Molecular dynamics studies of chemical processes in zeolites (*)
F. DELOGU, P. DEMONTIS, G. B. SUFFRITTIand A. TILOCCA
Dipartimento di Chimica, Università di Sassari - Via Vienna 2, I-07100 Sassari (Italy)
(ricevuto il 28 Febbraio 1997; approvato l’8 Maggio 1997)
Summary. — The use of classical Molecular Dynamics simulations for the study of chemical processes in zeolites is discussed. Some examples including recent results on the diffusion of binary mixtures, on the energy relaxation of vibrationally excited molecules and on the recombination of photodissociated I2molecule in silicalite are
illustrated.
PACS 31.15.Qg – Molecular dynamics and other numerical methods. PACS 31.70.Dk – Environmental and solvent effects.
PACS 82.30 – Specific chemical reactions; reaction mechanisms. PACS 83.80.Pc – Inorganic materials: zeolites.
PACS 01.30.Cc – Conference proceedings.
1. – Introduction
Zeolites are well-known crystalline microporous aluminosilicates of natural or synthetic origin widely used in chemical industry as adsorbents, molecular sieves, and especially as catalysts.
In the catalytic action of zeolites, at least five different aspects can be distinguished. The most frequently mentioned are the selectivity of the reactants, the selectivity of products and the very chemical effect of acid-base and/or transition metal catalysis caused by protons, cations or transition metal atoms which are present on the surface of the micropores.
However, there are at least two other properties of zeolites which can influence the reactivity of the sorbed species: the heat bath effect of the framework, which can dissipate the excess energy of a chemical process or furnish thermal energy to reactants or products, and the influence of the (often locally strong) electric fields present in the micropores on the electronic energy states of the sorbates, which help in stabilizing reaction intermediates, such as radicals and ions.
One of the most popular techniques which can be adopted to study zeolites,
(*) Paper presented at the “First International Workshop on Reactivity of Oxide Materials. Theory and Experiment”, Como, 8, 9 November 1996.
including adsorbed species, at a microscopic scale, is Molecular Dynamics (MD) [1, 2]. MD makes use of classical dynamics to generate a phase space sampling of the system as an approximation of the much more complex quantum mechanics to derive structural and dynamical information.
In order to apply MD simulations to the study of chemical reactions all the above-mentioned aspects of a chemical reaction should be accounted for. The selectivity of reactants and products is essentially a steric effect, and it was thoroughly shown [3], in connection with the MD study of diffusive processes, that MD is a valuable tool for simulating this kind of phenomena. However, when a reactive process occurs in a zeolite, the simultaneous diffusion of different species (reactants, products, intermediates) must be considered, and the MD study of this class of diffusive phenomena is just at the beginning [4, 5].
The heat bath effect is well reproduced by MD, and its importance and effectiveness were proven by computer simulations [6-9]. The two remaining effects are of strictly quantum-mechanical nature. However, the catalytic action could be simulated (with some approximations) by MD if a good smooth fit of a reliable potential energy hypersurface of the reactive process is available. The evaluation of these hypersurface must be performed by quantum-mechanical methods. The problems connected with the quantum calculations in the field of zeolites are thoroughly discussed by Sauer et
al. [10] in a recent review article.
Although the evaluation of realistic potential energy hypersurfaces for complex reactive mechanisms often could be computationally awkward, it could not be so for simple radicalic reactions. The last is an example of a class of reactions for which reasonable model potentials could be adequate for meaningful simulations.
If the hypersurface shows potential energy barriers higher than the available thermal energy, special but well-known techniques are required in order to use MD [2, 3].
The last remaining effect, i.e. the influence of the electric field, if it is not included in the potential energy hypersurface, can be accounted for directly in the simulations by using the Car-Parrinello (CP) method [11].
Therefore, it appears that MD could be currently used to simulate chemical reactions in zeolites, but, to our knowledge, only one or two attempts have been made. It seems that some research groups have been discouraged, by the apparent complexity of the puzzle, to try to put together all the pieces, in spite of the fact that they are available. To our knowledge, the first (and the only published as yet) example of the study of a chemical reaction in zeolites was performed by June et al. [12]. The reaction was simply the isomerization between conformers of butane and hexane in rigid silicalite, but the adopted procedure is similar to the one that should be followed in any other case, as complex as it may be.
We shall outline in this paper some contributions of our group on this topic.
2. – Results and discussion
In order to verify the ability of MD to study some of the above-discussed basic phenomena involved in a chemical reaction in zeolites, we choose some models, as simplest as possible, to simulate the simultaneous diffusion of different species, to investigate the relaxation of the excess energy of a molecule in a zeolite framework
and, finally, to study a simple radicalic recombination reaction in a zeolite and to compare it with the same one in a liquid solvent.
2.1. Diffusion of mixtures of different sorbates. – The simultaneous diffusion of different guest species was simulated using MD by Chitra and Yashonath [4] in order to understand the factors controlling the diffusion mechanisms. In particular, they evaluated the diffusion coefficient of two Lennard-Jones different particles, with the same mass, in zeolite Na Y with a loading of two molecules per cage. One of the species (labeled 1) had the mass and the dimensions of xenon, while the diameter of the other one (labeled 2) was varied. By plotting the ratio of the diffusion coefficients z 4D1/D2
against the ratio of the corresponding sorbate diameters, one obtains a decreasing function with an anomalous peak corresponding to the superdiffusivity of the species labeled 2 when its dimensions fit the diameter of the windows connecting the cages.
This finding can be explained by considering that, when the size of the sorbate molecule fits the diameter of the micropores the radial force acting on a sorbate molecule is nearly zero, giving rise to a: “floating molecule” or “levitation” or superdiffusivity effect. It is worthwhile to note that these MD simulations supplement the earlier work of Derouane and co-workers [13] on the mobility of Lennard-Jones particles in a zeolite and the possibility of observing higher mobility in the channels of silicalite as pointed out by Demontis et al. [7].
In our laboratory the investigation on binary mixtures of Lennard-Jones sorbates was extended to silicalite [5]. This zeolite is the all-silica analogue of the well-known catalyst ZSM-5. Its structure [14] is characterized by two channel systems, straight along y and sinusoidal along x, which intersect with each other giving rise to elongated cavities of about 9 Å in diameter. The cross-section of the channels is about 5.5 Å.
The MD simulations were carried out for a system containing 2304 framework atoms and 16 Lennard-Jones particles having the mass of argon, but the diameter (or better the parameter s of the Lennard-Jones potential) of 8 of them was varied. Framework vibrations and flexibility were ensured by a model potential representing the interactions between framework atoms through harmonic springs connecting nearest-neighbour atoms. This model has been developed in our laboratory and yields a reasonable representation of the structure and vibrational spectrum of silicalite [15]. Each MD run lasted 3 ns, after equilibration for 150 ps.
The diffusion coefficient was evaluated for the mixtures and compared with the corresponding ones for homogeneous sorbates at the same loading.
Preliminary results show that in all the considered cases the diffusion coefficient of a species is slightly increased for the mixtures with respect to the homogeneous sorbates but with irregular trend, although superdiffusivity conditions were not met.
It seems that some co-operative mechanism is acting, and work is in progress to thoroughly ascertain its features.
2.2. Vibrational relaxation of a diatomic molecule. – The vibrational relaxation in silicalite of a diatomic molecule representing a united-atoms approximation of ethane (CH3 groups represented by one centre of force) was studied through MD
simulations [16]. The adopted model accounted for the vibrations of the system using the above-mentioned harmonic potential for the framework and a Morse potential for the diatomic molecule.
The parameters of the Morse potential were varied in order to probe the relaxation rate as a function of the vibrational frequency of the sorbed molecules. The results
Fig. 1. – Energy transfer rate from the diatomics to the zeolite framework vs. frequency of the oscillator (upper curve). For comparison, the computed vibrational spectrum of silicalite (lower continuous curve) and the experimental one (dashed curve) are also reported.
show that the framework favours the relaxation of diatomics oscillating at frequencies near to its characteristic vibrational frequencies, leading in such cases to shorter relaxation times and to an increase in the energy exchanged per collision, as illustrated in fig. 1.
Therefore, in these classical simulations, resonances between the diatomics and the framework vibrations provide an approximation of the quantum-mechanical V-V energy transfer.
As a conclusion, it was shown that the zeolite framework can be effective in dissipating excess internal energy of a sorbed molecule on a picosecond time scale. This property is important for stabilizing the newly formed products of a chemical reaction, and can be used to elucidate reaction mechanisms in zeolites. Moreover, on the basis of the principle of microscopic time reversibility, these considerations can be applied to explain the ability of zeolites to supply kinetic energy to the reactants in order to overcome potential energy barriers.
2.3. Simulation of the recombination reaction of I2in silicalite. – As an example of
an MD simulation of a chemical reaction in zeolites, we attempted [17] a qualitative study of recombination reactions of I2 in silicalite and in liquid CCl4. The reaction in
liquid phase was simulated, in order to get a comparison both with experimental data [18, 19] and with previous statistical mechanical [20, 21] and MD investiga-tions [22, 23]. The reaction is radicalic, possessing small or negligible potential energy barrier, so that standard MD simulations can be performed.
Fig. 2. – Trend of the kinetic energy of the iodine atoms in the first 10 ps following the dissociation. A) in tetrachloromethane; B) in silicalite.
A simplified model has been developed to study the reactive process. The potential acting between I atoms is represented by a Morse potential function. The two iodine atoms are embedded in a Lennard-Jones liquid simulating CCl4 or in a vibrating
silicalite lattice. After equilibration and 10 ps of free diffusion, a photodissociation is simulated by giving the iodine atoms a suitable velocity, and the evolution of the system is then studied for 60 ps.
The observed fate of the two iodine atoms can be a primary recombination (the direct formation of a stable I2 molecule through a quick relaxation of the excess
energy), a dissociation or a more complex behaviour, with the atoms undergoing one or more collisions before a recombination. The direct reaction is favoured in the liquid, where, if the atoms are trapped in the same solvent cage, they loose quickly kinetic energy and recombine. On the contrary, in silicalite the free atoms, to dissipate energy, must collide with a relatively smooth environment showing preferential directions of easy diffusion, or (not frequently) with each other, so that they spend a longer time to thermalize (see fig. 2).
However, as it appears in fig. 3, once the molecule is formed, the excess energy transfer in the liquid phase, occurring via a vibrational-translational coupling, is less efficient than in silicalite, where the energy dissipation faster occurs by vibrational-vibrational coupling. However, it is hard to find a clear dependence of the behaviour of the iodine atoms on the region of the channel system (sinusoidal or straight channels, or intersections) where the collision occurs.
Fig. 3. – Average evolution of the internal energy of the iodine molecule in the first 50 ps after recombination. A) in tetrachloromethane; B) in silicalite.
The fraction of the dissociated molecules which undergoes recombination is slightly smaller in silicalite than in the liquid. Further study on this subject is in progress.
3. – Conclusions
From the results reported above, it appears that it is possible to apply classical Molecular Dynamics simulations to study, at least qualitatively, some interesting aspects of chemical reactions in zeolites. Work is in progress to extend and verify this kind of calculations thoroughly and to develop simulation techniques through which quantum-mechanical phenomena involved in chemical reactions catalyzed by zeolites could be taken into account.
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