Polanyi-Bronsted relation

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 ° ... 

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. 

Scheme 4.1 illustrates this relation between change in activation energy 5Eact and change in reaction energy 6Er. According to the Bronsted-Polanyi rule, when there is no change in the reaction path... 

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. 

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%. 

The important point about the illustration is that the Bronsted relation is seen to be a straightforward consequence of the Polanyi relation. These empirical relations are very general, and do not depend on the details of the catalytic sequence or the nature of its rate-determining step. Their usefulness lies in the possibility of predicting a rate from a purely thermodynamic quantity, A a, provided that the proportionality constant and a have been determined by means of experiments with a series of acids (or bases). 

The Bronsted relation obtained from Polanyi relation ... 

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... 

These simple considerations yield several corollaries, sometimes known together as the Bell-Evans-Polanyi (BEP) principle [14]. First, there is an approximately linear relation between the barrier height and the reaction energy this is the basis of the Bronsted relation (and other LFERs). Second, the proportionality constant a in Eq. (19.2) tends to be smaller for exothermic reactions (but larger for endothermic reactions). Third, the position of the crossing point between the curves lies closer to the reactants for more exothermic reactions this is the basis of the Hammond postulate, that the TS for a more exothermic reaction more closely resembles the reactants (and that for a more endothermic reaction more closely resembles the products). 

The main catalytic influence of the nature of the electrode material is through the adsorption of intermediates of complex electrode reactions. Hortiuti and Polanyi [50] suggested that the activation energy of an electrode reaction should be related to the heat of adsorption of adsorbed intermediates by a relationship of the form of the Bronsted rule in homogeneous solutions. This corresponds to a vertical shift of the potential energy curves by an amount with p a... 

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

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