Concentration polarization inhibition

It should be understood that even for micro surface features the potential is uniform and the ohmic resistance through the bath to peaks and valleys is about the same. Also, electrode potential against SCE will be uniform. What is different is that over micro patterns the boundary of the diffusion layer does not quite follow the pattern contour (Fig. 12.3). Rather, it thus lies farther from depth or vias than from bump peaks. The effective thickness, 8N, of the diffusion layer shows greater variations. This variation of 8N over a micro profile therefore produces a variation in the amount of concentration polarization locally. Since the potential is virtually uniform, differences in the local rate of metal deposition result if it is controlled by the diffusion rate of either the depositing ions or the inhibiting addition (leveling) agents. 

In an environment with a constant redox condition (e.g., permanently aerated and/or constant pH), a condition not uncommon in industrial and environmental situations, corr could shift in the positive direction for a number of reasons. Incongruent dissolution of an alloy could lead to surface ennoblement. Alternatively, as corrosion progresses, the formation of a corrosion product deposit could polarize (i.e., increase the overpotential, i), for) the anodic reaction as illustrated in the Evans diagram of Fig. 4. Polarization in this manner may be due to the introduction of anodic concentration polarization in the deposit as the rate of transport of dissolved metal species away from the corroding surface becomes steadily inhibited by the thickening of the surface deposit i.e., the anodic half-reaction becomes transport controlled. 

When macromolecular substrates are involved in the transformation under study, concentration polarization phenomena affect the EMR performance more severely. Diffusion limitations of macromolecular substrates hamper the use of immobilized enzymes in the hydrolysis of high-molecu-lar-weight substrates. By selecting membranes with an appropriate molecular weight cut-off, both enzyme and substrate are retained in an EMR in touch with each other, and hydrolysis products and/or inhibitors are continuously removed from the system. Soluble enzymes can then act directly on substrate macromolecules without diffusion limitations and steric hindrance imposed by enzyme fixation to a solid support. The stirring features of CST EMRs moreover assures that substrates and/or inhibitors within the reactor vessel are maintained at the lowest possible concentration level. Such reactor configuration is then extremely useful when substrate inhibited reaction patterns are involved, or when inhibiting species are assumed to exist in the feed stream. 

Coupled Effect of Concentration Polarization and Inhibition by Carbon Monoxide... 

In order to discuss on the separate effect of concentration polarization and inhibition by CO, the system shown in Figure 14.1 is considered. Referring to this sketch, three different zones can be identified ... 

Both forward and backward permeation are considered in order to analyze both cases where the membrane behaves as hydrogen purifier (forward permeation) or hydrogen supplier (backward permeation). The permeation process is considered to be divided into several elementary steps, each of which is characterized by its own model equations. The details of such a model can be found elsewhere where the model introduced in was modified in some steps to take into account the presence of an inhibitor species (CO). The same approach was followed by Catalano et al., who analyzed the inhibiting effect of CO without considering the concentration polarization. ... 

In the following sub-section, concentration polarization coefficient (CPC) and inhibition coefficient (IC) will be introduced separately in order to show their different contribution on the overall permeance reduction. 

Definition of Concentration Polarization Coefficient in the Presence of Inhibition... 

The definition of concentration polarization coefficient adopted in the previous section (eqns (14.8) to (14.10)) is general and, thus, can be conveniently applied to different situations. In particular, CPC can be also used in a situation in which permeation is affected by inhibition, as reported in eqn (14.13) in terms of both driving forces and permeances ... 

According to their definitions, CPC and IC provide quantitative measures of the flux decrease due to concentration polarization and inhibition, respectively. However, it is sometimes useful to have an indication of the overall flux... 

For this aim, an overall permeance reduction coelScient , PRCP was introduced, to take into account the permeation reduction owing to both concentration polarization and inhibition at the same time. Its definition, reported in eqn (14.19), arises from the simple consideration that the lowest permeance is evaluated at bulk conditions when both polarization and inhibition affect the membrane system, whereas, on the other hand, the ideal membrane behavior and the maximum permeance can be found under pure hydrogen conditions ... 

In this section, the analysis is focussed on the direct effect that inhibition by CO and concentration polarization have on hydrogen permeance and transmembrane flux. To do that, the operating conditions reported in Table 14.4 are considered.As shown in the table, two mixtures are considered to separate the CO contribution to concentration polarization and inhibition. 

According to its definition, the coefficient PRC is able to deal with the possible situations in which a membrane system affected by concentration polarization and inhibition can operate (Table 14.5). 

In Figure 14.4, all the three reduction coefficients are reported as functions of upstream CO partial pressure. The dashed line indicates the concentration polarization presence without considering the inhibition by CO. 

However, considering that the plateau value of IC indicates the maximum level after which the system cannot be affected by inhibition anymore, a method to quantify separately the effect of inhibition and polarization can be developed, even when only CO and H2 are present (mixture 2). In fact, the case represented by the second mixture clearly shows that it is theoretically impossible to reach the plateau value by performing only permeation tests, since after a certain level of CO the polarization begins to be appreciable. However, the polarization effect is progressively lower as higher membrane thicknesses are considered. Therefore, the equilibrium value can be estimated with good approximation and, thus, the difference between thin and thick membrane behavior can be attributed to concentration polarization. 

A novel result shown in this and in the previous figure is represented by the diiference between systems with and without inhibition i.e. with CO considered as inert). This last (virtual) case, shown at 1000 kPa only to evidence that inhibition and concentration polarization aifect each other, clearly demonstrates that in the presence of inhibiting species the polarization decreases because of a lower permeating flux. 

Finally, in order to observe quantitatively both the influence of concentration polarization and inhibition by CO, the behavior of the overall permeation reduction coeificient is shown in Figure 14.7, which represents a map analogous to the ones presented for CPC and IC. 

In this chapter, an innovative approach dealing with the combined effect of concentration polarization and inhibition by CO in Pd-based membranes is discussed and analyzed by means of appropriate coefficients measuring the permeation reduction due to these phenomena. 

According to their definition, these coefficients - namely, concentration polarization coefficient CPC), inhibition coefficient IC) and the overall... 

A remarkable result obtained from such an investigation consisted in the quantification of the mutual interactions between concentration polarization and inhibition, for which the non-additivity of the effects was shown in terms of their respective coefficients. In fact, it was mathematically demonstrated that the physical phenomenon according to which the concentration polarization in the presence of inhibition is less than in its absence due to a lower permeating flux. 

To ensure the inhibition of concentration polarization (keeping the dark electrode unpolarized), [F] must be twice as large as [B] ... 

Analysis of practical A, B, C photogalvanic cells has shown that the concentration of Y and Z (the inorganic iron couple) helps induce the required homogeneous kinetics [12, 23, 24]. The concentrations of the iron redox couple aid the prevention of concentration polarization at the dark electrode, while trapping A at the illuminated electrode ([Fe " )] and inhibiting destruction of B or C in the electrolyte ([Fe )]. 

Concentration polarization represents the energy losses associated with mass transport effects. For instance, the performance of an electrode reaction may be inhibited by the inability for reactants to diffuse to or products to diffuse away from the reaction site. In fact, at some current, the limiting current density a situation will be reached wherein the current will be completely limited by the diffusion processes (see Fig. 42.2). Concentration polarization can be represented by... 

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