Heterogeneous catalysis models

Growth of oscillations for heterogeneous catalysis model with poisoning A = amplitude, Tp = period... 

The specific models we will analyse in this section are an isothermal autocatalytic scheme due to Hudson and Rossler (1984), a non-isothermal CSTR in which two exothermic reactions are taking place, and, briefly, an extension of the model of chapter 2, in which autocatalysis and temperature effects contribute together. In the first of these, chaotic behaviour has been designed in much the same way that oscillations were obtained from multiplicity with the heterogeneous catalysis model of 12.5.2. In the second, the analysis is firmly based on the critical Floquet multiplier as described above, and complex periodic and aperiodic responses are observed about a unique (and unstable) stationary state. The third scheme has coexisting multiple stationary states and higher-order periodicities. 

The microscopic understanding of tire chemical reactivity of surfaces is of fundamental interest in chemical physics and important for heterogeneous catalysis. Cluster science provides a new approach for tire study of tire microscopic mechanisms of surface chemical reactivity [48]. Surfaces of small clusters possess a very rich variation of chemisoriDtion sites and are ideal models for bulk surfaces. Chemical reactivity of many transition-metal clusters has been investigated [49]. Transition-metal clusters are produced using laser vaporization, and tire chemical reactivity studies are carried out typically in a flow tube reactor in which tire clusters interact witli a reactant gas at a given temperature and pressure for a fixed period of time. Reaction products are measured at various pressures or temperatures and reaction rates are derived. It has been found tliat tire reactivity of small transition-metal clusters witli simple molecules such as H2 and NH can vary dramatically witli cluster size and stmcture [48, 49, M and 52]. 

Of these, the most extensive use is to identify adsorbed molecules and molecular intermediates on metal single-crystal surfaces. On these well-defined surfaces, a wealth of information can be gained about adlayers, including the nature of the surface chemical bond, molecular structural determination and geometrical orientation, evidence for surface-site specificity, and lateral (adsorbate-adsorbate) interactions. Adsorption and reaction processes in model studies relevant to heterogeneous catalysis, materials science, electrochemistry, and microelectronics device failure and fabrication have been studied by this technique. 

P. Meakin, D. J. Scalapino. Simple models for heterogeneous catalysis Phase transitions-like behavior in nonequilibrium systems. J Chem Phys 57 731-741, 1987. 

M. Kolb, Y. Boudeville. Kinetic model for heterogeneous catalysis Cluster and percolation properties. J Chem Phys 92 3935-3945, 1990. 

E. V. Albano. Irreversible saturation transitions in dimer-dimer reaction models of heterogeneous catalysis. J Phys A (Math Gen) 25 2557-2568, 1992 Corrigendum. J Phys A (Math Gen) 26.3661, 1993. 

Models and theories have been developed by scientists that allow a good description of the double layers at each side of the surface either at equilibrium, under steady-state conditions, or under transition conditions. Only the surface has remained out of reach of the science developed, which cannot provide a quantitative model that describes the surface and surface variations during electrochemical reactions. For this reason electrochemistry, in the form of heterogeneous catalysis or heterogeneous catalysis has remained an empirical part of physical chemistry. However, advances in experimental methods during the past decade, which allow the observation... 

R.M. Lambert, F. Williams, A. Palermo, and M.S. Tikhov, Modelling alkali promotion in heterogeneous catalysis in situ electrochemical control of catalytic reactions, Topics in Catalysis 13, 91-98 (2000). 

In cases of spillover in heterogeneous catalysis the usual kinetic models can no longer be applied in a direct way. The creation of new surface sites or... 

The low-temperature oxidation of hydrogen as in the cap of a lead-acid storage battery is an example of heterogeneous catalysis. It is proposed to model this reaction as if it were homogeneous ... 

All these steps can influence the overall reaction rate. The reactor models of Chapter 9 are used to predict the bulk, gas-phase concentrations of reactants and products at point (r, z) in the reactor. They directly model only Steps 1 and 9, and the effects of Steps 2 through 8 are lumped into the pseudohomoge-neous rate expression, a, b,. ..), where a,b,. .. are the bulk, gas-phase concentrations. The overall reaction mechanism is complex, and the rate expression is necessarily empirical. Heterogeneous catalysis remains an experimental science. The techniques of this chapter are useful to interpret experimental results. Their predictive value is limited. 

Steps 1 through 9 constitute a model for heterogeneous catalysis in a fixed-bed reactor. There are many variations, particularly for Steps 4 through 6. For example, the Eley-Rideal mechanism described in Problem 10.4 envisions an adsorbed molecule reacting directly with a molecule in the gas phase. Other models contemplate a mixture of surface sites that can have different catalytic activity. For example, the platinum and the alumina used for hydrocarbon reforming may catalyze different reactions. Alternative models lead to rate expressions that differ in the details, but the functional forms for the rate expressions are usually similar. 

Equation (10.12) is the simplest—and most generally useful—model that reflects heterogeneous catalysis. The active sites S are fixed in number, and the gas-phase molecules of component A compete for them. When the gas-phase concentration of component A is low, the k a term in Equation (10.12) is small, and the reaction is first order in a. When a is large, all the active sites are occupied, and the reaction rate reaches a saturation value of kjkd-The constant in the denominator, is formed from ratios of rate constants. This makes it less sensitive to temperature than k, which is a normal rate constant. 

This equation gives (0) = 0, a maximum at =. /Km/K2, and (oo) = 0. The assumed mechanism involves a first-order surface reaction with inhibition of the reaction if a second substrate molecule is adsorbed. A similar functional form for (s) can be obtained by assuming a second-order, dual-site model. As in the case of gas-solid heterogeneous catalysis, it is not possible to verify reaction mechanisms simply by steady-state rate measurements. 

Research into cluster catalysis has been driven by both intrinsic interest and utilitarian potential. Catalysis involving "very mixed -metal clusters is of particular interest as many established heterogeneously catalyzed processes couple mid and late transition metals (e.g., hydrodesulfurization and petroleum reforming). Attempts to model catalytic transformations arc summarized in Section II.F.I., while the use of "very mixed -metal clusters as homogeneous and heterogeneous catalysis precursors are discussed in Sections I1.F.2. and I1.F.3., respectively. The general area of mixed-metal cluster catalysis has been summarized in excellent reviews by Braunstein and Rose while the tabulated results are intended to be comprehensive in scope, the discussion below focuses on the more recent results. 

Reactivity studies of organic ligands with mixed-metal clusters have been utilized in an attempt to shed light on the fundamental steps that occur in heterogeneous catalysis (Table VIII), although the correspondence between cluster chemistry and surface-adsorbate interactions is often poor. While some of these studies have been mentioned in Section ll.D., it is useful to revisit them in the context of the catalytic process for which they are models. Shapley and co-workers have examined the solution chemistry of tungsten-iridium clusters in an effort to understand hydrogenolysis of butane. The reaction of excess diphenylacetylene with... 

D.A. Rudd, L.A. Apuvicio, J.E. Bekoske and A.A. Trevino, The Microkinetics of Heterogeneous Catalysis (1993), American Chemical Society, Washington DC]. Ideally, as many parameters as can be determined by surface science studies of adsorption and of elementary steps, as well as results from computational studies, are used as the input in a kinetic model, so that fitting of parameters, as employed in Section 7.2, can be avoided. We shall use the synthesis of ammonia as a worked example [P. Stoltze and J.K. Norskov, Phys. Rev. Lett. 55 (1985) 2502 J. Catal. 110 (1988) Ij. 

The examples of the model studies presented show how the meshing of modern surface techniques with reaction kinetics can provide valuable Insights Into the mechanisms of surface reactions and serve as a useful complement to the more traditional techniques. Close correlations between these two areas holds great promise for a better understanding of the many subtleties of heterogeneous catalysis. 

In spite of the importance of having an accurate description of the real electrochemical environment for obtaining absolute values, it seems that for these systems many trends and relative features can be obtained within a somewhat simpler framework. To make use of the wide range of theoretical tools and models developed within the fields of surface science and heterogeneous catalysis, we will concentrate on the effect of the surface and the electronic structure of the catalyst material. Importantly, we will extend the analysis by introducing a simple technique to account for the electrode potential. Hence, the aim of this chapter is to link the successful theoretical surface science framework with the complicated electrochemical environment in a model simple enough to allow for the development of both trends and general conclusions. 

Corma A, Serra JM, SemaP, MolinerM. 2005. Integrating the high-throughput characterization into combinatorial heterogeneous catalysis unsupervised constmction of quantitative stracture/property relationship models. J Catal 232 335-341. 

In addition, it sustains CO electro-oxidation at relatively low overpotential, and there are crystal face dependences for both the ORR and CO oxidation. Since Au is also a system that exhibits both particle size and support effects in heterogeneous catalysis, it provides an interesting model system for smdying such effects in electrocatalysis. 

Froment, G.F., "Model Discrimination and Parameter Estimation in Heterogeneous Catalysis", AIChE. 1, 21 1041 (1975). 

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