CuII, cysteine and p‐nitrophenol) were studied by square‐wave voltammetry to examine whether their redox kinetics can be measured by using the phenomenon of the ‘quasireversible maximum’. This is explained in detail. The following standard rate constants are obtained: EuSal complex ks = 720 ± 31 s−1, SeIV/CuII, log [ks/(cms−1)] = 0.94 ± 0.9, cysteine, log [ks/(cms−1)] = 0.6 ± 0.9 and p‐nitrophenol, ks > 1200 ± 50 s−1.

Measurements of redox kinetics of adsorbed azobenzene by “a quasireversible maximum” in square-wave voltammetry

The standard redox reaction rate constants of azobenzene adsorbed to the mercury electrode are k s = 350 ± 25 s − 1 in the acidic perchlorate medium (pH 2) and k s = 175 ± 20 s − 1 in the acetate buffer pH 4.7. Under the influence of 0.2%, 0.5% and 1% acetonitrile in these electrolytes, the rate constants are reduced to 265 ± 5 s − 1, 160 ± 20 s −1 and 77 ± 10 s −1, at pH 2, and to 150 ± 5 s −1 and 56 ± 13 s −1 at pH 4.7.

Square-wave voltammetry of quasi-reversible surface redox reactions

Abstract A “quasi-reversible maximum” in square-wave voltammetry can be used for the determination of the standard reaction rate constant of a redox reaction between an adsorbed reactant and a product if their adsorption constants satisfy the condition 0.1 ⩽ K ox K red ⩽ 10 . By plotting the ratio of peak current and frequency as a function of frequency, the critical frequency fmax, for which this ratio is at the maximum, can be determined. Theoretically it is shown that the rate constant is related to fmax by the equation ks = κmaxfmax, where κmax is the critical kinetic parameter which depends on the transfer coefficient of the surface redox reaction. If α = 0.55 ± 0.5, κmax = 1.13, and if α is not known, the average value gk max = 1.18 ± 0.05 , which applied to 0.25 ⩽ α ⩽ 0.85, can be used. For other α values, the corresponding κmax parameters are given by the formula κmax = 1.13 + 1.13(α − 0.55)2. The method was applied to the redox reaction of adsorbed azobenzene in perchlorate and acetate electrolytes of various pH. The rate constants are ks = (62 − 12pH)s−1 for pH ⩽ 4 and ks = 28 s−1 for pH 4.65.

A square‐wave voltammetry in a cathodic stripping mode

AbstractA model of cathodic stripping square‐wave voltammetry (SWV) of insoluble mercuric salt accumulated at the mercury drop electrode surface is developed. Theoretical relationships between the properties of responses and the parameters of both the redox reaction and the SWV signal are analyzed. Both reversible and quasireversible redox reactions are considered. The nature of quasireversible maximum is discussed. Numerical simulations are compared qualitatively with the SW stripping voltammograms of electrodeposited HgS.

Theory of square-wave stripping voltammetry and chronoamperometry of immobilized reactants

Square-wave stripping voltammograms of redox reactions which involve immobilized reactants and dissolved products are analysed theoretically. The model applies to anodic or cathodic stripping of the material accumulated at an electrode surface by electrodeposition, abrasion, adsorption or the formation of a thin amalgam film. Reversible, quasi-reversible and totally irreversible reactions are considered. The origin of the so-called “quasi-reversible maximum”, which could be used for electrode kinetic measurements, is explained using a study of the chronoamperometric properties of these reactions.