Evans-Polanyi relation

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 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. 

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. 

This subsection begins with a short summary of particle-size-dependence observations of chemical bond activation. Next, the Bronsted-Evans-Polanyi relation that relates activation energies of elementary surface reaction steps with the corresponding reaction energies is introduced. In the subsections that follow, the... 

As long as the structures of ttansition state and dissociated state are close, changes in metal-atom interactions will lead to the Bronsted-Evans-Polanyi relation between activation energy and reaction energy of a surface elementary reaction. Interestingly, microscopic reversibility imphes that the Bronsted-Evans-Polanyi proportionality constant for recombination is typically 0.1. This implies that the ratio of the energy of the surface fragments in the transition state compared to the dissociated state is a constant and on the order of 90%. 

Table 3.4. CO transition-state energies according to the Br0nsted—Evans-Polanyi relation (kJ/mol).

The Br0nsted-Evans-Polanyi relation applied to the CO dissociation reaction results in Table 3.4. The quantum-chemical result upon which this is based is the dissociation of CO over Ru(OOOl) with 2x2 coverage. 

The large value of a in these Brpnsted-Evans-Polanyi relations is consistent with a late transition state for the dissociation reactions as discussed in Chapter 2. The only parameter in the universal relations is the reaction energy Er, which can be easily calculated. 

Reactant or product states of surface reactions are often (de-)stabilized by the presence of other adsorbates. This implies a change in the reaction energy as a function of overlayer composition. The Brpnsted-Evans-Polanyi relation again provides an elegant procedure to estimate the effect of lateral interactions on changes in the activation energies. 

The foregoing discussion deals with the stmcture effect on A (or entropy change). The stmcture effect on the activation energy (or reaction enthalpy change) is described by the Evans-Polanyi relation, with just two parameters Eo and a) for each single event type, which generally are obtained from model-compound experiments. 

Cushing GW, Navin JK, Donald SB, et al C-H bond activation oflight alkanes on Pt(lll) dissociative sticking coefficients, Evans-Polanyi relation, and gas-surface energy transfer, JPhys Chem C 114(40) 17222-17232, 2010. 

Voj vodic A, Calle-Vallejo F, Guo W, Wang S, Toftelund A, Studt F, Shen J, Man IC, Rossmeisl J, Bligaard T, Nprskov JK, Abild-Pedersen F. On the behavior of Brpnsted-Evans-Polanyi relations for transition metal oxides. J Chem Phys 2011 134 244509. 

Wang SG, Temel B, Shen JA, Jones G, Grabow LC, Studt F, Bligaard T, Abild-Pedersen F, Christensen CH, Nprskov JK. Universal Brpnsted-Evans-Polanyi relations for C-C, C-O, C-N, N-O, N-N, and 0-0 dissociation reactions. Catal Lett 2011 141 370-373. 

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