Theoretical Aspects of a Surface Electrode Reaction Coupled with Preceding and Regenerative Chemical Steps: Square‐wave Voltammetry of a Surface CEC’ Mechanism

Large number of lipophilic substances, whose electrochemical transformation takes place from adsorbed state, belong to the class of so‐called “surface‐redox reactions”. Of these, especially important are the enzymatic redox reactions. With the technique named “protein‐film voltammetry” we can get insight into the chemical features of many lipophilic redox enzymes. Electrochemical processes of many redox adsorbates, occurring at a surface of working electrode, are very often coupled with chemical reactions. In this work, we focus on the application of square‐wave voltammetry (SWV) to study the theoretical features of a surface electrode reaction coupled with two chemical steps. The starting electroactive form Ox_(ads) in this mechanism gets initially generated via preceding chemical reaction. After undergoing redox transformation at the working electrode, Ox_(ads) species got additionally regenerated via chemical reaction of electrochemically generated product Red_(ads) with a given substrate Y. The theory of this so‐called surface CEC’ mechanism is presented for the first time under conditions of square‐wave voltammetry. While we present plenty of calculated voltammograms of this complex electrode mechanism, we focus on the effect of rate of regenerative (catalytic) step to simulated voltammograms. We consider both, electrochemical reactions featuring moderate and fast electron transfer. The obtained voltammetric patterns are very specific, having sometime hybrid‐like features of voltammograms as typical for CE, EC and EC’ mechanisms. We give diagnostic criteria to recognize this complex mechanism in SWV, but we also present hints to access the kinetic and thermodynamic parameters relevant to both chemical steps, and the electrochemical reaction, too. Indeed, the results presented in this work can help experimentalists to design proper experiments to study chemical features of important lipophilic systems.     

Square‐wave Voltammetry of Two‐step Surface Electrode Mechanisms Coupled with Chemical Reactions – A Theoretical Overview

Square‐wave voltammetry (SWV) of so‐called “surface redox reactions” is seen as a simple and efficient tool to quantify large number of drugs, physiologically active substances and other important chemicals. It also provides elegant methods to get access to relevant kinetic and thermodynamic parameters related to many lipophilic compounds. Moreover, with this technique we can study activity of various enzymes by exploring the “protein‐film voltammetry” set up. In this work, we focus on theoretical SWV features of four complex surface electrode mechanisms, in which the electron exchange between the working electrode and the studied redox substrate takes place in two successive steps. While we present large number of calculated square‐wave voltammograms, we give hints to recognize particular two‐step surface mechanism, but also to distinguish it from other similar mechanisms. We present plenty of relevant aspects of surface two‐step surface EE, two‐step surface ECE and surface catalytic EEC’ mechanisms. Moreover, we present for the first time a series of theoretical results related to two‐step surface EECrev mechanism (i. e. two‐step surface reaction coupled to follow‐up reversible chemical step). The simulated voltammetric patterns presented in this work can bring relevant aspects to resolve some experimental situations met in voltammetry of many redox enzymes and other important substances whose electrochemical transformation occurs in two‐steps.     

Square‐wave Amplitude Effect in Cathodic and Anodic Stripping Square‐wave Voltammetry

In this paper a theoretical study of stripping processes at planar electrodes under conditions of square‐wave voltammetry is presented. A mechanistic examination for cathodic stripping electrode mechanisms, a simple anodic striping mechanism, and anodic stripping mechanisms coupled with adsorption equilibrium of the analyte are discussed using varying square‐wave amplitudes. The methodologies described here use two typical features: the peak potential separation of square‐wave components and the amplitude‐based quasireversible maximum. Both methods can be applied at a constant frequency, i. e., constant scan rate. The received data are combined with the critical parameters of electrode reaction kinetics. Thus, the established methodologies allow for a simple kinetic characterization. The received diagnostic criteria are verified with experiments at a glassy carbon electrode for lead ions.     

Theoretical Contribution towards Understanding Specific Behaviour of “Simple” Protein‐film Reactions in Square‐wave Voltammetry

Surface reactions of uniformly adsorbed redox molecules at working electrode surface are seen as adequate models to studying chemical reactivity of many lipophilic enzymes. When considered under pulse voltammetric techniques, these systems show several uncommon features, whose origin is still not completely clear. The phenomena of “quasireverible maximum”, “splitting” of the net peak in square‐wave voltammetry, and the very steep descent of Faradaic currents of simple surface redox reactions exhibiting fast electron transfer are just some of the features that make these systems quite interesting for further elaborations. In this work, we present a set of theoretical calculations under conditions of square‐wave voltammetry in order try to explain some of aforementioned phenomena. The major goal of our work is to get insight to some voltammetric and chrono‐amperometric features of two considered surface reactions, i. e. (1) the “simple” surface redox reaction, and (2) surface redox reaction coupled to follow‐up irreversible chemical reaction of electrochemically generated redox species (or surface ECirr). We focus on the role of created Red(ads) (here in the reduction pulses only) to the current components of calculated square‐wave voltammograms exhibiting fast electrode reaction. We show that the irreversible chemical removal of electrochemically generated Red(ads) species, created in the potential pulses where half‐reaction of reduction Ox(ads)+ne‐?→Red(ads) is “defined” to take place, causes significant increase of all square‐wave current components. The results presented in this work show how complex the chrono‐amperometric features of surface redox reactions under pulse voltammetric conditions might be. In addition, we point out that both half reactions of a given simple surface redox process can occur, at both, “only reduction” and “only oxidation” potential pulses in square‐wave voltammetry. This, in turn, contributes to the occurrence of many phenomena observed in simple protein‐film voltammetry reactions. The effects of chemical reaction rate to the features of calculated square‐wave voltammograms of surface ECirr systems with fast electrode reaction are reported for the first time in this work.     

Square‐Wave Voltammetry of Quasi‐Reversible CE Reactions at Spherical Microelectrodes

A mathematical model for the CE mechanism in which the chemical together with the electrochemical reactions are quasi‐reversible at the surface of spherical macro and micro‐electrodes is presented for the case of square‐wave voltammetry. The analysis of voltammometric responses considers the influence of rate and equilibrium constants, together with the electrode radius, and their dependence on the square‐wave frequency (f). Both kinetics and the sphericity effect act synergistically on the electrochemical response. Also, the apparent electrode sphericity and the reversibility of the chemical as well as the electrochemical reactions are jointly affected by the variation of f. Disregarding the sphericity contribution in the calculation of kinetic parameters at a microelectrode may introduce errors even higher than one order of magnitude. The model allows the analysis of a more realistic and complex electrochemical system that requires not only the dependence of experimental responses on f, but also their fit with theoretical voltammograms, in order to provide some useful mechanistic information. Finally, concentration profiles are also studied to realize how the chemical contribution is buffering the absences of oxidized species at the electrode surface, and how those profiles are modified for the case of spherical macro and micro‐electrodes.     

Theoretical Analysis of a Surface Catalytic Mechanism Associated with Reversible Chemical Reaction Under Conditions of Cyclic Staircase Voltammetry

In this work, we present theoretical results in cyclic staircase voltammetry of a surface catalytic mechanism that features reversible chemical step, the so‐called “surface catalytic EC_rev’ mechanism”. We consider specific surface regenerative mechanism, in which both of the electro‐inactive substrates are present in large excess in electrochemical cell from the beginning of the experiment. The chemical reversibility brings at this mechanism more complexity in respect to the features of well‐elaborated surface catalytic EC’ mechanism coupled with chemically irreversible regenerative reaction. As we present plenty of simulated cyclic voltammograms, we also propose methods to get insight to kinetics and thermodynamics parameters relevant to chemical regenerative step. The elaboreted results can be important in analysing the kinetics and thermodynamics of many drug‐drug and drug‐DNA interactions, for example. In addition, with the results elaborated in this work we can access relevant information about the chemistry of important lipophilic enzymes studied in protein‐film voltammetry set up.     

Theoretical Treatment of a Cathodic Stripping Mechanism of an Insoluble Salt Coupled with a Chemical Reaction in Conditions of Square Wave Voltammetry. Application to 6‐Mercaptopurine‐9‐D‐Riboside in the Presence of Ni(II)

Cathodic stripping mechanism of an insoluble salt coupled with a homogenous chemical reaction is considered both theoretically and experimentally under conditions of square‐wave voltammetry. For the mercury electrode in aqueous solution, the electrode reaction is described as L(aq)+Hg(l)=HgL(s)+2e^?, where L(aq) is the reactive ligand that forms a sparingly soluble compound HgL(s). The electrode reaction is coupled with a homogenous, first‐order chemical reaction, A(aq)=L(aq). Theoretical predictions are confirmed by experiments with 6‐mercaptopurine‐9‐D‐riboside in the presence of nickel(II) ions.     

A computational methodology for accurate predictions of rate constants in solution: Application to the assessment of primary antioxidant activity

The accurate prediction of rate constants for chemical reactions in solution, using computational methods, is a challenging task. In this work, a computational protocol designed to be a reliable tool in the study of radical‐molecule reactions in solution is presented. It is referred to as quantum mechanics‐based test for overall free radical scavenging activity (QM‐ORSA) because it is mainly intended to provide a universal and quantitative way of evaluating the free radical scavenging activity of chemical compounds. That is, its primary antioxidant activity. However, it can also be successfully applied to obtain accurate kinetic data for other chemical reactions in solution. The QM‐ORSA protocol has been validated by comparison with experimental results, and its uncertainties have been proven to be no larger than those arising from experiments. Further applications of QM‐ORSA are expected to contribute increasing the kinetic data for free radical‐molecule reactions relevant to oxidative stress, which is currently rather scarce. © 2013 Wiley Periodicals, Inc.     

Determination of Electrochemical Electron‐Transfer Reaction Standard Rate Constants at Nanoelectrodes: Standard Rate Constants for Ferrocenylmethyltrimethylammonium(III)/(II) and Hexacyanoferrate(III)/(II)

The most common approximation of electroneutrality is inappropriate for analyzing the voltammetric response of nanoelectrodes. Therefore, the microelectrode theory for extracting the standard rate constant k⁰ for electron transfer from steady‐state voltammograms is invalid for nanoelectrodes. Unlike previous approaches, we considered the influence of the interfacial potential distribution caused by the absence of electroneutrality. We estimated the magnitude of the error at low overpotential incurred as a result of ignoring the absence of electroneutrality and found that it was small. In this region, electrochemical reaction appears to be limited by the rate of electron transfer. Under these conditions, k⁰ can be obtained from steady‐state voltammogram data in a low overpotential region according to an approximate form of the Butler–Volmer equation. This procedure can greatly simplify analysis and calculation of the rate constant k⁰ at nanoelectrodes. Steady‐state voltammogram of equal‐concentration hexacyanoferrate(III)/(II) (Fe(CN) /Fe(CN) ) and ferrocenylmethyltrimethylammonium(III)/(II) (FcTMA²⁺/FcTMA⁺) redox couples were investigated at Pt? Ir nanoelectrodes in the presence of a support electrolyte. k⁰ for Fe(CN) /Fe(CN) and FcTMA²⁺/FcTMA⁺ at Pt? Ir nanoelectrodes were evaluated.