Sur la détermination générale de l'impédance de concentration (diffusion convective et réaction chimique) pour une électrode à disque tournant

A general relation is demonstrated between the concentration impedance in the presence of a homogeneous chemical reaction and the impedance due to convective diffusion. This relation is specified for the case where the diffusion coefficients of the substances involved in the reaction are equal. It can be used to treat experimental results if the impedance of convective diffusion can be obtained in an analytical form. Three approximation formulas for this relation are given, valid respectively for low, medium, and high values of the module of a dimensionless complex variable which is a function of the frequency and the rate constants. Examples are given of numerical applications of these formulas for predicting the value of the concentration impedance, given the frequency, the Schmidt number, the rate constants of the reaction, and the disc rotation rate.     

Computing steady-state metal flux at microorganism and bioanalogical sensor interfaces in multiligand systems. A reaction layer approximation and its comparison with the rigorous solution

In complicated environmental or biological systems, the fluxes of chemical species at a consuming interface, like an organism or an analytical sensor, involve many coupled chemical and diffusion processes. Computation of such fluxes thus becomes difficult. The present paper describes an approximate approach, based on the so-called reaction layer concept, which enables one to obtain a simple analytical solution for the steady-state flux of a metal ion at a consuming interface, in the presence of many ligands, which are in excess with respect to the test metal ion. This model can be used for an unlimited number of ligands and complexes, without limit for the values of the association/dissociation rate constants or diffusion coefficients. This approximate solution is compared with a rigorous approach for the computation of the fluxes based on an extension of a previously published method (J. Galceran, J. Puy, J. Salvador, J. Cecília, F. Mas and J. L. Garcés, Phys. Chem. Chem. Phys., 2003, 5, 5091-5100). The comparison is performed for a very wide range of the key parameters: rate constants and diffusion coefficients, equilibrium constants and ligand concentrations. Their combined influence is studied in the whole domain of fully labile to non-labile complexes, via two combination parameters: the lability index, L, and the reaction layer thickness, mu. The results show that the approximate solution provides accurate results in most cases. However, for particular combinations of metal complexes with specific values of L or mu, significant differences between the approximate and rigorous solutions may occur. They are evaluated and discussed. These results are important for three reasons: (i) they enable the use of the approximate solution in a fully reliable manner, (ii) when present, the differences between approximate and rigorous solution are largely due to the coupling of chemical reactions, whose importance can thus be estimated, (iii) due to its simple mathematical expression, the individual contribution of each metal species to the overall flux can be computed.     

ECE and disproportionation: Part VI. General resolution. Application to potential step chronoamperometry

The competition between homogeneous and heterogeneous electron transfers in ECE-DISP mechanisms: A+eB BC C+eD B+C→A+D is analyzed in the context of potential step chronoamperometry. Starting from the expressions of the apparent number of electrons for the limiting situation, ECE, DISP1, DISP2, the transition between two of these “pure” mechanisms is systematically investigated. The general system is then analyzed for large values of the kinetic parameters, i.e., in the particular case of a stationary state arising from mutual compensation of diffusion and chemical reaction (“pure kinetic” conditions). This provides an estimation of the range of parameters where numerical analysis of the general case is actually necessary together with tests of accuracy of the numerical computation procedures. In this framework the analysis of the most general case involving no particular assumption about the magnitude of the thermodynamic and kinetic parameters leads to a three-dimensional kinetic zone diagram which allows to predict the effects of the intrinsic (equilibrium and rate constants) and operational (time, concentration) parameters on the displacement of the system from one limiting situation to the other. On these bases, the practical effectiveness of single-step techniques in discriminating between the limiting mechanisms is discussed. It is shown that the discrimination between DISP2 and either ECE and DISP1 can be easily carried out in terms of either concentration or time dependence of the current response. The discrimination between ECE and DISP1 is much more difficult and requires a high experimental accuracy to be effective.     

A study of the charge propagation in nanoparticles of Fe2O3 core-cobalt hexacyanoferrate shell by chronoamperometry and electrochemical impedance spectroscopy

A composite electrode comprised of graphite, Nujol, and nanoparticles of Fe₂O₃ core–cobalt hexacyanoferrate shell was prepared and the charge transport processes in the bulk of this composite were studied. The electrode/solution interface was assumed as a binary electrolyte whose charge transport occurred between redox sites of the nanoparticles present in the composite and counter cations present in the solution. Using cyclic voltammetry, the diffusion of counter cation in the shell was investigated. Using chronoamperometry, an effective diffusion coefficient and its dependency on the applied potential was obtained. In the Nyquist diagrams, different time constants were appeared with relation to different physical and electrochemical processes. Percolation of electron in the shell of the nanoparticles appeared at very high frequencies and exhibited the feature of a diffusion process with a transmissive boundary condition at interface of core–shell structure/graphite particles. The diffusion coefficients of electron and counter cation and the standard rate constants of each individual electrochemical reaction were obtained.     

Electrochemical behavior of 2'-halogenated derivatives of N,N-dimethyl-4-aminoazobenzene at mercury electrode.

The electrochemical behavior of 2'-halogeno-N,N-dimethyl-4-aminoazobenzene derivatives was investigated using various polarographic and voltammetric methods. The peak potentials of these derivatives were observed to shift towards negative values along with an increase in the pH. A reduction of the azo linkage took place via two electrons at pH > 4, but four electrons at pH < 4 in aqueous-ethanol mixtures. The standard rate constants were determined with (Laviron technique) or without (Nicholson technique) taking the adsorption phenomena into account. The diffusion coefficients were calculated from the cyclic voltammetric data using a method developed by Garrido. The amount of adsorbed substances and transfer coefficients for the electron transfer were also determined. A mechanism for the electrode reaction is proposed. These compounds can be quantitatively determined between 1 x 10(-5) M and 1 x 10(-7) with DPP and CV.     

Physicochemical quantities in catalytic reactions measured simultaneously by gas chromatography

Summary A small volume of reactant, 1-butene, is injected onto a catalytic bed and is allowed to diffuse away from it together with the product butane, along a narrow empty chromatographic tube; the latter is connected perpendicularly to the middle point of another similar tube through which hydrogen flows as reactant and carrier gas, transferring both 1-butene and butane to the detector through an analytical column. By using the reversed-flow GC technique, extra peaks are obtained in the chromatographic trace, sampling the concentration of both the readtant and product at the junction of the two tubes as a function of time. These concentrations are the result of the diffusion of the substances along the narrow empty tube, modified by the adsorption-desorption rates and the rate of the catalytic reaction. From the extra peaks of the reactant and product, a number of physicochemical quantities pertaining to the catalytic reaction can be calculated simultaneously, using appropriate mathematical analysis. These include adsorption rate constants, reaction rate constants, desorption rate constants, partition coefficients, and the overall mass transfer coefficients of the reactant across the gas-solid boundary of the catalytic bed. Presented at the 17th International Symposium on Chromatography, September 25–30, 1988, Vienna, Austria.     

Factors influencing the analytical performance of an atmospheric sampling glow discharge ionization source as revealed via ionization dynamics modeling

A kinetic model is developed for the dynamic events occurring within an atmospheric sampling glow discharge that affect its performance as an ion source for analytical mass spectrometry. The differential equations incorporate secondary electron generation and thermalization, reagent and analyte ion formation via electron capture and ion-molecule reactions, ion loss via recombination processes, diffusion, and ion-molecule reactions with matrix components, and the sampling and pumping parameters of the source. Because the ion source has a flow-through configuration, the number densities of selected species can be estimated by applying the steady-state assumption. However, understanding of its operation is aided by knowledge of the dynamic behavior, so numerical methods are applied to examine the time dependence of those species as well. As in other plasma ionization sources, the ionization efficiency is essentially determined by the ratio of the relevant ion formation and recombination rates. Although thermal electron and positive reagent ion number densities are comparable, the electron capture/ion-molecule reaction rate coefficient ratio is normally quite large and the ion-electron recombination rate coefficient is about an order of magnitude greater than that for ion-ion recombination. Consequently, the efficiency for negative analyte ion formation via electron capture is generally superior to that for positive analyte ion generation via ion-molecule reaction. However, the efficiency for positive analyte ion formation should be equal to or better than that for negative analyte ions when both ionization processes occur via ion-molecule reaction processes (with comparable rate coefficients), since the negative reagent ion density is considerably less than that for positive reagent ions. Furthermore, the particularly high number densities of thermal electrons and reagent ions leads to a large dynamic range of linear response for the source. Simulation results also suggest that analyte ion number densities might be enhanced by modification of the standard physical and operating parameters of the source.     

Mass transfer to tubular electrodes: ECE process

The mathematical model of mass transport for linear sweep voltammetry under hydro-dynamic conditions at tubular electrodes has been studied for ECE processes in which an irreversible chemical reaction is coupled between two reversible charge transfer reactions. The resulting boundary value problem is converted into system of two integral equations, which is solved numerically. The effects of axial flow rate, scan rate, potential difference, variation of chemical reaction rate and the effect of the ratio of number of electrons (n ₂/n ₁) involved in two charge transfer reactions on CV-voltammograms are investigated and shown graphically.     

Redox reactions without direct contact of the reactants. Electron and ion coupled transport through polyaniline membrane

It is demonstrated that Fe3+ in one solution can be reduced to Fe2+ by ascorbic acid in another solution when both aqueous solutions are separated by polyaniline membrane. This transmembrane redox process is possible due to electron/anion coupled counter transport through polyaniline membrane. It was demonstrated that at least one of the solutions must have acidic pH to initiate the transmembrane redox reaction. Both redox processes on the solution/membrane interfaces and the electron/ion coupled transport through the membrane play important role in determining the rate of transmembrane reaction. Possible kinetic mechanism is proposed. Apparent "diffusion coefficients" for redox equivalents inside polyaniline membrane and the rate constants of redox reactions on both solution/membrane interfaces are estimated. Maximal transmembrane reaction rate is 2 x 10(-9) mol/(s cm2) in terms of transport of redox equivalents through the membrane and formation of Fe2+. This value is much higher than the typical values of the rates of respiration in mitochondria expressed in the same units. For thin membranes, the rates of transmembrane redox reactions are determined by interface processes and characteristic times are comparable to those in biomembranes.     

Conductivity‐Dependent Completion of Oxygen Reduction on Oxide Catalysts

The electric conductivity‐dependence of the number of electrons transferred during the oxygen reduction reaction is presented. Intensive properties, such as the number of electrons transferred, are difficult to be considered conductivity‐dependent. Four different perovskite oxide catalysts of different conductivities were investigated with varying carbon contents. More conductive environments surrounding active sites, achieved by more conductive catalysts (providing internal electric pathways) or higher carbon content (providing external electric pathways), resulted in higher number of electrons transferred toward more complete 4e reduction of oxygen, and also changed the rate‐determining steps from two‐step 2e process to a single‐step 1e process. Experimental evidence of the conductivity dependency was described by a microscopic ohmic polarization model based on effective potential localized nearby the active sites.     

Electroreduction of 6-amino-5-nitroso-1,3-dimethyluracil on polycrystalline platinum and nickel cathodes in acid aqueous solution

The reduction of 6-amino-5-nitroso-1,3-dimethyluracil (ANDMU) is a key step in caffeine synthesis. Electroreduction technology is a promising green chemical process. The voltammetric behavior of ANDMU at polycrystalline platinum and nickel cathodes was studied. The Nicholson theory was used to resolve the reduction process semi-quantitatively. The results show that ANDMU mainly undergoes an ECE (electron transfer, chemical reaction, electron transfer) process involving four electrons on the platinum and nickel cathodes in which the two electron-transfer steps occur at almost the same potential and the rate of the coupling chemical reaction between two electron-transfer steps is very fast. Apparent kinetic data and diffusion coefficient were determined for the platinum rotating-disk electrode.     

Synthesis, spectroscopic and electrochemical studies on bis-[1,3-substituted (Cl, Br) phenyl-5-phenyl formazanato]nickel(II) complexes

In this study, new 1:2 Ni complexes of 1,3-substituted phenyl-5-phenylformazans were synthesized with -Cl, -Br substituents in the o-, m-, p-positions of the 1-phenyl ring and -NO(2) group in the m-position of the 3-phenyl ring. Their structures were elucidated and spectral behaviors were investigated with the use of elemental analysis, GC-Mass, (1)H NMR, (13)C NMR, FTIR, UV-vis spectra. Furthermore electrochemical properties such as number of electrons transferred (n), diffusion coefficients (D) and possible reaction mechanism of the compounds were determined with the use of cyclic voltammetry, ultramicrodisc electrode and chronoamperometry. The relation between their absorption properties and electrochemical properties was examined. A linear correlation was obtained between Hammett substituent coefficients with lambda(max) values.     

2,2’-二氨基苯氧基二硫化物的电极过程动力学研究

利用循环伏安法、线性伏安法及旋转圆盘电极技术，研究了2,2’-二氨基苯氧基二硫化物(DAPOD)在含有0.1 mol•L－1 LiClO4电解质的乙腈/四氢呋喃有机溶液中，铂、金、玻碳及石墨电极上的电化学行为.伏安结果表明DAPOD中的二硫键与硫巯基之间的氧化还原反应属动力学不可逆过程，这种在室温下表现出的电化学反应不可逆性是有机二硫化物普遍存在的不足，必须通过分子内或分子间的电催化来改善其可逆性能.旋转圆盘电极测试结果显示， DAPOD的阴极还原反应级数为0.5，阳极氧化反应级数为1.由此推知DAPOD电还原属两电子转移反应，分两步完成：第一步为平衡的化学反应步骤；第二步为电子转移步骤，属决速步.同时还测定了DAPOD的阴极与阳极传递系数、交换电流、平衡电势及标准速率常数等相关的动力学常数.通过比较铂、金、玻碳及石墨四种不同材料电极对DAPOD的电极过程的影响,发现石墨对DAPOD的还原过程具有电催化作用.     

Simulation of the electron transfer between the tetraheme subunit and the special pair of the photosynthetic reaction center using a microstate description

Charge transfer through biological macromolecules is essential for many biological processes such as, for instance, photosynthesis and respiration. Protons or electrons are transferred between titratable residues or redox-active cofactors, respectively. Transfer rates between these sites depend on the current charge configuration of neighboring sites. Here, we formulate the kinetics of charge-transfer systems in a microstate formalism. A unique transfer rate constant can be assigned to the interconversion of microstates. Mutual interactions between sites participating in the transfer reactions are naturally taken into account. The formalism is applied to the kinetics of electron transfer in the tetraheme subunit and the special pair of the reaction center of Blastochloris viridis. It is shown that continuum electrostatic calculations can be used in combination with an existing empirical rate law to obtain electron-transfer rate constants. The re-reduction kinetics of the photo-oxidized special pair simulated in a microstate formalism is shown to be in good agreement with experimental data. A flux analysis is used to follow the individual electron-transfer steps.     

Coulometry on the Voltammetric Timescale: Microdisk Potential‐Step Chronoamperometry in Aprotic Solvents Reliably Measures the Number of Electrons Transferred in an Electrode Process Simultaneously with the Diffusion Coefficients of the Electroactive Species

Microdisk, single potential‐step chronoamperometry, is applied to a range of organic substrates in the aprotic solvents tetrahydrofuran, propylene carbonate, acetonitrile and the room temperature ionic liquid [C₄dmim][N(Tf)₂]. Fitting of the chronoamperometric transients was achieved using the Shoup and Szabo method [3]. Accurate values for the diffusion coefficients, D, and the number of electron(s) transferred, n, in the electrode process have been simultaneously and consistently obtained. This method is shown to be generally applicable and reliable for the determination of the number of electrons transferred in faradaic processes uncomplicated by relatively slow coupled homogeneous kinetics. Since the experiment is conducted essentially on typical voltammetric timescales it can be commended as a complementary technique for classical coulometry which is only possible on much longer timescales. The chronoamperometric method is therefore likely to be of greater relevance to the interpretation of voltammetric data.     

Electrochemical investigation of 1,3,5-triphenylformazan and its nitro derivatives in dimethyl sulfoxide.

Cyclic voltammetric (CV) and chronoamperometric (CA) behaviors of 1,3,5-triphenylformazan (TPF), 3-(p-nitrophenyl)-1,5-diphenylformazan (PNF) and 3-(m-nitrophenyl)-1,5-diphenylformazan (MNF) were studied in dimethyl sulfoxide medium. TPF was found to give a single sharp cathodic CV peak corresponding to a gain of one-electron per molecule. The diffusion coefficient and the number of electrons transferred were calculated using the Baranski equation with the CV-data obtained by an ultramicroelectrode. Standard rate constants for the reduction were calculated by the Klingler-Kochi technique. The electrochemical data obtained support the mechanism proposed by Umemoto.     

Electrochemical reduction of 1-([(4-halophenyl)imino]methyl)-2-naphthols in aprotic media.

The electrochemical reduction of 1-([(4-halophenyl)imino]methyl)-2-naphthols on graphite electrodes was studied using cyclic voltammetry, chronoamperometry, constant-potential coulometry and preparative constant-potential electrolysis techniques. The data revealed that the reduction on graphite was irreversible and followed an EC mechanism. The diffusion coefficients and the number of electrons transferred were determined using the chronoamperometric Cottrell slope and the ultramicro disc Pt-electrode steady-state current. The number of electrons was also determined by bulk electrolysis. The compounds were subjected to constant-potential preparative electrolysis and the electrolysis products were purified and identified by spectroscopic methods. Based on these findings, a mechanism for the electro-reduction process is proposed.     

LBGK method coupled to time splitting technique for solving reaction-diffusion processes in complex systems

A new approach to numerically solve a reaction-diffusion system is given, specifically developed for complex systems including many reacting/diffusing species with broad ranges of rate constants and diffusion coefficients, as well as complicated geometry of reacting interfaces. The approach combines a Lattice Boltzmann (LB) method with a splitting time technique. In the present work, the proposed approach is tested by focusing on the typical reaction process between a metal ion M and a ligand L, to form a complex ML with M being consumed at an electrode. The aim of the paper is to systematically study the convergence conditions of the associated numerical scheme. We find that the combination of LB with the time splitting method allows us to solve the problem for any value of association and dissociation rate constant of the reaction process. Also, the method can be extended to a mixture of ligands. We stress two main points: (1) the LB approach is particularly convenient for the flux computation of M and (2) the splitting time procedure is very well suited for reaction processes involving association-dissociation rate constants varying on many orders of magnitude.     

Kopplung von chemischen reaktionen und diffusions-prozessen bei nichtisothermen reaktionen

It was investigated, how a chemical reaction was affected by diffusion processes. The analytical solution of the problem is presented for three sample geometries (plate, cylinder, sphere). Furthermore we perform an analysis of the dimensions and get the result, that four dimensionless parameters are essential for the reaction rate. The influence of these parameters on the thermogravimetric curves is discussed and the results are compared with experimental findings.     

Kinetic modeling of liquid-phase adsorption of phosphate on dolomite

The adsorption of phosphate from aqueous solution on dolomite was investigated at 20 and 40 degrees C in terms of pseudo-second-order mechanism for chemical adsorption as well as an intraparticle diffusion mechanism process. Adsorption was changed with increased contact time, initial phosphate concentration, temperature, solution pH. A pseudo-second-order model and intraparticle diffusion model have been developed to predict the rate constants of adsorption and equilibrium capacities.The activation energy of adsorption can be evaluated using the pseudo-second-order rate constants. The adsorption of phosphate onto dolomite are an exothermically activated process. A relatively low activation energy and a model highly fitting to intraparticle diffusion suggest that the adsorption of phosphate by dolomite may involve not only physical but also chemisorption. This was likely due to its combined control of chemisorption and intraparticle diffusion. However, for phosphate/dolomite system chemical reaction is important and significant in the rate-controlling step, and for the adsorption of phosphate onto dolomite the pseudo-second-order chemical reaction kinetics provides the best correlation of the experimental data.