Brpnsted-Evans-Polanyi Relationships

In this section, we move from the elucidation of molecular and atomic adsorption to the fundamental features that control smface reactivity. We start by initially describing dissociative adsorption processes. We focus on elucidating surface chemistry as well as the understanding of how the metal substrate influences the intrinsic surface reactivity. We will also pay attention to geometric ensemble-size related requirements. The Brpnsted-Evans Polanyi relationship between transition-state energy and reaction energy discussed in Chapter 2 is particularly useful in understanding differences in reactivity between different metal surfaces. 

One can then assume a Brpnsted-Evans-Polanyi relationship to relate the dependence of rate constant fc i to the overpotential E ... 

Diatomic molecules adsorbed to transition-metal surfaces dissociate through tight transition states. A general Brpnsted-Evans-Polanyi relationship can then be defined which is valid for nearly all diatomic molecules that dissociate along a similar reaction path ... 

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. 

Recently, semiempirical methods based on DFT calculations have been developed for catalyst screening. These methods include linear scaling relationships [41, 42] to transfer thermochemistry from one metal to another and Brpnsted-Evans-Polanyi (BEP) relationships [43 7]. Here, these methods and also methods for estimation of the surface entropy and heat capacity are briefly discussed. Because of their screening capabilities, semiempirical methods can be used to produce a first-pass microkinetic model. This first-pass model can then be refined using more detailed theory aided by analytical tools that identify key features of the model. The empirical bond-order conservation (BOC) method, which has shown good success in developing microkinetic models of small molecules, has recently been reviewed [11] and will not be covered here. 

FIGURE 11.8 Potential energy profiles for reducing one OH in the half-dissociated water network by a proton from the water layer at three different potentials. Inset shows the Brpnsted-Evans-Polanyi (BEP) relationship for the charge transfer process. The fine represents a fit to the data showing a transfer coefficient (y in Eq. 6.5) of 0.5. Adapted from Tripkovic et al. (2010). (See insert for color representation of the figure.)... 

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