Electrode polarization mass transfer

The constants characterizing the electrode reaction can be found from this type of polarization curve in the following manner. The quantity k"e is determined directly from the half-wave potential value (Eq. 5.4.27) if E0r is known and the mass transfer coefficient kQx is determined from the limiting current density (Eq. 5.4.20). The charge transfer coefficient oc is determined from the slope of the dependence of In [(yd —/)//] on E. 

The results reviewed above suggest that gas-phase diffusion can contribute significantly to polarization as O2 concentrations as high as a few percent and are not necessarily identifiable as a separate feature in the impedance. Workers studying the P02 -dependence of the electrode kinetics are therefore urged to eliminate as much external mass-transfer resistance in their experiments as possible and verify experimentally (using variations in balance gas or total pressure) that gas-phase effects are not obscuring their results. 

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... 

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. 

Manipulation of the mass transfer resistances is another possibility. Let us assume that the analyte is an electrically neutral species, but the major interferant is charged. By placing an ion-exchange membrane with immobile charge of opposite polarity to that of the interferant in front of the electrode, the access of the charged interferant becomes blocked by the electrostatic repulsion. These selectivity design strategies can be summarized in a statement that applies also to other life situations. In amperometric sensors, the information is obtained from the current path of least resistance. 

Under working conditions, with a current density j, the cell voltage E(J) decreases greatly as the result of three limiting factors the overvoltages r a and r c at both electrodes due to a rather low reaction rate of the electrochemical processes (activation polarization), the ohmic drop RJ in the electrolyte and interface resistance Re, and mass transfer limitations for reactants and products (concentration polarization). 

The standard potentials are valid at "zero current"—that is, before any electrons are ever moved. In practical cells and when finite currents are passed, the cell potentials are affected by the finite resistance R of the electrolyte, which causes an "IR drop" across the cell, and also by "overpotentials," due to polarizations of the solution caused by (i) a finite mass transfer rate, (ii) a preceding reaction, or (iii) charge-transfer. If the "IR drop" is less than 0.002 V, then two-electrode cells are adequate for reproducible measurements (e.g., in polarography). 

An ideal unpolarized cell would have R = 0 and infinite current an ideal polarized cell would have a fixed R independent of and thus a constant current. Reality is somewhere in between There are several sources of "polarization" that can be considered as finite contributions to the overall resistance R > 0 (or better, the impedance Z). The IR drop, from whatever source, is also called the overpotential t] (i.e., IR > 0), which always decreases the overall E remember that R is always a function of time and E. The causes of polarization are (1) diffusion-limited mass transfer of ions from bulk to electrode (2) chemical side reactions (if any), and (3) slow electron transfer at the electrode between the adsorbed species to be oxidized and the adsorbed species to be reduced. 

In the polarization curve, three parts can be observed kinetic, ohmic, and mass transfer. In the kinetic part, the cell voltage drop is due to the charge-transfer kinetics, i.e., the 02 reduction and H2 oxidation rate at the electrode surface, which is dominated by the kinetic I-rj equation (Equation 1.37). In the ohmic part, the cell voltage drop is mainly due to the internal resistance of the fuel cell, including electrolyte membrane resistance, catalyst layer resistance, and contact resistance. In the mass transfer part, the voltage drop is due to the transfer speed of H2 and 02 to the electrode surface. 

Ahn et al. have developed fibre-based composite electrode structures suitable for oxygen reduction in fuel cell cathodes (containing high electrochemically active surface areas and high void volumes) [22], The impedance data obtained at -450 mV (vs. SCE), in the linear region of the polarization curves, are shown in Figure 6.22. Ohmic, kinetic, and mass transfer resistances were determined by fitting the impedance spectra with an appropriate equivalent circuit model. 

Compared with a Teflon -bonded commercial electrode, the composite electrode showed lower polarization losses at high current densities, even though the composite material did not contain Pt. The ohmic and mass transfer resistances were lower in the composite electrode than in the commercial electrode. The sintered contacts and interlocked networks formed in the composite structure permitted better electrical and physical contact between the carbon fibres and metal fibres, leading to a composite electrode with a high void volume and large macroscopic porosity, which increased the accessibility of carbon to the reactants [22],... 

M. Eisenberg, C. W. Tobias, and C. R. Wilke, "Ionic Mass Transfer and Concentration Polarization at Rotating Electrodes," Journal of The Electrochemical Society, 101 (1954) 306-319. 

Chemical reactions can happen before or after the charge-transfer step. Any step can be rate determining, that is, the slowest one determines the total reaction rate. As the electrode polarizes, the resulting overpotential consists of several factors. The most important ones are activation, concentration, and resistance overpotentials. The activation overpotential results from the limited rate of a charge-transfer step, concentration overpotential from the mass-transfer step, and resistance overpotential is the result of ohmic resistances such as solution resistance. Depending on the nature of the slowest step, the reaction is activation, mass transfer, or resistance controlled. 

The thickness distribution of electrodeposits depends on the current distribution over the cathode, which determines the local current density on the surface. The current distribution is determined by the geometrical characteristics of the electrodes and the cell, the polarization at the electrode surface, and the mass transfer in the electrolyte. The primary current distribution depends only on the current and resistance of the electrolyte on the path from anode to cathode. The reaction overpotential (activation overpotential) and the concentration overpotential (diffusion overpotential) are neglected. The secondary... 

The reactions (20) to (22) form the copper equilibrium on the electrode surfaces. Concentration of Cu(I) on the cathode surface affects the deposition rate. The maximum net rate of Cu+ production is at about —50 mV versus Cu/CuSC>4 and at higher overpotentials it decreases. Disturbing the Cu(II)—Cu(I)—Cu equilibrium can cause the formation of copper powder, but this is more a problem on the anode. For the current densities commonly used in electrorefining, the cathode overpotential is between 50 and 100 mV. The system is mainly charge transfer controlled and the effect of mass-transfer polarization is small. If Cu(I) concentration on the cathode surface decreases, mass-transfer polarization will increase, causing more uneven deposit. 

Equation (A.2.5) indicates that the establishment of the Nemstian concentrations (0 at the electrode requires that mass transfer of analyte to and from the electrode be controlled and limited by diffusion due to a concentration difference only, called complete concentration polarization. Once the analyte reaches the electrode surface, the rate of electron transfer must be rapid (i.e., mass transfer not electron transfer limits the rate of... 

Concentration polarization occurs because of the finite rate of mass transfer from the solution to the electrode surface. Electron transfer between a reactive species in a solution and an electrode can take place only from the interfacial region located immediately adjacent to the surface of the electrode this region is only a fraction of a nanometer in thickness and contains a limited number of reactive ions or molecules. For there to be a steady current in a cell, the interfacial region must be continuously replenished with reactant from the bulk of the solution. That is, as... 

Voltammetry is based on the measurement of current in an electrochemical cell under conditions of complete concentration polarization in which the rate of oxidation or reduction of the analyte is limited by the rate of mass transfer of the analyte to the electrode surface. Voltammetry differs from electrogravimetry and coidometry in that in the latter tw o methods, measures are taken to minimize or compensate for the effects of concentration polarization. Furthermore, in voltammetry a minimal consumption of analyte takes place, whereas in electrogravimetry and coidometry essentially all of the analyte is converted to product. 

The polarization curve for silver electrodeposition from nitrate solution, 0.5 M AgN03 in 0.2M HNO3, onto a graphite electrode is shown in Fig. 15. As shown earlier,7 the polarization curves for silver deposition from nitrate solution onto a graphite electrode and on graphite covered with a nonporous surface film of silver (hence, on a massive silver electrode) are practically the same. The polarization curve in Fig. 15 is very similar to that in Fig. 7, which means that mass-transfer limitations were decreased or even eliminated. The SEM photomicrographs of the deposit corresponding to the points from Fig. 15 are shown in Fig. 16. 

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