Electrode surfaces reactant diffusion process

Now let us consider the situation in which convective diffusion is very fast and species A partitions into the film quickly yet no processes operate to convert A to B inside the film (e.g., process 4 in Figure 14.4.1). If the heterogeneous conversion of A is fast, then the overall process is entirely controlled by the rate at which the primary reactant. A, can arrive at the electrode surface by diffusion through the film. 

Figure 2.1 Schematic of the electrode electron-transfer and reactant diffusion process in an electrochemical system. Cb(0,t) is the surface concentration of oxidant species, ChlO.t) is the surface concentration of reductant species, Co(x,f) is the bulk solution concentration of oxidant, and Cr(x, ) is the bulk solution concentration of reductant species. In these four expressions of concentration, tis the reaction time. (For color version of this figure, the reader is referred to the online version of this book.)...

Electrogenerated chemiluminescence (ECL) is the process whereby a chemiluminescence emission is produced directly, or indirectly, as a result of electrochemical reactions. It is also commonly known as electrochemiluminescence and electroluminescence. In general, electrically generated reactants diffuse from one or more electrodes, and undergo high-energy electron transfer reactions either with one another or with chemicals in the bulk solution. This process yields excited-state molecules, which produce a chemiluminescent emission in the vicinity of the electrode surface. 

The theory for cyclic voltammetry was developed by Nicholson and Shain [80]. The mid-peak potential of the anodic and cathodic peak potentials obtained under our experimental conditions defines an electrolyte-dependent formal electrode potential for the [Fe(CN)g] /[Fe(CN)g]" couple E°, whose meaning is close to the genuine thermodynamic, electrolyte-independent, electrode potential E° [79, 80]. For electrochemically reversible systems, the value of7i° (= ( pc- - pa)/2) remains constant upon varying the potential scan rate, while the peak potential separation provides information on the number of electrons involved in the electrochemical process (Epa - pc) = 59/n mV at 298 K [79, 80]. Another interesting relationship is provided by the variation of peak current on the potential scan rate for diffusion-controlled processes, tp becomes proportional to the square root of the potential scan rate, while in the case of reactants confined to the electrode surface, ip is proportional to V [79]. 

Mass transport processes - diffusion, migration, and - convection are the three possible mass transport processes accompanying an - electrode reaction. Diffusion should always be considered because, as the reagent is consumed or the product is formed at the electrode, concentration gradients between the vicinity of the electrode and the bulk solution arise, which will induce diffusion processes. Reactant species move in the direction of the electrode surface and product molecules leave the interfacial region (- interface, -> interphase) [i-v]. The - Nernst-Planck equation provides a general description of the mass transport processes. Mass transport is frequently called mass transfer however, it is better to reserve that term for the case that mass is transferred from one phase to another phase. 

Such an energy transfer is taken into account in the encounter pre-equilibrium model [131, 133], which considers the outer-sphere electrode reaction to be a two-step process. In the first step the reactant diffuses to the reaction zone with a thickness dr at the electrode surface, where the probability of the charge transfer process between reactant and electrode is significant [133]. Here the electrode and reactant in the reaction zone are similar to a pair of reactants which exchange the electrons in a homogeneous reaction. 

In order to undergo a redox process, the reactant must be present within the electrode-reaction layer, in an amount limited by the rate of mass transport of Yg, to the electrode surface. In electrolyte media, four types of mass-transport control, namely convection, diffusion, adsorption and chemical-reaction kinetics, must be considered. The details of the voltammetric procedure, e.g., whether the solution is stirred or quiet, tell whether convection is possible. In a quiet solution, the maximum currents of simple electrode processes may be governed by diffusion. Adsorption of either reactant or product on the electrode may complicate the electrode process and, unless adsorption, crystallization or related surface effects are being studied, it is to be avoided, typically... 

For disk-type electrodes, usually with a radius of O.l-l.O cm the thickness of the diffusion layer that is depleted of reactant is much smaller than the electrode size so that mass transport can be described in terms of planar diffusion of the electroactive species from the bulk solution to the electrode surface as schematized in Figure 1.2a, where semi-infinite diffusion conditions apply. The thickness of the diffusion layer can be estimated as for a time electrolysis t and usually ranges between 0.01 and 0.1 mm (Bard et al., 2008). For an electrochemically reversible -electron transfer process in the absence of parallel chemical reactions, the variation of the faradaic current with time is then given by the Cottrell equation ... 

As a matter of fact, the confinement of high concentrations of catalytic centres on an electrode, up to 1 M, is of potential interest only in the case where all, or almost all of these centres retain their electroactivity. In other words, what are the factors which control the electroactivity of an immobilized species on an electrode surface, and how does one maintain rapid electrochemical reactions This theoretical aspect of the mode of operation of polymer modified electrodes has been mainly considered by research groups from Bard [182], Anson [16,17], Saveant [183], Murray [184], and Laviron [185]. The elementary kinetic steps of the overall catalytic process have been identified, i.e., the diffiision of the reactants from the electrolytic medium to the reacting centre, the transport of electrons from the electrode to the catalytic centre, the catalytic reaction itself and the diffusion of the products to the electrolytic medium. 

Suppose an electrochemical cell is operated at some potential in the plateau region of Fig. 3. Solute transported by the electrode surface is immediately converted, thereby creating a void of reactant immediately adjacent to the surface. A concentration gradient now exists out in the bulk solution, the concentration is the same as before the reaction, but near the surface it is zero. New analyte molecules diffuse from bulk solution to the surface to fill the void and are also reacted. Mathematically, the process is a simple application of Fisk s first law of diffusion, which states that the flux (J) at the electrode surface is given by the product of the diffusion coefficient (D) of the solute in the mobile phase and the concentration gradient at the electrode surface ... 

Several other factors are also responsible for important differences in electrochemical behaviour in different solvent systems. More viscous solvents impede the mass transfer processes, by which reactants are brought to the electrode surface and products are swept away. In such solvents the solution resistivities are high with consequently large heating effects, power wastage and the exacerbation of experimental problems associated with the maintenance of uniform electrical conditions across the electrode surface. However, the choice of viscous solvents such as glycerol or sulpholane is advantageous when diffusion phenomena are under study. Solution resistivity problems also arise when the solvent fails to promote complete dissociation of the electrolyte or permits extensive ion association. 

Emulsion processes are of considerable importance and cyclic voltammetry allows these to be investigated. Texter et al. [23, 121] and Rusling et al. [122] voltammetrically studied processes in optically clear, stabilised microemulsions, in which the droplet size was smaller than 100 nm. Processes monitored were shown to be consistent with a CE-type reaction scheme in which reactant diffused from the organic emulsion droplet towards the electrode surface. 

To understand the interplay of enzyme catalysis and mass transfer within polymer film, it is essential to develop models that take account of these effects, then compare the models predictions with experiment. Fig. 9.13 illustrates the physicochemical processes involved in the enzymic turnover of substrate to product within a polymer film. Such processes include mass transport of substrate and product either to or from the film, partition of these species across the polymer-solution interface, transport of reactants and products within the film (by diffusion), and electrochemical reaction with enzymic products at the electrode surface. Effects of migration of charged species within the film are usually ignored. 

Equation (2.10) and Figure 2.7 illustrate the diffusion process from an electrode surface positioned at x = 0 whether it is the export of reaction products or the import of reactants the other way. Equation (2.10) also illustrates that physical processes in electrochemistry... 

The effects caused by the main step of those mentioned are shortly reviewed in the following sections, considering first the electrochemical processes in which reactants, intermediates, and products are freely diffusing solution species, not interacting with the electrode surface. 

Diffusion process at a constant electrode potential. Assuming that Reaction (2-II) is a totally reversible reaction, and the reductant is insoluble (CR(0,f) = 1). According to the Nernst Eqn (2.24), the oxidant s surface concentration should be constant if the electrode potential is held as a constant. In this case, Co(0, t) = Cq = constant (Cq is the reactant concentration at electrode surface). Using the other three conditions as (1) the diffusion coefficient (Do) is constant, independent on the reactant concentration (2) at the beginning of reaction (t=0), the reactant concentration is uniform across the entire electrolyte solution, that is,Co(x,0)= C and (3) at any time, the reactant concentration at unlimited distance is not changed with reaction process, that is, Co(°o,t) = C, Eqn (2.40) can be resolved to give the expression of Co(x,t) ... 

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