Frumkin and Temkin

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. 

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. 

This uncertainty makes the kinetic analysis in terms of Frumkin and Temkin adsorption isotherms also uncertain. As long as there is no clear evidence to the contrary, it may be safer to rely on a simple form of a kinetic equation consistent with the Langmuir adsorption isotherm. Therefore, it is usually accepted that in not too concentrated acids the OER occurs on Pt according to... 

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. 

The Slygin-Frumkin (1935) and Temkin (1940) isotherms can be explained by the following rate expressions ... 

In the early 1930s, Polanyi visited the Soviet Union and became friends with Soviet chemists, especially with Alexander Frumkin and Nikolai N. Semyenov (Semenoff, Semyonov, Semenov). Both of them were members of the Editorial Board of Acta Physicochimica URSS. Besides Semyenov (Nobel prize in chemistry, 1956) and Frumkin, some outstanding scientists hallmarked this journal, such as J. Frenkel and N. Kumakov, and later P. Rehbinder and M. Temkin (Tyemkin) (Fig. 12.16). Polanyi published several papers also in other Soviet scientific journals such as in Uspekhi Khimii and Phys. Z. Sowjetunion in 1932 and 1933. Acta Physicochimica URSS published by the Academy of Sciences of the USSR was an excellent foreign-language journal (cost 4/volume), and Polanyi certainly... 

Neither the reactant-pair mechanism [19] nor the water discharge mechanism [25] are in agreement with the pH dependence for the oxidation of type I species. The pH dependence may be explained as suggested by Frumkin and Podlovchenko [4] in their discussion of the mechanism of ethanol oxidation. A chemical reaction between adsorbed carbonaceous species and OH d is supposed rate-determining on a heterogeneous surface of the Temkin type [34]. The discussion is the same as that for the oxidation mechanism of chemisorbed carbonaceous species in section 11 of chapter IX. 

In order to overcome this difficulty Temkin and Pyzhev proposed to abandon the Langmuir adsorption concept, which basically assumes the surface of the catalyst to be energetically uniform. Instead they chose to use for the adsorption equilibrium the isotherm proposed by Frumkin and Slygin [19],... 

Let us now compare the preexponential factors for an ordinary discharge and a barrierless discharge. For an ordinary discharge, it is impossible to completely overcome the difficulties associated with the determination of the entropy of an activated complex, and the contribution from AS°, the entropy of an individual electrode process, since the value of this quantity cannot be determined by purely thermodynamic methods. Temkin[10] proposed an approximate method for estimating these quantities. He proceeded from the fact established by Frumkin and Jofa[104] that the hydrogen overpotential is independent of the activity coefficient for H30 ions. In the absolute rate theory, this experimental result can be described as a relation between the activity coefficients of the activated complex and hydrogen ions ... 

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... 

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... 

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). 

As to when to use Frumkin s approach or that of Temkin, as long as one is willing to accept the approximation leading to Eq. (7.156), it does not matter as far as the resulting kinetic equations (see below) are concerned. However, the thought process behind Frumkin s equation is to take account of the interaction between the adsorbed entities and that behind Temkin s is to allow for the difference in adsorption energies in different sites on the surface equation. 

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... 

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... 

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. 

Temkin, on the other hand, refers to a study by Federova and Frumkin (351a), who found that the heat of solution of hydrogen in the /3-phase of palladium depends largely on the concentration. 

The easiest test concerns Eq. (22a) describing the LJ-type dissociation. The equation establishes the linear correlation between the dissociation barrier A for a homonuclear admolecule A2 and the atomic heat of chemisorption Qh with the slope of k = 3/2. As seen from Table V, for H2, 02, and N2 dissociated on surfaces of metals as varied as Fe, Ni, Cu, W, and Pt, the experimental values of k lie within the range k = 1.4-1.7, that is, within 10-15% of the theoretical LJ value of k = 1.5. It should be stressed that, unlike similar linear relations between the activation barriers and the heats of reactions (Brpnsted, Polanyi, Frumkin-Temkin-Semye-nov, etc.), Eq. (22a) is not a postulate but a corollary of the general principle (BOC-MP) applied to the one-dimensional dissociation ABS As + Bs. 

Changes with time in the isotopic exchange reaction rate between H2 and HDO(v) over a hydrophobic Pt-catalyst induced by the addition of HN03 were studied experimentally The HN03 poisoning was found to be reversible and was well explained in terms of the competitive adsorption of HNO, with H2 or HDO onto the catalytic active sites. The adsorption equilibrium for HN03 could be expressed by the Frumkin-Temkin equation and the time evolution of the activity was well expressed by the Zeldovich rate equation. 

This is the Frumkin-Temkin adsorption equation considering adsorption heat,7). Substituting Eq.(l I) and Eq,(l6) into Eq.(19), we get a normalized reaction rate at a poisoned steady state as follows. 

---