Bronsted-Evans Polanyi

Bronsted-Evans-Polanyi (BEP) linear activation energy-reaction energy relationships ... 

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-... 

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

Reactions involving simple reactants and products often offer simple descriptions of activity or selectivity. The Bronsted-Evans-Polanyi (BEP) relation, for instance, states that the activation barrier, Ea, and the heat of reaction, AE, of elementary dissociation reactions are often linearly correlated (Fig. 1). Extensive DFT calculations have supported this empirical relation for a large number of elementary dissociation reactions and suggest that it is due to the structural similarities between the transition state and the product states. When such a dissociation step is rate-limiting, knowing AE is sufficient to capture the activity of the overall reaction, which exhibits volcano-shaped... 

Estimated transition state energies (in units of kJ/mol) for CO dissociation from the Bronsted-Evans-Polanyi formula extrapolated from ruthenium (after Ref. (25))... 

Figure 7.6. Volcano curve for CO methanation (T. Bligaard, J.K. Norskov, S. Dahl, J. Matthiesen, C.H. Christensen, J. Sehested, The Bronsted-Evans Polanyi relation and the volcano curve in heterogeneous catalysis, Journal of Catalysis 224 (2004) 206).

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%. 

Other methods for calculating the activation energies of the ORR have been reported in the literature. Based on the linear Bronsted-Evans-Polanyi relationship, Norskov et al. [85] proposed a method to estimate the least activation energy by calculating the stability of the reaction intermediate. With this simple model, the study reported a Tafel slope of 60 mV at 300 K (71 mV at 357 K). The value was consistent with experimental results. 

Scaling Relations for Transition States The Bronsted-Evans-Polanyi Relationship... 

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