Concentration polarization limit values

Further, as the current density of the fuel cell increases, a point is inevitably reached where the transport of reactants to or products from the surface of the electrode becomes limited by diffusion. A concentration polarization is estabhshed at the elec trode, which diminishes the cell operating potential. The magnitude of this effect depends on many design and operating variables, and its value must be obtained empirically. 

The transmembrane potential derived from a concentration gradient is calculable by means of the Nemst equation. If K+ were the only permeable ion then the membrane potential would be given by Eq. 1. With an ion activity (concentration) gradient for K+ of 10 1 from one side to the other of the membrane at 20 °C, the membrane potential that develops on addition of Valinomycin approaches a limiting value of 58 mV87). This is what is calculated from Eq. 1 and indicates that cation over anion selectivity is essentially total. As the conformation of Valinomycin in nonpolar solvents in the absence of cation is similar to that of the cation complex 105), it is quite understandable that anions have no location for interaction. One could with the Valinomycin structure construct a conformation in which a polar core were formed with six peptide N—H moieties directed inward in place of the C—O moieties but... 

The polarization equation describes polarization as a fnnction of current density. In the case of concentration polarization, the form of the polarization eqnation is nnre-lated to the natnre of reaction or electrode. In the case of activation polarization, the parameters of the polarization eqnations depend decisively on the natnre of the reaction. At identical values of current density and otherwise identical conditions, the values of polarization for different reactions will vary within wide limits, from less than 1 mV to more than 2 or 3 V. However, these equations still have common features. A relatively simple set of equations is obtained for simple redox reactions of the type... 

Curve 1 of Fig. 6.4a shows a plot of CD against AE which corresponds to Eq. (6.42) with n = 2. At zero polarization the current is zero. Under anodic polarization the current tends toward its limiting value We can see from Fig. 6.4b that the surface concentration then falls to zero, while the value of increases to [cf. (4.15)]. Under cathodic polarization, similarly, the current tends toward a limiting value of the surface concentration of Ox falls to zero, and the surface concentration of Red increases to + (Rox/ ed)< v,ox-... 

Eigures 6.7 and 6.8 show polarization curves that correspond to the eqnations obtained in the particnlar case where a = P = 0.5 (n = 1) and 4,red id,ox (since and Kq, have similar values, this implies that — Curve 1 of Fig. 6.7 shows the case of pure concentration polarization (i° has a very large valne) the other curves show the influence of decreasing exchange CD (decreasing reaction rate constants), which is revealed at constant valnes of the limiting-cnrrent densities. 

The additional potential required to maintain a current flowing in a cell when the concentration of the electroactive species at the electrode surface is less than that in the bulk solution. In extreme cases, the cell current reaches a limiting value determined by the rate of transport of the electroactive species to the electrode surface from the bulk solution. The current is then independent of cell potential and the electrode or cell is said to be completely polarized. Concentration overpotential decreases with stirring and with increasing electrode area, temperature and ionic strength. 

Zone III the E vs ln(l — j/ji ) logarithmic curve corresponds to concentration polarization, which results from the limiting value ji of the mass transfer limiting current density for the reactive species and reaction products to and/or from the electrode active sites an increase inji from 1.4 to 2.2 Acm leads to a further... 

We saw previously that concentration polarization results in the decrease of solute concentration near the permselective interface (right at the interface in the electro-neutral version) where most of the system s resistance thus concentrates, and where the space charge develops. The system is expected to be sensitive to the minimum concentration value, and because of nonlinearity nontrivial effects, could be anticipated in response to unsteady disturbances of this value (e.g., provided by harmonic modulation superimposed upon a constant voltage applied to the system). Since it is easier to increase the minimal concentration (close to zero at the limiting current) than to decrease it, we might expect a positive rectification effect for the direct current component, counterintuitive ( anomalous ) in the present system with a convex stationary VC curve. Thus the topic of this section is the rectification effects that arise in the stationary concentration polarization in response to a harmonic voltage modulation. 

For components rejected by the membrane (Ea < 1) the enrichment Ea produced by the membrane lies between 1 and 0. The concentration polarization modulus Cijcib then lies between 1 (no concentration polarization) and a maximum value of 2.72. That is, the flux of the less permeable component cannot be more than 2.72 times higher than that in the absence of concentration polarization. In contrast, for a component enriched by the membrane in the permeate (Ea > 1), no such limitation on the magnitude of concentration polarization exists. For dilute solutions (cib small) and selective membranes, the intrinsic enrichment can be 100 to 1000 or more. The concentration polarization modulus can then change from 1 (no concentration polarization) to close to zero (complete concentration polarization). These two cases are illustrated in Figure 4.8. 

A fluorophore free in solution can have a low polarization value, whereas when it is bound to a macromolecule, its polarization increases. The polarization unit is a dimensionless entity, i.e., the value of P does not depend on the intensity of emitted light and the fluorophore concentration. However, this is the theory the reality is quite different. In fact, measuring polarization at high fluorophore concentrations yields erroneous values, and in many cases, instead of reading the correct values of P and A, values that neighbor the limiting values are recorded. 

As the current flow increases, the smaller is the (Cu)s value and the larger is the polarization this is known as concentration polarization. When [Cu]s approaches zero, the current density is known as the limiting current density. 

For other values of Ka other expressions are obtained. For Du = 1, reduces to -ErcosO, l.e. only the applied field remains. For Du = 0 a more negative value for is predicted, as expected. In the extreme case of Du = the double layer conducts so well that no concentration polarization can be created In that limit V (r = a) becomes independent of 0. Expression ]3.13.4] may also be formally formulated in terms of the Induced dipole moment... 

It was established by Yeliseyeva and Bakaeva (1968) that in the polymerization of polar monomers (MA) the decrease of emulsifier adsorption depends on tbe structure of the latter and for some types of emulsifiers may reach limiting values. This was observed in tbe polymerization ofMA in the presence of a mixed type of emulsifier, partially sulfurated with sulfuric acid oxyethylated alkylphenol (emulsifier C-I0 ). Its adsorption on the particle surface increases with the initial concentration and reaches > 100% filling of the adsorption layer, conditionally corresponding to 0.3S nm per molecule. Stable, concentrated latexes with small particles are formed. Therefore, emulsifier adsorption and the mechanism ctf particle formation associated with it depends not only on monomer polarity but also on the chemical structure of the emulsifier. 

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