Claude P. Andrieux

Catalysis of electrochemical reactions at redox polymer electrodes: Kinetic model for stationary voltammetric techniques

Abstract A kinetic model describing the catalytic activity of redox polymer film electrodes is presented and discussed for reaction schemes in which the primary reaction between the active form of the catalyst and the substrate is the rate-determining step. The derivations are given for stationary techniques, such as rotating disc electrode voltammetry. Besides the diffusion of the substrate from the bulk of the solution to the film—solution interface, three kinetic factors determine the magnitude of the catalytic current: “diffusion” of electrons from the electrode surface to the film—solution interface; diffusion of the substrate in the opposite direction; rate of the rate-determining step of the catalytic reaction. Correspondingly, the kinetics of the diffusion—reaction process can be entirely described by only three dimensionless parameters expressing the relative rates of the rate-controlling processes. Provision is made for the partition coefficient of the substrate between the film and the solution to be different from unity. A finite-difference resolution of the kinetics is developed, but attention is mainly focused on the search of characteristic behaviors depending upon a lesser number of parameters and expressed by simple closed-form equations which are particularly convenient to use in the processing of experimental data. These are essentially of four types. 1. (1) The electron and substrate diffusion of the film are so fast that the rate-controlling phenomenon in the film is the catalytic reaction. 2. (2) The cataytic reaction is so fast that the kinetics is controlled jointly by the two diffusion process. 3. (3) When “diffusion” of electron is faster than diffusion of substrate in the film a pure kinetic situation may arise by mutual compensation of the latter process and the catalytic reaction. 4. (4) In the opposite case a pure kinetic situation may again arise resulting this time from mutual compensation of electron “diffusion” and catalytic reaction. The kinetics observed in intermediary situations is also described, as well as the variations of the parameters that are required to pass from one limiting behavior to the other. It is shown that, according to the kinetic situation prevailing in the film, a second wave way appear which features the direct reduction of the substrate at the electrode surface after it has diffused through the film. Diagnostic criteria of the various limiting situation are presented, being based on the variations of the height of the catalytic wave with the rotation speed and the solution concentration of the substrate, as well as on the existence and height of the second wave. The electron “diffusion” through the film can be characterized independently by means of experiments involving the oxido-reduction of the film in the absence of substrate. Conversely, the substrate diffusion in the film can be characterized using analogous system in wich catalysis is absent. With the help of these data, the catalytic reaction occuring in the film can be quantitatively characterized. It is shown that this does not require exact knowledge of the film thickness. Such application of the kinetic model to actual experimental systems are illustrated by the discussion of experimental data from the literature.

Homogeneous redox catalysis of electrochemical reactions: Part V. Cyclic voltammetry

Abstract Cyclic voltammetry appears as a more convenient tool for studying homogeneous redox catalysis than polarography, due to the recording of the current potential being much faster and the control of the diffusion process more accurate and involving a much more extended range of rates. The theory of homogeneous redox catalysis in the context of cyclic voltammetry is presented for the EC reaction scheme, i.e. the simplest of the mechanisms in which the initial electron-transfer process is followed by chemical reaction. The treatment involves a stationary-state assumption regarding the initial product of the electron transfer The dimensionless voltammograms then depend upon two kinetic parameters and of the ratio of the substrate and catalyst concentrations. Two limiting situations are found for the kinetic control of the catalytic process according to the relative magnitude of the, follow-up chemical reaction and the backward electron-transfer rates. In one of these the kinetic control is by the forward homogeneous electron transfer, while in the other it is by the follow-up chemical reactions. In these two cases the system depends upon only two parameters, allowing a detailed discussion of the shape and characteristics of the voltammograms to be presented, as well a set of working curves giving the relative catalytic increase of the peak current as a function of the pertinent kinetic parameter and of the substrate—catalyst concentration ratio. A numerical procedure is presented for the resolution of the general case involving a mixed kinetic control by the two reactions. Diagnostic criteria for the recognition of the two limiting cases and the transition to mixed kinetic control are given, as well as procedures for determining the characteristic rate constants. The theory is then extended to the more frequently encountered two-electron processes which involves only a slight modification of the results pertaining to the EC scheme. Experimental illustrations of the main theoretical results are given in the context of the reduction of aromatic halides in aprotic media. The results obtained in this study have as their main application the determination, through the redox catalytic method, of the rate and equilibrium parameters for irreversible systems that would be far beyond the possibilities offered by the standard use of electrochemical techniques.

Homogeneous redox catalysis of electrochemical reactions: Part I. Introduction

Abstract In redox homogeneous catalysis the catalyst couple merely plays the role of an electron carrier by contrast with chemical catalysis which involves the transitory formation of catalyst-substrate adduct. A detailed kinetic analysis of redox catalysis in the case of an EC-type electrode reaction is given involving the following reaction sequence B → k C A + 1 e ⇌ B B → C } direct electrode reduction of the substrate The Hush-Marcus relationship between heterogeneous and homogeneous electron transfer rate constants is used to select the range of the parameter variations and to predict the magnitude of the catalytic efficiency as a function of the potential separation between the catalyst reduction and the direct substrate reduction, the ratio of the catalyst over the substrate concentration and the electrochemical standard rate constant of the substrate. Two situations are of particular interest for the kinetic analysis of the experimental data: (a) kinetic control of the direct substrate reduction by the follow-up chemical reaction with diffusion by charge transfer with activation or diffusion control of the solution electron exchange, the rate determining step of the catalytic sequence being A+Q→P+B. In these conditions, kinetic information on the substrate reduction process is obtainable which could not have been derived from a direct electrochemical analysis.

Kinetics of electrochemical reactions mediated by redox polymer films: Reversible cross-exchange reactions

Abstract While the previous rigorous treatments of the problem have been restricted to completely irreversible substrate-mediator cross-exchange reactions, the present analysis aims at the kinetic description of systems in which the cross-exchange equilibrium constant may take any value. According to the value of the standard potential difference between the redox polymer and substrate couple and to the oxido-reduction kinetics of the latter, three different situations of practical interest are discussed. For each. the parameters of the system are specified and their role is analyzed in the context of stationary techniques such as rotating disk voltammetry. Besides the magnitude of the equilibrium constant of the cross-exchange reaction and the diffusion of the substrate between the bulk of the solution and the film-solution interface, there are three other current-limiting factors: kinetics of the cross-exchange reaction, diffusion of the substrate and diffusion-like propagation of the electrons in the film. The formulation of the results is greatly simplified by the expression of the latter four factors in terms of characteristic currents. A numerical method for obtaining the current in the general case is described. However, attention is mainly focused on characteristic limiting behavior in which one or two of the three rate-limiting phenomena occurring in the film control the magnitude of the current. In these limiting situations, closed-form expressions of the current are obtained. How one passes from one situation to the other is discussed in terms of characteristic current ratios. Attention is mainly directed toward the expression of the plateau currents of the first and second waves, but an approximate description of the potential localtion of the waves is also given. Details of the mathematical derivations are not given. They are available upon request in any specific case.

Electrodimerization: VII. Electrode and solution electron transfers in the radical-substrate coupling mechanism. discriminative criteria from the other mechanisms in voltammetric studies (Linear sweep, rotating disc, polarography)

Summary The interference of solution electron transfer, as well as electrode electron transfer in radical-substrate electrochemical coupling mechanisms is studied as a particular case of the e.c.e. vs. disproportionation problem. Discriminative criteria between the various possible electrodimerization reaction schemes and procedures for rate constant determination are derived for the techniques of linear sweep voltammetry, rotating disc electrode voltammetry and classical polarography.

Fast sweep cyclic voltammetry at ultra-microelectrodes: Evaluation of the method for fast electron-transfer kinetic measurements

With ultra-microelectrodes (in the 10 μ m diameter range), it is possible to decrease the ohmic drop to values that allow the use of very high scan rates in cyclic voltammetry (10–1000 kV s−1. Although reduced as compared with standard size microelectrodes, the ohmic drop is, however, not negligible and thus must be appropriately corrected for. On the other hand, at these high sweep rates the double-layer charging current is a substantial portion of the total current. The correct treatment of the cyclic voltammetric data thus necessitates an ohmic drop correction that takes into account the mutual dependence of the faradaic and double-layer charging currents. Such a treatment is applied to the reduction of anthracene in dimethylformamide, a test example of very fast electron-transfer kinetics (kSap = 3.5 cm s−1), at sweep rates ranging from 20 to 250 kV s−1. The system is analysed both by direct simulation of the cyclic voltammograms and by means of convolution of the voltammograms with the diffusion function (πt)−12. The effect of band-pass limitations of the potentiostat and current measurer on the cyclic voltammetric responses is also discussed.

Homogeneous redox catalysis of electrochemical reactions: Part II. Rate determining electron transfer, evaluation of rate and equilibrium parameters

Abstract The reduction of chlorobenzene in DMF with tetrabutylammonium as supporting cation is taken as an example illustrating the occurrence of homogeneous catalysis under the following conditions: (a) charge tranfer control of the uncatalyzed reduction of the substrate, (b) activation and diffusion control of the solution electron exchange between substrate and catalyst. Since chlorobenzene is reduced according to a two-electron process, the kinetic treatment previously given for a simple EC mechanism is extended to the two-electron case considering the occurrence of the second electron uptake either at the electrode or in solution. Eight catalyst couples involving aromatic hydrocarbons and heterocycles were employed to evaluate the catalytic efficiency as a function of the half-wave potential separation ΔE1/2. The variations of the catalytic efficiency with the excess factor for a given catalyst show that the rate determining step is in almost all cases the forward solution electron exchange. This allows a relatively simple determination of the rate constant of this reaction as a function of ΔE1/2. Two distinct regions in ΔE1/2 clearly appear corresponding to activation and diffusion control of the solution electron transfer, respectively. The behavior in the activation controlled region fits satisfactorily with a simplified version of the Marcus theory in which the quadratic term is neglected. Analysis of the results allows an indirect determination of the electrochemical standard rate constant, the standard potential and the isotopic homogeneous rate constant which could not have been obtained through standard electrochemical methods. The relationship between the homogeneous and heterogeneous reorganization energies is discussed in terms of Hush and Marcus theories.

Kinetics of electrochemical reactions mediated by redox polymer films: New formulation and strategies for analysis and optimization

Abstract A new formulation of the kinetics of electrochemical reactions mediated by redox films is proposed for the case of an irreversible cross-exchange reaction in the context of rotating disc electrode voltammetry. It involves the normalization of the substrate concentration versus its value at the film boundary interface. The overall kinetics are then shown to depend on only two dimensionless parameters. Procedures for analysing the effects of the rotation speed and the other experimental parameters are proposed. The construction of a kinetic zone diagram summarizing the variation of the kinetic control with the various parameters is useful for defining the optimal performances of the film.

Homogeneous redox catalysis of electrochemical reactions: Part IV. Kinetic controls in the homogeneous process as characterized by stationary and quasi-stationary electrochemical techniques

Abstract The analysis of homogeneous redox catalysis of an EC electrochemical reaction: Electrode process Catalytic process A + 1 e ⇌ B ( I el ) P + 1 e ⇌ Q ( 0 ) Q + A ⇌ k 2 k 1 B + P ( I sol ) B → k C ( II ) is greatly simplified if the stationary-state assumption can be made for species B. Two limiting situations are then obtained for extreme values of k/k2 involving kinetic control of the overall reaction either by the forward reaction (I sol) or by reaction (II) with (I sol) as a preequilibrium. The polarization problem has been numerically solved for these two limiting cases as well as for the transition between them in the context of stationary or quasi-stationary electrochemical methods such as rotating disc voltammetry or classical polarography. The scope and limitations are discussed showing that it can be safety applied in the application of homogeneous redox catalysis to the determination of equilibrium and rate parameters of irreversible systems that are inaccessible through the standard use, of electrochemical kinetic techniques. The treatment has been extended to more complex processes, i.e. those involving the overall exchange of two electrons along an ECE or a solution electron-transfer mechanism. Procedures for the practical determination of the equilibrium and rate parameters of an irreversible system from homogeneous redox catalysis data are discussed.

Homolytic and heterolytic radical cleavage in the Kolbe reaction: Electrochemical oxidation of arylmethyl carboxylate ions

Abstract The mechanism of oxidative decarboxylation of arylmethyl carboxylate ions is derived from the analysis of the cyclic voltammetric responses of an extended series of compounds, and, in a few selected cases, of product distribution. In all cases, the removal of the first electron and the cleavage of the bond that results in the formation of CO2, are successive rather than concerted processes. In a majority of cases, the unpaired electron is located on carboxyl oxygen of the acyloxy radical which undergoes a fast homolytic cleavage. The reaction is kinetically controlled by the first electron step. The resulting alkyl radical is formed so close to the electrode surface that it is oxidized before having time to dimerize thus yielding exclusively carbocation-derived products (non-Kolbe reaction). When the aromatic portion of the carboxylate ion is easier to oxidize, as with the 4-dimethylamino-benzyl and 9-anthracenyl-methyl derivatives, the acyloxy radical has a zwitterionic character, the cleavage is slower and follows a heterolytic mechanism (involving an intramolecular dissociative electron transfer). This is the reason that the kinetic control passes progressively to the cleavage step. The slower cleavage is also the cause of the formation of a substantial amount of dimer together with carbocation-derived products.