Voltammetry at spatially heterogeneous electrodes

Recent advances are overviewed which enable simulation of the voltammetric behaviour of surfaces which respond in an electrochemically spatially heterogeneous fashion. By use of the concept of a “diffusion domain” computationally expensive three-dimensional simulations may be reduced to tractable two-dimensional equivalents. In this way the electrochemical response of partially blocked electrodes and microelectrode arrays may be predicted, and are found to be consistent with experimental data. It is, furthermore, possible to adapt the “blocked” electrode analysis to enable the voltammetric sizing of inert particles present on an electrode surface. Finally theory of this type predicts the voltammetric behaviour of electrochemically heterogeneous electrodes—for example composites whose different spatial zones display contrasting electrochemical behaviour toward the same redox couple.     

Microstructures by Selective Desorption of Self‐Assembled Monolayer from Polycrystalline Gold Electrodes

Potential‐controlled partial reductive desorption of a self‐assembled monolayer of mercaptopropionic acid (MPA) formed on polycrystalline gold electrodes is used to expose subdomains of bare gold to the electrolyte solution. Two sets of cathodic waves are observed in the reduction scan with MPA self‐assembled on a polycrystalline gold electrode. The origin of the two waves is ambiguous but there are indications that the waves are correlated with reductive desorption from the (111) and then simultaneously (100) and (110) index faces of a polycrystalline gold electrode. Consecutive reduction scans with reversing the potential direction after the first peak (but before the onset of the second wave) results in disappearance of the first wave. The exposed domains are then blocked by an assembling process of longer chain alkanethiols to create a mixed self‐assembled monolayer on polycrystalline gold electrodes. Desorption of the remaining MPA creates a partially blocked electrode and the blocking behavior towards hexacyanoferrate(III) is analyzed using the theory of partially blocked electrodes and indicates an array of interacting centers. The approach of partial reductive desorption may be exploited for use in biosensing applications where the exposed gold domains could be used for anchoring of DNA probes.     

Reticulated vitreous carbon-plant tissue composite bioelectrodes

The construction and dynamic response characteristics of a tissue-porous electrode combination, composed of a plant tissue which is packed into reticulated vitreous carbon (RVC), are described. The open-cell structure of RVC thus serves as a template for the biocomponent. The immediate proximity of the tissue to the carbon surface results in a very rapid response. High sensitivity accrues from the high tissue “loading” and large electrode area. Such advantages are illustrated with mushroom-, potato- and horseradish root-packed RVC matrices. Bioaccumulation at alga-“loaded” RVC composites is also demonstrated. The effects of various operational variables on the response were evaluated. The tissue-RVC composite electrodes exhibit sigmoidal cyclic voltammograms, characteristic of partially blocked surfaces.     

Simulation of electrochemical behavior of partially blocked electrodes under linear potential sweep conditions

The paper presents nonlinear model which stands for effective digital simulation of electrochemical behavior of partially blocked electrodes under linear potential sweep and cyclic voltammetry conditions. The model is based on a system of diffusion equations, also involving the Nernst diffusion layer. The mass transport is assumed to be regular in the entire diffusion space. The influence of the thickness of the resist layer on the behavior of the partially blocked electrodes is investigated. The agreement between the theoretical results and experimental ones is obtained to be admirable for several model electrodes with different blocking degree.     

Modeling of Current Distribution on Smooth and Columnar Platinum Structures

Studying the growth and stability of anisotropic or isotropic disordered surfaces in electrodeposition is of importance in catalytic electrochemistry. In some cases, the metallic nature of the electrode defines the topography and roughness, which are also controlled by the experimental time and applied external potential. Because of the experimental restrictions in conventional electrochemical techniques and ex situ electron microscopies, a theoretical model of the surface geometry could aid in understanding the electrodeposition process and current distributions. In spite of applying a complex theory such as dynamic scaling method or perturbation theories, the resolution of mixed mass‐/charge‐transfer equations (tertiary distribution) for the electrodeposition process would give reliable information. One of the main problems with this type of distribution is the mathematics when solving the spatial n‐dimensional differential equations. Use of a primary current distribution is proposed here to simplify the differential equations; however it limits wide application of the first assumption. Distributions of concentration profile, current density, and electrode potential are presented here as a function of the distance normal to the surface for the cases of smooth and rough platinum growth. In the particular case of columnar surfaces, cycloid curves are used to model the electrode, from which the concentration profile is presented in a parameterized form after solving a first‐type curvilinear integral. The concentration contour results in a combination of a trigonometric inverse function and a linear distribution leading to a negative concavity curve. The calculation of the current density and electrode potential contours also show trigonometric shapes exhibiting forbidden imaginary values only at the minimal values of the trochoid curve.     

Electrochemical Detection of Protons Produced in an Electrode Reaction Using Interdigitated Microarray Electrodes

This work describes the use of interdigitated array electrodes (IDAE) for proton detection. Methanol electrooxidation in sulfuric acid solution was exemplified. Reduction currents originating in the reaction product generated by methanol electrooxidation on a Pt generator electrode were observed at the Pt collector electrode, the potential of which was fixed in the hydrogen evolution region. In order to reduce the background current of hydrogen evolution, an Hg‐plated Pt collector electrode was fabricated. Compared to the Pt collector electrode, the reduction current observed at the Hg collector electrode was extremely small. The product detected was found to be a proton from the current responses observed at Pt and Hg collector electrodes.     

The control of potential in continuous flow systems

The control of the potential of the working electrode in closed loop flowing systems is discussed. Various relative positions of the reference electrode are considered. No satisfactory arrangement of a three electrode configuration is possible for the general case; only when all but one of the current paths are blocked is a three electrode system satisfactory. Generally, however, a five electrode arrangement is adequate for all purposes. Electrical circuits for practical operation are given. With suitably designed tube electrodes reactions with very high exchange currents can be studied free from any uncertainty due to ohmic resistances. An application to the control of parasitic current corrosion is noted.     

Dual microband electrodes: current distributions and diffusion layer ‘titrations’. Implications for electroanalytical measurements

The simulation of transport to double microband electrodes in generator–collector mode is reported focusing especially on the ‘titration curve’ approach to electroanalysis in which a titrant is electrogenerated from a redox active precursor on the generator electrode and reacts homogeneously with the target analyte. The current on the detector electrode reflects the amount of titrant ‘surviving’ passage between the two electrodes. The form of the titration curve – plots of detector current as a function of generator current – is shown to be highly sensitive to the electrode kinetics of the redox couple driven at the generator electrode. Accordingly the naïve use of such methodology for analysis without accompanying simulation and kinetic analysis is fraught with danger. Use of the conformal mapping approach in combination with the ADI method for investigation of the ‘titration’ current distributions at the double band system gives fast and precise simulation of this and similar problems. Convergence analysis is described which allows for the automatic selection of the simulation grid size so as to obtain a chosen accuracy (for example 1%) of the current for all experimentally meaningful values of the geometrical and physico-chemical parameters of the system to be investigated.     

Abrasively modified electrodes: mathematical modelling and numerical simulation of electrochemical dissolution/growth processes under cyclic voltammetric conditions

An approximate mathematical model for electrochemical dissolution/growth processes of diffusionally independent and well-separated particles randomly dispersed on an inert conducting electrode surface is presented and solved using numerical simulation. The model, mimicking abrasively modified electrodes where particles of electroactive voltammograms solid are immobilised on an electrode surface, provides clear insights into the effects of different parameters on the voltammetric response of such systems and permits the exploration of the competition taking place between mass transport and surface processes. The mathematical model is then compared with experimental data obtained with basal plane pyrolytic graphite electrode abrasively modified with solid particles of perinaphthenone and studied in aqueous solution.Dedicated to Professor Dr. Alan M. Bond on the occasion of his 60th birthday.     

Application of a Power Time Current to the Study of a Catalytic Mechanism in Chronopotentiometry and Reciprocal Derivative Chronopotentiometry. Advantages of a Cyclic Stationary Response

This paper develops the theory for a pseudo‐first order catalytic mechanism in chronopotentiometry with a power time current, I(t)=I₀t^u (u≥?1/2), applied to a spherical electrode of any size, and the advantages of the use of small electrodes and ultramicroelectrodes are discussed. The advantages of using a cyclic power time current to reach a stationary response suitable for characterizing a catalytic mechanism easily and accurately are reported. The reciprocal derivative (dt/dE?E) curves, which present peaks quantitatively related to the kinetic parameters of the chemical reaction, have been obtained from the potential‐time responses. The influence of the homogeneous kinetic, the electrode radius and the power of time current in the achievement of a stationary response is analyzed. Methods for determining thermodynamic and kinetic parameters of the chemical reaction are proposed.     

Precapacitive processes in single potential-step chronoamperometry

Extremely short-lived anodic currents were observed in the early parts of the transient response following the application of a cathodic potential step to a mercury working electrode. It is proposed that this phenomenon is due to the existence of a brief precapacitive period, which precedes full development of the double-layer charging current, and which allows momentary reaction (reduction) of species present at the electrode surface. The observed anodic currents are explained in terms of a re-oxidation of such "resident" species that were reduced during this precapacitive period. The subsequent capacitive surge produced by the charging of the electrical double layer leads to an anodic shift of the electrode potential that can be sufficient for the re-oxidation of the precapacitive amalgam. The anodic peak is linearly related to depolarizer concentration and varies with supporting electrolyte concentration, ion mobility and potential step size. Cathodic preconcentration of the depolarizer enhances the effect.     

Electrode “edge effects” analyzed by the Green function method

An exact method based on Green's equation is used to find the diffusion-controlled faradaic current for certain electrode geometries that incorporate edges and vertices. Thereby the magnitudes of the time-independent current density associated with angled electrode/electrode and electrode/insulator junctions are calculated. As well, the square-root-of-time-dependent currents associated with vertices, receive attention. These terms extend to longer times, the Cottrell formulation appropriate for short times. Though most of the problems solved here have been tackled previously, the novel Green function approach is shown to be straightforward and intuitive.     

Theory of porous electrodes: Calculation of overall cathode characteristics for the case where the polarization curve has segments with different slopes

It is demonstrated how one should carry on with calculations of overall currents and other parameters that characterize active layers of porous electrodes in the case where polarization curves for the catalyst display two or more segments with different slopes and exchange currents. A calculation of overall currents presumes that the active layer of an electrode has an optimum thickness, over which the current reaches a maximum. The entire range of values of the cathode potential is considered, specifically, the high potentials (from a steady-state potential up to the point where there is observed an inflection in the polarization curve), the intermediate potentials (near the front surface and near the rear surface of the active layer there are realized segments of the polarization curve with different slopes), and the low potentials (throughout the entire thickness of the active layer there is observed a second segment of the polarization curve). To give an example, calculations of overall characteristics of a cathode with Nafion and platinum are performed.     

Microband electrodes of ideal and nonideal geometries: AC impedance spectroscopy

The AC impedance behavior of microband electrode geometries which deviate from the ideal is derived via numerical modelling of the chronoamperometric response under diffusion-only conditions. Specifically attention is given to four electrode shapes in addition to the ideal microband geometry: elevated microband electrodes (with conducting supporting sides), recessed microband electrodes (with insulating pit walls), platform electrodes (with insulating supporting sides) and, for the purposes of comparison, a hypothetical line electrode without any support which permits diffusional mass transport to both sides of the infinitesimally thin electrode. Simple analytical expressions are established for the frequency dependence of the AC impedance in each case.     

Polarization Curve of a Porous Hydrophobized Electrode for Electrosynthesis Involving a Side Electrochemical Reaction

A polarization curve, suggested for electrosynthesis in a porous hydrophobized electrode operating in an inner-kinetic mode at a current efficiency for the target product below 100%, depends on the balance between exchange currents and slopes of the side and target reactions and the difference between the equilibrium potential of the side reaction and the steady-state electrode potential. At different slopes of the side and the target reactions, the current efficiency depends on the polarization. Experimental and calculated data satisfactory agree.     

Modelling the electric potential distribution in the dark in nanoporous semiconductor electrodes

This study concerns the electric potential distribution in the dark in nanocrystalline porous semiconductor electrodes, in full depletion conditions. Since band bending in a single colloidal particle is small, the idea is to develop a model that accounts for the total potential drop resulting from the equilibration between the Fermi level and the redox potential in the solution. As preliminary steps, the band bending and potential distribution in a planar electrode and also in a colloidal semiconductor particle are reviewed. In order to overcome the limitations of results based on these geometries, a model based on a columnar shape is developed. The Poisson equation is solved in the columnar electrode, with careful consideration of the boundary conditions. A large potential drop is shown to take place at the back contact. To complete the study, the effect of the depletion zone in the transparent conducting oxide is analysed. Simple expressions are derived that permit evaluation of how the total potential drop is distributed between the electrode and the substrate. From this, the strength and spatial range of the electric field in the electrode can be estimated. Received: 25 June 1998 / Accepted: 15 December 1998     

Hydrodynamic Microgap Voltammetry under Couette Flow Conditions: Electrochemistry at a Rotating Drum in Viscous Poly(ethylene glycol)

Electrochemical processes in highly viscous media such as poly(ethylene glycol) (herein PEG200) are interesting for energy‐conversion applications, but problematic due to slow diffusion causing low current densities. Here, a hydrodynamic microgap experiment based on Couette flow is introduced for an inlaid disc electrode approaching a rotating drum. Steady‐state voltammetric currents are independent of viscosity and readily increased by two orders of magnitude with further potential to go to higher rotation rates and nanogaps. A quantitative theory is derived for the prediction of currents under high‐shear Couette flow conditions and generalised for different electrode shapes. The 1,1′‐ferrocene dimethanol redox probe in PEG200 (D=1.4×10^?11 m² s^?1) is employed and data are compared with 1) a Levich‐type equation expressing the diffusion–convection‐limited current and 2) a COMSOL simulation model providing a potential‐dependent current trace.     

Some studies of electrodes made from single crystals of TTF /sd TCNQ

Electrodes made from single crystals of tetrathiafulvalenium tetracyanoquinodimethanide (TTF. TCNQ) have been used to study the electrochemistry of the conducting organic salt and to investigate the mechanism of the electrochemical oxidation of glucose oxidase at conducting salt electrodes.The single crystal electrodes exhibit much lower non-Faradaic currents than the corresponding polycrystalline electrodes prepared as sublimed films or as pressed pellets. This leads to much lower background current levels and hence more clearly defined electrochemistry for solution species. Studies of the ac impedance behaviour and the electrochemistry of outer sphere redox species indicate that TTF·TCNQ electrodes behave as conventional metallic electrodes within their stable potential range.Results for the electrochemistry of glucose oxidase at the single crystal electrodes are inconsistent with a simple homogeneous mediation mechanism or with simple heterogeneous redox catalysis. Similarities with results obtained for TTF modified glucose oxidase suggest that the enzyme may undergo direct electrochemistry after modification by hydrophobic interaction with TTF molecules derived from the conducting salt electrode.     

Modeling the Electrochemical Response of Mesoporous Materials Toward Its Application to Biomolecular Detection

The performance of an electrochemical sensor based on the ability of a probe to cross a mesoporous membrane partially blocked by an analyte is predicted using a numerical model. The system comprehends a membrane placed close to the working electrode and the signal is generated by applying square wave voltammetry. The digital simulation allows comparing the responses for different situations regarding the way in which the membrane is blocked by the sample. The developed model is compared with experimental results. The effect of the sizes of the pore, analyte and probe on the system response is evaluated.     

Coupling between electroosmotically driven flow and bipolar faradaic depolarization processes in electron-conducting microchannels

A quantitative theory is proposed for the analysis of steady electroosmotically driven flows within conducting cylindrical microchannels. Beyond a threshold value of the electric field applied in the electrolyte solution and parallel to the conducting surface, electrochemical oxidation and reduction reactions take place at the two extremities of the substrate. The spatial distribution of the corresponding local faradaic currents along the bipolar electrode is intrinsically coupled to that of the electric field in solution. The nonuniform distribution of the electric field alters the double layer composition, and in particular the zeta-potential value, along the conducting surface via the occurrence of concomitant electronic and ionic double layer charging processes. The combined spatial dependencies of the lateral electric field and electrokinetic potential considerably affects the distribution of the electroosmotic velocity field in the directions parallel and perpendicular to the surface depolarized by faradaic processes. In this paper, the coupling between bipolar electrodic behavior and electroosmosis is explicitly investigated for the case of irreversible--that is, kinetically controlled--electron transfer reactions. Typical simulation results are presented and illustrate the possibility of controlling and optimizing electroosmotic flows in conducting channels by electrochemical means.