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2.4. ELECTROCATALYSISFROMTHEORY 37 The CHE model has been applied to several systems. As mentioned, Nørskov et al. [152] applied it to studying the ORR. Their work identified that possible improvements in activity beyond Pt might be possible, and the work subsequently inspired research into new Pt3X alloys[189]. The superior activity of Pt3X alloys versus pure Pt has been verified experimentally[189–191]. This shows that the CHE method can lead to results that have practical predictive power. Rossmeisl et al. used the CHE method to study the oxygen evolution reaction (OER) from metal [192] and oxide[107] surfaces and Hansen et al. [108] used it for studying the chlorine evolution reaction (ClER) on rutile oxides. These studies identified a connection between the adsorption energy of O on the rutile oxide surface and the activities for both OER and for ClER. To summarize, the CHE model enables reaction free energies of electrochemi- cal surface reactions to be determined using adsorption energies obtained from standard DFT calculations, and the results obtained have been found to compare favorably with experiments. 2.4 Understanding of heterogeneous (electro)catalysis from electronic structure theory By using the methods outlined in the preceding sections, the energetics of molecules and materials can be evaluated accurately. It has also been indicated how the CHE model can be used to model the effects of electrode potential on adsorption ener- gies. In the following sections, the connection between these methods and hetero- geneous electrocatalysis will be made, and it will be described how these methods can be used to understand activity trends of different catalysts. A more thorough description can be found in the introductory textbook by Nørskov et al. [109]. 2.4.1 Brønsted-Evans-Polanyi relations The rate of a chemical reaction is determined by the activation energy for the re- action, the difference between the energy of the transition state and the energy of the reactants. In the Arrhenius rate expression there is also the attempt rate, but the dominating effect is the height of the barrier. In general, then, the energy of the transition state needs to be determined to be able to predict the rate of a re- action. The description of how heterogeneous (electro)catalysis can be modeled has so far only been based on reaction free energies and not on activation energies. The reason why reaction rates can be understood without calculation of activation energies is that many reactions exhibit so-called Brønsted-Evans-Polanyi (BEP) relationships, where the activation energy of a certain reaction step is linearly de- pendent on the reaction free energy of the step itself (which can be evaluated in thePDF Image | Studies of Electrode Processes in Industrial Electrosynthesis
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