Charge transfer coefficient adsorption

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. 

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). 

It is evident that m + 2 = 1- The quantities ni and H2 are called the formal (thermodynamic, macroscopic) charge-transfer coefficients. In the case of adsorption of Ox, the process may stop at stage (52), and, in the case of adsorption of Red, it may stop at stage (53). It can be shown [57] that the formal charge-transfer coefficients are determined by the relationships ... 

With the activation energies the following rate equations can be derived. For adsorption (a cathodic process with the charge transfer coefficient aj... 

V. Marecek, Z. Samec, and J. Weber, The Dependence of the Electrochemical Charge-Transfer Coefficient on the Electrode Potential. Study of the Hexacyanoferrate (III) Hexacyanferrate (IV) Redox Reaction on Polycrystalline Gold Electrode in Potassium Fluoride Solutions, J. Electroanal. Chem. Interfacial Electrochem. 94, 169-185 (1978) cf. also J. Weber, Z. Samec, and V. Marecek, The Effect of Anion Adsorption on the Kinetics of the Iron (3 + )/Iron (2. ) Reaction on Platinum and Gold Electrodes in Perchloric Acid, J. Electroanal. Chem. Interfacial Electrochem. 89, 271-288 (1978). 

Here X is the partial charge-transfer coefficient, namely, the fraction of electron charge transferred from a sulfur atom to the mercury upon adsorption, and a is the degree of dissociation of the sulfhydryl group. Since partial electron transfer from the sulfhydryl groups and their deprotonation are strictly correlated events, a and X are expected to assume close values. The Hg notation is merely used to denote chemisorption of the RSH thiol on Hg, and has no stoichiometric implications. As a matter of fact, under conditions of total charge transfer (a = 2. = 1), formation of mercurous [3, 69] or both mercurous and mercuric [77, 79] thiolate monolayers has been postulated. However, no definite... 

The calculations were performed near the potential of zero charge, when the outer potential of the metal and solution are equal. The charge transfer coefficients were calculated for energy widths of A = 0.5eV and A = — leV, which is a reasonable range for weak adsorption. The degrees of adatom adsorption were set at 0 = 1/3 and o = 2/3. o = 0, which corresponds to the vacuum is also shown. Experimental values of the electrosorption valenciesare shown in the last column of the table. 

Nonetheless, the conclusion can be drawn that in the case of sufficiently small 0, the impact of adsorption on the orders of electrochemical reaction is not significant, especially if they are determined maintaining the constant electrode potential. However, this cannot be said when speaking about such kinetic parameters as charge transfer coefficients or standard rate constants. It is desirable that their effective values determined without analyzing adsorption phenomena should be corrected for DEL effects. 

The rate constants k and k vary with the adsorption energy in the opposite direction. This is indicated in the diagram of Figure 2.43 where the activation energies for the formation of the intermediate and its consecutive electrochemical formation of H2 are qualitatively shown for the three cases (a) -AG < AGh (b) -AG = AGh and (c) AGa AG . AGh is the free energy for the formation of one H atom from H2 without interaction with a surface. With k = exp(-AG /A r) and the charge transfer coefficients pi pj, one can easily derive that 0 1 in case (a) and 0 -> 0 in case (c). In case (b) 0 will have an intermediate value. In... 

Impedance spectroscopy may provide quantitative information about the conductance, the dielectric coefficient, the static properties of a system at the interfaces, and its dynamic changes due to adsorption or charge-transfer phenomena. Since in this technique an alternating current with low amplitude is employed, a noninvasive observation of samples with no or low influence on the electrochemical state is possible. 

Subscript (ads) denotes adsorption via a thiolate linkage, while (ps) stands for a physisorbed and/or adsorbed state via different interactions. However, large dimensions of the studied molecules and their amphiphilic nature make the surface reaction mechanism more complex than in case of cystine/cysteine. Interfacial microstructure plays an important role in the determination of the surface behavior of the adsorbed molecules. From the study on the charge-transfer kinetics, the transfer coefficient a was calculated as slightly less than 0.50, while the rate constant (based on Laviron s derivations [105]) was of the order of 10 s k The same authors [106] have shown earlier that the adsorption rate constant of porcine pancreatic phospholipase A2 at mercury via one of its disulfide groups is of the order of 10 s h... 

The ratios given in Eq. (4.66) are only dependent on the electrode shape and size but not on parameters related to the electrode reaction, like the number of transferred electrons, the initial concentration of oxidized species, or the diffusion coefficient D. For fixed time and size, the values of f or Qf2 are characteristic for a simple charge transfer (see Fig. 4.4 for the plot of Qf2 calculated at time (ti + T2) for planar, spherical, and disc electrodes) and, as a consequence, deviations from this value are indicative of the presence of lateral processes (chemical instabilities, adsorption, non-idealities, etc.) [4, 32]. Additionally, for nonplanar electrodes, these values allow to the estimation of the electrode radius when simple electrode processes are considered. 

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