Mass transfer electroactive

Here, m = is the electrode kinetic parameter typical for surface electrode processes (see Sect. 2.5.1) and 7= rg is dimensionless diffusion parameter. The latter parameter represents the inflnence of the mass transfer of electroactive species. 

The effect of the volume and the surface catalytic reaction is sketched in Figs. 2.80 and 2.81, respectively. Obviously, the voltammetric behavior of the mechanism (2.188) is substantially different compared to the simple catalytic reaction described in Sect. 2.4.4. In the current mechanism, the effect of the volume catalytic reaction is remarkably different to the surface catalytic reaction, revealing that SWV can discriminate between the volume and the surface follow-up chemical reactions. The extremely high maxima shown in Fig. 2.81 correspond to the exhaustive reuse of the electroactive material adsorbed on the electrode surface, as a consequence of the synchronization of the surface catalytic reaction rate, adsorption equilibria, mass transfer rate of the electroactive species, and duration of the SW potential pulses. These results clearly reveal how powerful square-wave voltammetry is for analytical purposes when a moderate adsorption is combined with a catalytic regeneration of the electroactive material. This is also illustrated by a comparative analysis of the mechanism (2.188) with the simple surface catalytic reaction (Sect. 2.5.3) and the simple catalytic reaction of a dissolved redox couple (Sect. 2.4.4), given in Fig. 2.82. 

In case (i), the chemical reaction is too slow to contribute to the mass transfer of the electroactive species involved. In case (iii), the chemical reaction is so fast that it is virtually in equilibrium and the reaction is controlled by diffusion of the electroactive and the electroinactive component together. Case (ii) leads to some simplification resulting, for example, in a linear relationship between — jrv2 and —... 

There are several ways in which the solvent-supporting electrolyte system can influence mass transfer, the electrode reaction (electron transfer), and the chemical reactions that are coupled to the electron transfer. The diffusion of an electroactive species will be affected not only by the viscosity of the medium but also by the strength of the solute-solvent interactions that determine the size of the solvation sphere. The solvent also plays a crucial role in proton mobility water and other protic solvents produce a much higher proton mobility because of fast solvent proton exchange, a phenomenon that does not exist in aprotic organic solvents. 

The first use of the SECM in a study of lateral mass transfer was reported by Unwin and Bard [79]. Several years later, the Unwin group studied the lateral mass transfer of a surfactant at the air-water (A-W) interface by analyzing transient current behavior [81]. The electroactive surfactant, A-octadecylferro-cenecarboxamide (CigFc0) was mixed with 1-octadecanol in a 1 1 ratio and spread onto water surface to form a Langmuir monolayer. A 25-pm diameter submarine tip (i.e., a Pt UME sealed in a U-shaped glass capillary with the conductive surface pointing upward) was placed 1-2 pm away from the A-W... 

The very fast metal-metal ion electrode processes, for which the exchange current density is very high. At steady state the overall rates of those electrode processes are controlled by the rates of mass transfer of the electroactive components to and from the electrode-melt interface. 

Electrochemical reactions consist of electron transfer at the electrode surface. These reactions mainly involve electrolyte resistance, adsorption of electroactive species, charge transfer at the electrode surface, and mass transfer from the bulk solution to the electrode surface. Each process can be considered as an electric component or a simple electric circuit. The whole reaction process can be represented by an electric circuit composed of resistance, capacitors, or constant phase elements combined in parallel or in series. The most popular electric circuit for a simple electrochemical reaction is the Randles-Ershler electric equivalent... 

Electrochemical reactions in fuel cells occurring on an electrode surface involve several steps. The electroactive species need to reach the electrode surface and adsorb on it, and then the electron transfer occurs at the electrode/electrolyte interface. The first step is mass transfer, and the second and third steps are electrode kinetics. If the mass transfer is fast, and the absorption and charge transfer are slow, the total reaction rate is determined by the electrochemical reaction kinetics. However, in the case of slow mass transfer and fast electrochemical kinetics, the mass transfer limits the whole reaction speed. In other words, the reactant that can reach the electrode surface will be consumed immediately, and the problem will be insufficient reactant on the electrode surface. 

So far the electrochemical techniques described have been based on diffusion as the mode of mass transfer of the electroactive reactants, that is, the concentration profiles develop according to Pick s second law (Eq. 22). The thickness of the diffusion... 

As mentioned in the preceding sections, mass transfer plays a crucial role in electrochemistry. The ubiquity of this phenomenon evidently arises because the electrons are exchanged at a two-dimensional surface boundary but the reactants and products are dispersed in a three-dimensional solution. Thus in the absence of mass transfer, only a small layer (of a few molecular radii thicknesses) would exchange electrons with each electrode, as is the case, for example, when the electroactive material is adsorbed at the electrode (Sec. III.D). As such, mass transfer is essential in controlling the success and rate of any preparative electrochemical reaction. 

Let us now discuss more precisely the relationship between current and mass transfer at the electrode surface. From Eq. (134) it is seen that the flux of electroactive species is given, in the absence of migration, by Eq. (140), at the electrode surface (x = 0). 

Electrolyses at an elevated or reduced pressure are generally avoided because of the added complexity in cell design, unless high pressures are needed to avoid evaporation of the solvent. Electrochemical reactors are often operated at elevated temperatures in order to enhance electrode reaction rates, improve mass transfer of electroactive species to the electrode surface, and to increase the conductivity of the electrolyte. Joule (IR) heating during current flow through the reaction medium in conjunction with exothermic electrode reactions may require extensive cooling of the electrochemical reactor. 

Here the symbol M refers to the mass transfer coefficient (cm/s). The concentrations for the electroactive species (x) and the currents are related by the equation... 

Thus, the addition of an excess of nonelectroactive ions (a supporting electrolyte) nearly eliminates the contribution of migration to the mass transfer of the electroactive species. In general, it simplifies the mathematical treatment of electrochemical systems by elimination of the V or dmass transport equations (e.g., equations 4.1.10 and 4.1.11). 

As we have just seen, it is possible to restrict mass transfer of an electroactive species near the electrode to the diffusive mode by using a supporting electrolyte and operating in a quiescent solution. Most electrochemical methods are built on the assumption that such conditions prevail thus diffusion is a process of central importance. It is appropriate that we now take a closer look at the phenomenon of diffusion and the mathematical models describing it (16-19). 

Suppose we now consider a series of step experiments in the anthracene solution discussed earlier. Between each experiment the solution is stirred, so that the initial conditions are always the same. Similarly, the initial potential (before the step) is chosen to be at a constant value where no faradaic processes occur. The change from experiment to experiment is in the step potential, as depicted in Figure 5.1.3a. Suppose, further, that experiment 1 involves a step to a potential at which anthracene is not yet electroactive that experiments 2 and 3 involve potentials where anthracene is reduced, but not so effectively that its surface concentration is zero and that experiments 4 and 5 have step potentials in the mass-transfer-limited region. Obviously experiment 1 yields no faradaic current, and experiments 4 and 5 yield the same current obtained in the chronoamperometric case above. In both 4 and 5, the surface concentration is zero hence anthracene arrives as fast as diffusion can bring it, and the current is limited by this factor. Once the electrode potential becomes so extreme that this condition applies, the potential no longer influences the electrolytic current. In experiments 2 and 3 the story is different because the reduction process is not so dominant that some anthracene cannot coexist with the electrode. Still, its concentration is less than the bulk value, so anthracene does diffuse to the surface where it must be eliminated by reduction. Since the difference between the bulk and surface concentrations is smaller than in the mass-transfer-limited case, less material arrives at the surface per unit time, and the currents for corresponding times are smaller than in experiments 4 and 5. Nonetheless, the depletion effect still applies, which means that the current still decays with time. 

If the potential is stepped to the mass-transfer controlled region, the concentration of the electroactive species is nearly zero at the electrode surface, and the current is totally controlled by mass transfer and, perhaps, by the kinetics of reactions in solution away from the electrode. Electrode kinetics no longer influence the current, hence the general i-E characteristic is not needed at all. For this case, / is independent of E. In Sections 5.2 and... 

The plateau current of a simple reversible wave is controlled by mass transfer and can be used to determine any single system parameter that affects the limiting flux of electroreactant at the electrode surface. For waves based on either the sampling of early transients or steady-state currents, the accessible parameters are the fi-value of the electrode reaction, the area of the electrode, and the diffusion coefficient and bulk concentration of the electroactive species. Certainly the most common application is to employ wave heights to determine concentrations, typically either by calibration or standard addition. The analytical application of sampled-current voltammetry is discussed more fully in Sections 7.1.3 and 7.3.6. 

There is a significant contrast here with Section 5.4.2(e), where we found that the results for reversible systems observed at spherical electrodes could be extended generally to electrodes of other shapes. This is true for a reversible system because the potential controls the surface concentration of the electroactive species directly and keeps it uniform across the surface. Mass transfer to each point, and hence the current, is consequently driven in a uniform way over the electrode surface. For quasireversible and irreversible systems, the potential controls rate constants, rather than surface concentrations, uniformly across the surface. The concentrations become defined indirectly by the local balance of interfacial electron-transfer rates and mass-transfer rates. When the electrode surface is not uniformly accessible, this balance varies over the surface in a way that is idiosyncratic to the geometry. This is a complicated situation that can be handled in a general way (i.e., for an arbitrary shape) by simulation. For UME disks, however, the geometric problem can be simplified by symmetry, and results exist in the literature to facilitate the quantitative analysis of voltammograms (12). 

In most respects, the SMDE presents a much simpler situation than the classical DME, because the drop is not growing during most of its life. In parallel with our discussion of diffusion-controlled currents at the DME, we confine our view now to the situation where the SMDE is held constantly at a potential in the mass-transfer controlled region. In the earliest stages of a drop s life (on the order of 50 ms), when the valve controlling mercury flow is open and the drop is growing, the system is convective. Mass transfer and current flow are not described simply. After the valve closes, and the drop stops growing, the current becomes controlled by the spherical diffusion of electroactive species. 

Notice that for given reaction conditions (Cq and m), a ring electrode will produce a larger current than a disk electrode of the same area. Thus, the analytical sensitivity of a ring electrode (i.e., the current caused by a mass-transfer-controlled reaction of an electroactive species divided by the residual current) is better than that of a disk electrode, and this is especially true of a thin ring electrode. However, it is usually more difficult to construct a rotating ring electrode than an RDE. 

When both the dissolved and adsorbed species are electroactive, the theoretical treatment involves the use of the full flux equation (14.3.1), along with adsorption isotherms, the usual diffusion equations, and the initial and semi-infinite conditions, as discussed in Chapter 6. Since the partial differential equations involving mass transfer must be employed, the mathematical treatment is more complicated and we consider here only the case for a nemstian electron-transfer reaction where either O (reactant) or R (product) is adsorbed, but not both (43). 

Mass transfer by migration of electroactive species under the influence of an applied voltage is rendered negligible by using a high concentration of supporting electrolyte (e.g., 0.1-M KCl). 

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