Mass charge transfer process

Many of the electrochemical techniques described in this book fulfill all of these criteria. By using an external potential to drive a charge transfer process (electron or ion transfer), mass transport (typically by diffusion) is well-defined and calculable, and the current provides a direct measurement of the interfacial reaction rate [8]. However, there is a whole class of spontaneous reactions, which do not involve net interfacial charge transfer, where these criteria are more difficult to implement. For this type of process, hydro-dynamic techniques become important, where mass transport is controlled by convection as well as diffusion. 

Study of the charge-transfer processes (step 3 above), free of the effects of mass transport, is possible by the use of transient techniques. In the transient techniques the interface at equilibrium is changed from an equilibrium state to a steady state characterized by a new potential difference A(/>. Analysis of the time dependence of this transition is the basis of transient electrochemical techniques. We will discuss galvanostatic and potentiostatic transient techniques for other techniques [e.g., alternating current (ac)], the reader is referred to Refs. 50 to 55. 

The analysis of the kinetics of the charge transfer is presented in Sect. 1.7 for the Butler-Volmer and Marcus-Hush formalisms, and in the latter, the extension to the Marcus-Hush-Chidsey model and a discussion on the adiabatic character of the charge transfer process are also included. The presence of mass transport and its influence on the current-potential response are discussed in Sect. 1.8. 

For an electrode reaction to be considered reversible, it is necessary to compare the rate of the charge transfer process and the rate of the mass transport of electroactive species. When the mass transport rate is slower than the charge transfer one, the electrode reaction is controlled by the transport rate and can be considered as electrochemically reversible in that the surface concentration fulfills the Nemst equation when a given potential is applied to the electrode. In Electrochemistry, knowledge of the behavior of reversible electrode processes is very important, since these can be used as a benchmark for more complex systems (see Chap. 5 in [1] and Sect. 1.8.4 for a detailed discussion). 

In this section, a non-reversible electrode reaction will be addressed. An exact definition of a slow charge transfer process is not possible because the charge transfer reaction can be reversible, quasi-reversible, or irreversible depending on the duration of the experiment and the mass transport rate. So, an electrode reaction can be slow or non-reversible when the mass transport rate has a value such that the measured current is lower than that corresponding to a reversible process because the rate of depletion of the surface species at the electrode surface is less than the diffusion rate at which it reaches the surface. Under these conditions, the potential values that reduce the O species and oxidize the R species become more negative and more positive, respectively, than those predicted by Nemst equation. 

From the voltammograms of Fig. 5.12, the evolution of the response from a reversible behavior for values of K hme > 10 to a totally irreversible one (for Kplane < 0.05) can be observed. The limits of the different reversibility zones of the charge transfer process depend on the electrochemical technique considered. For Normal or Single Pulse Voltammetry, this question was analyzed in Sect. 3.2.1.4, and the relation between the heterogeneous rate constant and the mass transport coefficient, m°, defined as the ratio between the surface flux and the difference of bulk and surface concentrations evaluated at the formal potential of the charge transfer process was considered [36, 37]. The expression of m° depends on the electrochemical technique considered (see for example Sect. 1.8.4). For CV or SCV it takes the form... 

The effects of the catalytic reaction on the CV curve are related to the value of dimensionless parameter A in whose expressions appear variables related to the chemical reaction and also to the geometry of the diffusion field. For small values of A, the surface concentration of species C is scarcely affected by the catalysis for any value of the electrode radius, such that r)7,> —> c c and the current becomes identical to that corresponding to a pseudo-first-order catalytic mechanism (see Eq. (6.203)). In contrast, for high values of A and f —> 1 (cathodic limit), the rate-determining step of the process is the mass transport. In this case, the catalytic limiting current coincides with that obtained for a simple charge transfer process. 

Mass transport limitation is more often encountered in electrode kinetics than in any other field of chemical kinetics because the activation-controlled charge-transfer rate can be accelerated (by applying a suitable potential) to the point that it is much faster than the consecutive step of mass transport, and therefore no longer controls the observed current. From the laboratory research point of view, mass transport is an added complication to be either avoided or corrected for quantitatively, in order to obtain the true kinetic parameters for the charge-transfer process. 

Rutherford and Vroom studied A1+ collisions with O2 and N2 at ion energies ranging from 1 to 5000 eV in a crossed beam apparatus involving a modulated neutral beam. ° The aluminum ions were produced by surface ionization of AICI3 vapor on a hot tungsten filament and product ions were detected mass spectrometrically. In the AI+ + O2 collision system, the 02" " formation cross section was found to be at the detection limit of 0.01 A at 1 keV ion energy ( 115 km/s), after which it rose to values above 0.1 A at 5 keV. N2" formation in A1+ -f N2 collisions was only measurable above 1.5 keV ( 150 km/s). The dissociative charge transfer processes ... 

By an increase of the overvoltage, i.e. the deviation from the redox potential, the rate of the heterogeneous charge transfer process is enhanced so as to cause the rate of the whole process to become controlled by mass transfer. Under these conditions the diffusion current, Id, is proportional to the concentration of the substance to be determined, So-... 

Effect of the Adsorbed Layer on the Mass- and Charge-Transfer Processes at the Electrode Solution Interface... 

There are two types of problems in the analysis of electrocatalytic reactions with mixed control kinetics reactant adsorption and combined considerations of mass and charge transfer processes in the current vs. potential profiles. The dependence of the current density, j, with the overpotential, x, can be expressed under r values larger than 0.12 V (in absolute values) through the Tafel expression corrected by the mass transfer effects ... 

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