Linear sweep voltammetry at the tubular electrode

The theory of linear sweep voltammetry at the tubular electrode has been developed for reversible electrode processes. The convective diffusion differential equations have been transformed to an integral equation which is solved numerically. The theoretical current—potential curves at different velocities of the solution have been calculated. Comparison with experiments using a tubular electrode shows satisfactory agreement.     

Modeling the measurements of cellular fluxes in microbioreactor devices using thin enzyme electrodes

An analytic approach to the modeling of stop-flow amperometric measurements of cellular metabolism with thin glucose oxidase and lactate oxidase electrodes would provide a mechanistic understanding of the various factors that affect the measured signals. We divide the problem into two parts: (1) analytic formulas that provide the boundary conditions for the substrate and the hydrogen peroxide at the outer surface of the enzyme electrode layers and the electrode current expressed through these boundary conditions, and (2) a simple diffusion problem in the liquid compartment with the provided boundary conditions, which can be solved analytically or numerically, depending on the geometry of the compartment. The current in an amperometric stop-flow measurement of cellular glucose or lactate consumption/excretion is obtained analytically for two geometries, corresponding to devices developed at the Vanderbilt Institute for Integrative Biosystems Research and Education: a multianalyte nanophysiometer with effective one-dimensional diffusion and a multianalyte microphysiometer, for which plentiful data for metabolic changes in cells are available. The data are calibrated and fitted with the obtained time dependences to extract several cellular fluxes. We conclude that the analytical approach is applicable to a wide variety of measurement geometries and flow protocols.     

Linear sweep voltammetry at the tubular graphite electrode: Part II. Totally irreversible processes

The theory of linear sweep voltammetry at the tubular graphite electrode has been developed for irreversible processes. The convective diffusion differential equations have been transformed into an integral equation which is solved numerically. The current-potential curves have been calculated theoretically and verified experimentally. The dependence of the current-potential curves on velocity has been studied. A procedure for the determination of kinetic parameters, i.e. standard rate constant and transfer coefficient, is presented.     

超微盘电极上统一的稳态伏安曲线方程式——传质时间法

本文提出了传质时间的新概念,并用于推导超微盘电极上同时控制包括Nernst扩散、对流扩散、化学反应和电极反应的稳态伏安曲线方程式,对电流、电位的性质进行了讨论。     

Fickian diffusion constrained on spherical surfaces: voltammetry.

A model is developed for the voltammetric response due to surface charge injection at a single point on the surface of a sphere on whose surface the electroactive material is confined. Accordingly, charge diffusion is constrained to the spherical surface and thus mimicks the voltammetric response of immobilised microparticles derivatised with electroactive material. The full cyclic voltammetric response is investigated, and the peak currents, the peak-to-peak separation and the symmetry of the voltammetric wave are shown to be indicative of the heterogeneous kinetics and the geometry of the adsorbed microparticle. The results show strong deviations from the responses expected for planar diffusion.     

Simulation of suspension separation by two-stage pressure-head flotation in a cylindrical direct-flow hydrocyclone

A mathematical model of separation of suspensions with a non-Newtonian dispersion medium by two-stage pressure-head flotation in a cylindrical direct-flow hydrocyclone was developed. A system of differential equations describing convective diffusion and motion of a particle-bubble complex was solved numerically. The concentration field was modeled and integral separation parameters were determined.     

A model for the propagation of a redox reaction through microcrystals

Chronoamperometry of reversible redox reactions with the insertion of cations into solid particles immobilised at an electrode surface is analysed theoretically using a semiinfinite planar diffusion model. A coupled diffusion of electrons and ions within the crystal lattice is separated in two differential equations. The redox reaction is initiated by the polarisation of the three-phase boundary, where the crystal is in contact with both the electrode and the solution. From this contact line the redox reaction advances on the surface and into the crystal body by the diffusion of ions and conductance of electrons. The effects of the geometry and conductivity of the particles on the current are discussed. Received: 28 December 1996 / Accepted: 17 February 1997     

Dynamic diffuse double-layer model for the electrochemistry of nanometer-sized electrodes

A dynamic diffuse double-layer model is developed for describing the electrode/electrolyte interface bearing a redox reaction. It overcomes the dilemma of the traditional voltammetric theories based on the depletion layer and Frumkin's model for double-layer effects in predicating the voltammetric behavior of nanometer-sized electrodes. Starting from the Nernst-Planck equation, a dynamic interfacial concentration distribution is derived, which has a similar form to the Boltzmann distribution equation but contains the influence of current density. Incorporation of the dynamic concentration distribution into the Poisson and Butler-Volmer equations, respectively, produces a dynamic potential distribution equation containing the influence of current and a voltammetric equation containing the double-layer effects. Computation based on these two equations gives both the interfacial structure (potential and concentration profiles) and voltammetric behavior. The results show that the electrochemical interface at electrodes of nanometer scales is more like an electric-double-layer, whereas the interface at electrodes larger than 100 nm can be treated as a concentration depletion layer. The double-layer nature of the electrode/electrolyte interface of nanometer scale causes the voltammetric responses to vary with electrode size, reactant charge, the value of formal redox potential, and the dielectric properties of the compact double-layer. These voltammetric features are novel in comparison to the traditional voltammetric theory based on the transport of redox molecules in the depletion layer.     

A non-conventional way to perform voltammetry

In a conventional voltammetric experiment, the electroactive species is dissolved in solution, and then diffuses from the solution phase to the electrode phase. In our proposed non-conventional voltammetric experiment, the electroactive species is trapped in the electrode phase instead of being dissolved in solution. A non-aqueous solvent was first used to trap the organic species in a porous surface layer and the modified electrode then transferred to an aqueous buffer to conduct voltammetry measurements.We tested the non-conventional voltammetric mode using a modified multi-walled carbon nanotube electrode containing mono-, di- and tri-nitroaromatic compounds trapped in the porous three-dimensional network of the CNTs. From these experiments, we conclude that the non-conventional mode produces higher peak currents and displacement of the peak potentials, yielding lower overpotentials. Furthermore, it is possible to obtain more selective voltammograms in the non-conventional mode, showing peaks that could not be resolved in the conventional mode.These results are due to a change in the mass transport regime, with thin layer diffusion being the main transport method in the non-conventional mode, compared to semi-infinite diffusion in the conventional mode.The proposed approach is an excellent alternative for performing voltammetric studies on insoluble or slightly soluble organic compounds.     

Nonlinear, electrocatalytic swimming in the presence of salt

A small, bimetallic particle in a hydrogen peroxide solution can propel itself by means of an electrocatalytic reaction. The swimming is driven by a flux of ions around the particle. We model this process for the presence of a monovalent salt, where reaction-driven proton currents induce salt ion currents. A theory for thin diffuse layers is employed, which yields nonlinear, coupled transport equations. The boundary conditions include a compact Stern layer of adsorbed ions. Electrochemical processes on the particle surface are modeled with a first order reaction of the Butler-Volmer type. The equations are solved numerically for the swimming speed. An analytical approximation is derived under the assumption that the decomposition of hydrogen peroxide occurs mainly without inducing an electric current. We find that the swimming speed increases linearly with hydrogen peroxide concentration for small concentrations. The influence of ion diffusion on the reaction rate can lead to a concave shape of the function of speed vs. hydrogen peroxide concentration. The compact layer of ions on the particle diminishes the reaction rate and consequently reduces the speed. Our results are consistent with published experimental data.     

Reduction of a simple ion at permeable film-coated stationary electrodes

Recently proposed chemically prepared electrodes are coated with a thin, permeable, insulating, inert film which does not react with the depolarizer, does not allow depolarization on its surface and does not change the standard constant of the depolarization rate. It only changes the diffusion coefficient of a certain ion near the surface of the electrode. In this article, the theory of a reversible reduction of a simple ion at a film-coated stationary planar electrode is developed. If the film thickness is comparable with a diffusion layer thickness, considerable changes on the i-t curves can occur, but the position of the half-wave potential will remain constant.     

Electrochemical determination of trace amounts of environmentally important dyes

A number of dyes exhibit genotoxic or ecotoxic properties leading to the need for sensitive and selective methods for their determination. Because of the easy reducibility of dyes, modern polarographic and voltammetric methods (differential pulse polarography on classical dropping mercury electrode, differential pulse voltammetry on hanging mercury drop electrode or adsorptive stripping voltammetry) are suitable for the determination of trace amounts of these substances in the general environment in the vicinity of production plants. The scope and limitations of these methods is reviewed and optimum conditions for recently developed methods are summarized. It is shown that the sensitivity of newly developed polarographic and voltammetric methods is sufficient even for the most demanding applications and their selectivity can be increased by their combination with preliminary separation using thin layer chromatography or liquid extraction.     

Electrochemical determination of trace amounts of environmentally important dyes

A number of dyes exhibit genotoxic or ecotoxic properties leading to the need for sensitive and selective methods for their determination. Because of the easy reducibility of dyes, modern polarographic and voltammetric methods (differential pulse polarography on classical dropping mercury electrode, differential pulse voltammetry on hanging mercury drop electrode or adsorptive stripping voltammetry) are suitable for the determination of trace amounts of these substances in the general environment in the vicinity of production plants. The scope and limitations of these methods is reviewed and optimum conditions for recently developed methods are summarized. It is shown that the sensitivity of newly developed polarographic and voltammetric methods is sufficient even for the most demanding applications and their selectivity can be increased by their combination with preliminary separation using thin layer chromatography or liquid extraction.     

Paired electrosynthesis: micro-flow cell processes with and without added electrolyte

The thin layer flow cell geometry with working and auxiliary electrodes directly facing each other, allows electrosynthetic processes to be conducted in flow-through mode. At sufficiently small cell height, the two diffusion layers of working and auxiliary electrode overlap or become ‘coupled’. As a result electro-generated acids or bases are instantaneously neutralised, products from anode and cathode can interact, and, more importantly, bulk electrolysis is possible without intentionally added electrolyte. In this preliminary report, the operation of a micro-flow cell with coupled diffusion layers is demonstrated for the one electron oxidation of ferrocene and for the two electron–two proton reduction of tetraethyl ethylenetetracarboxylate dissolved in ethanol. In proof-of-principle bulk electrolysis experiments without intentionally added electrolyte, high yields of the product, tetraethyl ethanetetracarboxylate are obtained at a nickel working electrode. It is demonstrated that a sufficient concentration of electrolyte for bulk electrolysis is generated locally and in situ between working and auxiliary electrode.     

Exact steady state solutions in symmetrical Nernst–Planck–Poisson electrodiffusive models

We compare three one-dimensional Nernst–Planck–Poisson systems that describe ion distribution near the electrode surfaces with planar, cylindrical and spherical symmetry respectively. These three models take into account ion diffusion and migration. In particular they describe the diffusive layers formed by Li+ ions in the vicinity of the graphite electrode particles. The three types of symmetry appear due to three different ways of particle ordering inside the electrode. In this paper we construct the exact steady state solutions to these systems and approximate solutions in form of power series. Then we solve the systems numerically and compare the results. We discuss the influence of symmetry in electrode particle ordering on the steady state distribution of ions in the diffusive layer.     

Activity of SiDbCl in the Electrooxidation of Ascorbic Acid,Dopamine, and Uric Acid

Selective electroanalytical responses for ascorbic acid, dopamine and uric acid at a carbon modified electrode based on 3‐n‐propyl‐1‐azonia‐4‐azabicyclo[2.2.2]octane silsesquioxane chloride (SiDbCl) is reported. The overlapped peaks observed at an unmodified electrode are resolved into three well defined voltammetric peaks allowing the simultaneous determination of the three species. Detection limits of 37, 0.3 and 0.1 μmo L⁻¹ of ascorbic acid, dopamine and uric acid, respectively, were calculated from calibration curves based on differential pulse voltammetric experiments performed in Britton ‐ Robinson buffer solution at pH 7.04.     

Layer-by-layer identification of copper alteration products in metallic works of art using the voltammetry of microparticles

An in situ technique for layer-by-layer electrochemical analysis of solid surfaces using the voltammetry of microparticles is presented. The method is based on the determination of several shape-dependent parameters for voltammetric curves recorded at a graphite pencil working electrode in contact with the sample, all immersed into aqueous electrolytes. Repetitive square wave voltammetry and sequential application of constant potential reductive steps and voltammetric scans yield discernible responses for the corrosion products distributed in stratified layers on metal-based surfaces. This methodology is applied to identify alteration products of copper and copper alloys distributed in different layers in copper coupons submitted to different corrosive treatments and a contemporary brass sculpture.     

微带电极上同时受扩散、化学反应、电极反应速率控制的伏安方程

运用积分变换的方法推导了超微带电极上同时受扩散、化学反应、电化学反应动力学控制的伏安关系,得到了前行化学反应、平行化学反应和后行化学反应的准可逆伏安方程,并列出了计算所得的典型伏安曲线。     

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.     

A dual-electrode approach for highly selective detection of glucose based on diffusion layer theory: experiments and simulation

A dual-electrode configuration for the highly selective detection of glucose in the diffusion layer of the substrate electrode is presented. In this approach, a glassy carbon electrode (GCE, substrate) modified with a conductive layer of glucose oxidase/Nafion/graphite (GNG) was used to create an interference-free region in its diffusion layer by electrochemical depletion of interfering electroactive species. A Pt microelectrode (tip, 5 microm in radius) was located in the diffusion layer of the GNG-modified GCE (GNG-G) with the help of scanning electrochemical microscopy. Consequently, the tip of the electrode could sense glucose selectively by detecting the amount of hydrogen peroxide (H2O2) formed from the oxidization of glucose on the glucose oxidase layer. The influences of parameters, including tip-substrate distance, substrate potential, and electrolyzing time, on the interference-removing efficiency of this dual-electrode approach have been investigated systematically. When the electrolyzing time was 30 s, the tip-substrate distance was 1.8 a (9.0 microm) (where a is the radius of the tip electrode), the potentials of the tip and substrate electrodes were 0.7 V and 0.4 V, respectively, and a mixture of ascorbic acid (0.3 mM), uric acid (0.3 mM), and 4-acetaminophen (0.3 mM) had no influence on the glucose detection. In addition, the current-time responses of the tip electrode at different tip-substrate distances in a solution containing interfering species were numerically simulated. The results from the simulation are in good agreement with the experimental data. This research provides a concept of detection in the diffusion layer of a substrate electrode, as an interference-free region, for developing novel microelectrochemical devices.