Grand Ensemble Monte Carlo Simulation of Simple Molecules

Roland J.M. Pellenq, and David Nicholson ... De Vito , Christophe Den Auwer , Pier Lorenzo Solari , Cécile Daniel , Yves Schuurman , and David Farrus...
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Langmuir 1995,11, 1626-1635

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Grand Ensemble Monte Carlo Simulation of Simple Molecules Adsorbed in Silicalite-I Zeolite Roland J.-M. Pellenqt and David Nicholson* Department of Chemistry, Imperial College of Science Technology and Medicine, London SW7 2AY, U.K. Received May 9, 1994. I n Final Form: October 17, 1994@ Grand ensemble simulations have been performed for Ar, Kr, and Xe adsorbed in silicalite-1. Two potential models were employed to model the adsorbate zeolite interactions: one originating from the work of Kiselev which has been widely used in previous work, and one developed in this work, which includes high order two-body dispersion, induced and three-body interactions, denoted PN1. Simulation data have been compared with experimental isotherms and isostericheat curves obtained from microcalorimetryand also with neutron scattering data. Neither of the potential models used was able to predict the transition observed in experimental isotherms, although the heat curve transitions are reproduced. These transitions are associated with adsorption at the substep preceding the transition. Decompositionof simulated heats into wall and molecule components facilitates an interpretation of these curves. From an analysis of neutron data and the thermodynamic data, we conclude that the step observed in the argon and krypton isotherms must be attributed to an adsorbent transition which possibly induces a rearrangement of the adsorbed phase. Therefore, this transition is not due to a disordered fluid to crystalline solid adsorbate transformation nor to commensurate-incommensurate phase changes. We demonstrate that the distorted lattice cannot be identified with the para-form which occurs duringp-xyleneadsorption. We concludewith a brief description of current ideas bearing on adsorbent lattice transformation and propose a tentative mechanism. A full atomic level interpretation awaits further investigation. 1. Introduction

Physical adsorption in the ZSM-5 zeolites has attracted a great deal of attention over the last 15years. One reason for this interest is the practical application which these materials find as catalysts. A second reason is that the well-defined and chemically simple nature of the pure silica form, silicalite-1, suggests that this would be a n ideal subject for investigations which aim a t gaining a better understanding of adsorption in microporous materials. Studies of physical adsorption and transport in silicalite-1 fall roughly into two categories: those centered around adsorbates related to practical applications and those which concentrate on adsorbates commonly used for characterization. The present study belongs to the second of these groups and forms part of a cooperative project involving both experimental and theoretical work. Our particular contribution has been concerned with the simulation (mainly low temperature) of physical adsorption of simple molecules, such a s the rare gases, nitrogen, and methane. Here we report simulation studies of the adsorption of argon and other rare gases into silicalite-1 at 77 K. A particularly interesting feature of the experiments is that adsorption isotherms for many simple adsorbates exhibit transitions-sometimes accompanied by hysteresis. For example argon and krypton isotherms both show a single transition during low temperature physisorption, but their isosteric heat curves are quite different; nitrogen has two transitions, although methane and xenon show none. Furthermore this variety of behavior is significantly modified when some lattice silicons are substituted by aluminum. The interpretation of these observations offers a considerable challenge. To model the adsorbate-adsorbent interactions we have used two different potentials. The first of these is based on the summation of simple 12-6 interactions between

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adsorbate and lattice oxygens introduced by Kiselev and co-workers1and referred to here as the Kiselev potential. The parameters were chosen using the scheme suggested in ref 1. The second was a more detailed potential function, described elsewhere2r3 and summarized below which included higher order two-bodyand three-body long range dispersion terms; for ease of reference we shall denote this as the PN1 potential. Previous simulations of adsorption into silicalites and similar materials have appeared in which potential functions of the Kiselev type were used; Pan and Mersmann4 studied the adsorption of Ar in silicalite a t low coverage and found substantial discrepancy in comparison with experiment. Other rare gas simulations in silicalite include Xe5,6and where Kr-Si as well as Kr-0 interactions were included. A number of simulations of diffusion and adsorption of rare gasesEand methaneg-ll in silicalite have been made using potentials of the 12-6 form in which parameters were adjusted to fit low coverage experimental data. One of the most important conclusions from the present work is that some of the transitions observed in adsorption isotherms must be associated with changes in the ad(1)Kiselev, A. V.; Lopatkin, A. A.; Shulga, A. A. Zeolites 1985,5,167. (2) Pellenq, R. J.-M.; Nicholson, D. Fundamentals of adsorption, Proceedings of the N t h International Conference, Suzuki, M., Ed.; Kodansha: Kyoto, 1993; p 515. (3)Pellenq, R.J.-M.; Nicholson, D. J. Phys. Chem., in press. (4)Pan, D. F.;Mersmann, A. Fundamentals of adsorption, Proceedings of the IIIrd International Conference; Mersmann, A., Scholl, s., Eds.; United Engineering Trustees, 1991. ( 5 ) Pickett, S. D.; Nowak, A. K.; Thomas, J. M.; Peterson, B. K.; Swift, J. F. P.; Cheetham, A. K.; den Ouden, C. J . J.; Smit, B.; Post, M. F. M. J.Phys. Chem. 1990,94,1233. (6) June, R. L.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1990, 94,8232. (7)Hope, A. T. J.; Leng, - C. A,; Catlow, C. R. A. Proc. R. SOC.London 1989,A424, 57. (8)Krasil'nikova, 0.K.; Bering, B. P.; Serpinskii, V. V.; Dubinin, M. M. Izu. Akad. Nauk SSSR, Ser. Khim. 1977,5,1194. (9) Goodbody, S. J.;Watanabe, K.; MacGowan, D.; Walton, J . P. R. B.;Quirke, N. J. Chem SOC.,Faraday Trans. 1991,87, 1951. (10)Catlow. C. R. A,: Freeman. C. M.: Vessal. B.: Tomlinson, S. M.: Leslie, M. J. Chem Soc., Faraday Trans. 1991,87, 1947. (11)June, R.L.;Bell, A. T.; Theodorou, D. N. J.Phys. Chem. 1990, 94,1508.

0 1995 American Chemical Society

Grand Ensemble Monte Carlo Simulation sorbent framework; any restructuring of the adsorbate is conditional upon these changes. Structural alteration of MFI zeolites is known to occur under certain circumstances. For example crystallographic12 and solid-state NMR studied3 have shown two distinct forms: orthorhombic, found a t high temperature, and a low temperature monoclinic form. The transition from one to the other is reversible and occurs for unloaded silicalite a t 340 K, when aluminum is substituted for silicon, the transition temperature is lowered. Only small changes of structure accompany this transition. The unit cell in the monoclinic structure has the dimensions a = 2.0107 nm, b = 1.879 nm, c = 1.3369 nm, and a = b ,' = ~ 1 2y, = 90.67' l4 while the orthorhombic structure has a = 2.007 nm, b = 1.992 nm, c = 1.342 nm, and a = ,6 = y = d 2 . The corresponding changes in channel dimension and structure are also small. The accepted dimensions15for the elliptical cross section of the straight channels in the orthorhombic form are 0.520 nm and 0.575 nm, while the sinusoidal channels have a cross section of 0.53 nm by 0.56 nm. In the monoclinic phase the dimensions of the corresponding channels are 0.52 nm by 0.58 nm for the straight channels and 0.52 nm by 0.58 nm for the sinusoidal ~ h a n n e 1 s . lIt~has also been observed that the adsorption of some small organic molecules, notably p-xylene a t room temperature, can induce crystal phase transitions, and van Koningsveld et al. have demonstrated changes from monoclinic to the so-called para form during adsorption of this molecule.16 The para form has a n orthorhombic unit cell but shows shifts of atom positions along the c-axis. Benzene and pyridine also induce this transition, but the slightly larger cyclohexane molecule does NMR evidence also points to the possibility of lattice distortion associated with the adsorption of some aromatic organic m01ecules.l~ The para structure is characterized by the dimensions a =2.121nm, b= 1.9820nm,andc= 1.3438nmandchannel dimensions 0.50 nm by 0.620 nm for the straight channels and 0.63 nm by 0.47 nm for the sinusoidal channels. In the context of this work, it is important to note that these cavity and channel diameters are established from the absolute atomic positions obtained by X-ray diffraction assuming a van der Waals radius for the framework oxygen atoms of 1.35 A. The remainder of the paper is organized as follows. In section 2 we describe briefly the grand canonical Monte Carlo (GCMC)simulation and the potential functions used. A full discussion of the derivation and validation of the PN1 potential has appeared e l ~ e w h e r e . Argon ~ , ~ adsorption in silicalite-1 is considered a t some length in section 3; a comparison of adsorption data at 195 K with simulation further supports the validity of the adsorbate adsorbent potential employed. Simulated isotherms, heats, and neutron scattering spectra for argon a t 77 K are compared with experiment. Section 4 describes and discusses similar results for krypton adsorbed at 77 K. A brief account of xenon adsorption a t higher temperature is made in section 5 . In the final section we summarize the evidence and previous models for adsorbent transitions in the light ofthese results and earlier findings; we propose a tentative mechanistic basis for such transitions and suggest directions for future investigation. (12)van Koningsveld, H.; Jansen, J. C.; van Bekkum, H. Zeolites 1987,7,564. (13) Klinowski, J.; Carpenter,T. A.; Gladden, L. F. Zeolites 1987,7, 73. (14)van Koningsveld, H.; Jansen, J. C.; van Bekkum, H. Zeolites 1990,10,235. (15)van Koningsveld, H.: van Bekkum H.; Jansen, J. C. Acta Crystallogr. 1987,B46,127. (16) van Koningsveld, H.; Tuinstra, F.; van Bekkum, H.; Jansen, J. C.Acta. Crystallogr. 1989,B45,423. (17) Snurr A. Q.;Bell, A. T.;Theodorou, D. N. J. Phys. Chem. 1993, 97,13742.

Langmuir, Vol. 11, No. 5, 1995 1627 2. Simulation and Potential Functions Monte Carlo simulation in the grand canonical @Vn ensemble is an established and widely used technique. Simulations were carried out at fmed chemical potential and the number of particles in the simulation was allowed to vary, which helps to minimize ergodic difficulties. This ensemble also has the attraction that p is one of the independent variables as is the case in many real situations. Of particular relevance in the present context is the study of adsorption isotherms where one is concerned with the value of (N)for fmed values of T andp. Creations and destructions were chosen for a trial with equal probability to maintain microscopic reversibility.18 In a creation trial the probability of a n acceptance is given by

6:'= min (1,ZV exp(-PAU$?) N+l where the initial number of molecules is N , AUN is the change in the total potential energy, z = exp(P,u)/A3,and A for a spherical particle is given by

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Control charts in the form of plots of number and internal energyversus the number ofMonte Carlo steps were used to monitor the approach to equilibrium. Acceptance rates for creation destruction were also followed. The step length was adjusted to give an acceptance rate for translation of 0.5. After equilibrium had been attained, all averages were reset and calculated over several million configurations. Isosteric heats of adsorption were obtained from fluctuations over the number of particles in the system and from fluctuations of the internal energy18

The isosteric heat of adsorption was split into two components: the adsorbate-adsorbent (qw)and the adsorbateadsorbate interactions (am).The isosteric heat of adsorption can be calculated in two ways: directly from expression 5 and from the sum of these two components. This procedure was used as a self-test for the simulation code. Because of fluctuations, it is clear that the accuracy of any quantity measured by computer simulation is accompanied by a n intrinsic error. This error can be evaluated from standard d e ~ i a t i 0 n s . l ~ In addition to isotherms and adsorption heats, molecular configurations a t equilibrium (snapshots) and singlet distribution functions were obtained. The latter were found by dividing the simulation box into a number of sections and calculating the average density in each subsystem. The simulation box was constructed from 27 unit cells and the periodic boundary conditions applied in three dimensions. (18) Nicholson, D.; Parsonage, N. G. Computer Simulation and the Statistical Mechanical Theory ofAdsorption; Academic Press: London, 1982. (19) Bakaev, A. V.; Steele W. A. Langmuir 1992,8, 148.

1628 Langmuir, Vol. 11, No. 5, 1995 The simulations were run mainly on i860 processors (supplied by Transtech, Ltd.) and also on silicon graphics machines. The adsorbate-adsorbate interactions were modeled by 12-6 functions using standard parameters for ( E I J Z , ~ ) for Ar (120 K, 0.3405 nm), Kr (169 K, 0.3595 nm), and Xe (281K, 0.3849 nm). These are effective parameters which give good results for the energy and other properties of homogeneousbulk phases. In the present application they must be regarded as a first approximation. We have addressed this question in greater detail elsewhere.z0 The adsorbate-adsorbent potential, as mentioned above, was represented either by the Kiselev potential or by the PNl2s3potential. Although the Kiselev potential gives surprisingly good results, it is not difficult to demonstrate its limitations. The PN1 potential was constructed so as to include high order two-body and threebody dispersion terms, first order induced interactions and Born Mayer repulsive terms for the adsorbate-oxygen and adsorbate-silicon interactions. The repulsive parameters were determined from zero coverage experimental data and the potential function was verified by testing the ability of the potential to predict other data.z,3 The attractive part of the potential required values of the dipole polarizability and the effective number of electrons for the lattice species, and methods for calculating these have been e s t a b l i ~ h e d . ~The , ~ ' PN1 function was determined initially for a n argon adsorbate, and extension to other adsorbate species necessitates a combination rule for the repulsive parameter^.^ No adjustable parameters were involved in extending the argon potential to Kr and Xe. The most significant difference between the two models in relation to the present work is that the PN1 potential predicts narrower pore spaces than the Kiselev potential. The reasons for this have been discussed el~ewhere.~ The adsorbate-adsorbent potential function is clearly too complicated to use directly in a simulation. We therefore used a grid-interpolation procedure in which a zeolite unit cell is split into a collection of small cubes with side length 0.02 nm. The total adsorbate-zeolite energy was calculated a t each corner of each cube with a cutoff of 1.8 nm. To reduce the size of grid required, the symmetry of a unit cell was exploited. The accuracy of the interpolation based on this cube size was high, except in the strongly repulsive regions of the potential, where the strength of the repulsion tends to be overestimated. In the Monte Carlo calculations however few acceptances are to be expected in this region, so that no serious error was incurred by interpolating the potential function from the grid. The accuracy of the interpolation was checked by comparing results a t zero coverage from integration of the Boltzmann factor, with simulations containing an average of less than two molecules per unit cell. A check a t higher pressure was also made using the Kiselev potential. The interpolation method gave 30.3 argon atoms per unit cell a t a pressure of 6.5 Pa, compared to 30.6 atoms when the potential was calculated directly. 3. Argon Adsorption 3.1. Adsorption of Argon at 195 K. Richardsz2has measured the adsorption of argon into silicalite a t 195 K (Figure 1). At this temperature the adsorption is in the Henry law region over the range of pressure studied (up to 3000 Pa) as found also in the simulation. The heat of (20)Femandez-Alonso, F.; Pellenq, R. J.-M.; Nicholson, D. Mol. Phys., in press, FBmandez-Alonso,F. Final year project report Imperial College, 1993. (21) Pellenq, R. J.-M.; Nicholson, D. J.Chem. Soc., Faraday Trans. 1993,89, 2499. (22) Richards, R. Thesis, University of London, 1986. ~~

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adsorption remained constant a t 14.7 k J mol-' with a negligible contribution ( < 0.05 k J mol-l) from moleculemolecule interactions. The simulation results shown include a small correction for surface excess; this is difficult to estimate accurately because of uncertainties in the internal volume which should be usedz3but amounts to no more than 0.012Ar per unit cell a t the highest pressure. The agreement between the PN1 potential and experiment is close,whereas the simulation using the Kiselev potential shows considerable deviation. This adds further confirmation to our previous c o n c l ~ s i o nthat ~ ~ ~the Kiselev potential overestimates the pore width in silicalite. 3.2. Adsorption Isotherms for Argon at 77 K. Figure 2 shows the adsorption isotherms obtained from simulation a t 77 K compared with the experimental isotherm measured by Llewellynet aLZ4The experimental (23) Kaneko, K.; Cracknell, R. F.; Nicholson, D. Langmuir 1994,10, 4606. (24) Llewellyn, P. L.; Coulomb, J. P.; Grillet, Y.; Patarin, J.;Lauter, H.; Reichert, H.; Rouquerol, J . Langmuir 1993, 19, 1846.

Langmuir, Vol. 11, No. 5, 1995 1629

Grand Ensemble Monte Carlo Simulation

error bar is f 0 . 8 Ar per unit cell.25 By use of the PN1 18 , , potential, the maximum amount adsorbed in the simulation is 23.6 argon atoms per unit cell, which is considerably 16 less than the maximum of 33 Ar per unit cell obtained with the Kiselev model. This is again consistent with the fact that a n argon atom “sees”narrower cavities with the PN1 model than with the Kiselev model. When compared -P8 14 to the experimental isotherm, it is clear that neither of a the potential models is able to reproduce the step obtained f 12 experimentally a t about 5 Pa. I t has been argued that this step from 24 to 30 argon atoms per unit cell in the experimental isotherm is the signature of a phase transition of the adsorbed phase from a localized fluid phase to A 4 I 9 L Y L 4 a more compact crystalline commensurate p h a ~ e . ~ ~ , ~ ~ L Muller et aLZ5have also obtained a step in an adsorption isotherm for argon in silicalite a t 77 K. In their measureI I 1 I , 1 .I 0 ments the step occurred a t the same pressure but the 0 5 10 15 20 25 30 35 transition was from 21 molecules per unit cell to a number of Arluc maximum loading of 26 argon atoms per unit cell. Figure 3. Isosteric heat of adsorption for Ar in silicalite-1 at However it seems probable that the correct experimental 77 K. (N) is the number of argons per unit cell. Experimental isotherm is the one which gives the higher loading. results are shown with a heavy line.24b26 Simulated heats using Recently Borghard et aLZ7have obtained a maximum PN1 potential: total heat (01,wall part (m), molecule part (A). loading of 29 Ar per unit cell a t 87 K. This underlines the Simulated heats using Kiselev potential: total heat (0). experimental problems which can arise as a consequence of crystal defects in such materials.28 Evidence that the Ar per unit cell in close correspondence with results for transition does indeed correspond to a n intracrystalline the orthorhombic structure. We conclude that neither of process, rather than a process occurring at a n external these structures can accommodate the number of molsurface, as suggested by these workers, is provided by the ecules (30) adsorbed after the transition has occurred. experiments of Muller et al. ,29 who compared isotherms Simulations with the PN1 model using the para structure obtained on two different samples of silicalite. The first given by van Koningsveld16resulted in a slightly higher sample consisted of large well-defined crystals; the second filling (25 molecules per unit cell) a t high pressure than contained small crystals. Although the external surface that found for the orthorhombic lattice. However this is was larger in the second sample, the isotherms exhibited still too far below the maximum filling found experimena smaller transition than the first sample with a negligible tally to offer strong evidence that this structure occurs external surface. One possible explanation for the absence during argon adsorption. In the case of p-xylene adsorpof a transition in the simulation is that this has occurred tion in silicalite a t room temperature, it has been shown17 a t a spuriously low pressure; the inset in Figure 2 that the isotherm step is due to a lattice solid-solid phase demonstrates that this is not the case for either of the transition. potential models used. In recent work30 hysteresis has 3.3. Isosteric Heats of Adsorption for Ar at 77 K. been found in the isotherm step. Neither of the potential Figure 3 shows the plots of the two theoretical isosteric models showed hysteresis when simulations were started heat curves versus coverage, compared with their exfrom maximum filling under high pressure. perimental counterpart. The simulation results also show Since previous work has confirmed that the PN1 the split of the total heat into the adsorbate-adsorbate potential gives superior predictions to the Kiselev potenand the adsorbate-zeolite contributions. The experitial, and since neither model leads to the observed mental heat curve remains nearly constant up to 20 Arluc transition, it would appear that the experimentally (unit cell) when it exhibits a sudden increase to 23 Arluc observed transition occurs, not as previously thought, in followed by a flat part from 23 to 28 Ar/uc, and a final the adsorbate alone, but primarily in the adsorbent. decrease from 28 to 31 Arluc. This behavior is not Possible candidate structures for the transformed adsorreproduced theoretically. Both the PN1 and the Kiselev bent are the monoclinic and para forms mentioned in the heat curves have similar shapes which are not in agreeintroduction. In the simulations reported the orthorment with experiment but are characteristic of type I hombic structure was chosen because the higher symmetry isotherms and therefore consistent with the simulated of this structure greatly reduces the size ofthe grid which isotherms. The error bar for the theoretical result is f 0 . 3 needs to be calculated and stored. However, as already k J mol-l over the whole of the range of coverage, while mentioned, the monoclinic structure is in fact the most the experimental error is f 0 . 5 k J mol-l a t low loading stable form for the unoccupied lattice a t 77 K. It is possible and about f l k J mol-l a t the transition. The PN1 model therefore that a monoclinic to orthorhombic transition predicts the correct maximum heat of adsorption (16 k J occurs during adsorption. A simulation using the PN1 mol-’) a t 23 Arluc, although it overestimates the experipotential was run on the monoclinic structure a t 77 K and mental heat curve at loadings between zero and 23 Arfuc. a pressure of 25 Pa. This run resulted in a filling of 23.1 In this respect the isosteric heat curve obtained with the Kiselev model is in better agreement with experiment up (25) Muller, U.; Reichert, J.; Robens, E.; Unger, K. K.; Grillet, Y.; to 20 Arluc. It is important to note that it is the beginning Rouquerol, F.; Rouquerol, J.; Pan, D. F.; Mersmann, A. Fresenius 2. of the step in the experimental isotherm (Le., the end of Anal. Chem. 1989,333,433. the first plateau) which corresponds to the maximum on (26) Llewellyn, P. L. Thesis, Brunel University, 1992. (27) Borghard, W. S.; Reichman, P. T.; Sheppard, E. W. J. Catal. the experimental heat curve; the step from 23 to 30 Arluc 1993,139,19. corresponds to the horizontal part and the final decrease (28) Cracknell, R. F.; Gubbins, K. E. Langmuir 1993,9,824. on the experimental isosteric curve. Thus the step on the (29) Muller, U.; Reichert, H.; Kokotailo, G. T.; Unger, K. K.; Grillet, Y.; Rouquerol, F.; Rouquerol, J. Fundamentals of Adsorption, Proceedexperimental isotherm and the sudden increase in the ings of the IIIrd International Conference; Mersmann, A,, Scholl, s., isosteric heat of adsorption are not coincident. It is notable Eds.; United Engineering Trustees, 1991; p 595. that the adsorbate-adsorbate contribution to the total (30)Tosi-Pellenq, N. J. M.; Coulomb, J. P. Private communication, PN1 isosteric heat increases steadily from the very 1993.

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1630 Langmuir, Vol. 11, No. 5, 1995 beginning ofthe adsorption process. This is a n interesting ~ ~ , the ~ ~ sudden result since it has been ~ u g g e s t e dthat increase in the experimental heat of adsorption is due to a cooperative effect among adsorbed species close to the transition. According to this interpretation the slowly varying part of the experimental heat curve from 0 to 20 Arfuc can be ascribed to the energetic homogeneity of the site distribution in the zeolite. However potential maps of zeolite pores and other evidence2s3imply that these materials cannot be homogeneous adsorbents in the commonly accepted sense. In the light of these simulation results it is clear that there are two competingmechanisms in the variation of the isosteric heat of adsorption with coverage: the adsorbate-zeolite contribution decreases with coverage as the adsorbate molecules occupy less and less favorable adsorption sites; this is balanced by the adsorbate-adsorbate interaction which increases as the loading increases. Similar observations have been made for Xe adsorbed in zeolite This interpretation implies that a description of the adsorption process in terms of a localized adsorption before the transition, in which the particles occupy discrete sites without interacting with each other, is not valid. I t is more realistic to picture an induced heterogeneity due to adsorbate-adsorbate interactions between particles confined within small volumes. Neither of the potential models used here is able to explain the adsorption process between 23 and 28 Ar atoms per unit cell, and the common shape of the theoretical isosteric heat curves indicates that the adsorption mechanism is essentially the same in both cases. However, the decrease in the experimental heat curve between 28 and 30 Arfuc can be explained with the aid of simulation results. The decrease of the PN1 isosteric heat after 22 Ar/uc is seen to be due to a decrease in the adsorbate-adsorbate contribution. An analysis of the argon-argon pair distribution function shows that a t this stage the argon atoms are on average a t 0.345 nm from each other which is considerably less than the equilibrium distance for a n isolated pair (0.376 nm) and comparable to the hard sphere distance (0.3405 nm). Jamesson et al.33have reported similar observations for xenon in zeolite NaA. Thus it is clear that a t high coverage adsorbate repulsion is the major cause of the decrease in the total heat curve. The stability of the adsorbate phase is maintained by the chemical potential. It is interesting to note that Borghardet aLZ7have obtained a n isosteric heat curve similar to that obtained with the PN1 model from calculations based on effective potentials (although their absolute value for qst a t zero coverage is clearly overestimated). If pressure is increased by 2 orders ofmagnitude, the adsorbate-zeolite contribution to the total heat curve decreases due to overlap between adsorbed molecules and framework species. Thus interpretation of the isosteric heat curve for molecules confined to small cavities contrasts with that for adsorption on planar surfaces or in larger pores. In these less confined systems such as argon on graphite34or argon in VPI-5 (pore dimension 1.3 nm),28there is a decrease in qstafter monolayer formation. Here simulation studies clearly demonstrate that this decrease is associated with adsorption into a weaker part of the adsorption field, more distant from the surface. 3.4. Argon Adsorbate Structure in Silicalite-1. Figure 4 shows a plot of the occupancy of different regions of the absorbent as a function of the total amount adsorbed calculated for the PN1 potential model. More detailed structural information can be obtained from the density ~~

(31)Sing, K. S. W.; Unger, K. K. Chem Znd. 1993. (32) Vernov, A.;Steele, W. A.; Abrams, L. J.Phys. Chem. 1993,97, 7660. (33) Jamesson, J.; de Dios, J. 3. Chem. Phys. 1991,97,417. (34)Nicholson, D.;Parsonage, N. G. J.Chem. Soc., Faraday Trans. 2 1986,82,1657.

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Figure4. Amount adsorbed in differentregions plotted against total amount adsorbed: V, channel intersections;0,sinusoidal channels; 0, straight channels. distributions a t the highest loading, shown for both potential models in Figure 5, and from the snapshots taken a t different stages of the adsorption with the PN1 model (Figure 6). The singlet distributions (Figure 5) are nearly identical for both potential models in thex-direction with the highest concentration of adsorbate molecules a t the intersections between the straight and the sinusoidal channels. In the sinusoidal channels of the adsorbate, the Kiselev model predicts a more ordered structure (narrower peaks) than the PN1 model, but the density plot in the y-direction is significantly different. Thus the peaks at the channel intersections exhibit shoulders which are not present in the PN1 density plot. These shoulders indicate that, in the Kiselev model, extra molecules are adsorbed near to the channel intersections. The PN1 density plots a t maximum loading (Figure 5) show that all argon atoms are a t the adsorption sites determined in earlier w ~ r k . ~ , ~ From a n examination of the snapshot pictures (Figure 6) we can identify the following steps in the filling process: (i)At a very low loading of about 2 molecules per unit cell (Figure 6a,b), adsorption is a t the strongest sites in the center of the straight pores. (ii)At higher coverages of about 8 molecules/unit cell (Figure 6c) these molecules tend to be pulled off these sites toward the sinusoidal pores which contain the majority of the adsorbate population. (iii) When filling reaches about 16 molecules/unit cell (Figure 6d),there is adsorptioninto most ofthe straight pores; the intersections now become favored sites, since molecules in these regions can interact with adsorbate in both the sinusoidal and in the straight pores. (iv)Finally (Figure 6e,f) the previously depleted regions of the pores are filled. This mechanism explains the smoothly rising (type I) isotherm shown in Figure 2; the snapshot pictures confirm that further filling beyond about 23 molecules/ unit cell would be accompanied by substantial repulsive overlap between adsorbate molecules. This mechanism illustrates the importance of the adsorbate-adsorbate interaction in the sorption process even a t low loading and is also compatible with Figure 4. Two possible mechanisms proposed for the transition can be refutedfiom the evidence of Figures 4-6. An early suggestion was that the channels filled first and that the transition occurred due to filling of the intersection^.^^ Figure 4 shows that sites close to the intersection are occupied at low loadings and that no part of the cavity remains unoccupied up to the transition. A second possibility is that a mechanism operates which is similar to the commensurate-incommensurate transitions ob-

Grand Ensemble Monte Carlo Simulation

Langmuir, Vol. 11, No. 5, 1995 1631

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x-axis (A) Figure 5. Singlet distributions along the x - and y-directions for the PN1 potential (A, B) the Kiselev potential (C,D).

served for some adsorbates on graphite surfaces, in which molecules initially occupy.highenergy sites, but are pulled off these by cooperative adsorbate interaction^.^^ A PN1 simulation was run using a starting configuration obtained from the coordinates of the 24 sites in the silicalite unit cell and the pressure was set to the experimental transition. The maximum loading remained unchanged (23.3Ar/uc). Indeed it could be argued that the proximity of the sites and the strength of the argon interactions are such as to eliminate this m e ~ h a n i s m .Furthermore ~~ simulation for adsorption of (spherical)nitrogen molecules in slit pores of different dimension have shown that commensurate-incommensurate transitions are largely frustrated by the adsorbate-adsorbate interactions induced by the confined space of small micro pore^.^^ 3.5. Neutron Diffraction Data for Ar Adsorbed in Silicalite-1. Neutron diffraction has proved to be a very powerful method for determining the structure of the adsorbed phase.37 A diffraction spectrum contains information on both adsorbate and adsorbent structure since neutrons are, in general, scattered by all nuclei. Llewellyn et aLZ4have followed the adsorption ofrare gases including argon in silicalite using neutron diffraction: the appear(35) Parsonage,N. G. J . Chem. SOC.,Faraday Trans. 1992,88,777. (36) Nicholson, D. J. Chem. SOC.,Faraday Trans. 1994, 90, 181. (37) Coulomb, J. P. J . Phase Transitions, 1991.

ance of new structures in the diffraction spectra after the transition was attributed to an orderingofthe argon atoms to a more compact phase. In order to compare experimental neutron diffraction spectra with the simulation results, our simulation code was interfaced with a program which calculates diffraction spectra from molecular configurations output from the simulation. Most of the calculations reported used 27 unit cells, but a few were carried out using a single unit cell. It is interesting to note that where 27 unit cells have been used to calculate the spectrum the base line exhibits a broad maximum similar to that found experimentally and reflecting disorder of the type observed for liquids. This can be attributed to the distribution of molecules among unit cells and is not found when only a single unit cell is used in the calculations. Using a larger number of unit cells also has the effect of narrowing and intensifying the peaks at maximum loading, suggesting that even better correspondence with experiment could be obtained from a larger simulation. The appearance of a broad maximum in the larger (27 unit cell) system suggests that the narrow maxima originate mainly from adsorbent or from adsorbate-adsorbent cross terms, rather than reflecting structure in the adsorbate. The comparison between the simulation results and the experimentaPs diffraction spectra, plotted as intensity

~

1632 Langmuir, Vol. 11, No. 5, 1995

Pellenq and Nicholson D

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Figure 6. Snapshots from the PN1 potential simulations for argon in silicalite-1. The lattice is viewed in the xy projection in a, c, d, and e and in the zy projection in b and f. In the first projection the straight pore is vertical and the sinusoidal pore is horizontal. The second projection views the zeolite along the axis of the straight pores. The pressures at which these snapshots were taken are 0.01 (a and b), 0.05 (c), 0.30 (d), and 10.0 Pa (e and f).

(on an arbitrary scale) versus the wave vector Q, is presented in Figure 7. The diffraction spectrum for the empty zeolite obtained from the simulation (D) is in good agreement with experiment. In the simulation, the zeolite structure is orthorhombic although a t this temperature the crystal is monoclinic. The difference between the two struc$ures can be seen on the diffraction spectra at Q = 1.55A-l where the monoclinic spectrum exhibits a doublet which is replaced by a singlet in the orthorhombic (simylated)structure. The peaks in the range Q = [1.6, 1.8 A-l] are characteristic of the zeolite structure. The second set of spectra shows the experimental spectrum before the transition (B) and the configuration obtained with the PN1 simulation a t maximum loading (E). The first striking feature is the strong decrease of the peaks a t Q = 0.6 A-l in the both spectra. This was attributed to destructive interferences between the adsorbed phase and the solid. Static simulations (obtained by placing adsorbates in the zeolite unit cell a t arbitrary positions) show that the decreaseof the left-hand peak in this doublet corresponds to an increasing occupancy in the straight channels; symmetrically the decrease of the right-hand peak corresponds to an increasing occupancy of the sinusoidal channel. Experimentally both peaks diminish simultaneously indicating that both types of zeolite channels are populated in the course of the adsorption process or that the channel intersections are always occupied. These results confirm the simulation snapshot (38) Coulomb,J.P.;Llewellyn, P. L.; Grillet, Y.; Rouquerol,J. Studies Surf Sci. Catal. 1994,87, 535.

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Figure 7. Neutron diffraction spectra for argon in silicalite-1. Comparison of experimental and simulated spectra. Plots on the left-hand side are from e ~ p e r i m e n twith , ~ ~ 36Arfor empty zeolite (A), loading of 24 molecules per unit cell (B), and 30 molecules per unit cell (C). Right-handside plots are calculated from simulation for the empty zeolite (D), PN1 potential with 27 unit cells and ( N ) = 24 argonshc (E),Kiselev potential with one unit cell and ( N ) = 30 argonshc (F),and Kiselev potential with 27 unit cells and (N) = 31 argonshc (G).

analysis which has shown the major role played by the intersections in the sorption mechanism. The second major feature is the appearance of significant new peaks commqn to the simylated and experimental spectTa a t Q = 1.4A-l and 1.5 A-l and in the range Q = [ 1.8 A-l, 2.2 A-1]. These new structures are attributed to the growing adsorbate phase in the zeolite. The width of the peaks reflects the fact that the adsorbed phase is not ordered. The peaks characteristic of the zeolite structure remained unchanged a t this stage of the sorption process. The third set of spectra in Figure 7 presents the experimental spectrum after the transition (C) and the spectrum obtained from the Kiselev simulation a t high loading (31Arhc)(F,G).On the experimental spectrum, one can identify several major features. Firstly, when comparing with the experimental spectrum before the transition, one can see that a doublFt of very jntense and thin peaks has grown a t Q = [1.8A-l, 1.95 A-l]. This was interpreted as the signature of an ordered phase adsorbed in the A se5ond set of new peaks have appeared at Q = [2.0 A-l, F.4Awl], Among these structures, the doublet at Q = [2.0 A-l, 2.1 A-l] has also been attributed to ordering of the adsorbed phase. Most of the experimental peaks are present in the simulated spectrum; the agreement is gcceptable for the peaks in the region Q = [2.0 A-l, 2.4 A-l]. There is however one major difference in the experimental spectrum: the intense doublet a t Q = Cl.8

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PressurelPa Figure 8. Neutron diffraction spectra at different loadings of 40Arin silicalite-1.39The heavy line is the experimentalisotherm;

Figure 9. Adsorptionisotherms for Kr at 77 K experimental ref 7 (A), this work39(v);simulated isotherms, data, ref 26 (O), PN1 potential (O), Kiselev potential (0).

A-l, 1.95 A-l] is not well reproduced in the simulated spectrum indicating that the adsorbed molecules in the Kiselev simulation are not as ordered as the experiments imply. To a first approximation, the most probable relative distance between adsorbed argon atoms is given by d = 2xIQ and can be identified with the first maximum of the pair distribution function. The peak width characterizes the correlation length. Thus the narrow, intense peak a t Q = 1.9 h;-l corresponds to a probable argon-argon distance of 0.33nm extended over a large domain. The first peak of the pair distribution function for argon atoms in the Kiselev simulation is a t 0.336nm compared to o = 0.3405nm and shows that the argon atoms are repelling each other, consistent with the decrease in the isosteric heat curve a t high coverage. Comparing the peaks chargcteristic of the zeolite structure in the region Q = L1.6A-l, 1.8A-ll on the experimental spectrum, one can see that one of these splits into two components after the transition, indicating that structural changes have occurred in the zeolite framework during the adsorption process. In the simulated spectrum these peaks of course remain unchanged, since the zeolite framework is kept rigid. Spectra have also been run using the isotope 40Ar which has a very small coherent diffusion length,39thereby enabling the evolution of the zeolite framework to be followed during adsorption. The results confirm that the zeolite peaks remain unchanged up to substep at 24 argon atoms per unit cell. After the transition one peak a t Q = 1.7 A-l is split, as shown in Figure 8. This adds further weight to the evidence that the zeolite crystal itself undergoes a phase transition to a new structure which allows more argon atoms to adsorb in the channels, evolving simultaneously to a more organized phase, as shown by the neutron diffraction experiment. The magnitude of the zeolite relaxation is difficult to assess since the new structure, after the transition, is not known.

Although all three experimental isotherms exhibit a step a t roughly the same pressure, one of them overestimates significantly the amount adsorbed compared to the other two. Indeed this isotherm24predicts a maximum amount of krypton adsorbed equal to that for argon a t the same temperature. This is surprising since krypton is 8%larger than argon. The other two isotherms agree in their estimate of a lower maximum adsorption, although the new isotherm reported in this exhibits a nearly vertical step, in contrast to the more gradual transition of the earlier work. The earlier isotherm of Hope et al.’ was measured on small zeolite crystals (3pm) while the new isotherm was measured on large and well-formed crystals (180pm crystal length) synthesized by Muller et aL40 The difference in the form of the transition step on the isotherm is consistent with other experimentsz9where different crystal sizes were used. Comparison of simulation with experiment shows a situation similar to that for argon: both the PN1 and the Kiselev models give type I isotherms but neither potential model predicts the transition. Here however the Kiselev isotherm overestimates the maximum amount adsorbed while the maximum adsorption on the PN1 isotherm corresponds to the substep plateau of the two lower experimental isotherms. These results again indicate that a maximum loading of around 30 krypton atoms per unit cell24is too high. The fact the Kiselev model does not reproduce the maximum amount of krypton adsorbed in this case suggests that the good agreement, between the experimental maximum loading and simulation, when this model is used for argon, may be fortuitous. 4.2. Isosteric Heats of Adsorption for Kr at 77 K. The most striking feature in the experimental isosteric heat of adsorption curvez6shown in Figure 10 is that there is a n endothermic transition. This result was obtained by microcalorimetry coupled to a volumetric apparatus from which the highest isotherm in Figure 9 was measured. The beginning of the substep occurs at the loading where the isosteric heat is a minimum after the endothermic transition. Thus the step on the experimental isotherm and the transition on the isosteric heat curve

the spectra from left to right are for the empty zeolite, the zeolite plus adsorbatejust before the step, and the zeolite plus adsorbate after the transition.

4. Krypton Adsorption 4.1. Krypton Isotherms at 77 K. Figure 9 compares the simulated adsorption isotherms with experiment. (39) Tosi-Pellenq, N.M.; Coulomb, J.-P.Private communication, 1993.

(40)Muller, U.; Unger K. K.; Pan D. F.; Mersmann, A,; Grillet, Y.; Rouquerol, F.;Rouquerol, J.Zeolites as Catalysts, Sorbentsand Detergent Builders; Karge, H. G., Weiktamp, J.,Eds.; Elsevier: Amsterdam, 1989.

Pellenq and Nicholson

1634 Langmuir, Vol. 11, No. 5, 1995 25 I

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Figure 10. Isosteric heats for krypton compared with PN1 potential. The heavy line is the experimentalcurve,24simulated points are for the PN1 potential: total heat (e),wall part (01, molecule part (A),

are not coincident. In fact the step on the isotherm corresponds to the end of the endothermic plateau (30 Kr/uc) and the final decrease of the isosteric heat curve. This situation corresponds to that found for argon, except that there the transition was exothermic. The isosteric heat obtained with the PN1 model successfully predicts a sharp endothermic transition of comparable magnitude to its experimental counterpart, although the number of molecules adsorbed per unit cell is smaller, as discussed in the previous section. However the PN1 model constantly overestimates the experimental isosteric heat since the total theoretical curve increases monotonically while the experimental curve remains flat until the transition. It has been demonstrated for argon that a better description of the adsorbate-adsorbate interaction suppresses the total isosteric heat up to the transition.z0 A similar effect would be expected for krypton adsorption. The sudden decrease in the total isosteric heat of adsorption a t the beginning of the substep arises from the interplay of its two components (Figure 10). An analysis of snapshots shows that the final increase in the kryptonkrypton contribution corresponds to the formation of clusters at the intersections of the zeolite channels. The interaction with the zeolite then becomes less and less favorable as the loading increases, accounting for the strong decrease a t 17 Kr/uc which also corresponds to the change of slope in the rising krypton-krypton contribution. When the loading reaches 18 Kr/uc, the adsorbed molecules start repelling each other rather than overlap with the zeolite wall. Consequently the aggregate structures in the vicinity of the channel intersections disappear. A loading of up to 20 Krhc can be squeezed into the pores under increasing pressure; the Kr-Kr contribution to qst now remains constant, but the wall contribution continues to decrease. Above this loading both components decrease, indicating that the zeolite cavities are totally filled. This mechanism emphasizes the importance ofthe adsorbateadsorbate interaction during the adsorption process. Neutron spectraz4 show features similar to those observed for argon. New peaks appear due to the adsorbed phase and a change in the zeolite structure can be observed. However Kr has a much smaller coherent diffusion length (0.074 nm compared to 0.243 nm for Ar) and consequently the peaks are not as intense, which

Figure 11. Isotherms for Xe adsorbed on silicalite-1at 195 K experimental results47(--), simulation (0).

makes simulated spectra more difficult to interpret. It is clear that the step in the adsorption isotherm, the endothermic plateau, and the final decrease in the isosteric heat curve cannot be explained by simulations with rigid zeolite frameworks. We therefore conclude once again that these phenomena are associated with zeolitic deformation consequent upon adsorbate loading.

5. Adsorption of Xenon in Silicalite-1 5.1. Xenon Isotherms. An experimental isotherm obtained a t 195 K for this system47is compared with the PN1 model in Figure 11. The isotherm is type I and exhibits no transitions. The general agreement is within error limits, and the maximum adsorption of 16 Xe/uc is in good agreement with the PN1 simulation and with a similar maximum obtained4z from experimental measurements over the range 121-358 K. The Kiselev potential gives a type I isotherm with a maximum adsorption of 18 molecules/uc. 5.2. Isosteric Heat Curves for Xe. Unfortunately there are no microcalorimetric measurements for this system. However, the isotherms measured by Bulow et al. ,41have been used to obtain heats. From their results, it can be seen that the isosteric heat steadily increases with loading and exhibits no characteristic features. The simulated heats (Figure 12) show the same behavior. The decomposition into wall and molecule parts indicates that the increase results mainly from the adsorbate interactions. The wall part remains constant, suggesting that all positions occupied in the microporous space are equivalent for xenon. The adsorbent can be said to be homogeneous for this adsorbate. It should be mentioned that methane adsorbed in silicalite a t 77 K behaves like Xe a t 121 K in that there is no step in the isotherm and the isosteric heat curve exhibits no special features. The neutron diffraction spectra for methane does not show any modification of the peaks characteristic of the zeolite.z6 6. Conclusions

Simulation studies have been made of three rare gas adsorbates in silicalite-1. Two potential models were used to describe the adsorbate-adsorbent interactions: a 12-6 model based on the model of Kiselev, and a new potential function denoted a s PN1, developed in this ~ o r k . The ~,~ (41)Bulow, M.; Hartel, U.; Muller, U.; Unger, K. K. Ber Busensges. Phys. Chem. 1990, 94, 74. (42)Pan, D.F.;Mersmann, A. Gus Sep. Purif. 1991,5,210.

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Number of atoms of Xe / uc Figure 12. Simulatedheats of adsorptionfor xenon in silicalite at 195 K from simulations using the PN1 potential: total heat (01,wall part (M), molecule part (A).

experimental isotherms for argon and krypton exhibit a clear transition, in contrast to those for xenon (and for methane, which has not been studied here). Simulation results obtained with either potential do not show the observed transitions, although the more accurate PN1 model gives good agreement with the xenon results and with high temperature argon results where no transition has been observed. Furthermore the PN1 potential gives a satisfactory prediction of the silicalite adsorption up to the top of the isotherm substep. This finding has prompted a reappraisal of isosteric heat and neutron scattering data which had previously been interpreted in terms of adsorption homogeneity and a disordered liquid-like to commensurate crystalline solid transition. Extensive use of simulated heat curves, decomposed into wall and molecule components, has revealed that the heat curve transition does not coincide with the isotherm step but with the substep plateau and can be identified, in the case of microporous adsorbents, with repulsive interactions engendered when adsorbate molecules are forced into the confined space ofthe cavities. Neutron scattering results from earlier work have been augmented by measurements with 40Ara s a n adsorbate. This molecule does not scatter neutrons, nevertheless there is a change in the spectra obtained before and after the transition. We conclude that the transition observed in Ar adsorption a t 77 K must be attributed to a restructuring of the adsorbent. A similar picture emerges for Kr, although some conflict exists between different isotherm measurements. A new Kr isotherm measured in this work predicts a maximum filling of about 23 molecules per unit cavity after the step, which is rather less than the maximum of 30 found in some earlier studies. The idea of zeolite deformation during adsorption was first proposed by Krasil’nikovas who developed a thermodynamic model. A phenomenological model, which invokes adsorbent transformation in order to explain isotherm steps, has also been developed.42 A satisfactory interpretation a t the molecular level awaits full scale

simulation studies in which adsorbent and adsorbate species are included. One question which needs to be answered is why the phenomenon appears to occur with some adsorbents and adsorbates but not with others. The case ofp-xylene has already been mentioned16and exhibits similarities with argon adsorption; for this adsorbate the isotherm exhibits a step from four to eight molecules per unit cell. The corresponding isosteric heat shows a n increase (exothermic) a t the end of the isotherm substep and remains constant43during the transition from four to eight molecules per unit cell. The accompanying change ~ 3the ~~ in framework structure is well d o c ~ m e n t e d . l ~ JOn other hand the larger cyclohexane molecule does not induce structural modifications in this adsorbent.45 Similarly there seems to be no such transition for methane at 77 K24 although it is larger than the molecules studied here; for this molecule, there is no step in the isotherm and the neutron scattering peaks which characterize the zeolite are retained at all coverages. Xenon also behaves like these molecules. A mechanism can be proposed along the following lines: For some adsorbate species there will be a misfit between adsorbate molecules and the pore space such that a small expansion of the adsorbent would enable further molecules to squeeze into the cavities, the increase in lattice energy being compensated by a reduction in adsorbate energy. Equally for some adsorbate-adsorbent combinations the structure could contract to reduce the misfit with the adsorbate; in this case there would be no step and the isotherm would remain type I. In some cases distortion of the framework does not lower the overall free energy and its structure is not modified a t high loading. This mechanism implies an energy compensation which may explain why the isotherm step occurs at nearly constant isosteric heat and why framework modification does not occur with Ar a t 195 K where the critical loading is not reached. The monoclinicto orthorhombic transition has been shown to be ferroelastic16in which the frequency of one of the acoustic modes approaches zero a t the transition. This soft mode permits displacement of the framework atoms and a second order transition occurs. If more than one mode is involved, it would not be necessary for the modes to approach zero frequency but merely to decrease by several orders of magnitude and the transition would be first order a s observed in the isotherms under di~cussion.~~

Acknowledgment. We thank the CEC for providing equipment and support to one of us (R.J.-M.P.). We are indebted to Dr. Jean-Paul Coulomb and Nathalie TosiPellenq for communicating their results from 40Arneutron spectra and Kr adsorption prior to publication and for discussions. We are also grateful to Dr. Neville Parsonage, Dr. Roger Cracknell, and Professor H. van Koningsveld for discussions. LA940381S (43)Thamm, H. J. Phys. Chem. 1987, 91, 8. (44) Fyfe, C. A.; Kennedy, G. J.; De Sehutter, C. T.; Kokotailo, G . T. J. Chem. SOC.,Chem. Commun. 1984, 541. (45) Muller, J. A.; Conner, W. C. J.Phys. Chem. 1993, 97, 1451. (46)Parsonage, N. G.; Staveley, L. A. K. Disorder i n crystals; Monographs on Chemistry; Rowlinson, J. S., Baldwin, J. E., Eds.; Clarendon Press: 1978. (47) Chen, D. Thesis, University of London, 1992.