Quantum adsorption kinetics

Numerous quantum mechanic calculations have been carried out to better understand the bonding of nitrogen oxide on transition metal surfaces. For instance, the group of Sautet et al have reported a comparative density-functional theory (DFT) study of the chemisorption and dissociation of NO molecules on the close-packed (111), the more open (100), and the stepped (511) surfaces of palladium and rhodium to estimate both energetics and kinetics of the reaction pathways [75], The structure sensitivity of the adsorption was found to correlate well with catalytic activity, as estimated from the calculated dissociation rate constants at 300 K. The latter were found to agree with numerous experimental observations, with (111) facets rather inactive towards NO dissociation and stepped surfaces far more active, and to follow the sequence Rh(100) > terraces in Rh(511) > steps in Rh(511) > steps in Pd(511) > Rh(lll) > Pd(100) > terraces in Pd (511) > Pd (111). The effect of the steps on activity was found to be clearly favorable on the Pd(511) surface but unfavorable on the Rh(511) surface, perhaps explaining the difference in activity between the two metals. The influence of... 

In a few instances, quantum mechanical calculations on the stability and reactivity of adsorbates have been combined with Monte Carlo simulations of dynamic or kinetic processes. In one example, both the ordering of NO on Rh(lll) during adsorption and its TPD under UHV conditions were reproduced using a dynamic Monte Carlo model involving lateral interactions derived from DFT calculations and different adsorption... 

In Chapter 7 general kinetics of electrode reactions is presented with kinetic parameters such as stoichiometric number, reaction order, and activation energy. In most cases the affinity of reactions is distributed in multiple steps rather than in a single particular rate step. Chapter 8 discusses the kinetics of electron transfer reactions across the electrode interfaces. Electron transfer proceeds through a quantum mechanical tunneling from an occupied electron level to a vacant electron level. Complexation and adsorption of redox particles influence the rate of electron transfer by shifting the electron level of redox particles. Chapter 9 discusses the kinetics of ion transfer reactions which are based upon activation processes of Boltzmann particles. 

Figure 3.32. H2 Sticking (dissociative adsorption) probability S on Pd(100) as a function of incident normal kinetic energy Et = En. Circles are experiment [304], dashed and solid line are 6D first principles quantum dynamics with H2 in the ground state and a thermal distribution appropriate to the experiments, respectively [109]. The inset is also 6D first principles quantum dynamics but based on a better PES [309]. From Ref. [2].

Kinetic studies of photoreactions on semiconductor nanoparticles are important for both science and practice. Of scientific interest are the so-called quantum size effects, which are most pronounced on these particles shifting the edge of adsorption band, participation of hot electrons in the reactions and recombination, dependence of the quantum yield of luminescence and reactions on the excitation wavelength, etc. In one way or another all these phenomena affect the features of photocatalytic reactions. At present photocatalysis on semiconductors is widely used for practical purposes, mainly for the removal of organic contamination from water and air. The most efficient commercial semiconductor photocatalysts (mainly the TiC>2 photocatalysts) have primary particles of size 10-20 nm, i.e., they consist of nanoparticles. Results of studying the photoprocesses on semiconductor particles (even of different nature) are used to explain the regularities of photocatalytic processes. This indicates the practical significance of these processes. 

A characteristic increase of 90 after the horizontal section is apparently more pronounced when the potassium oxalate K2C2O4 is used as the electron donor instead of the sulfide ions (Fig. 2.25). A qualitative similarity of the adsorption isotherms and the MO concentration dependence on the initial quantum yield indicates that the adsorbed dye molecules take part in the reaction. Note that all kinetic curves attain the same value of the stationary quantum yield ratio depends on the nature of polymeric surfactant used for stabilization of CdS colloid. With PAA, this ratio equals ca. 0.5, and 0.6 with PVS. 

The reliability of high-dimensional quantum calculations based on ab initio potential energy surfaces is also demonstrated in Fig. 6, where the sticking probability of H2/Cu(l 0 0) obtained by sixdimensional wave packet calculations [32] is compared to experimental results derived from an analysis of adsorption and desorption experiments [27]. The measured experimental sticking probabilities and, via the principle of detailed balance, also desorption distributions had been fitted to the following analytical form of the vibrationally resolved sticking probability as a function of the kinetic energy ... 

Generally first-order kinetics with respect to the concentration of the pollutant is observed for most AOPs in water. The compounds, which exhibit non-first-order kinetics also show quantum yields greater than one. These apparent higher quantum yields are due to sensitized oxidations. The kinetics for photocatalytic oxidation (PCO) can be expressed as one of Langmuir-Hinshelwood type, thus depending on both the degradation rate and the adsorption rate constant of the pollutant. 

Theoretical studies of the properties of the individual components of nanocat-alytic systems (including metal nanoclusters, finite or extended supporting substrates, and molecular reactants and products), and of their assemblies (that is, a metal cluster anchored to the surface of a solid support material with molecular reactants adsorbed on either the cluster, the support surface, or both), employ an arsenal of diverse theoretical methodologies and techniques for a recent perspective article about computations in materials science and condensed matter studies [254], These theoretical tools include quantum mechanical electronic structure calculations coupled with structural optimizations (that is, determination of equilibrium, ground state nuclear configurations), searches for reaction pathways and microscopic reaction mechanisms, ab initio investigations of the dynamics of adsorption and reactive processes, statistical mechanical techniques (quantum, semiclassical, and classical) for determination of reaction rates, and evaluation of probabilities for reactive encounters between adsorbed reactants using kinetic equation for multiparticle adsorption, surface diffusion, and collisions between mobile adsorbed species, as well as explorations of spatiotemporal distributions of reactants and products. 

We are concerned with the kinetics of zeolite-catalyzed reactions. Emphasis is put on the use of the results of simulation studies for the prediction of the overall kinetics of a heterogeneous catalytic reaction. As we will see later, whereas for an analysis of reactivity the results of mechanistic quantum-chemical studies are relevant, to study adsorption and diffusion, statistical mechanical techniques that are based on empirical potentials have to be used. 

We now report how theoretical methods can be used to provide information on the adsorption, diffusion, and reactivity of hydrocarbons within acidic zeolite catalysts. In Section A, dealing with adsorption, the physical chemistry of molecules adsorbed in zeolites is reviewed. Furthermore, in this section the results of hydrocarbon diffusion as these data are obtained from the use of the same theoretical methods are described. In Section B we summarize the capability of the quantum-chemical approaches. In this section, the contribution of the theoretical approaches to the understanding of physical chemistry of zeolite catalysis is reported. Finally, in Section C, using this information, we study the kinetics of a reaction catalyzed by acidic zeolite. This last section also illustrates the gaps that persist in the theoretical approaches to allow the investigation of a full catalytic cycle. 

Clearly, the quantum yield is a constant only if n = 0 and m = 1. Work by Emeline et al. (1998a, 2000c) has established that the reaction orders m and n can be interdependent. That is, the reaction order m varies with reagent concentration [M] and the order n depends on photon flow p. Eor example, for the photodegradation of phenol over TiOi and the photostimulated adsorption of oxygen on ZrOi, m 1 if n O, whereas n 1 if m 0. Results of kinetic studies (see Fig. 5.17) of both photostimulated processes have shown that the interdependence of the reaction rate can be generalised by eq. 5.91, which is identical with eq. 5.65. 

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