Theory_of_Zeolite_Catalysis

08/16/2001 05:42 PM Chemical Engineering-v28 PS069-11.tex PS069-11.xml APserialsv2(2000/12/19) Textures 2.0 THEORY OF ZEOLITE CATALYSIS R. A. van Santen* and X. Rozanska Schuit Institute of Catalysis, Eindhoven University of Technology Eindhoven 5600 MB, The Netherlands I. Introduction 400 II. The Rate of a Catalytic Reaction 401 III. Zeolites as Solid Acid Catalysts 403 IV. Theoretical Approaches Applied to Zeolite Catalysis 407 A. Simulation of Alkane Adsorption and Diffusion 407 B. Hydrocarbon Activation by Zeolitic Protons 414 C. Kinetics 427 V. Concluding Remarks 432 References 433 The reactivity of acidic zeolites to the activation of hydrocarbons is used to illustrate different modeling approaches applied to catalysis. Quantum-chemical calculations of transition-state and ground-state energies can be used to determine elementary rate constants. But to predict overall kinetics, quantum-mechanical studies have to be com- plemented with statistical methods to compute adsorption isotherms and diffusion constants as a function of micropore occupation. The relatively low turnover frequencies of zeolite-catalyzed reactions com- pared to superacid-catalyzed reactions are due mainly to high activa- tion energies of the elementary rate constants of the proton-activated reactions. These high values are counteracted by the significant in- teraction energies of hydrocarbons with the zeolite micropore wall dominated by van der Waals interactions. ©C 2001 Academic Press. *To whom correspondence should be addressed. 399 Copyright ©C 2001 by Academic Press All rights of reproduction in any form reserved. ADVANCES IN CHEMICAL ENGINEERING, VOL. 28 0065-2377/01 $35.00 08/16/2001 05:42 PM Chemical Engineering-v28 PS069-11.tex PS069-11.xml APserialsv2(2000/12/19) Textures 2.0 400 R. A. VAN SANTEN AND X. ROZANSKA I. Introduction Predictability of activity, selectivity, and stability based on known struc- tures of catalysts can be considered the main aim of the theoretical ap- proaches applied to catalysis. Here, for a particular class of heterogeneous catalysts, namely, acidic zeolites, we present the theoretical approaches that are available to accomplish this goal, which lead to a better understand- ing of molecular motion within the zeolitic micropores and the reactivity of zeolitic protons. It is not our aim to introduce the methods as such, since introductory treatments on those can be found elsewhere. Rather we focus on their application and use to solve questions on mechanisms and reactivity in zeolites. The discussion is focused on an understanding of the kinetics of zeolite-catalyzed reactions. We use the activation of linear alkanes and their conversion to isomers and cracked products as the main motive of our discussion. This class of reactions catalyzed by acidic zeolites is an ideal choice to illustrate the state of the art of theoretical molecular heterogeneous catalysis, because the reaction mechanisms, zeolite micropore structure, and structure of the catalytically reactive sites are rather well understood. Whereas simulation methods are available to model zeolite structures as a function of their composition as well as their topology [1–9], we do not discuss FIG. 1. The catalytic cycle of a zeolite-catalyzed reaction. 08/16/2001 05:42 PM Chemical Engineering-v28 PS069-11.tex PS069-11.xml APserialsv2(2000/12/19) Textures 2.0 THEORY OF ZEOLITE CATALYSIS 401 those techniques and their results here but refer to some of the results when discussing chemical reactivity and adsorption. Perpetual improvements in both computers and ab initio codes allow nowadays calculations on realistic structures [10–12]. Also, we do not present an overview of the deep mech- anistic insights that have been obtained recently on a molecular level for many hydrocarbon conversion reactions. Most of the practically important reactions have now been analyzed by quantum-chemical techniques [13–31] (viz., reactions with aromatic species [13–16], olefins and alkanes [17–22], water and methanol [23–26], metallic clusters supported on zeolite or metal exchanged zeolites [27–30], and acetonitrile [31]). We are concerned with the kinetics of zeolite-catalyzed reactions. Empha- sis 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. II. The Rate of a Catalytic Reaction A catalytic reaction is the result of a cyclic process that consists of many elementary reaction steps. The essence of a catalytic reaction is that the cat- alytic reactive center reappears after each cycle in which reactant molecules are converted into products. Since zeolites are microporous systems, a spe- cial feature is the coupling of reaction at the protonic centers with diffusion of the molecules through the micropores to and from the zeolite exterior. The zeolite catalytic cycle is sketched in Fig. 1. To reach the catalytic reactive center, molecules have to adsorb in the mouth of a micropore and diffuse to the catalytic center, where they can react. Product molecules have to dif- fuse away and, once they reach the micropore mouth, will desorb. Clearly, then, one has to complement quantum-chemical information on reactivity, concerned with the interaction of zeolite protons with reactants, with infor- mation on diffusion and on adsorption of reactants and products. Again, we do not exhaustively discuss molecular theories of diffusion and adsorption in zeolites but refer to other studies [32–34]. However, we highlight some important results significant to the kinetic analysis we are presenting. A characteristic time scale of a catalytic reaction event such as proton- activated isomerization of an adsorbed alkene molecule is 102 s. However, quantum-chemical calculations predict energies of electrons with character- istic time scales of 10−16 s. Of use to us are the potential energies that such 08/16/2001 05:42 PM Chemical Engineering-v28 PS069-11.tex PS069-11.xml APserialsv2(2000/12/19) Textures 2.0 402 R. A. VAN SANTEN AND X. ROZANSKA methods generate that determine the forces that act on the nuclei, which determine the vibrational frequencies. The characteristic time of vibrational motion is 10−12 s. In zeolites, diffusional times can be as short as 10−8 s and adsorption time scales are typically 10−6 s. Dependent on the free energies of adsorption, the time scale of desorption of a molecule is 10−4 s or longer. The time scales of the proton-activated elementary reactions are of the or- der of 10−4 s due to their high activation energies. The long time scale of reaction compared to that of vibrational motion implies that thermal energy exchange between reaction molecule and zeolite wall is fast. This is the jus- tification for the use of transition reaction rate theory [35–37]. In its most elementary form, the rate expression, rTST = kTh e (�S#/R) e−(Eact/RT ), (1) can be shown to be rigorously valid, if the rate of energy exchange is fast. In Eq. (1), the probability of passing the activation energy barrier by reactants with sufficient energy has been assumed to be equal to one. In this equa- tion, k is Boltzmann’s constant, h is Planck’s constant, �S# is the activation entropy, and Eact is the transition state barrier height. R is the gas constant. The major advance of the past decade is that, using quantum-chemical computations, activation energies (Eact) as well as activation entropies (�S#) can be predicted a priori for systems of catalytic interest. This implies much more reliable use of the transition-state reaction rate expression than be- fore, since no assumption of the transition state-structure is necessary. This transition-state structure can now be predicted. However, the estimated ab- solute accuracy of computed transition states is approximately of the order of 20–30 kJ/mol. Here, we do not provide an extensive introduction to mod- ern quantum-chemical theory that has led to this state of affairs: excellent introductions can be found elsewhere [38, 39]. Instead, we use the results of these techniques to provide structural and energetic information on catalytic intermediates and transition states. Because of the size of the reaction centers to be considered, a break- through in quantum chemistry had been necessary to make computational studies feasible on systems of catalytic interest. This breakthrough has been provided by density functional theory (DFT). Whereas in Hartree–Fock- based methods, used mainly before the introduction of DFT, electron ex- change had to be accounted for by computation of integrals that contain products of four occupied orbitals, in DFT these integrals are replaced by functionals that depend only on the electron density. An exchange-correla- tion functional can be defined that accounts for exchange as well as correla- tion energy. The correlation energy is the error made in Hartree–Fock-type theories by the use of the mean-field approximation for electronic motion. 08/16/2001 05:42 PM Chemical Engineering-v28 PS069-11.tex PS069-11.xml APserialsv2(2000/12/19) Textures 2.0 THEORY OF ZEOLITE CATALYSIS 403 The still unresolved problem is the determination of a rigorously exact func- tional, as all currently used DFT functionals are approximate. By computation of the stationary points of the n-dimensional energy di- agram of the interacting system, the structure of local energy minima as well as the transition state can be determined. For many systems, these in- teraction energies have an accuracy of the order of 5–15 kJ/mol. For this reason, as we illustrate later, discrepancies between theoretical calculation and experiment can be often related to shortcomings in model assumptions rather than to quantum-chemical approximations. Around the ground-state energy minimum and the transition-state saddle point, the potential can be expanded as a function of displacement of the normal coordinates with re- spect to their stationary values. Within the harmonic approximation, the vibrational spectrum and hence the corresponding entropy can be easily computed. The entropy follows from the expression S = −k ln p f (2a) = −k ln �i 11 − e−(hvi /kT ) , (2b) where i sums over the n normal vibration modes of the ground-state system and the n − 1 normal modes of the transition state. pf stands for the partition function and vi is the normal mode frequency. III. Zeolites as Solid Acid Catalysts The structure of a zeolite is illustrated in Fig. 2, using mordenite as an example. The zeolitic framework can consist of four valent (Si), three valent (Al, Ga, Fe), or five valent (P) cations, tetrahedrally coordinated with four oxygen atoms. The oxygen atoms bridge two framework cations. When the lattice cation is Si+IV, the framework charge is neutral. When Al+III substi- tutes for Si+IV, the framework becomes negatively charged. Zeolites of such a composition can exist when extra framework cations are ion exchanged into the zeolite cavities. In the case where this cation is NH+4 , the heating of the material induces ammonia to desorb. The proton that is left behind will bind to an oxygen atom bridging Al and Si framework cations (see Fig. 3). For an extensive discussion of zeolite crystals of catalytic interest, refer to Refs. 40 and 41. Also, several available reviews discuss the nature of the proton bonded to the bridging oxygen atom [42–45]. Although strongly covalently bonded to the zeolite, hydrogen attached to the bridging oxygen atom reacts as a proton with reactant molecules and 08/16/2001 05:42 PM Chemical Engineering-v28 PS069-11.tex PS069-11.xml APserialsv2(2000/12/19) Textures 2.0 404 R. A. VAN SANTEN AND X. ROZANSKA FIG. 2. The structure of mordenite zeolite. hence induces transformation reactions known also from superacid catalysis [46–48]. However, as will be explained, the detailed mechanism of activa- tion is very different from that known in superacid catalysis. Whereas in su- peracids low-temperature reactions generate carbonium and carbenium ions as stable but sometimes short-lived intermediates, the nature of carbonium FIG. 3. Hydrogen bonded to a bridging O atom in mordenite. 08/16/2001 05:42 PM Chemical Engineering-v28 PS069-11.tex PS069-11.xml APserialsv2(2000/12/19) Textures 2.0 THEORY OF ZEOLITE CATALYSIS 405 and carbenium ion intermediates is often quite different in solid acid catal- ysis. Essentially, carbonium and carbenium cation intermediates are parts of transition states or activated intermediate states through which reactions proceed. The high activation barriers of the elementary reaction steps im- ply that zeolitic solid acids are weakly acidic compared to superacids. One way to understand this is that, different from superacid media, the dielectric constant of a zeolite is low (ε ∼ 4) [49–51] and hence charge separation has a high energy cost [3]. It is now also well established that the zeolite framework has some flex- ibility. Due to the dominance of directed covalent bonding, the tetrahedra are rather rigid, but the bond-bending potential energy curve for bending of the Si–O–Si angle is rather flat. Local distortions of the framework can be easily accommodated because of the low energy cost of bending of the Si–O–Si angle. This is important because, as we will see later, attachment of a proton to the bridging oxygen atom increases the Si–O and Al–O dis- tances and hence requires a larger volume than a free Si–O–Al unit. Upon deprotonation the Si–O and Al–O bonds decrease and hence the effective volume of the concerned tetrahedron decreases. For low Al/Si ratio zeolites, differences in acidity of the zeolitic proton relate to slight differences in the local relaxability of the zeolite lattice around the protons [1–9]. For zeolites with a high Al/Si ratio, the zeolite proton interaction increases. Compositional variations may cause the deprotonation energy to vary by ∼1–5%. For a proper understanding of the interaction of hydrocarbons with ze- olitic protons, it is important to realize that the oxygen atoms, with a com- puted charge close to −1, and the Si atoms, with a computed charge close to +2, have very different sizes. This is illustrated in Fig. 4. Oxygen atoms are relative large and the framework cations are small. This implies that hydrocarbon molecules, when adsorbed in the zeolite micropores, will expe- rience mainly interactions with the large oxygen atoms, which inhibit direct interactions with the smaller lattice cations. Bonding within the zeolite framework is mainly covalent, and ionic bond- ing contributes only ∼10% [52–54]. The attractive interaction between the siliceous zeolite framework and hydrocarbons can best be described as a van der Waals dispersive interaction due to the attraction of fluctuating dipole moments of electronic motion on the oxygen atoms and hydrocar- bons [55–59]. The van der Waals interaction Vv·W = −Cαiα j ri j (3) is proportional to the polarizabilities αi of zeolitic oxygen atoms and, for instance, for alkanes the polarizabilities α j of CH2 or CH3 units. The polar- izability αi is approximately proportional to the volume of a molecular unit. 08/16/2001 05:42 PM Chemical Engineering-v28 PS069-11.tex PS069-11.xml APserialsv2(2000/12/19) Textures 2.0 406 R. A. VAN SANTEN AND X. ROZANSKA FIG. 4. Hexane occlude in a zeolite micropore. In Eq. (3), C is a constant, and ri j the distance between the centers of mass of units i and j [55–57]. Density functional theory quantum-chemical codes do not predict this van der Waals dispersive interaction accurately [60, 61]. One has to include the repulsive contribution to obtain the interaction potential. In the Lennard–Jones expression, the attractive and repulsive con- tributions can be described by Vv·W = −4εi j ( ( σi j ri j )6 − ( σi j ri j )12 ) , (4a) where σi j is the sum of the van der Waals radius of i and j, and εi j the well depth [62]. However, the repulsive part of the potential is best described by the Born repulsion expression, leading to the Buckingham interaction potential: Vv·W = −Cαiα j r 6i j + Ae−ari j . (4b) The Born repulsion expression stems from the Pauli principle, which re- sults from the prohibition of electrons with the same spin occupying the same wavefunction, a situation that occurs when doubly occupied orbitals interact. Whereas the van der Waals interaction cannot be computed accurately from 08/16/2001 05:42 PM Chemical Engineering-v28 PS069-11.tex PS069-11.xml APserialsv2(2000/12/19) Textures 2.0 THEORY OF ZEOLITE CATALYSIS 407 DFT quantum-chemical codes, the Born repulsive interaction is accurately computed. Expressions (4a) and (4b) are two-body interaction potentials commonly used in codes that predict energies or geometries based on em- pirical potentials. IV. Theoretical Approaches Applied to Zeolite Catalysis We now report how theoretical methods can be used to provide infor- mation 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. A. SIMULATION OF ALKANE ADSORPTION AND DIFFUSION 1. Methods and Theory Configurationally biased Monte Carlo techniques [63–65] have made it possible to compute adsorption isotherms for linear and branched hydrocar- bons in the micropores of a siliceous zeolite framework. Apart from Monte Carlo techniques, docking techniques [69] have also been implemented in some available computer codes. Docking techniques are convenient tech- niques that determine, by simulated annealing and subsequent freezing tech- niques, local energy minima of adsorbed molecules based on Lennard–Jones- or Buckingham-type interaction potentials. The interaction energy is determined by potentials as defined in Eq. (4). Bond-bending energy terms within the hydrocarbons are also included. The parameters of the interaction potential with zeolite have to be determined by a fit of experiment with theory. June et al. [66] and Smit and Maesen [67] used slightly different parameters (see Table I). The latter used pa- rameters fitted on experimental adsorption isotherms of hexane in silicalite. Whereas in siliceous materials the dominant interaction term is given by the 08/16/2001 05:42 PM Chemical Engineering-v28 PS069-11.tex PS069-11.xml APserialsv2(2000/12/19) Textures 2.0 408 R. A. VAN SANTEN AND X. ROZANSKA TABLE I VAN DER WAALS INTERACTION POTENTIALS FOR HYDROCARBONS ADSORBED IN ZEOLITES Parameter set σCH3,O = σCH2,O (A˚) εCH3,O (K) εCH2,O (K) June et al. [66] 3.364 83.8 83.8 Smit and Maesen [67] 3.64 87.5 54.4 Buckingham potential, in zeolites with protons or cations additional interac- tion terms become important. We discuss the interactions with protons later, but here we comment briefly on the effect of the presence of cations in zeo- lite micropores. Kiselev and Quang Du [68] were among the first to analyze adsorption in the hydrocarbon–zeolite system. Cations other than protons have a charge close to their