Frumkin-Temkin Isotherm

Hydrogen evolution reaction, mechanism, 1135, 1151, 1163, 1164, 1189 catalytic pathway, 1163,1194, 1255 electrocatalysis, 1280 Frumkin-Temkin isotherm, 1194 Langmuir isotherm, 1194 Hydrogen coadsorption... 

When Should One Use the Frumkin-Temkin Isotherms in Kinetics Rather than the Simple Langmuir Approach ... 

In the following discussion, an example is given that serves to show that introducing a Frumkin-Temkin isotherm does affect the kinetic relation between the current density, i, and the corresponding overpotential. The example chosen will use the hydrogen evolution reaction once more because it is relatively simple but at the same time involves consecutive steps and alternative pathways thus it has characteristics of many practical electrode reactions likely to be met in practice.68... 

Irreversible reaction, 1251, 1419 Isoconic, definition, 933, 978, 982 Isotherm, 932, 964, 1197 applicability, 941 and charge transfer, 954, 955 Conway and Angersein-Kozlowska, 943 definition, 933 in electrode kinetics, 1197 Flory—Huggins type, 941,942, 944, 965 Frumkin, 938, 942, 965 Frumkin-Temkin, 1197, 1198 Habib-Bockris, 943... 

Consider, now the dependence of 0 upon potential under the condition that AGe varies with 0. It will he less dramatic (i.e., d dV will be much smaller) than in the situation represented by the original, simpler, corresponding, Langmuir equation [Eq. (7.153)]. If the latter isotherm is applicable to a variation of 0 with potential at constant concentration, the surface is effectively either empty of intermediate (0 1) or near to 0 = 1. With Frumkin-Temkin in control, 0 varies linearly and more slowly with V than it does with the Langmuir equation. Thus, from (7.156), at constant cp... 

If the relative values of the rate constants among the consecutive or parallel steps in reactions such as that of hydrogen evolution have the most decisive influence here, Frumkin-Temkin should be used. If they lead to a situation in which the intermediate radical coverage tends toward zero or one, the matter is decided. As remarked above, for 0 — 0 or 0 — 1, the Frumkin and Temkin isotherms coincide in effect with that of Langmuir. 

This (Frumkin-Temkin) expression is to be compared with that using a Langmuir isotherm in Eq. (7.158). The value of... 

In the limit of a - 0, the ideal Langmuir adsorption isotherm is obtained. See - Frumkin isotherm, and for the role of surface heterogeneity - Temkin isotherm. Refs. [i] Horanyi G (2002) Specific adsorption. State of art Present knowledge and understanding. In Bard A], Stratmann M, Gileadi M, Urbakh M (eds) Thermodynamics and electrified interfaces. Encyclopedia of electrochemistry, vol. I. Wiley-VCH Verlag, Weinheim, pp 349-382 [ii] Calvo EJ (1986) Fundamentals. The basics of electrode reactions. In Bamford CH, Compton RG (eds) Comprehensive chemical kinetics, vol. 26. Elsevier, Amsterdam, pp 1-78... 

Disregarding for a moment the electrochemical aspect of this isotherm, we note that 0 is proportional to logC, (as opposed to the Langmuir isotherm, where it is proportional to a linear function of the concentration.) A simitar "logarithmic isotherm" was developed by Temkin. His derivation is much more complex, but in the final analysis it is based on the same physical assumptions. It has, therefore, become common to refer to Eq. 141 as the Temkin isotherm, although Temkin has never used it in this form. It is this approximate form of the Frumkin isotherm which is applied to electrode kinetics, as we shall see below. 

We neglect the preexponential term in 0 and substitute for the exponential term from the Temkin isotherm (i.e., the Frumkin isotherm for intermediate values of the coverage). For the first step at quasi equilibrium this leads to ... 

The adsorption of either ions or neutral molecules on the electrode surface depends on qn, i.e., on the apphed electric potential. Correspondingly, the electric field at the electrochemical interface is an additional free-energy contribution that either favors or restricts the adsorption of species on the electrode from the ionic conducting phase. A variety of adsorption isotherms has been proposed to account for the behavior of different electrochemical systems. Among them are the Langmuir, Frumkin, and Temkin isotherms [2]. Frumkin and Temkin isotherms, at variance with the Langmuir one, include effects such as adsorbate—adsorbate or adsorbate—surface interactions. 

Whatever is the mechanism of OHad and Oad formation, the principal point of this adsorption theory is that Pt surface atoms are stable in their positions in the lattice and the integrity of the Pt lattice is retained after an adsorption-desorption cycle in the voltammetry studies. The formation of adsorbed layer is described quantitatively by adsorption isotherms at equilibrium, e.g., Temkin or Frumkin adsorption isotherms and corresponding kinetic equations such as the Elovich equation. Intrinsic to the adsorption theory is the concept of the maximum surface concentration corresponding to monolayer coverage by the ad-particles on all available adsorption sites. " ... 

The kinetic behavior corresponding to this equation is often referred to as Temkin kinetics in relation to the Temkin isotherm [M. I. Temkin, Zh. Fiz. Khim. 15, 296 (1941) see also A. N. Frumkin, Z. Phys. Chem. 116, 466 (1925)], but the latter refers to heterogeneity rather than interaction effects with regard to the origin of the exp - rdj) term. 

The Frumkin isotherm can be regarded as a general isotherm from which both the Temkin and Langmuir isotherms can be obtained as special cases. Szklarska-Smialowski and Wieczorek found that the adsorption of various aliphatic compounds (acids, alcohols and amines) on steel in H2SO4 conformed with the Frumkin isotherm. 

CI2 evolution reaction, 38 56 electrochemical desorption, 38 53-54 electrode kinetics, 38 55-56 factors that determine, 38 55 ketone reduction, 38 56-57 Langmuir adsorption isotherm, 38 52 recombination desorption, 38 53 surface reaction-order factor, 38 52 Temkin and Frumkin isotherm, 38 53 real-area factor, 38 57-58 regular heterogeneous catalysis, 38 10-16 anodic oxidation of ammonia, 38 13 binding energy quantification, 38 15-16 Haber-Bosch atrunonia synthesis, 38 12-13... 

With this in mind, some important adsorption isotherms were introduced, and we found that each of them describes important characteristics of the adsorption process (Table 6.10). Thus, the Langmuir isotherm considers the basic step in the adsorption process the Frumkin isotherm was one of the first isotherms involving lateral interactions the Temkin is a surface heterogeneity isotherm and the Flory-Huggins-type isotherms include the substitution step of replacing adsorbed water molecules by the adsorbed entities (Fig. 6.98). 

Significantly later, foreign scientists reached a similar conclusion regarding the Freundlich isotherm. In the USSR, a theory of adsorption on an inhomogeneous surface was developed independently by M. I. Temkin of the Karpov Physico-Chemical Institute in connection with electrochemical research by Academician A. N. Frumkin. M. I. Temkin s work on a logarithmic isotherm was cited in [74] and published in [75]. The theory of adsorption and catalysis on an inhomogeneous surface was especially extensively developed by S. Z. Roginskii. 

This empirical equation of the adsorption isotherm, giving the relationship between 6 and the pressure, excellently represents many characteristics of chemisorption. Equation (72) is introduced by Frumkin and Slygin (366), who derived it from their electrochemical investigations on hydrogen electrodes. The equation has played an extensive role in the successful theory of ammonia catalysis of Temkin (367) and it has in literature been termed the Temkin equation (368), although Temkin himself and other Russian investigators call it the logarithmic adsorption isotherm. 

When reactants or intermediates are adsorbed, the rate of the reaction may no longer be related to the concentration by a simple law. This situation is best understood where a reactant is nonspecifically adsorbed in the outer -> Helmholtz plane. The effect of such adsorption on the electrode kinetics is usually termed the -> Frumkin effect. Physical and chemical adsorption on the electrode surface is usually described by means of an -> adsorption isotherm and kinetic equations compatible with various isotherms such as the - Langmuir, -> Temkin, -> Frumkin isotherms are known. 

Of course, other types of adsorption isotherms commonly represent the adsorption processes in heterogeneous catalysis, for example, the Freundlich isotherm and, especially in electrode processes, the Temkin and Frumkin isotherms (99). In the latter case... 

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