Kinetics concentration polarization

The concentration polarization is a result of decreasing surface concentration of reactant. The restriction can be a result of gas-phase transport limits, impurity absorption at the catalyst surface, liquid blockage in low-temperature fuel cells, or other reasons. The thermodynamic (Nernst) and kinetic concentration polarization at an electrode can be written as... 

Equations for concentration polarization are often used in conjunction with the diffusion and kinetic equations hence, it will be more convenient here to use concentrations rather than activities.)... 

The kinetic and polarization equations described in Sections 6.1 and 6.2 have been derived under the assumption that the component concentrations do not change during the reaction. Therefore, the current density appearing in these equations is the kinetic current density 4. Similarly, the current density appearing in the equations of Section 6.3 is the diffusion current density When the two types of polarization are effective simultaneously, the real current density i (Fig. 6.6, curve 3) will be smaller than current densities and ij (Fig. 6.6, curves 1 and 2) for a given value of polarization. 

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 ... 

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. 

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 ). 

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 ... 

Figure 7. (A, top) Simple battery circuit diagram, where Cdl represents the capacitance of the electrical double layer at the electrode—solution interface (cf. discussion of supercapacitors below), W depicts the Warburg impedance for diffusion processes, Rj is the internal resistance, and Zanode and Zcathode are the impedances of the electrode reactions. These are sometimes represented as a series resistance capacitance network with values derived from the Argand diagram. This reaction capacitance can be 10 times the size of the double-layer capacitance. The reaction resistance component of Z is related to the exchange current for the kinetics of the reaction. (B, bottom) Corresponding Argand diagram of the behavior of impedance with frequency, f, for an idealized battery system, where the characteristic behaviors of ohmic, activation, and diffusion or concentration polarizations are depicted.

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... 

In deriving eqn. (80), limitations due to mass transport at the interface were not considered. Strictly speaking, this is not realistic and as the reaction rate increases with overpotential in each direction a variation of the concentrations of reactant and product at the surface operates and concentration polarization becomes more important. Each exponential expression in eqn. (80) must be multiplied by the ratio of surface to bulk concentrations, ci s/ci b. The effect of mass transfer in electrode kinetics has been discussed in Sect. 2.4. 

Kinetic factors may induce a variation of electrode potential with current the difference between this potential and the thermodynamic equilibrium potential is known as the overvoltage and the electrode is said to be polarized. In a plating bath this change of potential can be attributed to the reduced concentration of depositing ions in the double layer which reduces the rate of transfer to the electrode, but the dissolution rate from the metal increases. Since the balance of these rates determines the electrode potential, a negative shift in the value occurs the concentration polarization Olconc)- Anodic effects are similar but in the opposite direction. 

The pressure-driven membrane processes can be operated at fixed pressure (FP) or fixed flux (FF), and FP tends to be lab and small scale and FF is large-scale commercial. Fouling for FP shows as a flux decline and for FF as TMP rise (Figure 6.1(b)). The fouling kinetics differ since FP becomes self-limiting as flux-driven fouling slows down, whereas for FF it is self-accelerating as foulants steadily accumulate and concentration polarization accelerates. These differences mean that extrapolation of FP trends to FF requires caution. 

Several reports have shown that the kinetics of P-gp transport activity can be sufficiently described by one-site Michaelis-Menten saturable kinetics (199-206). Where JP.g ) is the flux mediated by P-gp transport activity,, /max is the maximal flux mediated by P-gp transport activity, Km is the Michaelis-Menten constant, and Ct is the concentration of substrate present at the target (binding) site of P-gp. When donor concentration is used in place of Ct, apparent Km and Jmax values are obtained. Binding affinity of the substrate to P-gp and the catalytic (ATPase) activity of P-gp combine to determine Km, and, /max is determined by the catalytic (ATPase) activity of P-gp and the expression of P-gp in the system (concentration of P-gp protein). It has recently been noted that since substrates must first partition or cross the membrane to access the binding site, accurate assessing of P-gp kinetics can be difficult (207). Furthermore, the requirement of first partitioning into the membrane has been shown to produce asymmetric apparent kinetics in polarized cells where AP and BL membrane compositions may be sufficiently different (206). 

Figure 3.3.7 Theoretical (dashed dotted) and real (solid) cell voltage (V) - current density (I) performance characteristics of a fuel cell. Overpotentials are responsible for the difference between theoretical and real performance and cause efficiency losses. They split into (i) activation polarization overpotentials at anode and cathode due to slow chemical kinetics, (ii) ohmic polarization overpotential due to ohmic voltage losses along the circuit, and (iii) concentration polarization overpotentials due to mass-transport limitations. The activation overpotentials of the cathode are typically the largest contribution to the total overvoltage.

Figures 3.84 and 3.85 do not yet suffice to give the electric field at any position in the double layer. On closer Inspection, three fields have to be considered the applied field. Just discussed, the field of the double layer and the polarization field caused by the concentration polarization. The applied field, characterized by parallel field lines far from the particle, is in most electro-kinetic experiments 0(10 V m ), that of the double layer is, at least for an unpolarized system, radially directed and decays from 0(10 V m" ) close to the surface to zero for distance r — The magnitude and extension of the...

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. 

At the high current densities suggested by Figure 4.44b, titanium dissolution and copper oxidation may be controlled by concentration polarization rather than Tafel kinetics. Under concentration polarization, the current does not increase proportional to... 

Yeliseyeva et ai. (1976) studied the polymerization kinetics of polar acrylic monomers using ethyl acrylate. The dependence of the polymerization rate on the initiator concentration (ammonium persulfate) was examined at equal ionic strength in the presence of two emulsifiers, sodium dodecylsuDate and oxyethylaled (30) cetyl alcohol- Polymerization was carried out hi a dilatometer at 4S C, monomer-water phase ratio 1 9, and ammonium persulfate concentration 0.44-4.4 x 10 mol/dm. The obtained loagrithinic dependence is shown in Fig. 16. In each cases the... 

Takeuchi et al. 7 reported a membrane reactor as a reaction system that provides higher productivity and lower separation cost in chemical reaction processes. In this paper, packed bed catalytic membrane reactor with palladium membrane for SMR reaction has been discussed. The numerical model consists of a full set of partial differential equations derived from conservation of mass, momentum, heat, and chemical species, respectively, with chemical kinetics and appropriate boundary conditions for the problem. The solution of this system was obtained by computational fluid dynamics (CFD). To perform CFD calculations, a commercial solver FLUENT has been used, and the selective permeation through the membrane has been modeled by user-defined functions. The CFD simulation results exhibited the flow distribution in the reactor by inserting a membrane protection tube, in addition to the temperature and concentration distribution in the axial and radial directions in the reactor, as reported in the membrane reactor numerical simulation. On the basis of the simulation results, effects of the flow distribution, concentration polarization, and mass transfer in the packed bed have been evaluated to design a membrane reactor system. 

Polarization is an electrode phenomenon that may affect either or both of the electrodes in a cell. The degree of polarization of an electrode varies widely. In some instances, it approaches zero, but in others it can be so large that the cutrent in the cell becomes independent of potential. Under this circumstance, polarization is said to be complete. Polarization phenomena can be divided into two categories concentration polarization and kinetic polarization. 

How do concentration polarization and kinetic polarization resemble one another How do they differ ... 

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. 

Polarization (1) In an electrochemical cell, a phenomenon in which the magnitude of the current is limited by the low rate of the electrode reactions (kinetic polarization) or the slowness of transport of reactants to the electrode surface (concentration polarization). (2) The process of causing electromagnetic radiation to vibrate in a definite pattern. 

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. 

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