Molecular Heterogeneous Catalysis, Wiley (2006), 352729662X

16 Chapter 1

Both the embedded atom method (EAM) and e ective medium theory (EMT) have been used with some success to model the structure and composition of metal systems. In EAM, the potential is not linear in the number of neighbors and depends on the

electron density. The parameters for both theories can be deduced from experiments[17] or theory[18] . These systems, for the most part, have been limited to looking only at

the properties of only the metal atoms without adsorbates since there were few metaladsorbate potentials. Recent simulations by van Beurden and Kramer[18] indicate that with some e ort modified embedded atom (MEAM) potentials can be established for adsorbates in order to simulate the dynamics of the species on metal substrates.

Statistical mechanical Monte Carlo[19] as well as classical molecular dynamic methods can be used to simulate structure, sorption, and, in some cases, even di usion in heterogeneous systems. Kinetic Monte Carlo simulation is characteristically di erent in that the simulations follow elementary kinetic surface processes which include adsorption, desorption, surface di usion, and reactivity[20]. The elementary rate constants for each of the elementary steps can be calculated from ab initio methods. Simulations then proceed event by event. The surface structure as well as the time are updated after each event. As such, the simulations map out the temporal changes in the atomic structure that occur over time or with respect to processing conditions.

A much more in-depth description of the full range of di erent ab initio quantum mechanical methods, free energy and kinetic Monte Carlo methods, molecular dynamics, ab initio molecular dynamics and linear scaling methods is given in the Appendix.

References

1.New Chemical Science and Engineering Technology. Vision 2020 Catalysis Report, Council for Chemical Research (1997) see; http://www.ccrhq.org/vision/index /roadmaps/catrep.html

2.National Research Council, Commission on Physical Sciences, Mathematics, and Applications, Catalysis Looks to the Future, National Academies Press, Washington, DC (1992)

3.Opportunities for Catalysis in the 21st Century: A Report from the Basic Energy Sciences Advisory Committee (May 2002)

4.R.E. Smalley, Rice University Department of Chemistry, presentation at Columbia University (September 2003), Our Energy Challenge

(see http:smalley.rice.edu)

5.Basic Research Needs to Assure a Secure Energy Future: A Report from Basic Energy Sciences Advisory Committee (February 2003)

6.Basic Research Needs for the Hydrogen Economy, Basic Energy Sciences Workshop on Hydrogen Production, Storage and Use (May 2003)

7.D. Miller, NSF Workshop Report: Catalysis for Biorenewables Conversion (April 2004)

8.W.G. Frankenburg, in Hydrogenation and Dehydrogenation Catalysis, Vol. 3, P.H. Emmett (ed.), Reinhold, New York (1995)

9.S.M. Auerbach, R.A, Currado, P.K. Dutta, Handbook of Zeolite Science and Tech-

nology, Marcel Dekker, New York (2003);

H.van Bekkum, E.M. Flanigan, J.C. Jansen, Introduction to Zeolite Science and Practice, Stud. Surf. Sci. and Catal. Vol. 58, Elsevier, Amsterdam (1991)

10.G. Ertl, Adv. Catal. 37, 213 (1990);

R.Imbihl, G. Ertl, Chem. Rev. 95, 697 (1995)

Introduction 17

11.P.V.R. Schleyer, N.L. Allinger, T. Clark, J. Gasteiger, P.A. Kolleman, H.F. Schaefer, P.R. Schreiner (eds.), The Encyclopedia of Computational Chemistry, Wiley, New York (1998)

12.S. Marti, M. Roca, J. Andres, V. Moliner, E. Silla, I. Tu˜non,

J.Bertran, Chem. Soc. Rev. 2, 98 (2004)

13.V. Pallassana, M. Neurock, G.C. Coulston, J. Phys. Chem. B103, 8973 (1999)

14.R.A. van Santen, M. Neurock, Catal. Rev. Sci. Eng. 37, 557 (1995)

15.R.G. Bell, D.W. Lewis, P. Voigt, C.M. Freeman, J.M. Thomas, C.R.A. Catlow, in

Zeolites and Related Microporous Materials, State of the Art 1994, Vol. 84, 2075-

2082 (1994);

C.R.A. Catlow, in: Handbook of Heterogeneous Catalysis, Vol. 3, VCH, Weinheim, 1149-1165 (1997)

16.G.J. Kramer, N.P. Farragher, B.W.H. van Beest, R.A. van Santen, Phys. Rev. B43, 5068 (1991);

K.de Boer, A.P.J. Jansen, R.A. van Santen, Phys. Rev. B52, 12579 (1995)

17.M.I. Baskes, Phys. Rev. B46, 2727 (1992);

M.S. Daw, S.M. Foiles, M.I. Baskes, Mater. Sci. Rep. 9, 251 (1993)

18.P. van Beurden, G.J. Kramer, Phys. Rev. B63, 165106 (2001)

19.D. Frenkel, B. Smit, Understanding Molecular Simulation, Academic Press 1996

20.a) M.Neurock, E.W. Hansen, Comput. Chem. Eng. 22, 1045 (1998);

b)E. Hansen, M. Neurock, J. Catal. 196, 2, 241, (2001);

c)R.J. Gelten, R.A. van Santen, A.P.J. Jansen, in Dynamic Monte Carlo Simulations of Oscillatory Heterogeneous Catalytic Reactions P.B. Balbuena (ed.), Elsevier,

Amsterdam (2000)

CHAPTER 2

Principles of Molecular Heterogeneous Catalysis

2.1 General Introduction

The three predominant criteria for the development and the design of new catalytic materials are that they:

1.are highly active

2.produce only the desired products and

3.maintain activity for prolonged periods of time.

All three of these factors are controlled by the kinetics of the elementary steps in the overall catalytic cycle. The activity is defined as the rate at which the overall catalytic cycle turns over and is dictated by the rate-limiting step or steps in the overall process. These steps can include adsorption, desorption, specific surface reaction steps and even surface di usion. The selectivity of a reaction is defined as the percentage of desired product molecules that are part of the product spectrum. A 100% selectivity is always desired but never fully realized. The lifetime of catalysts is related to the selectivity of a desired coproduct poisoning the catalyst. As discussed in the previous chapter, theory along with fundamental experiments have advanced considerably over the past decade and can be used to determine the energetics for elementary reaction steps as well as the overall thermodynamics. This information can be used to help determine the kinetics by the application of theories or kinetic principles in physical chemistry including the Sabatier principle, transition state theory, and the Brønsted–Evans–Polanyi relationship , thus allowing one to relate overall thermodynamic parameters to the rates of catalytic reactions. In this chapter we describe the development and application of these principles to modeling heterogeneous catalytic systems.

Catalytic reactivity is controlled by the combination of intrinsic chemical reactivity and the extrinsic heat and mass transfer e ects related to the catalyst morphology and reactor configuration. We will mainly focus on the intrinsic activity except in the cases where it is di cult to uncouple these phenomena such as in the reaction and di usion in porous materials, which is covered in Chapter 4.

The kinetics of a catalytic system are dictated by the nature of the chemical complex formed as the result of the interactions between atoms in the catalyst and the adsorbate. The reactivity of the complex is controlled by local as well as long range chemical e ects. A classical question in heterogeneous catalysis is whether the catalytic sites can be described with either a Langmuir[1] or Taylor[2] model. These models refer to local descriptions of the active site. According to the Langmuir model, all sites are considered to be similar. In the Taylor model, however, there is a distribution of di erent sites, and catalysis occurs at a small fraction of unique sites.

A second important question involves the range of the chemical interactions. It is now well known that the nature of the reaction environment about the active catalytic site can be just as important in describing and potentially controlling the catalytic performance as the intrinsic chemical interactions in the catalytic complex. The reaction environment includes the influence of the solvent media; solid state matrix, i.e. the e ects of the cavity, the support, alloy composition and structure, and defects at the catalyst surface; long-range electrostatic forces between the catalyst and the reactive complex; relaxation and reconstruction of the surface; promoters and lateral interactions between surface adsorbates that change with reaction conditions.

Molecular Heterogeneous Catalysis. Rutger Anthony van Santen and Matthew Neurock

Copyright © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-29662-X

20 Chapter 2

The third predominant issue refers to whether the active site and its environment can be treated statically or whether one must follow their dynamics. Interesting physical e ects and phenomena can arise from the coupling of the surface mobility along with intrinsic chemical reactivity which include kinetic oscillations and self organized pattern formation under particular catalytic conditions. As an organizing principle for the chapter, we use the concepts outlined above, and for this reason, di erent catalytic systems will be discussed under the same headings.

This chapter proceeds with a general discussion of the overall catalytic cycle and Sabatier’s principle in order to illustrate the comparison of relative kinetic and thermodynamic steps in the overall cycle. This is followed by a fundamental discussion of the intrinsic surface chemistry and the application of transition state theory to the description of the surface reactivity. We discuss the important problem of the pressure and material gap in relating intrinsic rates with overall catalytic behavior and then describe the influence of the “tatic” reaction environment including promoters, cluster size, support, defects, ensemble, coadsorption and stereochemistry. Lastly, we discuss the transient changes to the surface structure as well as intermediates and their influence on catalytic performance.

2.1.1 The Catalytic Cycle

2.1.1.1 The Sabatier Principle

When the concept of catalysis was first formulated, the idea that the catalytic reaction is actually a catalytic cycle was not at all obvious. In 1836 Berzelius defined “catalytic force” as the process responsible for catalysis in which the decomposition of bodies was caused by the action of another simple or compound body. Faraday later showed that a catalytically reactive surface was chemically altered by contact with reacting gases. It was not, however, until after chemical thermodynamics had been developed that a more scientific understanding of catalysis was formulated. In 1896 Van’t Ho demonstrated that the rate of a catalytic reaction depended upon the amount of catalyst. Soon after Ostwald defined a catalyst to be a substance that changes the velocity of a reaction without itself being altered in the process. A catalyst, however, must operate within the thermodynamic limits of the reacting system[3] .

The reaction conditions for a specific system are defined by the overall thermodynamics of the reaction. The catalyst facilitates the adsorption of the reactants and their subsequent conversion into products. An important feature, however, is that the products must be rapidly removed from the surface in order to regenerate active surface sites. These ideas led to the concept that the catalytic reaction is comprised of a “cycle” which is made up of elementary physicochemical processes. At the most basic level, catalysis is comprised of at least five elementary steps:

–Chemisorption

–Dissociation/activation

–Di usion

–Recombination

–Desorption

The incorporation of these steps into a cycle and the overall concept of the catalytic cycle are illustrated for the catalytic decomposition of N2O over a catalytic substrate in Fig. 2.1. N2O is an environmentally detrimental molecule. It is produced as an undesirable product

Figure 2.1. Schematic illustration of the catalytic cycle of reaction events for the decomposition reaction of N2 O.

in automotive exhaust catalysis as well as in nitric acid synthesis. It is a precursor to nitric acid production in the stratosphere. Conventional catalysts for N2O decomposition are the transition metals and the transition-metal oxides.

Chemisorption is defined as the adsorption of reactants or intermediates on the catalyst substrate with an interaction energy with the surface which is strong enough to form chemical bonds between the adsorbate and the surface and to weaken internal bonds within the adsorbate. This helps to aid dissociation processes. In order for the N2O molecule to decompose it must bind strongly to the catalyst surface, thus weakening the internal N–O bonds. The interaction energy must therefore be strong enough to overcome the N–O bond energy in N2O. When N2O decomposition is the rate limiting step, the rate of the catalytic reaction should increase with increase of the N2O-catalyst interaction energy. On the other hand, the fragment molecules generated on the surface by decomposition of N2O have to desorb in order to regenerate the free catalytic sites necessary to continue the cycle. Hence, when the interaction between product molecules and the catalyst becomes too strong the desorption of product molecules becomes rate limiting. The rate will then decrease with increasing interaction energy of products with the catalyst. This ultimately leads to a balance of the catalyst-adsorbate bond strength so as to activate the adsorbate but avoid poisoning of the surface. This balance results in a volcano-type plot of rate against reactant-interaction strength whereby the rate increases up to a particular interaction strength known as the Sabatier maximum and then decreases. This shape of the plot is a consequence of the Sabatier principle (see Fig. 2.2). The rate of a catalytic reaction is maximized at an optimum interaction strength of the reactants with catalyst[4] . This provides a rational strategy for the optimization of catalytic rates. For instance, by comparing di erent catalysts for the same reaction and measuring the reactant-adsorption energies and catalytic rate, one can determine whether the reaction rate increases or decreases with adsorption energy of the reactants. If one then uses trends in measured or computed adsorption energies as a function of material, one can select surfaces that might improve catalytic performance.

The order for a monomolecular reaction changes from positive in the reactant concentration to the left of the Sabatier maximum to zero or negative order in the reactant

22 Chapter 2

Figure 2.2. Sabatier principle. Catalytic rate is a maximum at optimum adsorption strength.

concentration to the right of the Sabatier maximum. This corresponds to a low surface concentration of adsorbed intermediates on the left side of the optimum and an increasing surface coverage to the right side.

Sabatier-type volcano plots have been constructed for a number of di erent commercially relevant systems[3] . A simple kinetic expression that simulates the Sabatier result is found when one realizes that the decomposition of molecules requires a vacant site for molecular fragments to adsorb on. For instance, in the N2O decomposition reaction, the dominant surface species (most abundant reaction intermediate)[5] is atomic oxygen (O), which is in equilibrium with the gas phase. When the slow step in the reaction is dissociative adsorption of N2O, the mean-field kinetic rate expression for N2O decomposition,

where kdec is the rate constant for N2O decomposition, θ0 is the coverage of surface oxygen and nitrogen atoms and [N2O] is the gas phase concentration of N2O.

While kinetic rate expressions such as Eq. (2.1) are widely used, they are considered as very approximate. Generally the rate constants, as well as the equilibrium constants, cannot be considered concentration independent and therefore are only e ective parameters. Therefore, when they are measured in the laboratory, they will inherently be a function of the conditions under which the reaction was performed. This will be described more extensively in Chapter 3 on metal catalysis.

On transition metals or transition metal oxides, the rate of O2 desorption (kdes) com-

petes with the rate of N2O decomposition (kdiss ). Each adsorbed oxygen atom blocks a site for N2O decomposition. Nitrogen will adsorb only weakly, but oxygen is e ectively a

poison to the reaction. Expression (2.1) can be rewritten as a function of equilibrium and rate constants to give

When the interaction energy of the adsorbate with the transition metal increases kdiss will increase. As we will see later in Section 2.3, the activation energy of a reaction decreases

when the adsorption energy increases. On the other hand, the rate for the associative desorption of O2 will also decrease. Hence if Eq. (2.2) is studied as a function of the adsorbate-surface interaction energy, it will follow the Sabatier volcano curve. The rate will increase with increase in the surface interaction energy up to a specific interaction energy whereby there is a maximum rate. The maximum occurs when kdes and kdiss N2O balance one another. Increasing the adsorbate-surface interaction energy beyond this point decreases the rate of reaction as the surface becomes covered with an oxygen overlayer.

An important topic in this book is the prediction of reaction mechanisms. Elucidating the mechanism is enhanced by the construction of reaction energy diagrams which follow the energy changes of the di erent reaction intermediates as the reaction proceeds through its reaction cycle.

The kinetic expressions which govern di erent reaction mechanisms are usually very di erent. We will illustrate this by comparing expression (2.2) with the kinetic expression of N2O decomposition found for zeolites. The N2O decomposition reaction has a very di erent reaction sequence when catalyzed by isolated Fe cations in a zeolite, as compared with the reaction sequence found for catalysis by transition metals.

As we will see in Chapter 4, in the zeolite system we find that reaction occurs in two steps:

where [ ] denotes a vacancy site. Both steps are thought to be irreversible. In the presence of water the reaction sequence dies due to the formation of the non-active Fe(OH)2+ intermediate. The equilibrium constant for H2O adsorption is K . In the presence of water the kinetic rate expression for N2O decomposition becomes[6]

The rate of N2O decomposition here remains linear in N2O partial pressure, also at high pressures. This is quite di erent to what is found in Eq. 2.2 for N2O decomposition over the metal. Once again Sabatier-type behavior is expected as a function of the metaloxygen interaction energy. The rate of reaction a (ka) increases with an increase in the metal-oxygen bond energy, whereas the rate of reaction b (kb) decreases.

More generally, for the reaction of R to product P which proceeds through the formation of adsorbed intermediates I1 and I2:

kads

one can deduce the following steady-state expressions:

24 Chapter 2

Figure 2.3. Schematic graph of the activity of hydrocarbon hydrogenation as a function of the adsorption coe cients of the respective substrate molecules[7a].

As the interaction between reactant and surface increases, the rate according to Eq. 3b will increase linearly at lower pressures and subsequently saturate to a constant value at higher pressures. The production of P shows a maximum which is defined here as Sabatier’s maximum when

kr ≈ kdes(2)

To the left of the Sabatier maximum the surface is predominantly covered by the reactant, to the right of the maximum the surface is predominantly covered by products. To the right of the maximum the rate decreases because of the decrease in the desorption rate.

An interesting illustration of this concept is given by a comparative study of the hydrogenation of unsaturated hydrocarbons presented in Fig. 2.3. The rate of hydrogenation of di erent hydrocarbons is given as function of their adsorption equilibrium constants. One notes the volcano-type dependence found experimentally. This behavior implies that the rate of hydrogenation is a direct function of the adsorption constant of the reactant molecule. Mittendorfer et al.[7b] have shown theoretically that the binding energies for C4 to C6 intermediates on Pt(111) increase in following order:

Benzene < Butene < Butadiene < Butylene

This ordering is consistent with the changes that occur along the x-axis in Fig. 2.3.

Sabatier’s principle provides a kinetic understanding of the catalytic cycle and its corresponding elementary reaction steps which include adsorption, surface reaction, desorption and catalyst self repair. The nature of the catalytic cycle implies that bonds at the surface of the catalyst that are disrupted during the reaction must be restored. A good catalyst has the unique property that it reacts with the reagent, but readily becomes liberated when the product is formed. This will be further discussed in Section 2.2, where we describe the kinetics of elementary surface reactions and their free energy relationships.

2.1.1.2 Reaction Cycles; Intermediate Reagents

We will note in Chapter 7 that biochemical systems often consist of reaction cycles where the key molecular intermediate is regenerated after the catalytic reaction. The intermediate itself can be a catalytic reagent. In the biochemical reaction cycle, enzymes catalyze reactions between di erent molecular components in order to convert and create the catalytic reagent. For instance, in the citric acid cycle, see Fig. 2.4, which produces energy, an activated acetyl unit reacts with oxaloacetate and CO2 is produced by the oxidation of molecular fragments[8] . The overall reaction involves the conversion of acetyl and the water to CO2 and H2 and metabolic energy.

Figure 2.4. Citric acid cycle. This series of reactions is catalyzed by the following enzymes as numbered in the diagram: (1) Citrate synthase, (2) Aconitase, (3) Aconitase, (4) Isocitrate dehydrogenase, (5) α-Ketoglutarate: dehydrogenase complex, 6) Succinyl CoA syntetase, (7) Succinate dehydrogenase, (8) Fumarase and (9) Malate dehydrogenase. Adapted from L. Stryer[8].

Each step in the citric acid cycle is catalyzed by an enzyme. Two CO2 molecules are split o in reaction steps 4 and 5. The addition of H2O helps to regenerate the catalytic oxaloacetate intermediate. While each step in the citric acid cycle in itself is catalytic, the regeneration of the catalytic reagent oxaloacetate within the cycle is critical for the overall cycle to proceed.

In chemocatalysis, an analogous cycle would involve the formation of a surface intermediate (catalytic molecule) within the reaction cycle by the catalytic reaction with reactant molecules. Free radical reaction schemes, as discussed in Chapter 4, can be considered analogues of the biochemical cycle, where a reactive chemical intermediate is regenerated