Electrode potentials reactant diffusion process

As demonstrated in Section 5.2, the electrode potential is determined by the rates of two opposing electrode reactions. The reactant in one of these reactions is always identical with the product of the other. However, the electrode potential can be determined by two electrode reactions that have nothing in common. For example, the dissolution of zinc in a mineral acid involves the evolution of hydrogen on the zinc surface with simultaneous ionization of zinc, where the divalent zinc ions diffuse away from the electrode. The sum of the partial currents corresponding to these two processes must equal zero (if the charging current for a change in the electrode potential is neglected). The potential attained by the metal under these conditions is termed the mixed potential Emix. If the polarization curves for both processes are known, then conditions can be determined such that the absolute values of the cathodic and anodic currents are identical (see Fig. 5.54A). The rate of dissolution of zinc is proportional to the partial anodic current. 

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]. 

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) ... 

This first chapter to Volume 2 Interfadal Kinetics and Mass Transport introduces the following sections, with particular focus on the distinctive feature of electrode reactions, namely, the exponential current-potential relationship, which reflects the strong effect of the interfacial electric field on the kinetics of chemical reactions at electrode surfaces. We then analyze the consequence of this accelerating effect on the reaction kinetics upon the surface concentration of reactants and products and the role played by mass transport on the current-potential curves. The theory of electron-transfer reactions, migration, and diffusion processes and digital simulation of convective-diffusion are analyzed in the first four chapters. New experimental evidence of mechanistic aspects in electrode kinetics from different in-situ spectroscopies and structural studies are discussed in the second section. The last... 

In most electrochemical reactions, except very fast diffusion-controlled processes, the adsorption of reactants is a relatively fast step compared with succeeding electron transfer steps and can be considered in quasi-equilibrium. A knowledge of reactant adsorption behavior is necessary for interpretation of the mechanism of the reaction. Equilibrium adsorption studies are directed toward the evaluation of the surface concentration of reactants in relation to the electrode potential, the temperature, the activity of reactants, and other species in the bulk and the energy of adsorption as a function of the partial coverage 0. Study of the surface coverage by adsorbed intermediates can in some cases give additional information to the kinetic approach. Determination of adsorbed intermediates would indicate the path which the reaction follows. 

Electrode potentials measure only the relative thermodynamic likelihood for various halfreactions. In practice, kinetic factors can comphcate matters. For instance, sometimes the electrode process is limited by the rate of diffusion of dissolved species to or from the electrode surface. At some cathodes, the rate of electron transfer from the electrode to a reactant is the rate-limiting step, and a higher voltage (called overvoltage) must be apphed to accom-... 

We saw that formal kinetic equations apart from kinetic parameters also contain surface concentrations Cj of electrically active species. It follows from the material presented in previous chapters that differs from the corresponding bulk values because a diffusion layer with certain concentration profiles forms at the electrode surface. Moreover, another reason due to which surface concentrations change is adsorption phenomena, which form a certain structure called a double electrode layer (DEL) at the boundary metal solution. It is clear that in kinetic equations, it is necessary to use local concentrations of reactants and products, that is, concentrations in that region of DEL where electrically active particles are located. The second effect produced by DEL is related to the fact that a potential in the localization of the electrically active complex (EAC) differs from the electrode potential. Therefore, activation energy of the electrochemical process does not depend on the entire jump of the potential at the boundary but on its part only, which characterizes the change in the potential in the reaction zone. In this connection, the so-called Frumkin correction appears in the electrochemical kinetic equations, which is related to the evaluation of the local potential i// [1]. 

The relation between E and t is S-shaped (curve 2 in Fig. 12.10). In the initial part we see the nonfaradaic charging current. The faradaic process starts when certain values of potential are attained, and a typical potential arrest arises in the curve. When zero reactant concentration is approached, the potential again moves strongly in the negative direction (toward potentials where a new electrode reaction will start, e.g., cathodic hydrogen evolution). It thus becomes possible to determine the transition time fiinj precisely. Knowing this time, we can use Eq. (11.9) to find the reactant s bulk concentration or, when the concentration is known, its diffusion coefficient. 

Concentration Polarization As a reactant is consumed at the electrode by electrochemical reaction, there is a loss of potential due to the inability of the surrounding material to maintain the initial concentration of the bulk fluid. That is, a concentration gradient is formed. Several processes may contribute to concentration polarization slow diffusion in the gas phase in the electrode pores, solution/dissolution of reactants/products into/out of the electrolyte, or diffusion of reactants/products through the electrolyte to/from the electrochemical reaction site. At practical current densities, slow transport of reactants/products to/from the electrochemical reaction site is a major contributor to concentration polarization ... 

Transport Processes. The velocity of electrode reactions is controlled by the charge-transfer rate of the electrode process, or by the velocity of the approach of the reactants, to the reaction site. The movement or trausport of reactants to and from the reaction site at the electrode interface is a common feature of all electrode reactions. Transport of reactants and products occurs by diffusion, by migration under a potential field, and by convection. The complete description of transport requires a solution to the transport equations. A full account is given in texts and discussions on hydrodynamic flow. Molecular diffusion in electrolytes is relatively slow. Although the process can be accelerated by stirring, enhanced mass transfer... 

Cathodic deposition of magnesium from various chloride melts on different substrates has been studied by several authors [288-290], In dilute solutions of Mg(II) species the cathode process has been found to be controlled by diffusion of the reactant. Alloy formation has been observed on platinum, as reported by Tunold [288] and Duan et al. [290], The rate constant of the charge transfer process on a Mg/Ni electrode in molten NaCl-CaCl2-MgCl2 was reported by Tunold to have a value of about 0.01 cm s 1. This author also reported underpotential deposition of a monolayer on iron electrodes, at potentials approximately 100 mV positive to the Mg deposition potential. 

Potential at half-height — (in voltammetry) This is a diagnostic criterion in -> linear scan voltammetry. The potential at half-height Ep/2 is the potential at which the current is equal to one-half of the peak current fp Ep/2 = h (/=/p/2)- I he first of two potentials at half-height, the one that precedes the peak potential (Ep) is considered only. If a simple electrode reaction is reversible (- reversibility) and controlled by the planar, semi-infinite - diffusion, the absolute value of the difference between Ep/2 and Ep is equal to 56.6/n mV and independent of the - scan rate. If the -> electrode reaction of dissolved reactant is totally irreversible (-> reversibility), the difference Ep/2 - Ep is equal to 47.7/an mV for the cathodic process and -47.7/(l - a)n mV for the anodic process. 

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. 

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