Coefficients charge transfer

Figure 6.23. Effect of partial charge transfer coefficient XD on catalyst performance for fixed X.A depending on dimensionless potential n, (a) electrophobic, (b) electrophilic, (c) volcano-type, (d) inverted volcano-type.

Xa partial charge transfer coefficient of electron acceptor A... 

In addition to the thermodynamic quantity E°, the electrode reaction is characterized by two kinetic quantities the charge transfer coefficient a and the conditional rate constant k°. These quantities are often sufficient for a complete description of an electrode reaction, assuming that they are constant over the given potential range. Table 5.1 lists some examples of the constant k. If the constant k° is small, then the electrode reaction occurs only at potentials considerably removed from the standard potential. At these potential values practically only one of the pair of electrode reactions proceeds which is the case of an irreversible or one-way electrode reaction. 

Table 5.1 Conditional electrode reaction rate constants k° and charge transfer coefficients a. (From R. Tamamushi)... 

The charge transfer coefficient oc can be found from the dependence of j0 on C0x Or cRed-... 

Fig. 5.2 Dependence of the relative current density j/j0 on the overpotential rj according to Eq. (5.2.28). Various values of the charge transfer coefficient a are indicated at each curve. Dashed curves indicate the partial current densities (Eqs 5.2.11 and 5.2.12 for a = 0.5). (According to K. Vetter)...

The charge transfer reaction (5.2.39) is characterized by the formal electrode potential the conditional rate constant of the electrode reaction kf and the charge transfer coefficient aly while the reaction (5.2.40) is characterized by the analogous quantities E2y kf and a2. If the rate constants of the electrode reactions, which are functions of the potential, are denoted as in Eqs (5.2.39) and (5.2.40) and the concentrations of substances Au A2 and A3 are cly c2 and c3, respectively, then... 

If the single-electron mechanism has not been demonstrated to be the rate-controlling process by an independent method, then, in the publication of the experimental results, it is preferable to replace the assumed quantity ax by the conventional value cm, provided that the charge number of the overall reaction is known (e.g. in an overall two-electron reaction it is preferable to replace = 0.5 by or = 0.25). If the independence of the charge transfer coefficient on the potential has not been demonstrated for the given potential range, then it is useful to determine it for the given potential from the relation for a cathodic electrode reaction (cf. Eq. 5.2.37) ... 

A similar relationship is valid for the charge transfer coefficient of the anodic electrode reaction, aa. 

Parsons, R., Electrode reaction orders, charge transfer coefficients and rate constants. Extension of definitions and recommendations for publication of parameters. Pure Appl. Chem., 52, 233 (1979). 

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. 

We assume that neither the preexponential factor of the conditional electrode reaction rate constant nor the charge transfer coefficient changes markedly in a series of substituted derivatives and that the diffusion coefficients are approximately equal. In view of (5.2.52) and (5.2.53),... 

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. 

Anodic charge-transfer coefficient It Mobility of ionic species i... 

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

Schultze and Koppitz [3] assume that g is typically of the order of 0.1 [see Eq. (18.12)]. Using this value, estimate the partial charge-transfer coefficient of the ions in Table 18.1. 

The charge number, x i, of the adsorbed ions is not always the same as the ionic valence z of the hydrated ions the difference between z andz is called the charge transfer coefficient, f>z, in the contact adsorption of ions as identified in Eqn. 5-48 ... 

Since the electron transfer of the interfacial redox reaction, + cm = H.a> on electrodes takes place between the iimer Helmholtz plane (adsorption plane at distance d ) and the electrode metal, the ratio of adsorption coverages 0h,j/ in electron transfer equilibrium (hence, the charge transfer coefficient, 6z) is given in Eqn. 5-58 as a function of the potential vid /diOMn across the inner Helmholtz layer ... 

The same approach may also apply to the adsorption of redox particles other than the adsorption of proton-hydrogen atom on metal electrodes. To understand electrosorption phenomena, various concepts have been proposed such as the charge transfer coefficient and the adsorption valence [Vetter-Schultze, 1972]. The concept of the redox electron level in adsorbed particles introduced in this textbook is usefiil in dealing with the adsorption of partially ionized particles at electrodes. 

A 0f is the standard potential difference between phases a and p for this ion, kf is the standard rate constant for transfer of ion / and a is the charge-transfer coefficient. Concentrations c (a) and c (/3) correspond to the immediate vicinity of the phase boundary and are functions of the potential differences in the diffuse double layers according to the Boltzmann relationship... 

The charge transfer coefficient, a, was introduced by Erdey-Gruz and Volmer in 1930 as being the proportion of the overpotential assisting electron transfer in the... 

Ve - Vo) is the overpotential, the potential required to initiate reactions at the electrode surface, the difference between the equilibrium potential Vo (no current flowing) and operating potential Ve (current flowing). The above kinetics indicate that the rate of electron transfer from the n-type semiconductor to the redox system depends on the surface electron concentration, while electron injection from the redox system into the conduction band is constant independent of applied potential [11,76,77]. If the Helmholtz layer potential (pn varies across the interface the description of electron transfer becomes considerably more complicated requiring a charge transfer coefficient in equation (3.4.34). 

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