Transition state theory desorption from surfaces

It is insti uctive to compare the values of pre-exponential factors for elementary step rate constants of simple surface reactions to those anticipated by transition state theory. Recall from Chapter 2 that the pre-exponential factor A is on the order ofkTjh= 10 s when the entropy change to form the transition state is negligible. Some pre-exponential factors for simple unimolecular desorption reactions are presented in Table 5.2.2. For the most part, the entries in the table are within a few orders of magnitude of 10 s . The very high values of the preexponential factor are likely attributed to large increases in the entropy upon formation of the transition state. Bimolecular surface reactions can be treated in the same way. However, one must explicitly account for the total number of surface... 

The classical approach for discussing adsorption states was through Lennard-Jones potential energy diagrams and for their desorption through the application of transition state theory. The essential assumption of this is that the reactants follow a potential energy surface where the products are separated from the reactants by a transition state. The concentration of the activated complex associated with the transition state is assumed to be in equilibrium... 

In this chapter, we discuss TPR and reduction theory in some detail, and show how TPR provides insight into the mechanism of reduction processes. Next, we present examples of TPO, TP sulfidation (TPS) and TPRS applied on supported catalysts. In the final section we describe how thermal desorption spectroscopy reveals adsorption energies of adsorbates from well-defined surfaces in vacuum. A short treatment of the transition state theory of reaction rates is included to provide the reader with a feeling for what a pre-exponential factor of desorption tells about a desorption mechanism. The chapter is completed with an example of TPRS applied in ultra-high vacuum (UHV), in order to illustrate how this method assists in unraveling complex reaction mechanisms. 

Reuter, Frenkel, and Scheffler have recently used DFT-based calculations to predict the CO turnover frequency on RuO2(110) as a function of 02 pressure, CO pressure, and temperature.31 This was an ambitious undertaking, and as we will see below, remarkably successful. Much of this work was motivated by the earlier success of ab initio thermodynamics, a topic that is reviewed more fully below in section 3.1. The goal of Reuter et al. s work was to derive a lattice model for adsorption, dissociation, surface diffusion, surface reaction, and desorption on defect-free Ru02(l 10) in which the rates of each elementary step were calculated from DFT via transition state theory (TST). As mentioned above, experimental evidence strongly indicates that surface defects do not play a dominant role in this system, so neglecting them entirely is a reasonable approach. The DFT calculations were performed using a GGA full-potential... 

The dynamic motion due to rapid energy exchange for the desorption of Xe atoms from a Pd(lOO) surface will be illustrated. Figure 5.9a shows the rate of Xe desorption as predicted according to transition-state theory. Figure 5.9b compares computed molecular-dynamics rates and the transition-state rates. The open data points are the computed desorption rates for Xe atoms that are allowed to readsorb once they have passed the transition-state barrier. The filled data points ignore the possibility of readsorption. The open data points, computed from the more exact theory, always remain lower than the transition-state result. Transition-state theory and molecular dynamics predict very similar rate constants for the desorption of xenon from palladium. 

Figure 5.9, (a) Arrhenius plot of the rate of xenon desorption from a palladium (100) surface as calculated with transition-state theory, (b) Difference between the rates from a molecular dynamics simulation based on expression (5.26) and those calculated according to transition-state theory. The open data points include the possibility of readsorption which is ignored in the simulations corresponding to the filled points (from A.P. J. Jansen, 1992). 

The general relation between rj and is sketched in Figure 5.8. Deviations from the transition-state expression always have to be considered carefully when activation energies are very low. The use of the transition-state expression in xenon desorption from the metal surface is appropriate because of the relative high value of the desorption energy compared to kT. Transition-state theory is not valid for surface diffusion of CO because of the low activation energy. Of course, quantitative methods are needed to predict a priori the transition state. This will be demonstrated in Chapter 6. 

Hsu et al. [6] state that lumped kinetic models developed by the top-down route have limited extrapolative power . To remedy this situation, many researchers have developed complex reaction schemes based on chemical first principles that involve thousands of chemical species. We can classify them into mechanistic models and pathway models. Mechanistic models track the chemical intermediates such as ions and free radicals that occur in the catalytic FCC process. Transition state theory helps in quantifying the rate constants involved in adsorption, reaction and desorption of reactant and product species from the catalyst surface. Froment and co-workers [19] have pioneered the use of such models in a refinery context and have developed a model for catalytic cracking of vacuum gas oil (VGO). Hsu et al. [6] claim that using this method is challenging because of its large size and reaction complexity. 

From the point of view of associative desorption, this reaction is an early barrier reaction. That is, the transition state resembles the reactants.46 Early barrier reactions are well known to channel large amounts of the reaction exoergicity into product vibration. For example, the famous chemical-laser reaction, F + H2 — HF(u) + H, is such a reaction producing a highly inverted HF vibrational distribution.47-50 Luntz and co-workers carried out classical trajectory calculation on the Born-Oppenheimer potential energy surface of Fig. 3(c) and found indeed that the properties of this early barrier reaction do include an inverted N2 vibrational distribution that peaks near v = 6 and extends to v = 11 (see Fig. 3(a)). In marked contrast to these theoretical predictions, the experimentally observed N2 vibrational distribution shown in Fig. 3(d) is skewed towards low values of v. The authors of Ref. 44 also employed the electronic friction theory of Tully and Head-Gordon35 in an attempt to model electronically nonadiabatic influences to the reaction. The results of these calculations are shown in... 

Temperature programmed desorption (TPD) or thermal desorption spectroscopy (TDS), as it is also called, can be used on technical catalysts, but is particularly useful in surface science, where one studies the desorption of gases from single crystals and polycrystalline foils into vacuum [2]. Figure 2.9 shows a set of desorption spectra of CO from two rhodium surfaces [14]. Because TDS offers interesting opportunities to interpret desorption in terms of reaction kinetic theories, such as the transition state formalism, we will discuss TDS in somewhat more detail than would be justified from the point of view of practical catalyst characterization alone. 

The removal of an electron from an acceptor level or a hole from a donor level denotes, as we have seen, not the desorption of the chemisorbed particle but merely its transition from a state of strong to a state of weak bonding with the surface. The neglect of this weak form of chemisorption (i.e., electrically neutral form) which is characteristic of all papers on the boundary-layer theory of adsorption makes it quite impossible to depict the chemisorbed particle in terms of an energy level, i.e., to apply the energy band scheme depicted in Fig. 10 and used in these papers. ... 

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