An improved algorithm for the numerical simulation of cyclic voltammetric curves affected by the ohmic potential drops and its application to the kinetics of bis(biphenyl)chromium(I) electroreduction

Previously published algorithms for the modeling of cyclic voltammetric curves affected by ohmic potential drops, in terms of the classical explicit finite differences method, are discussed briefly. A fast and efficient numerical procedure suitable for such simulations is described. This approach exhibits high numerical stability for both high scan rates and large uncompensated ohmic resistances. The procedure is based on the calculation of the faradaic current as a root of the non-linear equation, with a simultaneous calculation of the capacitive current. Comparison of the cyclic voltammograms obtained using this method with those calculated using alternative published procedures proves its validity. For comparison with the experimental data, the cyclic voltammetric response for the reduction of bis(biphenyl)chromium(I) tetraphenylborate in N,N-dimethylformamide is shown and the kinetic parameters of this process are fitted. Compared to earlier modelings, they show better concordance with the results of studies at microelectrodes. In conjunction with earlier successful applications of the analogous numerical procedure to the realistic modeling of electrochemical oscillations and multistability at a constant external voltage, the algorithm presented appears to be one of the most applicable methods of calculation of the electrochemical responses affected by the ohmic potential drops.     

Digital simulation of fast cyclic voltammogram by integration of the double layer charging current

A new digital simulation method considering the influence of ohmic drop on the cyclic voltammogram was developed, which eliminated the time-consuming iterations (successive approximations) for the calculations of the effective (real) electrode potentials by the integration of the charging current. In this simulation the total current I_t (sum of the faradaic and charging currents) and charging current (I_c) were calculated on the basis of the equivalent circuit of the electrochemical cell. The simulated pure charging current, total current, and peak potentials were compared with those calculated by the numerical resolution method to test the accuracy of this simulation method. The computation speed of this digital simulation was also assessed. High simulation accuracy, simple programming, and very short computation time are the main advantages of this new method.     

Electrochemical studies on c-type cytochromes at microelectrodes

The aim of this work is to use microelectrodes as a current approach for the study of unmediated electrochemistry of redox proteins. An electrochemical study of monohemic cytochromes c₅₅₂ from Pseudomonas nautica 617, cytochrome c₅₅₃ from Desulfovibrio vulgaris and horse heart cytochrome c is presented at inlaid disk microelectrodes of platinum, gold and carbon. Different electrochemical techniques were used such as linear scan, differential pulse and square wave voltammetry. The electrochemical response was also analysed at conventional size (macro) electrodes for comparison. In all situations a promoter was used. The electrochemical behaviour was evaluated in terms of kinetics of the electrode processes and the formal potentials determined. Diffusion coefficients were also calculated from the voltammetric data. A critical comparison of the results obtained is carried out and the advantages of microelectrodes for electrochemical studies of metalloproteins are pointed out.     

Re-examination of the potential step chronoamperometry method through numerical inversion of Laplace transforms. II. Application examples

In the first part of this work, we proposed the so-called GS-, FE- and FT-PSCA algorithms to investigate a wide range of electrode geometry and chemical, electrochemical and one-dimensional mass-transport processes by the potential-step chronoamperometry (PSCA) method. Each algorithm provides a full explicit formulation of Faradaic current with respect to time, applied potential and electrochemical parameters (initial concentrations, geometrical parameter(s), standard potential, electrochemical and chemical rate constants and diffusion coefficients). Application examples relative to diffusion equations with spherical electrode geometry are presented in this second article by way of illustration of the potentialities of GS- and FT-PSCA algorithms. First, the case of one-step electrochemical reactions at spherical and hemispherical electrodes of any radius is investigated when both implicated species are soluble in the electrolytic solution. The numerical solution obtained from GS-PSCA algorithm is favourably compared to previous results in the electrochemical literature. Next, we use the FT-PSCA algorithm for investigating spherical diffusion with amalgamation reaction. Finally, the characteristic features of chronoamperograms and sampled-current voltammograms pertaining to the above reaction are examined and discussed.     

Electrochemical anion doping of poly[(tetraethyldisilanylene) oligot 2,5-thienylene)] derivatives and their p-type semiconducting properties

Chemically synthesized poly[(tetraethyldisilanylene)oligo(2,5-thienylene)] derivatives (DS/mT; m = 3 to 5) have been successfully anion-doped by electrochemical oxidation. Band-gap energies of 2.52, 2.65, 2.82 and 3.27 eV were evaluated for DS5T, DS4T, DS3T and DS2T respectively. The DS5T, DS4T and DS3T films exhibited electrical conductivities of the order of 10^?3 to 10^?4 S cm^?1 when doped with BF₄^?. The work functions of the films changed from 5.1 to ca. 5.5 eV with electrochemical anion doping. In cyclic voltammograms of the polymer films for anion doping and dedoping, an anodic peak potential and a cathodic one (E_pc.) shifted to the positive direction as the number m of thienylene units decreased. E_pcs at a sweep rate of 100 mV s^?1 were about 0.8, 0.9 and 1.0V for DS5T, DS4T and DS3T respectively. Reversible electrochemical doping and dedoping of the DS5T film were feasible when the potential was cycled between 0 and 1.2 V. At potentials more positive than 1.2 V, however, both overoxidation of the oligo(thienylene) unit and Si-Si bond cleavage took place, leading to decreases in conductivity and work function of the film.     

Re-examination of the potential-step chronoamperometry method through numerical inversion of Laplace transforms. I. General formulation and numerical solution

Re-examination of the potential-step chronoamperometry (PSCA) method through numerical inversion of Laplace transforms is proposed in this work. First, a general expression is derived in the Laplace domain for the current transient following the application of a potential step of arbitrary amplitude. The formulation applies to first-order electrochemical–chemical reactions (E, EC and CE reactions) with one-dimensional mass-transport processes of implicated species in the electrolytic solution or the electrode. Next, numerical inversion of the relevant Laplace transform is performed by the Gaver–Stehfest (GS), Fourier–Euler (FE) and ‘fixed’ Talbot (FT) methods. The so-called GS-, FE- and FT-PSCA algorithms in this work make it possible to investigate a wide range of electrode geometry and chemical, electrochemical and one-dimensional mass-transport processes by the PSCA method. Each algorithm provides a full explicit formulation of Faradaic current with respect to time, applied potential and electrochemical parameters (initial concentrations, geometrical parameter(s), standard potential, electrochemical and chemical rate constants and diffusion coefficients), which greatly simplifies the computation of potentiostatic current transients. Some application examples relative to diffusion equations with spherical electrode geometry will be presented in the second part of this work.     

Modelling and numerical simulation of hydrodynamical processes in a confined rotating electrode configuration

This work presents an extensive hydrodynamic study of the rotating disk electrode in a confined electrochemical cell configuration. The deviation, particularly on the axis, with a classical Von Cochran expression is evaluated. The mathematical model of the hydrodynamic properties is presented and demonstrated. The numerical resolution of the equation system obtained is made using the Patankar finite volumes method using in the Fluent^® code. The three stationary and transient velocity components of the flow, the gauge pressure and the stream function cartography have been calculated using nonstationary algorithms for rotation velocities ω∈{10⁰;5×10⁰;10¹;5×10¹;10²} rad s^?1 over the whole reactor volume. These results have been validated in the vicinity of the rotating disk by means of the classical analytical Cochran expressions. The results are in good agreement for large radial distances from the axis and for small axial distances from the electrode, which is important for electrochemical species fluxes, whereas an almost 40% difference has been calculated for the axial velocity profile component on the axis. This point is important because the first term of the truncated Cochran equation is widely used to estimate convective reactive species transport at the electrode surface. These expressions are good evaluations for peripheral profiles and there are few consequences for large surface electrodes. Validation “far from the electrode”, in the bulk has been made using LDA measurements. Good accordance between numerical and experimental data are obtained with problems arising at high rotation speeds. Very large turbulence intensities were measured at the chemical boundary layer frontier.     

New approach of electrochemical systems dynamics in the time domain under small-signal conditions: II. Modelling the responses of electrochemical systems by numerical inversion of Laplace transforms

In the first part of this work, we showed that numerical inversion of Laplace transform (NILT) methods could be readily applied to compute the responses of electrochemical systems to small input signals from any reasonable model of the system immittance that is the impedance for current-controlled techniques and the admittance for potential-controlled techniques. The aim of this second article is to provide some applications examples in different fields of electrochemical kinetics. The response of a polymer exchange membrane fuel cell to a small current pulse is computed. The responses of corrosion systems to small potential step/ramp signals are also dealt with. The response of electrochemical systems to a sinusoidal perturbation of electrode potential is investigated. Finally, both Faradaic and non-Faradaic components of the total current are computed by NILT methods under potential- and current-controlled conditions.     

Thermally enhanced conformational relaxation during electrochemical oxidation of polypyrrole

Oxidation of polypyrrole which was previously prepolarized at highly negative potentials is limited by the ability of polymeric chains to undergo conformational changes. As is well known, polymeric chains can vary their conformational state only when some energetic requirements are fulfilled. This allows the study of how conformational relaxation processes associated with electrochemical doping in conducting polymers are affected by changes in the experimental conditions used. In this work, the influence of temperature on the rate of conformational relaxation in polypyrrole is evaluated, on the basis of our electrochemical relaxation model. The comparison between experimental data and theoretical predictions from the model allows the activation energy ΔH* for the conformational changes associated with polypyrrole doping to be obtained, together with the evolution of structural and electrochemical features of the polymer with the temperature. A new technique of electrochemical thermocurrents is proposed to obtain information about interactions between polymer, solvent and ions.     

Weak adsorption of anions on gold: measurement of partial charge transfer using Fast Fourier Transform electrochemical impedance spectroscopy

Using electrochemical impedance spectroscopy (EIS) based on the Fast Fourier Transform (FFT) method, we have investigated the adsorption properties of F^?, NO₃^? and CH₃COO^? on Au in aqueous electrolytes. The results show that these anions adsorb on Au in considerably small amounts. The adsorption reactions are associated with partial charge transfer across the interface. We present a theoretical framework to analyze these data. Certain previously reported impedance features of simple adsorption reactions are found as special cases of the present analysis. By combining theory and experiment, we determine the double layer capacitance, adsorption capacitance, and the amount of partial charge transfer as functions of the applied voltage. The theoretical framework of the present work can be applied to both cases of weak and strong adsorption, and can be extended to describe coadsorption of different anions.     

Theoretical and experimental study of the ECE mechanism at microring electrodes

Microring electrodes are useful for the investigation of reaction kinetics due to their large perimeter to area ratio and compact nature but have hitherto been limited in application due to the absence of the underpinning theory. In this paper, we apply the conformal mapping technique recently developed by Amatore et al. [C. Amatore, A.I. Oleinick, I.B. Svir, J. Electroanal. Chem. 564 (2004) 245] for the simulation of chronoamperometry at very thin microring electrodes, where an ECE-type mechanism is in operation. The simulated results are compared with data obtained from chronoamperometry experiments with bromonitrobenzenes at lithographically fabricated gold microring electrodes. Best fit parameters for the experimental system are determined using an automatic fitting procedure. The dark electrochemical reduction of ortho-bromonitrobenzene (o-BNB) in 0.1 M tetrabutylammonium/acetonitrile solution is consistent with an ECE-type mechanism and a value of 20 s^?1 is theoretically determined for the unimolecular cleavage of the o-BNB radical anion, in good agreement with that previously reported for similar chemical systems.     

Linear sweep voltammetric and chronopotentiometric charge/potential curves for non reversible redox monolayers

A simple equation for the charge/potential (Q/E) dependence of an electroactive monolayer is presented. This equation is valid for any chronopotentiometric or voltammetric electrochemical technique, whatever the degree of reversibility of the molecular film. Particular expressions corresponding to linear sweep and cyclic voltammetry and to chronopotentiometry with a power time programmed current have been deduced, and analogies with the current/potential curves obtained in electrochemical systems under semi-infinite diffusion mass transport control under transient and steady state conditions has been established. Reversible Q/E curves present a time-independent and universal behaviour, which does not depend on the electrochemical technique employed to obtain them. The irreversible charge/potential curves exhibit different behaviour depending on which electrochemical method has been used. Easy methods for estimating thermodynamic and kinetic parameters of the electroactive film in both chronopotentiometric and voltammetric techniques are proposed.     

Applicability of electrochemical methods to carwash wastewaters for reuse. Part 2: Electrocoagulation and anodic oxidation integrated process

In this work a combined two-step process consisting in the electrochemical coagulation with iron anodes and the electrochemical oxidation with boron-doped diamond anode (BDD) was developed for the treatment of a real carwash wastewater. The effects of important operating parameters such as current density, electrolysis time and pH on the surfactants oxidation, COD removal and energy consumptions during electrocoagulation have been explored. Furthermore, the effect of current density on the performance of anodic oxidation has been studied. The experimental results revealed that in the optimal experimental conditions (actual pH 6.4, electrolysis time 6 min and applied current 2 mA cm⁻²) the electrocoagulation method is able to remove 75% of COD in with low energy consumption, about 0.14 kWh m⁻³. The complete COD removal of the wastewater was achieved by the overall combined process where the residual organics coming from the electrocoagulation are degraded by electrochemical oxidation applying a current of 10 mA cm⁻². The energy consumption and the electrolysis time for the complete mineralization of the carwash wastewater were 12 kWh m⁻³ and 100 min, respectively.     

Information entropy production for steady-state electrochemical systems

In this work, we develop non-equilibrium information theory formalism for the investigation of the steady-state heterogeneous electron transfer. In order to analyze the information transfer, we introduce the concept of information potential and information affinity. These new functions allow us to describe the transformation from the initial to final state by means of Fokker–Planck type equation. Accordingly, the transformation can be viewed as a diffusion process within the phase space. Also, we are able to determine the information entropy production. We show that the Shannon information entropy production is equal to zero for a reversible system. However, the change in the relative entropy or Kullback–Leibler measure of information distance is positive for an irreversible system. In all cases, we find that a non-negative information entropy production is always observed during the experiments. Here, we demonstrate the self-consistency of the non-equilibrium formalism in the information theory for studying steady-state electrochemical systems.     

Proton transport through the bc complex of photosynthetic bacteria and the significance of in-situ potentiometry of midpoint potentials

The significance of potentiometric titrations carried out in situ, i.e. within the biological membrane, is discussed with respect to the pH dependence of formal potentials. Results obtained using this method on membrane-bound proteins constituting the bc complex of photosynthetic bacteria are reconsidered. The discussion is based on the theoretical treatment of a recent electrochemical investigation into cytochrome c carried out by Ikeshoji and coworkers in 1989. These authors drew attention to differences between equilibrium reaction and conformational transition coupled protonations. Reasons are given as to why in-situ titrations are not able to differentiate these. The relevance of this to current working hypotheses of the bc complex are considered. A novel working hypothesis for proton transport by this complex is presented, including both equilibrium and conformation coupled protonations. Reaction kinetic calculations supporting this hypothesis are performed.     

An electrochemical impedance study of Alloy-22 in NaCl brine at elevated temperature: II. Reaction mechanism analysis

The development of deterministic models for predicting the accumulation of corrosion damage to high level nuclear waste (HLNW) canisters requires the acquisition of values for various model parameters. In the present work, we describe the extraction of values for various parameters in the point defect model (PDM) for the growth of passive films on Alloy-22, from electrochemical impedance data for this alloy measured in saturated NaCl brine (6.2 m, m = mol kg^?1) at 80 °C, as described in Part I. The barrier layer of the passive film on Alloy-22 in the passive region (V < 0.6 V_SHE) is postulated to be defective chromic oxide (Cr_2 + xO_3 ? y) with n-type electronic character. The data suggest that the barrier layer is cation rich (x > y) with cation interstitials being the principal defect, but it is not possible to exclude oxygen vacancies, unequivocally, as being the principal defect. If the barrier layer is cation rich, the phase is estimated to have the composition Cr_2.028O₃ close to the metal|film interface, whereas if it is oxygen deficient, the stoichiometry is estimated to be Cr₂O_2.981 at the same location. The thickness of the barrier layer in the passive region is found to increase linearly with voltage while the passive current density is constant. In the transpassive range (V > 0.6 V_SHE), the passive film is found to be a p-type semi conductor, and the thickness of the barrier layer decreases, while the log of the passive current increases, with increasing applied potential. These observations are consistent with the predictions of the PDM for passive films on metals and alloys, including the transition from the passive to the transpassive states, which is predicted to coincide with a change in oxidation state of the chromium species being ejected from the barrier layer from Cr(III) to Cr(VI) and with the oxidative dissolution of the film. The principal defect in the barrier layer in the transpassive state appears to be the Cr(III) cation vacancy, which is generated by the oxidative ejection of cations from the barrier layer. Optimization of the PDM on the impedance data has yielded a set of parameter values for the passive state that can be used in deterministic models for predicting the accumulation of general corrosion damage to Alloy-22 in HLNW repositories.     

Electrodissolution of Ti and p-Si in acidic fluoride media: formation ratio of oxide layers from electrochemical impedance spectroscopy

The electrodissolution of Ti and p-Si electrodes in acidic fluoride solutions has been investigated by electrochemical impedance spectroscopy as a function of potential E, fluoride concentration, pH and angular speed of the electrode, with the aim of characterising the oxide layers covering both materials. The impedance diagrams have been analysed to obtain the low frequency capacitance C_lf, the high frequency capacitance C_hf and the product R_hfI (where R_hf is the high frequency resistance and I the steady-state current). In the potential domain where the oxide thickness x is proportional to E, the formation ratio dx/dE has been computed from C_lf, C_hf and R_hfI. The calculated values have been found to be in good mutual agreement and close to the ones found in the literature.     

The multi-dimensional upwinding method as a new simulation tool for the analysis of multi-ion electrolytes controlled by diffusion,convection and migration. Part 1. Steady state analysis of a parallel plane flow channel

A new numerical method is presented for the calculation of concentration, potential and current distributions in two-dimensional electrochemical cells controlled by diffusion, convection and migration of ions. The numerical model, for reasons of generality developed for an explicit time-dependent solution, has been made implicit such that it can easily deal with electrochemical cells at steady-state involving multiple ions. The electrolyte solutions are considered to be dilute and at a constant temperature. This new method, the multi-dimensional upwinding method, originates from the field of fluid mechanics. It is an alternative approach to both finite element methods and finite volume methods.In order to evaluate the method, steady-state computations have been performed on two plane, parallel electrodes embedded in the walls of a flow channel. Tertiary current distributions have been calculated using Butler-Volmer polarisation laws and with the applied cell voltage as a driving force for concentration and potential gradients. Electrolytes with two and three ions were considered and the results, in case of an excessive amount of supporting electrolyte, were compared with the Levecque solution. In all cases, the numerical results are found to be in good agreement with analytical or numerical solutions from literature.     

Analysis of the hydrogen electrode reaction mechanism in thin-layer cells. 1. Theory

This work develops the equations that relate the kinetic parameters of the hydrogen electrode reaction (HER) with the current density (j) vs. potential (E) dependences of a thin-layer cell (TLC). Two operation modes of the TLC are analyzed. The first one proposes to examine the j(E) dependence of the hydrogen evolution reaction (her) on one electrode while the paired electrode oxidized the dissolved H₂ back to H⁺ under diffusion control. The second mode proposes to analyze the j(E) dependence of the hydrogen oxidation reaction (hor) on one electrode while the other generates dissolved H₂ from H⁺ under diffusion control. In both cases, as very high mass-transport rates are reached for distances in the micrometer range, the j(E) curves are sensitive to the complete set of kinetic parameters even for very large reaction rates. Possible ways to incorporate these equations in the theoretical formalisms of well-established TLC-based techniques such as scanning electrochemical microscopy are discussed.     

The electrochemical characteristics of blue copper protein monolayers on gold

Site-specifically engineered disulphide or surface cysteine residues have been introduced into two blue copper proteins, Pseudomonas aeruginosa azurin and Populus nigra plastocyanin, in order to facilitate protein chemisorption on gold electrodes. The subsequently formed well-defined protein monolayers gave rise to robust electrochemical responses and electron transfer rates comparable to those observed at modified electrode surfaces. Proximal probe characterisation confirms the presence, at high coverage, of well-ordered protein adlayers. Additionally, gold-metalloprotein affinity is such that molecular-level tunnelling and topographic analyses can be carried out under aqueous solution. The approaches outlined in this work can, in principal, be extended to the generation of arrays of any redox-active biomolecule.