An investigation of a potential step at a channel electrode

The present paper deals with a theoretical investigation of a potential step at a channel electrode. The study consists in the numerical solution of the partial differential equations relevant to the transient mass balance in the vicinity of the electrode, taking into account the convective term. Although such an equation has been investigated previously for both heat and mass transfer, we present the results obtained with the help of two packages relying upon either the numerical method of lines (DSS/2) or a derived Gear technique (LSODA). Results of the simulation — concentration profile and wall concentration gradient — are reported and a comparison with previous results is carried out. Both packages used yield very similar current variations which are observed to be in a good agreement with experimental data.     

On computer curve-fitting data-evaluation of relaxation techniques for electrode kinetic investigations

An important, hitherto unrecognized advantage of curve-fitting data-evaluation of relaxation techniques is its ability to determine the optimum time scale of the experiment, that is, to determine experimentally the time window where data contain the most information about the parameter to be measured. In the past, the optimum time window could only be estimated and, for a narrow time window, a poor estimate seriously limited the sensitivity of the kinetic measurements. The advantage of the curve-fitting method is demonstrated for galvanostatic, coulostatic and potentiostatic pulse measurements.     

On the effect of the uncompensated solution resistance on the applicability of the galvanostatic relaxation techniques and comparison to steady-state techniques for electrode kinetic measurements

The effect of the uncompensated resistance between the reference and working electrodes was investigated on the applicability fields of the single and double pulse galvanostatic relaxation techniques for the determination of exchange current density. The applicability field is defined in terms of three characteristic times of the electrode system: τ_c, the time constant of the double layer capacitance—reaction resistance system; τ_d, the time constant of the diffusion impedence—reaction resistance system; and τ_r, the time constant of the double layer capacitance—uncompensated solution resistance system. Within the boundaries of this field, the exchange current density can be determined with a maximum error of ±20%. It was found that the techniques are limited by the uncompensated solution resistance to τ_r ? 0.2τ_c. An applicability diagram was also constructed for steady-state measurement techniques. In this case, the applicability field is defined in terms of k₀ (the apparent standard rate constant of the reaction), k_m (rate constant of diffusion), and τ_r and τ_c. A comparison reveals that, at small τ_c values, the relaxation techniques can be used for systems with larger k_o values than can the steady-state techniques, but at large τ_c the situation is reversed. The crossover point depends on the specific techniques compared; for example, for the double pulse galvanostatic technique with computer curve-fitting data evaluation compared to the rotating disc electrode steady-state technique, the crossover is τ_c τ~ 10^?2 s.     

A further study of diffusion and its role in electrode reactions: The development of a novel double potential step technique

A novel double potential step technique is described. It is based on the concept that the product of an electrode process diffusing away from the surface may react with another potentially electroactive species; the fluxes of the two species are balanced during the first pulse and this leads to a rising i-t response during the second pulse at a potential where only the latter species is electroactive. The experiments have been simulated and the shape and timescale of the transient have been shown to depend on the nature and rate of the chemical reaction. These concepts are tested with three systems.     

Comparison of computer curve-fitting and graphical data evaluations of the galvanostatic relaxation technique for the measurement of kinetics of electrode reactions

It is shown that the maximum measurable standard heterogeneous rate constant is not a sufficient indication of the limitations of a relaxation method. The errors of the measurement, and consequently the limits of applicability, can only be described generally by certain characteristic times of the electrode system. These are τ_c, the time constant of the double layer capacitance—reaction resistance system and τ_d, the time constant of the diffusion impedance—reaction resistance system. A graphical representation of the field of applicability of a technique is introduced using the log κ vs log τ_c diagram, where κ, the rate constant parameter, is equal to (π/4τ_d)^{$\text{1}\text{2}$}. Within the field of applicability, the technique can be used to obtain the exchange current density with an error of less than ± 20%. Such a representation is completely general and can be useful not only for the evaluation of the galvanostatic technique but for a meaningful comparison of all relaxation techniques. Such diagrams are presented for the galvanostatic technique with graphical and computer curve-fitting data evaluations. The comparison of the two methods reveals a general superiority of the computer curve-fitting evaluation. It extends the field of applicability by at least one unit of log τ_c at all levels of κ. Furthermore, it always results in an equal or more accurate determination of the exchange current density without requiring the prior exact knowledge of the double layer capacitance and the diffusion coefficients. As a matter of fact, the computer curve-fitting method could potentially be used to determine the values of these quantities. The computer program requires an initial guess of the exchange current density, the diffusion coefficients, and the double layer capacitance to start the calculations and the method is very sensitive to errors in these guesses. To achieve the field of applicability indicated in this paper, the initial guesses must be within a factor of two of the true values; they can be readily obtained within these error limits by the less exact graphical data-evaluation method.     

Applicability of the potential step relaxation technique in the nonlinear current density—overpotential range

Previously, detailed error analyses have been published only for one of the simplest (graphical) and for one of the most complex (all-numerical) data-evaluation methods of the potentiostatic relaxation technique in the nonlinear current density—overpotential range. The latter extends the range of applicability of the technique to several orders-of-magnitude faster reactions but at the price of extensive computational requirements. There is a need for an intermediate range data-evaluation method for reactions with rates too fast for the classical, graphical method but not fast enough to justify extensive computations. Such an intermediate range data-evaluation method is described and evaluated in this paper. It is based on a computer curve-fitting method using the classical relaxation equation of Gerischer and Vielstich. The limitations of this method are described, and applicability diagrams are presented. For the determination of the exchange current density of an electrode reaction, this intermediate method is limited to one to three orders-of-magnitude slower reactions, as contrasted to the all-numerical data-evaluation method, which consists of coupling a numerical diffusion equation solver routine with the nonlinear multidimensional least-squares curve-fitting program. The reason for this limited applicability is that the classical relaxation equation was derived by using several simplification in the model of the electrode reaction system. The most damaging of these simplifications is the neglect of the effects of the uncompensated solution resistance between the working and reference electrodes. The use of this intermediate applicability data-evaluation method is still justified, when applicable, by an about one order-of-magnitude decreased computational time requirement.     

Study of pyrite oxidation by cyclic voltammetric, impedance spectroscopic and potential step techniques

Pyrite oxidation in chloride solutions was investigated with cyclic voltammetry, a.c. impedance and potential step techniques. The oxidation reactions of pyrite were examined by cyclic voltammetric technique and a two-step reaction with a passivation film forming as a first-step product was proposed. An equivalent circuit was then postulated based on the oxidation reactions. Parameters indicated in the equivalent circuit such as reaction resistance and pseudo-capacitance caused by the passivation film, were determined by a.c. impedance measurements. A mathematical formula was derived from the concept of the equivalent circuit to explain the depression of the semicircle in the complex plane plot. When the semicircle is depressed, the mathematical formula indicates that the reaction resistance should be obtained from the intersection of the semi-circle with Z-axis instead of the semicircle diameter. Potential step chronoamperometric technique was then applied to measure the charging current, which is caused by the pseudo-capacitance of the passivation film, to examine the proposed equivalent circuit. The peak charging current densities at 1.10 and 0.90 V vs SHE obtained from the equivalent circuit and the a.c. impedance measurements are 110 and 75 mA cm^–2, respectively. They are consistent with the peak current densities of 105 and 69 mA cm^–2 at 1.10 and 0.90 V, respectively, determined by the potential step chronoamperometric measurements.     

Discussion of three models used for the investigation of insertion/extraction processes by the potential step chronoamperometry technique

Three models used in electrochemical literature to fit experimental data for insertion/extraction processes investigated by the potential step chronoamperometry (PSCA) technique are examined and compared in this article. The first model (M_I) gives a theoretical expression of Faradaic current transient taking reaction kinetics at the electrode surface, diffusion process in the host material and Ohmic drop effects into consideration. The ‘cell-impedance controlled diffusion’ constraint is used in the second model (M_II) together with the diffusion equations and boundary conditions. Finally, the third model (M_III) applies when the diffusion flux of injected/extracted species at the electrode surface is limited by interfacial charge transfer kinetics represented by the Butler-Volmer equation. The use of a finite-difference method is required to numerically solve models M_II and M_III. First, the theoretical predictions from models M_I, M_II and M_III are compared when a small potential step is applied on the electrode. It is stated that the theoretical expression of current transient derived from model M_I is the analytical solution of both models M_II and M_III under small-signal (linearization) conditions. Next, the three models are numerically compared under Langmuir isotherm conditions, assuming a constant diffusion coefficient of guest species in the host material. It is shown that the ‘cell-impedance controlled diffusion’ constraint used in model M_II does not work very well when a large potential step is applied on the electrode. Finally, an alternative formulation of the boundary condition at the host material|electrolyte interface (model M_III) is used to study the influence of Ohmic drop, together with the use of large potential steps.     

Primary and secondary distributions after a small-amplitude potential step at disk electrode coated with conducting film

The set of equations and boundary conditions for the “primary potential/current distribution” after a small-amplitude potential step has been analyzed for a film-coated disk electrode in contact with an electrolyte. The solution of these equations provides the overall short-time resistance of this system, R_tot, which is determined by the short-time resistance of the electrolyte solution in contact with the bare disk electrode, R_s, and the short-time film resistance to the current passage in the normal direction, (r_o, disk radius; L_f, film thickness; κ_f, its specific conductivity). The deviation of R_tot from the sum of these resistances, R_s + R_f, originates from a three-dimensional potential/current distribution in solution. Procedures to calculate the film resistance and its specific conductivity on the basis of the measured values of R_tot and R_s have been proposed. Similar analysis has also been carried out for the “secondary potential/current distribution” in the same system. The overall resistance for this regime is related to the short-time solution resistance, R_s, and to the total resistance of the electrode, equal to the sum of the resistance, R_f, and two interfacial resistances, R_m/f and R_f/s. A method to determine the bulk-film parameters, R_f and κ_f, from data for the secondary distribution is discussed. Advantages and restrictions of the proposed route to transport parameters of a film at the electrode surface are analyzed, in comparison with existing methods of their determination.     

Transient solutions of potential steps at the rotating disc electrode with steady state initial concentration profiles for one electron transfer reactions

In this paper the transient solution of a potential step at a rotating disc electrode (RDE) for irreversible and quasireversible one electron transfer reactions is derived by Nernst diffusion layer approximation and separation of variables. This is then compared to finite element simulation results. For the initial conditions steady state concentrations are chosen, such that with this theory it is possible to fit and simulate quasi steady-state linear sweep RDE measurements or other quasi steady-state sequences of potential steps.It was found that it is possible to derive accurate closed form solutions for the initial parts of the transient response. However, the Nernst diffusion layer approximation leads to inaccuracies in the intermediate times with relative errors of up to 10%.By fitting the initial transient to the closed form solution it is possible to extract steady state background currents. Additionally, we use the potential step theory to derive an expression for kinetically controlled transition times and show that these can exceed the mass transport controlled transition time.     

Mechanisms of electroless metal plating. III. Mixed potential theory and the interdependence of partial reactions

Electroless plating reactions are classified according to four overall reaction schemes in which each partial reaction is either under diffusion control or electrochemical control. The theory of a technique based on the observation of the mixed potential as a function of agitation, concentration of the reducing agent and concentration of metal ions is presented. Using this technique it is shown that in electroless copper plating the copper deposition reaction is diffusion-controlled while the formaldehyde decomposition reaction is activation-controlled. Values of the kinetic and mechanistic parameters for the partial reactions obtained by this method and by other electrochemical methods indicate that the two partial reactions are not independent of each other.Nomenclature a Tafel slope intercept - A electrode area - b _M Tafel slope for cathodic partial reaction - b _R Tafel slope for anodic partial reaction - B _M diffusion parameter for CuEDTA^2– complex - diffusion parameter for dissolved oxygen - B _R diffusion parameter for HCHO - C _M bulk concentration of copper ions - bulk concentration of dissolved oxygen - C _R ^a surface concentration of HCHO - C _R bulk concentration of HCHO - D _R diffusion coefficient of HCHO - E electrode potential - E _M thermodynamic reversible potential for the metal deposition reaction - E _M ⁰ standard electrode potential for copper deposition - E _MP mixed potential - E _R thermodynamic reversible potential for reducing agent reaction - E _R ⁰ standard electrode potential for HCHO - F Faraday constant - i _M current density for metal deposition - i _M total cathodic current density - i _M ^k kinetic controlled current density for metal deposition - i _M ⁰ exchange current density for metal deposition - i _M ^D diffusion-limited current density for metal deposition - i _M ^D diffusion-limited current density for total cathodic reactions - current density for oxygen reduction - i _plat plating current density - i _R current density for HCHO oxidation - i _R ⁰ exchange current density for HCHO oxidation - i _R ^D diffusion-limited current density for HCHO oxidation - n _M number of electrons transferred in metal deposition reaction - n _R number of electrons transferred in the HCHO oxidation reaction - R gas constant - T absolute temperature - stoichiometric number - _M transfer coefficient for metal deposition - _R transfer coefficient for HCHO oxidation - _M symmetry factor - number of steps prior to rate determining step - _M overpotential for metal deposition - _R overpotential for HCHO oxidation - v kinematic viscosity - rotation rate of electrode     

动态现场原位(operando)表征技术在多相催化反应中的应用与进展

动态现场原位（operando）表征是在接近过程工业反应条件下,揭示催化反应机理及工业催化剂结构演变的新兴动态结构解析技术。本文综述了operando表征技术在多相催化反应中的应用及发展趋势,从operando红外、operando拉曼、operando X射线衍射、operando穆斯堡尔谱、operando X射线吸收谱及operando X射线光电子能谱6个方面概述了operando技术的最新进展。此外,还介绍了正在兴起的operando联用技术,该技术综合多种operando技术为一体,能够在反应过程中对催化剂的结构全貌进行深度表征,实现工业催化剂的理性设计,将成为未来多相催化研究的重要手段。然而,目前operando技术的时间分辨率和空间分辨率仍需进一步提升,其巨大潜力依然有待开发。     

Modelling the kinetics of fast catalytic cracking reactions

Instantaneous kinetic constants and gasoline selectivities have been determined for catalytic cracking of n-hexadecane. The pulse technique was used in order to model the sequential build-up of coke which occurs on cracking catalyst within a riser transport-line reactor. The total amount of hydrocarbon injected per unit weight of catalyst was between 0 and 10. The mathematical model used to analyze the data was based on the unsteady state mass balance of the microcatalytic reactor with the assumption of plug flow. Results suggest a fast deactivation process during the run with fresh catalyst, while regenerated catalyst showed a slower deactivation. The catalyst regenerated three times evidenced a low apparent activation energy when temperature was increased from 500°C to 550°C.     

极片电压高低与电解槽运行状况的关系探讨

从电解槽内部结构入手,通过单元槽内电压、电流、电阻三者之间的变化关系解释了极片电压与单元槽运行状况的关系.     

Recycling techniques for enhancing the selectivity of complex chemical reactions

It is demonstrated by the examples of reversible parallel and consecutive reactions that recycling of by-products provides a means to attain high conversion and selectivity. Analytical expressions are obtained for the minimum reactor volume theoretically required for complete conversion and 100% selectivity.     

Rheological investigation of form relaxation and interface relaxation processes in polymer blends

Summary Transmission electron microscopical and rheological investigations have been performed on polymer blend systems of the type A/B, A/A-b-B/B, and A/C-b-B/B, where B is poly(methyl methacrylate) as the continuous and A is polystyrene as the dispersed phase. A-b-B is the corresponding diblock copolymer, and C-b-B is a diblock copolymer with poly(cyclohexyl methacrylate) (C) being thermodynamically miscible with A. The sphere-size distribution was estimated from the TEM data and found to be monomodal for all blends. Smaller sphere sizes in the A/C-b-B/B blends compared with the A/A-b-B/B blends prove the efficiency of the enthalpic acting compatibilizer.The rheological material functions G and G were used to calculate relaxation time spectra and to determine characteristic relaxation times. The form relaxation time ₁ for the relaxation of the ellipsoidally deformed soft PS-particles back to spheres have been verified for all blends no matter whether they where compatibilized or not. An additional relaxation time was found for both types of compatibilized blends. This time is assigned to a non-isotropic interfacial stress, which may arise from relaxation processes of the block copolymers at the interface.     

Slow drift modeling and compensation in the glass electrode dynamics for the fast measurement of pH

Glass electrodes for measuring pH in solutions show relatively fast responses with slow drifts. To design compensators to remove the drifts that hinder fast measurements of pH, a dynamic model that consists of ordinary and partial differential equations is proposed. It can explain such two-time scale responses of glass electrodes. The fitting accuracies of the proposed model are experimentally evaluated in frequency-domain and time-domain. The frequency responses obtained from the square wave responses show the fitting abilities of the proposed model, and the step responses also support this. The step responses filtered based on the proposed model show that pH measurements can be made considerably faster. The proposed model can be used to improve the dynamics of glass pH electrodes by compensating dynamic elements causing slow drifts.     

On the origin of voltammetric pre-peaks and cathodic potential shifts during anodic substitution reactions

During voltammetric pyridination of 9-phenylanthracene a pre-peak was observed, the height of which was in direct relation to the stoichiometric ratio of 9-phenylanthracene and pyridine. In order to determine whether or not the latter result could be taken as evidence for a nucleophile assisted electron transfer, a “non-assisted” mechanism was simulated. It was found that an ecec mechanism gave substantial cathodic shifts of the peak potential for oxidation of a substrate in presence of a reactant, and if the rate constants were sufficiently high not only a cathodic shift, but also a pre-peak was observed during simulation. Thus, the experimental observations cannot be used as evidence for an assisted mechanism.     

Towards paired and coupled electrode reactions for clean organic microreactor electrosyntheses

Electrosynthesis offers a powerful tool for the formation of anion and cation radical intermediates and for driving clean synthetic reactions without the need for additional chemical reagents. Recent advances in microfluidic reactor technologies triggered an opportunity for new microflow electrolysis reactions to be developed for novel and clean electrosynthetic processes. Naturally, two electrodes, anode and cathode, are required in all electrochemical processes and combining the two electrode processes into one “paired” reaction allows waste to be minimised. By decreasing the inter-electrode gap “paired” reactions may be further “coupled” by overlapping diffusion layers. The concept of “coupling” electrode processes is new and in some cases coupled processes in micro-flow cells are possible even in the absence of intentionally added electrolyte. The charged intermediates in the inter-electrode gap act as electrolyte and processes become “self-supported”. Hardly any examples of “coupled” paired electrochemical processes are known to date and both “paired” and “coupled” processes are reviewed here. Coupled electrode processes remain a challenge. In future “pairing” and “coupling” electrode processes into more complex reaction sequences will be the key to novel and clean flow-through microreactor processes and to novel chemistry.