Tafel Slope and Exchange Current Density

Kinetic parameters other than the Tafel slopes and exchange current density already given have not been determined. 

Here, i is the measured current density, 4 is the kinetic current density, io is the diffusion limited current density, n is the number of electrons transferred per oxygen molecule, F is the Faraday constant (96485 C moF ), D is the diffusion coefficient of the molecular O2, Co is the concentration of molecular O2 in the electrolyte, v is the kinematic viscosity of electrolyte, and co is the angular rotation rate (rad s ). Plotting versus. yields n from the slope and 4 from the intercept on the 4 axis. The f obtained from the Koutecky-Levich plot can also be utilized to obtain the Tafel plot, logf versus E, to determine the Tafel slope and exchange current density (io). 

Once I-E curve is obtained, one can extract Tafel slope and exchange current density for HER. However, due to high surface area of practical catalysts, ESA has to be determined otherwise exchange current can be estimated erroneously. Described voltammetric methods (Section 3.1.2) are not used in this case, and usually impedance measurements are done at several cathodic overvoltages to determine double layer capacitance and to extract ESA [13]. Another possibility is to derive kinetic equation based on HER mechanism and to fit measured I-E curve into this equation to extract rate constant for each reaction step (see for example [78]). Comparison of catalyst performance is rather simple in this case. One can use extracted exchange current densities (normalized by ESA), but this is justified only is Tafel slopes are identical. 

Figure 3. Mixed potential diagram illustrating controls on the kinetics of corrosion at a pitted, oxide-covered metal. The potential range is from -700 to +300 mV/NHE. Arrows (B) corrosion current at the bottom of the pit, controlled by Fe Fe + (acid) and 2H - H2 (M) corrosion current at the mouth of the pit, controlled by the partial currents for Fe -> Fe2+ (passivated) and RX RH (Pit) corrosion current for the short-circuited pit, controlled by Fe Fe + (acid) and RX - RH. The three solid curves are generated using the Tafel equation and exchange current densities and Tafel slopes from reference (9). The dashed curve was measured at 5 mV s in pH 8.4 borate buffer, using methods described in reference (9).

Figure 83 Different combinations of partial current potential diagrams to explain anomalous codeposition with preferential deposition of the less noble component in the gray areas the less noble component is preferentially deposited, (a) A and B kinetically controlled, different Tafel slopes, similar exchange current densities, (b) A and B kinetically controlled, different Tafel slopes and different exchange current densities (i q > Jq ), (c) A kinetically controlled, B diffusion controlled, different exchange current densities (Iq > Jq ), (d) A diffusion controlled, B kinetically controlled, similar exchange current densities. (Reproduaxl with permission from Ref. [6], 1994, Elsevier.)...

From Eqs. (1222) and (12.23), it is clear that the corrosion current depends upon the exchange currents (i.e., available areas and exchange-current densities), Tafel slopes, and equilibrium potentials for both the metal-dissolution and electronation reactions. To obtain an explicit expression for the corrosion current [cf. Eq. (12.22)], one has first to solve Eqs. (12.22) and (12.23) for A0corr. If, however, simplifying assumptions are not made, the algebra becomes unwieldy and leads to highly cumbersome equations. 

Nonplatinum tungsten carbides have also been investigated for electrocatalytic ethanol oxidation. Pd/W2C-C and Pd/W2C-MWCNT (MW = multiwall) were tested in a half cell mode with 1 mol dm KOH and 1 mol dm ethanol, with Hg/HgO (1.0 mol dm KOH) reference electrode under various temperatures (61). Pd/WC-C and PdTWC-MWCNT electrocatalysts exhibited higher specific activities (mA/cm ), Tafel slope (mV/dec), and exchange current density (A/cm ) than Pd/C, Pd/MWCNT for ethanol oxidation. Especially, the WC-containing... 

The exchange current density is mainly reported on Pt and Pt alloys catalysts. As there are two Tafel regions, two exchange current densities have been reported. The extrapolation from the lower slope gave the value close to 10 A cm and from the higher, the value close to 10 A cm. On the other catalysts the exchange current density has occasionally been determined and their values vary on the catalysts, as well as, on the research method. 

The sohd line in Figure 3 represents the potential vs the measured (or the appHed) current density. Measured or appHed current is the current actually measured in an external circuit ie, the amount of external current that must be appHed to the electrode in order to move the potential to each desired point. The corrosion potential and corrosion current density can also be deterrnined from the potential vs measured current behavior, which is referred to as polarization curve rather than an Evans diagram, by extrapolation of either or both the anodic or cathodic portion of the curve. This latter procedure does not require specific knowledge of the equiHbrium potentials, exchange current densities, and Tafel slope values of the specific reactions involved. Thus Evans diagrams, constmcted from information contained in the Hterature, and polarization curves, generated by experimentation, can be used to predict and analyze uniform and other forms of corrosion. Further treatment of these subjects can be found elsewhere (1—3,6,18). 

Turning now to the acidic situation, a report on the electrochemical behaviour of platinum exposed to 0-1m sodium bicarbonate containing oxygen up to 3970 kPa and at temperatures of 162 and 238°C is available. Anodic and cathodic polarisation curves and Tafel slopes are presented whilst limiting current densities, exchange current densities and reversible electrode potentials are tabulated. In weak acid and neutral solutions containing chloride ions, the passivity of platinum is always associated with the presence of adsorbed oxygen or oxide layer on the surface In concentrated hydrochloric acid solutions, the possible retardation of dissolution is more likely because of an adsorbed layer of atomic chlorine ... 

The method permits the simultaneous determination of reaction order, m, and reaction rate constant, k, from the slope and the intercept of the straight line. The procedure can be repeated for various potential values below the limiting current plateau to yield k as a function of electrode potential. The exchange current density and the Tafel slope of the electrode reaction can be then evaluated from the k vs. potential curves. 

FTIR revealed that the modification with nickel altered the polymer bonds creating Ni-AN (for Pani and Ppy-based catalysts) and Ni-AS bonds (for P3MT -based catalysts), while TGA showed that the incorporation of nickel improved the thermal stability of the catalysts at high temperatures (above 400 °C). The Tafel slopes were very similar for all catalysts tested (-0.11-0.2) however, Ppy-C-Ni had the highest exchange current density ( 4 10 5 mAcm 2j followed by P3MT-C-Ni and Ppy-C ( 3.5 10 5 and 2.5 10 5 mAcm 2 respectively). Based on these results, it was concluded that Ppy-C-Ni was the most suitable catalyst for ORR in acidic medium [222],... 

The most important electrokinetic data pertinent to fuel cell models are the specific interfacial area in the catalyst layer, a, the exchange current density of the oxygen reduction reaction (ORR), io, and Tafel slope of ORR. The specific interfacial area is proportional to the catalyst loading and inversely proportional to the catalyst layer thickness. It is also a strong function of the catalyst layer fabrication methods and procedures. The exchange current density and Tafel slope of ORR have been well documented in refs 28—31. 

Figure 5. Measurement and analysis of steady-state i— V characteristics, (a) Following subtraction of ohmic losses (determined from impedance or current-interrupt measurements), the electrode overpotential rj is plotted vs ln(i). For systems governed by classic electrochemical kinetics, the slope at high overpotential yields anodic and cathodic transfer coefficients (Ua and aj while the intercept yields the exchange current density (i o). These parameters can be used in an empirical rate expression for the kinetics (Butler—Volmer equation) or related to more specific parameters associated with individual reaction steps.(b) Example of Mn(IV) reduction to Mn(III) at a Pt electrode in 7.5 M H2SO4 solution at 25 Below limiting current the system obeys Tafel kinetics with Ua 1/4. Data are from ref 363. (Reprinted with permission from ref 362. Copyright 2001 John Wiley Sons.)...

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