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A model of desorption from the surface of rotating disk into the solution of surface active substance is developed for Frumkin isotherm. The time needed to approach the first equilibrium within 1% of error is investigated. For desorption this means to acquire the highest surface coverage, and for adsorption the lowest coverage that is in the equilibrium with the bulk of solution. If the equilibrium isotherm is S shaped, the near equilibrium isotherms are characterised by big changes of coverage that are caused by small increments of bulk concentrations. These changes require very long near equilibrating times because they are driven by small fluxes of dissolved surfactant. These times are the second component of the hysteresis.

A model of cyclic staircase voltammetry of enzymatic reactions on the rotating disk electrode is developed and the inhibition by the product is investigated. The responses are mostly time - dependent current - potential curves with maxima in the forward but not in the backward branch. If the maxima appear in both branches, the inhibition is potential - dependent either directly or indirectly. The source of the second maximum is explained.

The accurate determination of the rate constant related to the electron transfer step of so-called “surface redox active compounds” by voltammetric measurements is very important because it is linked to the reactivity and stability of many biological and chemical systems such as redox enzymes, vitamins, hormones, and many more. Evaluation of the kinetics of the electron transfer is often challenging, especially when chemical equilibria are coupled to the electron transfer step. In this work, we theoretically consider some critical aspects of the time-related methodologies in square-wave voltammetry (SWV), which is designed to analyze the kinetics of the electron transfer step of surface mechanisms coupled with chemical reactions. We demonstrate with a series of simulated scenarios that caution must be taken when exploring the time-related analysis for kinetic characterizations for both surface CE and EC mechanisms. The main concern stems from the fact that the SW frequency simultaneously affects both the kinetics of electron transfer and that of chemical reactions as well. Under defined conditions, the SW frequency variation in the case of surface EC and CE mechanisms may produce unexpected features of the voltammetric patterns. In many scenarios, time-independent analysis, such as those related to the square-wave amplitude and potential increment, are seen as alternative tools to evaluate the rate parameter of electrode reactions.

Near equilibrium Frumkin adsorption isotherms created by the steady state diffusion at the surface of rotating disk are calculated. The difference between the equilibrium and the near equilibrium isotherms is explained by the time components of the later.

Kinetic currents caused by the interaction of dissolved catalyst and substrate are calculated. Sigmoidal dependence of currents on the bulk concentration of catalyst can be tested and the rate constant of redox reaction can be calculated by the proposed method. The applicability limits are discussed.

Theoretical single scan staircase voltammograms of homogeneous electrocatalytic reactions on the rotating disk electrode are calculated by the digital simulation. A simple relationship between steady state current and dimensionless kinetic parameter is discovered and the influence of the backward component of chemical reaction is demonstrated. A thickness of kinetic layer is discussed.

Totally irreversible electro-oxidation of dissolved reactant that is inhibited by the formation of oxide on the electrode surface is analysed theoretically. In the reverse, cathodic branch of staircase cyclic voltammogram these two parallel reactions exhibit both cathodic minimum and anodic maximum. The potentials of these extremes depend on the kinetics of oxide formation.

An oxidation peak in the cathodic branch of a cyclic voltammogram can be explained by the reversible deactivation and reactivation of the electrode surface. This phenomenon could be caused by the potential-dependent adsorption of the product of an irreversible electrode reaction. Keywords: Voltammetry, Adsorption, Electrode reactivation, Theory

An expanding plane model of polarogram influenced by the reactant adsorption is developed and applied to the Frumkin isotherm. It is shown that the polarogram may consist of the main wave and post-wave that are separated by the maximum and minimum. The origin of these extremes are investigated by the calculation of currents that flow during a single mercury drop. This work is licensed under a Creative Commons Attribution 4.0 International License.

A model of irreversible reduction complicated by the reactant adsorption is developed for the constant electrode potential. Chronoamperograms, or dc polarograms consist of two components that flow simultaneously and correspond to the volume and surface electrode reactions. The total response is a wave with the maximum that originates from the dependence of the kinetics of electrode reactions on the surface coverage. The dependence of peak potentials on the reactant concentration is demonstrated and explained. The difference between reversible and irreversible reductions is discussed.

Two reversible electrode reactions that are connected by either reversible or totally irreversible chemical reactions are theoretically analysed by staircase cyclic voltammetry. The dependence of peak potentials on the thermodynamic and kinetic parameters is calculated. If the mechanism is permanently in equilibrium, the stability constant of the reversible chemical reaction can be determined. Furthermore, the critical kinetic parameter is determined and its application to the measurement of the forward rate constant of the chemical reaction is demonstrated. Also, the influence of the kinetics of electrode reactions is discussed. Keywords: ECE mechanism; Cyclic voltammetry; Theory

Redox mechanisms in which the redox transformation is coupled to other chemical reactions are of significant interest since they are regarded as relevant models for many physiological systems. Protein-film voltammetry, based on surface confined electrochemical processes, is a methodology of exceptional importance, which is designed to provide information on enzyme redox chemistry. In this work, we address some theoretical aspects of surface confined electrode mechanisms under conditions of square-wave voltammetry (SWV). Attention is paid to a collection of specific voltammetric features of a surface electrode reaction coupled with a follow-up (ECrev), preceding (CrevE) and regenerative (EC’) chemical reaction. While presenting a collection of numerically calculated square-wave voltammograms, several intriguing and simple features enabling kinetic characterization of studied mechanisms in time-independent experiments (i.e., voltammetric experiments at a constant scan rate) are addressed. The aim of the work is to help in designing a suitable experimental set-up for studying surface electrode processes, as well as to provide a means for determination of kinetic and/or thermodynamic parameters of both electrode and chemical steps.

Normal pulse voltammetry and chronoamperometry of reversible electro-oxidation complicated by the reactant adsorption on the surface of stationary, planar electrode is investigated theoretically. A simple model of chronoamperometry is compared with a rigorous model of voltammetry. The solution of former is analytical, but it applies to the linear isotherm. However, it explains the origin of maximum of the current-potential curves and its relationship with the pulse duration. The second model is based on digital simulation and describes voltammograms that correspond to the Langmuir isotherm. The accumulation of the reactant during the potential scan is calculated. The limits of electroanalytical application of the normal pulse voltammetry are determined. This work is licensed under a Creative Commons Attribution 4.0 International License.

A model of electro-catalytic reaction inhibited by the product is developed. It is assumed that the stability constant of inhibiting complex depends on the electrode potential directly or indirectly. The resulting steady-state responses are characterised by maxima.

A theory of square wave voltammetry of three step electrode reaction of amalgam forming ions is developed for a thin mercury film electrode. It is assumed that the first and the second electron transfers are kinetically controlled while the third one is reversible and that the intermediates are thermodynamically unstable. The responses to the cathodic and anodic scan directions are analyzed.

Relationships between dimensionless anodic stripping square-wave voltammetric net peak currents and the dimensionless inverse electrode radius are curves with two asymptotes that depend on the duration of accumulation. The theory applies to reversible reduction of amalgam forming ions on stationary mac-ro and micro spherical and hemispherical mercury electrodes.

An electron transfer reaction at graphite electrode that is covered by a thin film of organic solvent, which is immiscible with water, and immersed into an aqueous electrolyte is considered theoretically. The redox couple is confined within the film and the conductivity is achieved by the transfer of anion of supporting electrolyte across the organic solvent / water interface. In linear scan voltammetry the peak potential depends on the initial concentration of either reactant, or the anion of supporting electrolyte in the film. A critical value of dimensionless kinetic parameter, which can be used for the determination of standard rate constant, is calculated.

The theory of three step electrode reaction is developed for square wave voltammetry on stationary spherical electrodes. It was assumed that all electroactive species are solution soluble. The dependence of the response on the thermodynamic stability of intermediates, on the electrode radius and the scan direction is investigated for the fast and reversible electrode reactions. The criterion of reversibility is postulated. Furthermore, the influence of electrode kinetics on the response was calculated for the cathodic and anodic scan directions. The difference in responses caused by the variation of scan direction is an indication of multiple electron transfers. The method for the estimation of transfer coefficient is demonstrated. This work is licensed under a Creative Commons Attribution 4.0 International License.

The influence of charge transfer kinetics and the rate of chemical reaction on square-wave voltammograms of electrode reaction followed by the dimerization of product is analyzed theoretically. The net peak potential is a linear function of the logarithm of reactant concentration if electrode reaction is reversible and the dimerization is either reversible, or totally irreversible. For the oxidation, the slopes of these relationships are −0.030 V and −0.022 V, respectively. Under the influence of electrode kinetics the linearity is lost. The relationship between net peak potential and the logarithm of frequency is linear either if electrode reaction is irreversible and the dimerization is reversible, or if electrode reaction is reversible and the dimerization is irreversible.

An influence of complexation of reactant and intermediate on square-wave voltammograms of reversible, two-step electrode reaction is analyzed theoretically. The potentials of the first and the second peak of the split net response depend on stability constants of complexes, the standard potentials of individual electron transfers and on the concentration of ligand: E P , 1 − E 1 0 = ( R T / F ) ( ln F M + − ln F M 2 + ) and E P , 2 − E 1 0 = E 2 0 − E 1 0 − ( R T / F ) ln F M + , where F M 2 + = 1 + β 1 , a c L − + β 2 , a c L − 2 + … and F M + = 1 + β 1 , b c L − + β 2 , b c L − 2 + … .

An influence of electron transfer kinetics on square-wave voltammograms of two-step electrode reaction is investigated theoretically. A phenomenon of "kinetic burden" of potential inversion is de- scribed for the case of equal kinetic parameters. A linear relationship between standard rate constant and the difference between standard potentials of the second and the first charge transfers is demonstrated for the reactions with thermodynamically unstable intermediate. (doi: 10.5562/cca2126)

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.

The standard rate constant of a simple electrode reaction Ox + n e − ↔ Red, in which both Ox and Red are solution soluble, can be determined by the variation of frequency in the square-wave voltammetry with inverted scan direction: log k s = log f 0 1/2 + log D 1/2 − 0.60 ± 0.01. In this equation log f 0 is the abscissa of the intersection of straight lines E p,2 = a log f + b and E p,2 = E 0 , where E p,2 is the potential of the second peak of the net response, E 0 is the standard potential, a = 2.3 RT /2(1 − α ) nF , b = E 0 − 2 a log k s + a log D − 0.0353/(1 − α ) n and D is a common diffusion coefficient.

Isopotential points in reverse square-wave voltammetry of irreversible electrode reactions are described for the first time. Experimental results (obtained with Eu 3+ in perchlorate solutions) and model calculations indicate that such an intersection appears when the net signals, recorded at increasing step potential, are plotted together. As long as the transfer coefficient is equal to 0.5, the isopoint appears at the standard potential E 0 , irrespective of the kinetic parameter κ . Otherwise, it is shifted positively or negatively. The effect could be used for determination of the standard potential, recognition of symmetric/asymmetric processes and testing the quality of experimental data.

Under the influence of previous experimental results, a new theoretical study of current–time relationship in differential pulse polarography was performed. In a reversible electrode reaction, complicated by the reactant adsorption on the static mercury drop electrode, the enhancement of the main peak with increasing drop life-time appears. The effect is explained by the change of reactant concentration at the electrode surface during the drop-life time. Non-Cottrell behavior becomes obvious if, in addition to the net response, its components are analyzed too.

The second order, reversible electrocatalytic mechanism followed by irreversible transformation of oxidized substrate is analyzed for chronoamperometry. The dependences of limiting current and half-wave potential on the measurement time and the concentrations of catalyst and substrate are investigated theoretically. These relationships can be used for the redox characterization of substrate and the measurement of its concentration.

A reversible electrode reaction that is followed by totally irreversible chemical reaction is investigated theoretically. The influence of chemical reaction on two components of the net response of differential pulse polarogram is analyzed. It is demonstrated that this EC mechanism depends on two kinetic parameters and that their critical values can be used for the measurement of the rate constant of chemical reaction.

The time dependence of analyte concentration at the surface of a flow-by potentiometric sensor in the flow-injection analysis was investigated theoretically. The relationships between the properties of response and experimental parameters, such as the sample volume and the distance between the injection point and the sensor, was calculated by finite difference numerical simulation.

A theory is provided for a reversible electro-oxidation of a neutral redox probe dissolved in room-temperature ionic liquid, which is sandwiched between an electrode surface and an aqueous solution as a thin film. If the peak potentials in cyclic voltammetry depend on the bulk concentration of electrolyte in water, the oxidation is most probably coupled to the transfer of anions from water into ionic liquid; but if the peak potentials are independent of the electrolyte concentration, the transfers of anions from water into ionic liquid and cations from ionic liquid into water are equally probable.

The adhesion of liposomes on a mercury electrode leads to capacitive signals due to the formation of islands of lecithin monolayers. Integration of the current-time transients gives charge-time transients that can be fitted by the empirical equation Q(t) = Q(0) + Q(1)(1 - exp(-t/tau(1))) + Q(2)(1 - exp(-t/tau(2))), where the first term on the right side is caused by the docking of the liposome on the mercury surface, the second term is caused by the opening of the liposome, and the third term is caused by the spreading of the lecithin island on the mercury surface. The temperature dependence of the two time constants tau(1) and tau(2) and the temperature dependence of the overall adhesion rate allow determination of the activation energies of the opening, the spreading, and the overall adhesion process both for gel-phase 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and for liquid-crystalline-phase DMPC liposomes. In all cases, the spreading is the rate-determining process. Negative apparent activation energies for the spreading and overall adhesion process of liquid-crystalline-phase DMPC liposomes can be explained by taking into account the weak adsorption equilibria of the intact liposomes and the opened but not yet spread liposomes. A formal kinetic analysis of the reaction scheme supports the empirical equation used for fitting the charge-time transients. The developed kinetic model of liposome adhesion on mercury is similar to kinetic models published earlier to describe the fusion of liposomes. The new approach can be used to probe the stability of liposome membranes.

In the theoretical model it is assumed that a graphite disk electrode is covered by a thin film of solution of decamethylferrocene (dmfc) and some electrolyte CX in nitrobenzene and immersed in an aqueous solution of the electrolyte MX. Oxidation of dmfc is accompanied by the transfer of anion X − from water into nitrobenzene since it is also assumed that cations dmfc + and C + are insoluble in water and cation M + is insoluble in nitrobenzene. Kinetic parameters of the electrode reaction can be determined if the total potential difference across the nitrobenzene/water interface is maintained constant by adding the electrolytes CX and MX in concentrations which are much higher than the initial concentration of dmfc in nitrobenzene.

A theoretical model of a surface electrode reaction coupled with a preceding chemical reaction (surface CE electrode mechanism) is theoretically studied under conditions of square-wave voltammetry. The position and the shape of the theoretical voltammograms are function of the redox kinetic parameter λ=ksf where ks is the standard electron exchange rate constant and f is the frequency of the potential modulation, chemical kinetic parameter z=kf+kbf, where kf and kb are the forward and backward rate constants of the preceding chemical reaction, respectively, and the equilibrium constant of the chemical reaction K. The influence of all these parameters to the theoretical square-wave voltammograms is investigated in detail. A theoretical methodology for estimation of the kinetic and thermodynamic parameters of the electrode mechanism is proposed. Keywords: Surface CE reaction, Square-wave voltammetry, Quasireversible maximum, Split SW voltammograms, Mathematical modelling

A comparative study of different types of cathodic stripping reactions under conditions of square-wave voltammetry is presented. Cathodic stripping processes involving reactions of second order as well as reactions coupled by adsorption of the reacting ligand are analysed The inherent parameters, controlling the overall voltammetric behaviour of each cathodic stripping electrode reaction are derived. The criteria for qualitative distinguishing of each mechanism are established as well as a methodology for redox kinetic measurements is proposed. The influence of the parameters of the excitation signal on the properties of the voltammetric response is analysed in order to find optimal conditions for analytical application. The theoretical results are illustrated by the experiments with a series of uracil derivatives.

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: Ox ( ads ) +n e − ⇆ Red ( ads ) → k s P ⇅ ⇅ ( Ox ( aq ) ) x=0 +n e − ⇆ ( Red ( aq ) ) x=0 → k v 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 ks, 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 kv. 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.

A theory of the influence of anion-induced adsorption of metal ions in pseudopolarography using the thin mercury film covered rotating disk electrode is developed. The model is developed assuming that the metal ion is forming several labile complexes with the ligand which is present in a great excess, and that only one complex species is adsorbed following a linear isotherm. The results obtained assuming steady-state conditions are compared with the simulation of transient processes using Galerkin and finite difference methods. It is shown that the adsorption of metal complexes on the disk electrode surface does not prevent the determination of the stability constants.

A theoretical model of electrocatalytic mechanism that is determined by Michaelis–Menten kinetics is developed for cyclic voltammetry. The adsorption and desorption of product of catalysis is considered and its influence on voltammograms is investigated. The rate constants of catalytic reaction and dissociation of the product from the surface can be estimated from the linear relationship between inverse limiting current and inverse concentration of substrate.