KINETICS OF CONCENTRATION POLARIZATION

B.B. Gupta, P. Blanpain and M.Y. Jaffrin, Permeate flux enhancement by pressure and flow pulsations in microfiltration with mineral membranes. /. Membr. Sci., 70 (1992) 257. M.Y. Jaffrin, L.H. Ding and J.M. Laurent, Kinetics of concentration polarization formation in crossflow filtration of plasma from blood experimental results. /. Membr. Sci., 72 (1992) 267. 

Transient measnrements (relaxation measurements) are made before transitory processes have ended, hence the current in the system consists of faradaic and non-faradaic components. Such measurements are made to determine the kinetic parameters of fast electrochemical reactions (by measuring the kinetic currents under conditions when the contribution of concentration polarization still is small) and also to determine the properties of electrode surfaces, in particular the EDL capacitance (by measuring the nonfaradaic current). In 1940, A. N. Frumkin, B. V. Ershler, and P. I. Dolin were the first to use a relaxation method for the study of fast kinetics when they used impedance measurements to study the kinetics of the hydrogen discharge on a platinum electrode. 

The discussion of concentration polarization so far has centred on the depletion of electroactive material on the electrolyte side of the interface. If the metal deposition and dissolution processes involve metastable active surface atoms, then the rate of formation or disappearance of these may be the critical factor in the overall electrode kinetics. Equation (2.69) can be rewritten for crystallization overvoltage as... 

While an ovapotential may be applied electrically, we are interested in the overpotential that is reached via chemical equilibrium with a second reaction. As mentioned previously, the oxidation of a metal requires a corresponding reduction reaction. As shown in Figure 4.34, both copper oxidation, and the corresponding reduction reaction may be plotted on the same scale to determine the chemical equilibrium between the two reactions. The intersection of the two curves in Figure 4.34 gives the mixed potential and the corrosion current. The intersection point depends upon several factors including (the reversible potential of the cathodic reaction), cu2+/cu> Tafel slopes and of each reaction, and whether the reactions are controlled by Tafel kinetics or concentration polarization. In addition, other reduction and oxidation reactions may occur simultaneously which will influence the mixed potential. 

Both kinetic and concentration polarization cause the potential of an electrode to be more negative than the thermodynamic value. Concentration polarization results from the slow rate at which reactants or products are transported to or away from the electrode surfaces. Kinetic polarization arises from the slow rate of the electrochemical reactions at the electrode surfaces. 

CST reactors have been more widely adopted, partly due to the possibility of concentration polarization control, and partly due to the easy modeling of enzyme kinetic behavior. In the literature, comprehensive mathematical descriptions of the kinetic behavior of enzymes located in CSTR UF units are reported 9 1-0 as far as low-molecular-weight substrates are concerned. 

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 )]. 

Using the method shown in Example 22-6, the thermodynamic potential for this cell can be shown to be 0.94 V. Thus, we expect no current at less-negatrve applied potentials at greater potentials, a linear increase in current should be observed in the absence of kinetic or concentration polarization. When a potential of about -2.5 V is applied to the cell, the initial current is about 1.5 A, as shown in Figure 24-la. The electrolytic deposition of copper is then completed at this applied potential... 

Example 5.3 Ohmic Losses in SOFC as a Function of Electrolyte Thickness Plot an ohmic-only polarization curve for a SOFC with (Zr02)o.92(Y203)o,o8 electrolyte at 1000°C for a 50-, 100-, and 300- xm-thick electrolyte and an OCV of0.997 V. That is, ignore kinetic and concentration polarization losses. Assume neat hydrogen and air at 1 atm back pressure is used. 

The kinetic equations describing the joint effects of activation and concentration polarization are very complex and we shall consider only the the case of a simple first-order reaction of the type (6.2) proceeding in the presence in the solntion of an excess of a foreign electrolyte. To simplify the appearance of these equations (which even in this case are very cnmbersome), in this section we use a more compact notation that contains two new kinetic parameters ... 

The current is recorded as a function of time. Since the potential also varies with time, the results are usually reported as the potential dependence of current, or plots of i vs. E (Fig.12.7), hence the name voltammetry. Curve 1 in Fig. 12.7 shows schematically the polarization curve recorded for an electrochemical reaction under steady-state conditions, and curve 2 shows the corresponding kinetic current 4 (the current in the absence of concentration changes). Unless the potential scan rate v is very low, there is no time for attainment of the steady state, and the reactant surface concentration will be higher than it would be in the steady state. For this reason the... 

Consider the case when the equilibrium concentration of substance Red, and hence its limiting CD due to diffusion from the bulk solution, is low. In this case the reactant species Red can be supplied to the reaction zone only as a result of the chemical step. When the electrochemical step is sufficiently fast and activation polarization is low, the overall behavior of the reaction will be determined precisely by the special features of the chemical step concentration polarization will be observed for the reaction at the electrode, not because of slow diffusion of the substance but because of a slow chemical step. We shall assume that the concentrations of substance A and of the reaction components are high enough so that they will remain practically unchanged when the chemical reaction proceeds. We shall assume, moreover, that reaction (13.37) follows first-order kinetics with respect to Red and A. We shall write Cg for the equilibrium (bulk) concentration of substance Red, and we shall write Cg and c for the surface concentration and the instantaneous concentration (to simplify the equations, we shall not use the subscript red ). 

At mercury and graphite electrodes the kinetics of reactions (15.21) and (15.22) can be studied separately (in different regions of potential). It follows from the experimental data (Fig. 15.6) that in acidic solutions the slope b 0.12 V. The reaction rate is proportional to the oxygen partial pressure (its solution concentration). At a given current density the electrode potential is independent of solution pH because of the shift of equilibrium potential, the electrode s polarization decreases by 0.06 V when the pH is raised by a unit. These data indicate that the rate-determining step is addition of the first electron to the oxygen molecule ... 

For isolating the overpotential of the working electrode, it is common practice to admit hydrogen to the counter-electrode (the anode in a PEMFC the cathode in a direct methanol fuel cell, DMFC) and create a so-called dynamic reference electrode. Furthermore, the overpotential comprises losses associated with sluggish electrochemical kinetics, as well as a concentration polarization related to hindered mass transport ... 

Although the improved extraction kinetics also increase the concentration of coextractives in the final extract, some degree of selectivity can be achieved by careful selection of the solvent or solvents used. Matrix co-extractives may be removed, or at least partially removed, by placing a suitable sorbent, such as alumina, at the exit of the extraction cell to remove lipid co-extractives. Excellent recoveries of both polar and nonpolar pesticides from a wide range of foodstuffs have been reported. Specific applications include organophosphorus and A-methylcarbamate pesticides. 

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