Diffusion mass transfer in a closed electrolytic microcell. Numerical simulation for the Cu/CuSO4(H2SO4)/Cu system

This paper reports the results of mathematical simulation of electrolysis in a closed electrolytic microcell in a Cu/CuSO₄(H₂SO₄)/Cu system, in which a two-stage electrode reaction, forming a relatively stable intermediate, and chemical reactions between the electrolyte components take place. The dependence of the current that flows through the cell on the electrolysis time and voltage on the cell electrodes was studied by numerical methods. The steady-state profiles of the concentrations of copper-containing species were calculated. The diffusion mass transfer rate in the cell was evaluated. The results were compared with the calculated data for the cell with a recessed electrode configuration with the indicator electrode lying at the bottom of a hole in the insulator. The mass transfer rate in the closed microcell was higher than on the recessed electrode.     

利用K-L方程估算旋转圆盘电极体系反应动力学电流的误差来源分析

旋转圆盘电极（RDE）体系主要用于低溶解度反应物的电极过程动力学研究. 在利用RDE技术研究不可逆电极反应动力学时,人们常利用Koutecky-Levich方程排除传质的影响,从总电流估算反应的动力学电流. 由于K-L方程是建立在系统满足稳态扩散模型的基础上,实际运用时如果体系偏离稳态扩散,就有可能对估算的动力学参数造成很大误差. 本文以氧气在多晶铂电极上的还原反应为例系统地估算了不同氧气浓度与电极转速下的误差,结果表明低氧气浓度与低圆盘转速的情况不满足稳态扩散条件,若此时仍根据K-L方程利用外推法进行分析,误差可达30%. 因此作者建议,在RDE体系中利用K-L方程估算动力学参数时,最好忽略低浓度与低转速下的数据,直接使用较高浓度与较高转速下的数据进行计算与分析.     

The influence of the adsorption of surface active substance on the rate constant of the electrode reaction

The electrode reaction of copper-EDTA complex was studied polarographically in the presence of polyvinylalcohol. The d.c. polarographic current-time curves were analyzed by using the equation given by Matsuda for the diffusion process of the depolarizer influenced by the adsorbates. The rate constants affected by the adsorption are assumed to be composed of two parts at relatively high coverage, i.e., one is the rate constant of the electrode reaction at free surface of DME and the other the rate constant of the electrode reaction through the adsorded layer. The rate constant at the uncovered surface was analyzed by a formula analogous to that proposed by Parsons and it was shown that one of the parameters involved in the formula depends on the electrode potential. On the other hand, it was shown that the electrode reaction at the covered surface is irreversible, and its cathodic rate constant depends on the electrode potential exponentially.     

Product distribution in preparative scale electrolysis: Part II. EC reaction schemes followed by competition between first-order chemical reaction and further electron transfer. One-electron systems

In many organic electrochemical reactions, the initially formed ion radical undergoes a rapid and irreversible reaction leading to an electrochemically and chemically reactive secondary radical. In the cases where this secondary radical is easier to reduce (or to oxidize) than the starting compound and at the same time undergoes a chemical reaction yielding an electroinactive species, a three-cornered ECC-ECE-Disp competition occurs involving the concurrent formation of two final products. The product distribution is determined as a function of the intrinsic-rates, rate ratios, diffusion coefficient- and operational-concentration, diffusion layer thickness and current density-parameters of the system. Two limiting situations are of particular interest, each corresponding to a two-term competition between chemical reaction and electron transfer, the latter process occurring predominantly at the electrode (ECE) or in the solution (Disp) respectively. Zone diagrams are drawn which provide a quick and convenient view of the effect of all the intrinsic and operational parameters on the ECC-ECE-Disp competition in terms of product distribution.     

On stability of model electrocatalytic process with frumkin adsorption isotherm occurring on spherical electrode

The method of impedance spectroscopy was used for theoretical studies of the conditions of appearance of Hopf instability in a model electrochemical system with a preceding homogeneous chemical reaction in the Nernst diffusion layer and electrocatalytic reaction on the spherical electrode surface under potentiostatic conditions. It is shown within the suggested electrochemical instability model based on the potential-dependent adsorption/desorption that the effective rate of the preceding homogeneous chemical reaction may affect the system stability. The effect diminishes at a decrease in the electrode radius. The instability region grows at an increase in the thickness of the Nernst diffusion layer.     

Biomolecular Release from Alginate‐modified Electrode Triggered by Chemical Inputs Processed through a Biocatalytic Cascade – Integration of Biomolecular Computing and Actuation

Biocatalytic cascades involving more than one or two enzyme‐catalyzed step are inefficient inside alginate hydrogel prepared on an electrode surface. The problem originates from slow diffusion of intermediate products through the hydrogel from one enzyme to another. However, enzyme activity can be improved by surface immobilization. We demonstrate that a complex cascade of four consecutive biocatalytic reactions can be designed, with the enzymes immobilized in an LBL‐assembled polymeric layer at the alginate‐modified electrode surface. The product, hydrogen peroxide, then induces dissolution of iron‐cross‐linked alginate, which results in release process of entrapped biomolecular species, here fluorescently marked oligonucleotides, denoted F‐DNA. The enzymatic cascade can be viewed as a biocomputing network of concatenated AND gates, activated by combinations of four chemical input signals, which trigger the release of F‐DNA. The reactions, and diffusion/release processes were investigated by means of theoretical modeling. A bottleneck reaction step associated with one of the enzymes was observed. The developed system provides a model for biochemical actuation triggered by a biocomputing network of reactions.     

The electrodissolution of magnetite: Part I. The electrochemistry of Fe3O4/C discs-potentiodynamic experiments

A simple technique is reported for the preparation of Fe₃O₄ compact electrodes by cold pressing of powdered magnetite admixed with carbon. The electrochemical behaviour of these compacts was shown to be similar with that of polycrystalline magnetite in respect of their potentiodynamic polarisation response. The variation of rest potential with solution composition is complex and indicates that there is oxidation of the surface to Fe₂O₃. Linear potentiodynamic polarisation curves are reported corresponding to unit concentration of ions for the pH range 3–9. The results provide evidence of an electrode process which is an irreversible single electron redox reaction. The current passing through the electrode is generally controlled by a solid-state diffusion process. It is postulated that the diffusing species is the H⁺ ion.     

Couple axial gradients of potential and concentration in a cylindrical pore electrode: an impedance model

The impedance of a cylindrical pore electrode in the case where the potential gradient due to the electrolyte resistivity is coupled to the axial concentration gradient of reacting species has been calculated semi-analytically from the approximate solution reported previously for the steady-state concentration and current profiles in the pore. Complex plane impedance plots, computed by an iteration technique for the transmission line, indicate: (i) a quasi-semi-circular diffusion loop at low frequencies due to diffusion control; and (ii) a high frequency loop in which the frequency dispersion is strongly dependent on the electrode parameters (electrolyte resistivity, diffusion coefficient of the reacting species, pore depth, Tafel coefficient of the electrochemical reaction and overall current flowing through the pore).     

The tube electrode and e.s.r.

The convective diffusion equation for the downstream distribution of products and intermediates produced on a tube electrode under conditions of laminar flow is solved. For distances which are large compared to the thickness of the electrode, an analytical solution in real space can be found. The solution of the equation has been applied to an apparatus in which the intermediates and products are detected by e.s.r. The species are transported by laminar flow from the electrode through an e.s.r. cavity. Results are presented for two systems and are found to be in good agreement with the theory.     

Pathways of diffusion mixed with subsequent reactions with examples of hydrogen extraction from hydride-forming electrode and oxygen reduction at gas diffusion electrode

This paper covers the role of the rate-determining step (RDS) in anodic hydrogen extraction from hydride-forming electrode. In general, hydrogen extraction from the electrode proceeds through the following steps: (1) hydrogen diffusion within the electrode, (2) hydrogen transfer from absorbed state to adsorbed state, (3) electrochemical oxidation of hydrogen to hydrogen ion involving charge transfer, and (4) hydrogen ion conduction through the electrolyte. In most theoretical and experimental investigations, it has been assumed that the RDS of anodic hydrogen extraction is hydrogen diffusion through the electrode. In real situation, however, the overall rate of hydrogen extraction is simultaneously determined by the rates of two or more reaction steps including hydrogen diffusion. The present work provides the overview of anodic hydrogen extraction in case that diffusion is coupled with interfacial charge transfer, interfacial hydrogen transfer, and hydrogen ion conduction through the electrolyte as well as the purely diffusion-controlled hydrogen extraction. In addition, the mixed controlled diffusion model was also exemplified with oxygen reduction at gas diffusion electrode of fuel cell system.     

Electrochemical behaviors of novel electroactive Au nanoparticles protected by self-assembled monolayers

There has been substantial recent interest in studying monolayer-protected gold clusters (MPCs) owing to their diverse applications. The present work is an electrochemical study of novel gold nanoparticles covered with a monolayer of mercapto-dodecanol ended chloro-dicyano-quinone (HS-C12O-CDQ), which was adsorbed on the electrode (CDQ-MPCs film). Our findings reveal a redox behavior for CDQ-MPCs film similar to the solution electrochemistry of dichloro-dicyano-quinone. Furthermore, a diffusion-like mechanism was found for electron transfer, which may have occurred due to proton diffusion towards or outwards the electrode through the film casted. Chronoamperometry confirmed diffusion behavior of the ET process. Finally, EIS was used to find the rate constant of ET process for the redox reaction that occurred and the contribution of MPCs in total interfacial capacitance.     

Lability of a mixture of metal complexes under steady-state planar diffusion in a finite domain

The rigorous analytical solution for the fluxes from a mixture of 1:1 metal complexes toward an active surface under steady-state planar diffusion in a finite domain and excess ligand conditions allows for the computation of the global degree of lability of the system as well as particular degrees of lability of each complex in the mixture. This kind of system is found in a variety of fields ranging from electrochemical techniques (such as stripping chronopotentiometry at scanned deposition potential, SSCP) to analytical devices (such as diffusion gradients in thin-film gels, DGT). Among the specific effects arising from the presence of a mixture of ligands competing for the metal we highlight the following: (i) The degree of lability of a complex in the mixture differs from its degree of lability in an unmixed system with the same ligand concentration, and (ii) the degree of lability of one complex depends on (i.e., can be modified with) the concentrations of the ligands in the mixture. The impact of these characteristics on the metal flux crossing the active surface reaches the highest value when both complexes are partially labile. The complex contribution to the metal flux goes through a maximum when the thickness of the diffusion domain is varied. Thus, the thickness of the diffusion domain can be chosen to enhance the contribution of one particular complex. Lability criteria for each complex of the mixture within the reaction layer approximation are also reported. In particular, the reaction layer formulation for a complex is discussed in detail for two limiting cases: the rest of complexes are all nonlabile or the rest of complexes are all labile.     

Pathways of diffusion mixed with subsequent reactions with examples of hydrogen extraction from hydride-forming electrode and oxygen reduction at gas diffusion electrode

This paper covers the role of the rate-determining step (RDS) in anodic hydrogen extraction from hydride-forming electrode. In general, hydrogen extraction from the electrode proceeds through the following steps: (1) hydrogen diffusion within the electrode, (2) hydrogen transfer from absorbed state to adsorbed state, (3) electrochemical oxidation of hydrogen to hydrogen ion involving charge transfer, and (4) hydrogen ion conduction through the electrolyte. In most theoretical and experimental investigations, it has been assumed that the RDS of anodic hydrogen extraction is hydrogen diffusion through the electrode. In real situation, however, the overall rate of hydrogen extraction is simultaneously determined by the rates of two or more reaction steps including hydrogen diffusion. The present work provides the overview of anodic hydrogen extraction in case that diffusion is coupled with interfacial charge transfer, interfacial hydrogen transfer, and hydrogen ion conduction through the electrolyte as well as the purely diffusion-controlled hydrogen extraction. In addition, the mixed controlled diffusion model was also exemplified with oxygen reduction at gas diffusion electrode of fuel cell system.

     

Voltammetry at a three-phase junction

When insoluble insulating crystals adhere to an electrode, the three-phase junction – where electrolyte solution, electrode and crystal meet – is the only feasible site for an electrochemical reaction. Moreover, sustained reaction is possible only if ions from the electrolyte solution are able to enter the crystal through the three-phase junction and disperse within the crystal. Here, order-of-magnitude calculations demonstrate that diffusion to the three-phase junction is well able to support voltammetry under standard experimental conditions. A model is built for cases of adherent cubes of uniform size and thereby the shapes of chronoamperograms, chronograviograms and cyclic voltammograms are predicted. The model assumes that the ion concentration at the three-phase junction plays a crucial role in the voltammetry, being determined by quasi-steady-state ion diffusion from the bulk, the thermodynamics of the electrode reaction, and the extent to which the crystal has already undergone reaction. Depending on the crystal size and scan rate, cyclic voltammograms may mimic solution-phase voltammograms from classical thin-layer experiments or from typical stripping experiments. The effect of size heterogeneity on cyclic voltammetry is simulated for lognormal distributions. Received: 5 January 1998 / Accepted: 17 April 1998     

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.     

Solid state reaction between α-naphthol and p-benzoquinone

The solid state reaction between α-naphthol and p-benzoquinone yields a red crystalline 1 : 1 adduct; in very concentrated solutions the red color can be seen, but it may be due either to Mulliken charge transfer or hydrogen bonding interactions. Kinetic studies of the solid state reaction by a capillary technique indicate that p-benzoquinone is the diffusing species, and that either surface migration or vaporphase diffusion plays an important role in the rate of complex formation. Microscopic examination of a single crystal of α-naphthol in the presence of p-benzoquinone vapor suggests that the reaction occurs only at defect centers on the α-naphthol surface. Since the reaction in the solid state goes to completion, it is suggested that cracks and crevices are formed, through which p-benzoquinone can diffuse easily into the lattice of the complex.     

Electrochemical aspects of the steel‐concrete system. A review

Steel in concrete is a very complex system where ionics and electrodics meet. From the perspective of ionics, the transport rate of oxidants (O₂) and aggressive species (CO₂, Cl^?) through the porous concrete cover defines the service life of structures. The study of these transport phenomena is a very complex task due to the changing nature of the pore network from the reaction of the matrix (pore walls) with the incoming species. At the steel–concrete interface, irreversible corrosion process occurs in parallel with reversible redox reactions involving Fe²⁺ and Fe³⁺ species that interfere in the electrochemical estimation of the corrosion rate. The present review is mainly to summarise the contributions of electrochemical impedance spectroscopy to investigate both the ionic transport and electrode reaction aspects of the problem.     

Investigations into the electroreduction of copper(II) ions on chalcocite in ammonia solutions using the rotating disc electrode method

Investigations into the electroreduction of copper(II) ions in ammonia solutions on a disc electrode made of synthetic chalcocite having a deficiency of copper atoms have been presented. It has been concluded that within the range of the diffusion controlled process copper(II) ions are the diffusing substance, at the same time in the course of the reaction two electrons are exchanged. The kinetic parameters for the electroactivating process have been estimated. With a higher concentration of copper in solution an inhibition process has been observed, probably caused by a slow transport rate of the species in the material of the electrode. In the system studied the phenomenon of a partially blocked electrode surface does not occur according to the Landsberg model.     

Electrochemical behavior of poly(ferrocenyldimethylsilane-b-dimethylsiloxane) films

The electrochemical behavior of poly(ferrocenyldimethylsilane-b-dimethylsiloxane) (PFDMS-b-PDMS) films deposited on a glassy carbon electrode was investigated by means of cyclic voltammetry (CV). The influences of the solvent, film thickness, temperature, and PDMS block length in PFDMS-b-PDMS on the electrode process were discussed. It was found that in 0.1 M aqueous LiClO(4) the electrochemical processes of the films on a glassy carbon electrode were complex and have a low rate of electron transport and mass diffusion. The kinetic parameters obtained indicated that the electrode process was controlled by both the electrode reaction and mass diffusion.     

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.