Cathodic charge transfer coefficient

Here ia is the exchange current density of the electrode reaction based on the bulk concentration aa and ac are the anodic and cathodic charge transfer coefficients, respectively and y is a dimensionless kinetic parameter. 

P Cathodic charge-transfer coefficient 0(A) Quantity of the order of magnitude... 

Electrokinetic parameters [10] Ideal potential Anodic preexponential coefficient Cathodic preexponential coefficient Anodic activation energy Cathodic activation energy Anode charge transfer coefficient Cathode charge transfer coefficient 0.8961 V 1.6e9 3.9e9 120 J mol-1 120 J mol-1 0a = 2, 0C = 1 ea = 1.4, 0C = 0.6... 

Experimentally, it is often found that the anodic and cathodic charge transfer coefficients are about 1/2. This is typically the case for outer-sphere electron transfer. Values between zero and one are found for several more complex reactions. We now consider whether this behavior is reasonable in the framework of the phenomenological model presented here. In an outer-sphere process, the oxidized and reduced species are outside the electrochemical double layer. The chemical potential of these species is then not influenced by the electrode potential, and the following is valid ... 

Here, n is the number of transferred electrons ( > 0), S the surface area, the cathodic rate constant, a the cathodic charge-transfer coefficient, and Zj the charge valence of the reactant. This expression should be modified to take into account the adsorption energies of the reactant and the product if the ET takes place for a species inside the compact layer [11]. The value of the coordinate, z, which determines the lr potential is a priori unknown. In most studies it was postulated that the ET took place at the species located at the outer Helmholtz plane (the boundary between the compact and diffuse layers). Then, ijf coincides with the potential drop within the diffuse layer, (poc, Eq. (17). 

Again the second step (26) has the lower activation barrier and will predominate for not too small ng. In n-type specimen, the kinetics will give an exponential voltage dependence with a formal cathodic charge transfer coefficient of 1. 

Anodic preexponential coefficient Cathodic preexponential coefficient Anodic activation energy Cathodic activation energy Anode charge transfer coefficient Cathode charge transfer coefficient... 

Voltammetric data, obtained for TEG-containing solutions, were transformed according to Eq. (9.15). Linear parts of NTP are observed over a certain range of potentials (Figure 9.30), where the normalized current density decreases with TEG concentration. It follows from NTP slopes that the cathodic charge transfer coefficient is equal to 0.50 0.03 and 0.40 0.02 for chloride- and bromide-containing solutions, respectively. The respective inhibiting action of TEG persists up to —0.03 and —0.1 V. Afterward, the process accelerates and i values approach those typical of surfactant-free solutions. 

The parameters in Equations 12.10 through 12.14 are defined as follows. AG(, and AG are the standard-state free energy of activation for chemisorptions (J/mol) at the cathode and anode, respectively, and A is the active cell area (cm ). k° and are the intrinsic rate constants (cm/s) for the cathode and anode reaction, respectively, and Ch o respectively the concentration of hydrogen ion and water at the membrane gas interface on the cathode side of the cell, is called the cathodic charge transfer coefficient or chemical activity parameter. R is the gas constant. The ohmic overvoltage can be represented using Ohm s law as discussed in Chapter 7 as... 

Here, C, is the species concentration i" that refers to fuel or oxidant, and Pi is the reaction order of species for the elementary charge transfer step. Oa and are the anodic and cathodic charge transfer coefficients, R is the universal constant, and T is the operating temperature, f is the Faraday s constant and rj is the surface overpotential ... 

In this expression, i represents the electrode current density, Zq is the exchange current density, R is the gas constant, T is the temperature, the anode and cathode charge transfer coefficients are often related by -I- = 1, zz is the number... 

Simplified Butler-Volmer Equation 3 Butler-Volmer Equation with Identical Charge Transfer Coefficients-sinh Simplification A very nice simplification can be made to the BV model if the anodic and cathodic charge transfer coefficients at the electrode are equivalent (i.e., Uc = a a). In this case, no approximation is needed, and a new form explicit in r] and mathematically equivalent to the original BV model can be written. This model is valid over all regions of the electrode polarization, as shown in Figure 4.25. 

Example 4.12 Calculating Crossover Losses In ref. [9], the authors noted a hydrogen crossover loss of 3.3 mA/cm for their automotive H2 PEFC applications. Calculate the mass crossover rate of hydrogen through the membrane. Also, calculate and plot the cathode activation overpotential loss at open circuit and 1 A/cm as a function of cathodic exchange current density. Assume the cathodic charge transfer coefficient at the cathode is 1.5 at a temperature of 353 K, and the fuel cell has a 50 cm geometric area. 

A sinh simplification for the case where the anodic and cathodic charge transfer coefficients are equal ... 

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