Temkin theory

Chapter 2 describes the evolution in fundamental concepts of chemical kinetics (in particular, that of heterogeneous catalysis) and the "prehis-tory of the problem, i.e. the period before the construction of the formal kinetics apparatus. Data are presented concerning the ideal adsorbed layer model and the Horiuti-Temkin theory of steady-state reactions. In what follows (Chapter 3), an apparatus for the modern formal kinetics is represented. This is based on the qualitative theory of differential equations, linear algebra and graphs theory. Closed and open systems are discussed separately (as a rule, only for isothermal cases). We will draw the reader s attention to the two results of considerable importance. 

It means that we consider only mono-, bi- and (rarely) termolecular reactions. The coefficients stoichiometric coefficients and stoichiometric numbers observed in the Horiuti-Temkin theory of steady-state reactions. The latter indicate the number by which the elementary step must be multiplied so that the addition of steps involved in one mechanism will provide a stoichiometric (brutto) equation containing no intermediates (they have been discussed in Chap. 2). 

In the framework of the Temkin theory of biographically nonuniform surfaces discussed in detail in Chapter 3, we introduce X= q-qo widi its highest value =l= i- o. The value of , (equal to the AG°/RT) depends on the surface site. If the Polanyi transfer coefficient a is equal for both steps from the general expressions of the rate constants of adsorption and... 

Temkin-Pyzhev equations mentioned above was in agreement with a number of kinetic measurement made on various catalysts such as Mo, W, Tc, Ru, Os and promoted Fe. One characteristic feature of ammonia synthesis rate is the retardation by the product ammonia, and reasonably explained by the Temkin theory. The assumption of rate determining step is also supported by the chemisorption of nitrogen. 

The first hypothesis of Temkin theory. The first hypothesis of Temkin theory is that active sites on catalyst surface exist a continuous distribution function in the following form,... 

The second hypothesis of Temkin. The second hypothesis of Temkin theory is that the relation between rate constants ki and equilibrium constants Ki = ki/k-i obeys a Bronsted-type relation ... 

The first application of Temkin theory in history was on cataljdic reaction for ammonia synthesis on iron catalyst. The famous reation rate equation of Temkin-Pyzhev was obtained, corresponding to the overall reaction ... 

A concept of distribution function 7 of active sites was introduced in the deduction of Temkin theory, from which well-known expressions for adsorption isotherms, such as Freundlich s and Prumkin-Temkin s isotherms and others, and for rate laws of adsorption such as Elovich s one were obtained. Analjdical forms of isotherms depend on the forms of adsorptive energy distribution function, because the physical meaning of these distribution function is based on the inherent non-uniform of catalyst surfaces and the interaction between adsorbed species. Therefore, this formulation accounts for two physical effects caused by non-ideality of adsorptive phase. 

A. Valance, C. Misbah, D. Temkin, K. Kassner. Analytic theory for parity breaking in lamellar eutectic growth. Phys Rev E 48 92A, 1993. 

Temkin S. I., Burshtein A. I. On the shape of the Q-branch of Raman scattering spectra in dense media. Theory, Chem. Phys. Lett. 66, 52-6 (1978). 

Introduction of stoichiometric number concept and linear transformation of the "conventional" QSSA equations (16) to the equivalent system (20) was essentially the major (and, possibly, only) result of theory of steady reactions developed independently by J. Horiuti in 1950s and M. I. Temkin in 1960s. 

This result has been explained by means of a complex theory due to Temkin and Pyzhev 23), but it can be explained equally well and more simply by the methods just described. The fraction of the surface covered by nitrogen atoms will be... 

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. 

A rather different theory of electron impact ionization was developed by Temkin (1982) it was based on the assumption that one of the electrons remains closer to the core than the other, so that the outer electron moves in the dipole field produced by the inner electron and the core. According to this Coulomb-dipole theory the ionization cross section has a modulated quasi-linear energy dependence of the form... 

The surface action law deduced by Temkin on the basis of the absolute rate theory [36] is of the form... 

The most general description for the kinetics of complex reactions in terms of the ideal adsorbed layer model was given in the Horiuti-Temkin steady-state reaction theory [43-47] (see Chap. 1). 

In the 1950s, Semenov and Voevodskii [148] made an attempt to apply the concepts of the branching-chain reaction theory to the kinetics of heterogeneous catalysts. They applied the concept of free valencies migrating over the catalyst surface and of "semi-chemisorbed radicals. But their attempt was criticized (see, for example, ref. 149 where Temkin, using hydrogenation of ethylene on palladium as an example, proved experimentally the inapplicability of the chain theory concepts). 

The application of the concept of "the rate along the basic route provides a possibility of obtaining a new formulation for the quasi-stationary conditions in terms of the Horiuti theory which is different from the ordinary one, i.e. "the formation of an intermediate is equal to that of its consumption . Temkin called the equations obtained "the conditions for the statio-narity of steps . In matrix form they are represented as... 

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. 

Faisal, F.H.M. and Temkin, A. (1972). Application of the adiabatic-nuclei theory to vibrational excitation, Phys. Rev. Lett. 28, 203-206. 

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