Polanyi relations

Linear relations between the activation energies and heats of adsorption or heats of reaction have long been assumed to be valid. Such relations are called Bronsted-Evans-Polanyi relations [N. Bronsted, Chem. Rev. 5 (1928) 231 M.G. Evans and M. Polanyi, Trans. Faraday Soc. 34 (1938) 11]. In catalysis such relations have recently been found to hold for the dissociation reactions summarized in Pig. 6.42, and also for a number of reactions involving small hydrocarbon fragments such as the hydro-... 

The fact that universal Brondsted-Evans-Polanyi relations appear to exist for these dissociation reactions raises the following questions. Why is the relationship between the activation energy and the adsorption energy of the dissociation products linear Why does it depend on structure Why is it independent of the adsorbates ... 

Explain the Bronsted-Evans-Polanyi relation in a simple potential energy scheme for an elementary reaction step. 

Bligaard T, Nprskov JK, Dahl S, Matthiesen J, Chistensen CH, Sehested J. 2004. The Br0nsted-Evans-Polanyi relation and the volcano curve in heterogeneous catalysis. J Catal 224 206-217. 

Logadottir A, Rod TH, N0rskov JK, Hammer B, Dahl S, Jacobsen CJH. 2001. The Br0nsted-Evans-Polanyi relation and the volcano plot for ammonia synthesis over transition metal catalysts. J Catal 197 229. 

In our simulations we use the following pragmatic approach. For a reaction we have a model of the lateral interactions that tells us how the energies of the initial and the final states (both minima) depend on the lateral interactions. We then use the Bronsted-Polanyi relation to relate the shifts in the initial and final state to a change in the activation energy ° ... 

In the present chapter, we have attempted to illustrate how surface bonding and catalytic activity are closely related. One of the main conclusions is that adsorption energies of the main intermediates in a surface catalyzed reaction is often a very good descriptor of the catalytic activity. The underlying reason is that we find correlations, Brpnsted-Evans-Polanyi relations, between activation barriers and reaction energies for a number of surface reactions. When combined with simple kinetic models such correlations lead to volcano-shaped relationships between catalytic activity and adsorption energies. 

For the reaction of H02 with H2 the Evans-Polanyi relation predicts E7 = 25 kcal. per mole. This in excellent agreement with Baldwins value (9) but not in very good agreement with the more reasonable value of E7 = 20 kcal. per mole required to bring the A factor down to a reasonable level. It could, however, be argued that H02 is somewhat more reactive than R02 and that a lower activation energy is in order 20 kcal. per mole is still about 6 kcal. per mole more than the endothermicity of the reaction. 

Hydrogen abstraction provides the chain propagation step that transfers hydrogen from a molecule to attacking radical. The kinetics of these processes often follow a Polanyi relation where e = E + a(AH ). Estimates of the pre-exponential factor sug-... 

According to the Polanyi relation, the change of the activation energy for dissociation 8Eact is proportional to the change in dissociation energy SAEdiss-... 

In addition, a variety of correlations often are used in the catalysis sci ence, which relate to the reaction rates and energies of the reaction inter mediates formation upon interaction of the catalyst with the initial reactants and transformation products. Many of these relations are known as the Broensted Polanyi relations. 

While identifying the rate determining parameters of the catalytic trans formation schemes under consideration, we understand better the reason for possible energy correlations in catalysis, the Broensted Polanyi relations for the transition state energies of surface transformations being typically apphed. Such an approach was intensively used in 1960s—1970s to... 

Let us estimate variations in the rate of a heterogeneous homogeneous reac tion on changes of the active phase (e.g., metal) particle size by considering the changes in the standard thermodynamic potential of the substance of the phase in terms of the correlation Broensted Polanyi relations. Consider the formation of adsorbate Kj in the course, for example, of an elementary gas solid phase reaction (4.85). Rate v of the elementary reaction is written as... 

One may suppose that changes in the particle size should result in changes of of the surface transition state, the changes being described correctly enough by the Broensted Polanyi relation with the increment Ak of substance K at its dispersing ... 

For analyzing more deeply the origin of free-radical persistence and the eventual activation barrier of their dimerization reactions, we have wondered whether the latter obey the Evans-Polanyi relation ... 

We pause to remark that the Bronsted coefficient a has often been used to describe TS structure via the Hammond postulate [15] or the Evans-Polanyi relation [45], where a is viewed as a measure of the relative TS structure along the reaction coordinate, usually a bond order or bond length. The important point is that, although adiabatic PT has a quite different, environmental, coordinate as the reaction coordinate, Eq. (10.12) is consistent with that general picture, with a proper recognition that quantum averages are involved. 

The discrepancies highlighted by Figs. 17.7 and 17.8 may be due to a breakdown of the Evans-Polanyi relation for a HAT reaction or alternatively the contribution of asynchronous PCET induced by the site-differentiation inherent to the metal oxidations as presented in Fig. 17.4. Studies that comprehensively treat the IE vs. 

The excellent linear plots confirm the Polanyi relation and lend considerable support to the values of the bond dissociation energies in the alkanes. It must be emphasized, however, that this type of relation is only applicable to reactions of radicals or atoms with a series of closely related compounds. It has been stressed by Benson and De More [385], from the example of the reactions of methyl radicals with a variety of substrates, that there is no way of relating the activation energies and enthalpy changes when the substrates are difficult classes of compounds. 

As may be deduced from Tables 38 and 39, the least reactive radicals and atoms have the highest values of a in the Polanyi relations. Despite attempts to relate the values of a to the properties of the reactant species, it is probably more realistic at the present time to consider the Polanyi relation as largely empirical. It should also be noted that the very small activation energies for the most reactive species, F and Cl, do not obey the Polanyi relation. 

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