VOLUME 105, NUMBER 31, AUGUST 9, 2001
© Copyright 2001 by the American Chemical Society
FEATURE ARTICLE Adsorption of Guest Molecules in Zeolitic Materials: Computational Aspects Alain H. Fuchs*,† and Anthony K. Cheetham Materials Research Laboratory, UniVersity of California, Santa Barbara, California 93106 ReceiVed: February 22, 2001; In Final Form: May 19, 2001
Recent progress in the computation of thermodynamic properties of guest molecules in zeolites, using classical molecular simulation techniques, is reviewed. It is shown that grand canonical Monte Carlo simulations, using statistical biaising for studying large anisotropic molecules, together with an appropriate guest-guest force field, may provide a reasonably accurate prediction of single component and binary mixture adsorption data for systems such as normal and branched alkanes, benzene, alkyl benzene isomers and halocarbon molecules in a variety of aluminosilicate hosts. The Monte Carlo algorithms used to obtain reliable thermodynamics data (adsorption isotherms and heats) are discussed as well as the newly developed semiempirical force fields, which allow a better transferability of the potential parameters from one guest/ host system to another.
I. Introduction Zeolitic materials and related open-framework inorganic materials are gaining increasing importance in industrial applications. In two of the most widespread applications, i.e., molecular sieving and catalysis, a crucial role is played by adsorption and transport of the guest molecules. From a more academic point of view, the behavior of fluids in confined geometries has also attracted much interest in the past few years. While the macroscopic science of this field is well developed, there is a need for a more fundamental microscopic understanding of the phenomena, as well as means for predicting thermodynamics and transport properties in a variety of guesthost systems. The properties of confined fluids are well described by analytical theory only in the case of model mesoporous materials such as slit pores or cylinders. However, atomic details need to be taken explicitly into account in order to reproduce the adsorption properties of fluids in micropores. Molecular simula* Corresponding author. † Permanent address: Laboratoire de Chimie Physique,Universite ´ de ParisSud, 91405 Orsay, France.
tion, in conjunction with experiments, has played an important role in the past few years in developing our understanding of the relation between microscopic and macroscopic properties of confined molecular fluids in zeolitic materials. The most recent developments in this field will be reviewed here. Two principal types of theoretical treatments of guest molecules in zeolite hosts can be found in the literature. On one hand, ab initio quantum chemistry techniques are used to address the problem of molecular chemisorption processes and reactions at Brønsted acid sites. On the other hand, classical Monte Carlo (MC)/molecular dynamics (MD) simulations are used to study adsorption and transport of molecules in zeolite pores. The quantum chemistry approach is rather time-consuming and, for this reason, calculations were often limited in the past to finite cluster models of zeolite. Modern ab initio MD codes can now be used to study larger systems, such as a methanol molecule interacting with the Brønsted site in a periodic model of chabazite.1,2 The classical MC/MD approach has been widely used to study the behavior of simple molecules (e.g., rare gases or simple hydrocarbon molecules) in siliceous zeolites such as silicalite.
10.1021/jp010702q CCC: $20.00 © 2001 American Chemical Society Published on Web 07/06/2001
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TABLE 1: Host-Guest Systems (pure components adsorption) Studied by Molecular Simulation guestf/hostV
FAU X
MFI
FAU Y
rare gases
11-23
26, 37, 95
24, 25,26, 95
N2 O2 H2 CO CO2 SF6 NH3 H2O methane
6, 19, 27 27
26-30,95 26-30, 95
26, 95 26, 95
ethane propane n-butane i-butane n-pentane 2-methyl alkane (C4-C9) neopentane n-hexane cyclohexane n-heptane n-octane n-nonane n-decane ethene, butene CF4 CF3Cl CF2Cl2 CFCl3 CHF3 chloroform trichloroethene isopropylamine acetonitrile benzene o-xylene m-xylene p-xylene other alkylbenzene m-dinitrobenzene phenol pyridine
other zeolitesa 21v,36v,23yz,31p,32pq, 33z,46um, 49v, 94w 26v, 37v 100, 101v
34 23 35 44 12,23,27,45,47,48, 50,51,52,53,54,55 12, 47, 52,60, 61,89 12,47,51, 52, 60, 61 39, 52, 60,61, 62,63, 67,68 52,55,60, 63, 67 60, 61, 62 63 52 55, 60, 61, 62
29 95 95 59
55, 60,61,62, 67 62 62 62, 67, 68 89 23
76, 77, 78
95 35, 95 42 25
33, 62$
35x 40v, 41y, 42v 23xz, 31p, 32pq, 36v, 45x, 49v, 56m, 57p, 58p 57p 57p, 64u, 65r 33v, 57p, 62xuvw, 64u, 65r
62$
57p, 62xuvw, 64u, 65r
33, 62$ 66 33, 62$ 62$ 62$ 62$
33v, 62xuvw, 64u, 65r
72 72,73 35
71 71 71, 74, 75 71 71 72 72,73 35
80, 98
79,80,96
84 84
25, 79, 81, 82, 83 25, 79,81, 82, 83, 97,102 86
33v, 62xuvw, 65r 62xuvw 62xuvw 62xuvw 69u, 70 23xz
35x 87x 79
76 75, 86, 99 78 35
35
86xms 85 35x
computed quantitiesb P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, S P, S P, I P, I Q, S P, I, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, S P, I, Q,S P, Q, S P, Q, S P, Q, S P, Q, S P, Q, S P, Q, S Q, S P, S P, I, Q, S P, S P, I, Q, S P, I, Q, S P, S P, S P, I, Q, K, S Q, S
a
x: Mordenite; y: Heulandite; z: Boggsite; t: Chabazite; u: Ferrierite; v: Zeolite A; w: Rho; m: Zeolite L; r: Zk-5; s: Mazzite; p: AlPO45; q: VPI-5. b P: interaction potential energy; I: adsorption isotherms; Q: heats of adsorption; K: Henry’s constants; S: structural data on the adsorbed phase.
A large number of different equilibrium configurations of the system can be generated through these techniques, enabling one to compute ensemble average quantities, which can be related to thermodynamics and transport properties of the guest molecules. This approach relies on semiempirical intermolecular potentials, which constitutes a main drawback of the classical methods. Bridging the gap between the quantum chemistry and the classical approaches is a major challenge in molecular simulation. Electronic density functional theory based MD codes are still far from being able to address long time diffusion and high loading adsorption processes. This is not only a problem of computing time. Basic theoretical problems remain open, such as the inclusion of long-range dispersion interaction in the models. The development of mixed quantum/classical methods, once the embedding problems are solved, is expected to yield new powerful methods for zeolite catalysis studies. For the time being, the classical, semiempirical, approach is the only feasible way of addressing thermodynamic and transport phenomena in complex guest/host systems in which no chemical reactivity takes place. Recent progress in the simulation of
thermodynamic properties of guest molecules in zeolites and other related porous materials is reviewed here. It is shown that the use of recently developed techniques allows the simulation of systems that a few years ago were considered impossible to study via computer simulation. Systems of relevance to commercial applications, such as normal and branched alkanes, benzene, alkyl benzene isomers, and halocarbon molecules in aluminosilicate hosts, are now being studied by molecular simulation. The MC algorithms used to obtain reliable thermodynamic data (adsorption isotherms and heats) are discussed as well as the newly developed semiempirical force fields, which allow a better transferability of the parameters from one guest/ host system to another. This topic, which dates back to the late 1970s, has been partly reviewed before,3-7 and we shall concentrate here on the substantial amount of work that has appeared in this area in the past decade (Tables 1 and 2,11-102). We do not intend to cover transport properties in any detail since two excellent reviews have already appeared in this area.8,9 Finally we should like to mention a very useful introduction to zeolite modeling that has appeared recently.10
Feature Article
J. Phys. Chem. B, Vol. 105, No. 31, 2001 7377
TABLE 2: Host-Guest Systems (binary mixtures adsorption) Studied by Molecular Simulation guestf/hostV
MFI
N2/O2 Ar/CH4/CF4 binary mixtures methane/ethane/ propane/butane binary mixtures ethane/ethene n-butane/i-butane n-pentane/2-methyl butane n-hexane/2-methyl pentane n-hexane/3-methyl pentane n-heptane/2-methyl hexane CF2Cl2/CO2 m-xylene/p-xylene a
FAU FAU other computed X Y zeolitesa quantitiesa 30
23, 88 51, 55
23xz
89 63 63, 90 63, 90 91 63, 90 85
92, 93 81-84
P, I, S P, I, Q, S P, I, Q P, I, Q, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, I, Q, K, S P, Q, K, S P, I, Q, S
Symbols as in Table 1.
II. Computational Methodologies Monte Carlo (MC) Simulations. MC simulations are particularly convenient for computing equilibrium thermodynamic quantities such as the average number of adsorbed molecules 〈N〉 , the isosteric heat of adsorption qst, and the Henry’s constants K. In addition, MC simulations provide detailed structural information, in particular the location and distribution of adsorbed molecules in the pores. Adsorption quantities are usually computed in the grand canonical (GC) statistical ensemble in which the chemical potential (µ), volume (V), and temperature (T) are fixed.103 These thermodynamic conditions are close to the experimental conditions where one wants to obtain information on the average number of particles in the porous material as a function of the external conditions. At equilibrium, the chemical potentials of the fluid bulk phase and the adsorbed phase are equal. The pressure in the reservoir fluid can be calculated from an equation of state, and it is thus directly related to the chemical potential in the adsorbed phase. The ensemble average number of molecules in the zeolite, 〈N〉 , is computed directly from the simulation. By performing simulations at various chemical potentials, at a given temperature, one obtains the adsorption isotherm. Experimental adsorption isotherms yields the excess number of molecules adsorbed in the porous medium which is not, in principle, directly comparable to 〈N〉 . Since zeolite pores are small, the correction is negligible under normal conditions. The isosteric heat of adsorption is another quantity of interest that can be obtained from GCMC simulations:103
qst ) RT -
( ) ∂UN ∂N
V.T.
) RT -
〈NUN〉 - 〈N〉〈UN〉 〈N2〉〈N〉2
(1)
where UN is the potential energy of the adsorbed phase. It is assumed in eq 1 that the gas phase is ideal. The Henry coefficient K is defined as the slope of the adsorption isotherm at zero pressure. It is directly related to the excess chemical potential of the adsorbed molecules:104
K ) β exp(-βµex)
(2)
Henry’s coefficients are usually computed in the NVT ensemble,47,67 in which the number of adsorbed molecules (N), volume (V), and temperature (T) are fixed. It should be stressed that the calculation of the Henry coefficient requires two simulations (one in the zeolite and one in the ideal gas phase) for molecules which contain internal nonbonded interactions. A full development of the statistical mechanics of the µVT and NVT ensembles and the description of the corresponding
Monte Carlo algorithms have been given in several publications (see for instance Smit and Frenkel104) and will not be repeated here. In a MC simulation, microscopic reversibility requires that gen acc ens gen acc Pens o ‚Pofn‚Pofn ) Pn ‚Pnfo‚Pnfo
(3)
where Pens is the ensemble probability of a microscopic state “o” (for “old”) or “n” (for “new”). Pgen and Pacc are the probabilities to generate and to accept the ofn or the nfo moves, respectively. In a standard GCMC simulation, three types of moves are performed. The first one is a thermal equilibration move. It consists of a displacement and/or rotation step in the case of a rigid molecule. In the case of nonrigid molecules, it also includes perturbation to intramolecular degrees of freedom. In the second type of move, a new molecule is inserted into the system (transferred from the gas to the zeolite) at a randomly chosen position with a randomly chosen orientation. In the third type of move, a molecule is randomly chosen and removed. In the case of a binary mixture, an additional type of trial (swap) can be used which consists of changing the identities of the adsorbed particles without changing their positions and orientations.105 When all of these Monte Carlo moves are randomly generated, gen Pgen ofn ) Pnfo and the acceptance probabilities depend only on the ensemble probabilities.82,104 These random moves are usually handled by the standard Metropolis sampling scheme.106 Standard GCMC simulations have proven successful in predicting adsorption behavior of a variety of simple guest molecules in zeolites (from rare gases to simple hydrocarbons, see Table 1). For more complex (anisotropic) molecules, such as long alkane chains and aromatic molecules, the acceptance rate of the insertion/deletion steps drops and convergence of the GCMC algorithm can be achieved only by implementing statistical bias techniques. In the statistical bias, the molecule is inserted at an energetically favorable region of space, thus increasing the acceptance rate of this step; in addition, by subsequently modifying the acceptance rules so that eq 3 is still satisfied, one can ensure that the GC ensemble is correctly sampled. Different bias schemes have been proposed in the literature. For alkane chains, the configurational-biais (CB) technique is used, based upon the Rosenbluth sampling scheme,107 which consists of inserting the chain, bead by bead, into the voids of the porous material.60,104 The insertion of a molecule in the pore first consists of generating a number of candidate positions for the atom to be inserted. Then one of these positions is selected according to the energy contributions from the external degrees of freedom of the molecule. As the molecule is constructed, a Rosenbluth weight is accumulated and used in the acceptance rule for insertions. This procedure, initially derived by Smit60 for CB-GCMC simulation of the adsorption of united atom (UA) linear alkane chain models, has recently been extended to branched alkanes63,68 and to all atom (AA) alkane models.68 The CB-GCMC scheme is obviously limited to flexible chain molecules, and other bias have to be used in the case of rigid molecules. In the case of aromatic molecules, Snurr et al.76 have introduced three biaised GCMC schemes. The first one is the cavity-bias first suggested by Mezei.108 It consists of only attempting a molecular insertion where the sorbate molecules leave a “cavity” which may accommodate the extra molecule. The second one is an energy-bias scheme. It involves attempting insertions more often in the energetically more favorable regions
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TABLE 3: Comparison of Standard GCMC and Biased GCMC Algorithms Computed Adsorption Quantitiesa low loading P ) 0.01 Pa insertion (p-xylene) standard I/D using Vacc using Vacc+CB using Vacc+CB+OB swap (50/50 mixture) swap OB-swap
high loading P ) 10 Pa
〈N〉
Pacc (%)
〈N〉
Pacc (%)
0.44 0.40 0.42 0.43 1.12 1.00
0.1 0.2 0.2 0.7 11.7 27.1
2.0
