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Adsorption of xenon in zeolite Y: a molecular dynamics study
Volume 177, number
I
CHEMICAL PHYSICS LETTERS
8 February 1991
Adsorption of xenon in zeolite Y: a molecular dynamics study * S. Yashonath Solid State andStructural Chemistry Unit, Indian Institute of Science, Bangalore, 560 012, India Received 13 March 1990; in final form I9 November 1990
A molecular dynamics calculation of a realistic model of xenon adsorprion in sodium-Y zeolite is reported. The equilibrium properties such as the energy distribution function, the centre-of-cage-centre-of-mass radial distribution function, and the cageoccupancy distribution function are obtained. The results are in reasonable agreement with those of earlier calculations. The dynamics is significantly slower than that observed for other small organic molecules. Xenon exhibits anisotropic motion in the large cavity.
and computational details. The results and discussion are presented in section 3.
1. Introduction Adsorption in zeolites has attracted much attention in recent times. The problem is complicated by the large number of factors influencing the adsorption in the channels and cages of the zeolites. Among these, geometrical as well as the chemical state of the zeolite determined by the %/Al ratio and the nature of the extraframework cations play important roles in determining the adsorption characteristics. Adsorption of xenon in faujasites has been studied by Rowlinson and co-workers by direct calculation of partition functions, and by a grand canonical Monte Carlo method [ 1,2]. These results have yielded interesting insights into the structure of the adsorbed fluid, distribution of occupancies and thermodynamic behaviour. Recently, some work on adsorption of small organic molecules in faujasites has also been reported [ 3-51. Here, we report a molecular dynamics calculation of xenon adsorbed in faujasite. Our interest is to study the equilibrium and the dynamical behaviour of the adsorbed xenon in faujasite and to compare our results with those of earlier calculations. In section 2, we discuss the details of the intermolecular potential
* Contribution istry Unit.
54
No. 691 from Solid State and Structural Chem-
0009-2614/91/$
2. The details of calculation The crystal structure of faujasite has been determined by several workers [ 6-8 1. The space group is Fd3m. In the present calculation, the atomic coordinates and the lattice parameter a=24.85 8, reported by Fitch et al. have been used [ 81. The zeolite lattice was kept rigid and only the xenon coordinates were included in the integration. The number of extraframework sodium cations were 48 per unit cell corresponding to a Si/AI ratio of 3.0. Of the 48 cations, 16 are in Si sites and the remaining 32 occupy S,, sites [ 4,8]. In the present calculation, we have adopted the model of Kiselev and co-workers [ 91 for the zeolite-xenon interaction. The interaction between the adsorbed xenon and the zeolite is confined to the oxygens and the sodiums. This is a reasonable assumption in view of the fact that the silicon and the aluminium are buried within the oxygen lattice, thus preventing the close approach of the xenon to these atoms. The xenon-(oxygen, sodium) interaction was taken to be of the LennardJones form [ 91,
@ik=-A$+$,i=Xe,k=O,Na. 03.50 0 1991 - Elsevier Science Publishers B.V. (North-Holland)
Volume 177,number 1
Table I Potential parameters for xenon-Nay zeolite at T= 375 K Atom
Xe
8 February 199I
CHEMICALPHYSICS LETTERS
A ( IO'kJ mol-’ A6)
B ( lo6 kJ mol-’ A’*)
0
Na
0
Na
8.2793
2.9143
Il.1345
7.9079
The dispersion parameters Aik were obtained from the Kirkwood-Muller expression and the repulsion parameters Blk by imposition of the constraint that the force should be zero at the equilibrium distance. The details are given in ref. [ lo]. The polarization energy is taken into account in the present calculation since this is a many-body term and would result in a considerable increase in the computational time. The xenon-xenon interaction was modelled by a Lennard-Jones potential,
(2) with a=4.10 8, and e/k=221 K [lo]. Molecular dynamics calculations were performed in the microcanonical ensemble with periodic boundary conditions. The system consisted of one unit cell of faujasite consisting of 384 oxygen, 48 sodium and eight xenon atoms. The xenon atoms were uniformly distributed at the start of the simulation in the large cavities or the supercages. A time step of 1.0 fs was employed for the integration. Equilibration was performed over a period of about 20 ps and averages accumulated over a fairly long period of 0.1 ns. A shifted potential with a potential truncation of IO A has been employed. Integration was carried out by means of a simple Verlet scheme [ 121.
and the calculated value of 17.25 kJ/mol obtained by Kiselev and Du [ 91 in view of the fact that the Si/Al ratio employed by us here is higher and qs,decreases with an increase in the Si/Al ratio [ 13 1. Part of the discrepancy is due to the neglect of the polarization interaction. It is difftcult to compare our results to those of Woods et al. due to the spherical potential approximation employed by them which does not correspond to any specific Si/Al ratio. Fig. 1 shows the interaction-energy distribution function, N(U). The curve shows a main peak near - 12 kJ/mol and a shoulder near - 15 kJ/mol. The shoulder arises from the xenon near the minimum energy or the adsorption site. The xenon atoms which are not near the adsorption site contribute to the higher-energy region comprising the main peak and the high-energy tail. This may be compared with the adsorption of methane in faujasite which showed a characteristic bimodal distribution. A similar bimodal distribution was also observed in the case of benzene [ 51. In contrast to these, the present results show an almost unimodal distribution with only a barely visible shoulder which seems to suggest the absence of two or more markedly distinct regions in the supercage for the case of xenon. Therefore, it is expected that a spherically averaged potential should be more appropriate for xenon adsorbed in faujasite than for methane and benzene for which there appear to exist several significantly different regions in the supercage. The higher-energy region, namely the region above - 8 kJ/mol, was initially thought to be
c
3. Results and discussion
O.lO2
The average temperature of the system is 375.9 K. The total interaction energy of a xenon atom is ( U) = ( U,) + ( Ugh), where ( V,) is the guestguest and ( Ugh) is the guest-host contribution. We have obtained a value of - 12.33 kJ/mol for ( U) . The guest-guest contribution to the total interaction energy was found to be small. The isosteric heat of adsorption, qa, is 15.46 kJ/mol. This compares reasonably with the experimentalvalue of 180.0 kJ/mol
z
0.00
- 20.0
-40
-12 0 U.kJ/mol
Fig. 1. Energy distribution function for xenon in zeolite NaY at a concentration of one atom per large cavity and a temperattire of 375 K.
55
Volume177,number I
CHEMICALPHYSICSLETTERS
due to xenon migrating from one large cavity to another. Closer examination, however, revealed that this is not so. The region with U> - 8 kJ/mol seems to be due to xenon in the proximity of the cage centre. The distribution of the methane in the supercage is shown in fig. 2. Here, the centre-of-cage-centre-ofmass (cot-corn) radial distribution function (rdf ) is plotted as a function of the distance of methane from the centre of the supercage. The cot-corn rdf shows a main peak near 4 A and a smaller one near 1 A. The main peak in the rdf suggests that the xenon atoms spend a large fraction of their time near the walls of the supercage. This is similar to the behaviour shown by methane and other molecules [ 5,141. This type of cot-corn rdf seems to be a characteristic feature of X,Y-type of zeolites. The shape of the coccorn rdf and the position of the peaks are strongly influenced by two factors: One is the nature of the interaction and the other is the geometry of the cage. The comparison with the results of Rowlinson and co-workers [ 21, who employed a spherically averaged potential, is worthwhile. The present results show a broader spread of the main peak extending to much smaller r values and a small peak near 1 A absent in the earlier study [2]. This means that the molecules are, in fact, able to stray significantly more often towards the centre of the cage than suggested by a spherically averaged potential. This view is in accordance with the fact that the sites in the large cavity are localized regions near the cage wall, and it is only in these regions that molecules spend a fairly large amount of time, thus contributing to the main 6
8 February1991
peak in the cot-corn rdf. Thus, if P(r, 0, 4) is the probability of finding a xenon atom at a point given by (r, 8, $), where r, 0, 9 are the polar coordinates of points within the large cavity, then it is evident that P( r, 19,4) varies as a function of i3and # as well as of r. This suggests that the potential function has strong angular dependence. It is not known if these anisotropies are also tetrahedral in symmetry reflecting the cage symmetry, since the potential felt by the guest atom arises not only from just the atoms comprising the inner walls of the large cavity but also from those beyond it. The tail near 6 A arises from the diffusion of xenon from one large cavity to another. This tail is likely to become increasingly prominent with increase in temperature. Fig. 3 shows the xenon-xenon radial distribution function. The main peak near 4.5 A corresponding to the minimum in the Xe-Xe interaction potential (0=4.10 A) suggests the existence of a significant population of dimer, even at this low concentration of one xenon per supercage. Such dimer formation has been observed for a one-site model of methane adsorbed in ZSM-5 [ 31. For a noble gas fluid, the second peak in the g(r) should appear at approximately $ r, where rl is the position of the first peak. It is interesting to note the second peak in the xenon-xenon rdf appears only beyond I 1 A. It is therefore, apparent that the zeolite influences the fluid structure strongly, at least at low loadings. The cage distribution function is shown in fig. 4. It is seen that the fraction of cages with zero-occupancy is 0.33 which is less than the fraction of cages with an occupancy of one. This is in contrast to a value of 0.37 obtained by Rowlinson and co-workers
/f-l
/
\
I
Fig. 2. Centre-of-cage-centre-of-mass radial distribution function for xenon in sodium-Y zeolite at a temperature of 375 K. 56
Fig. 3. Xenon-xenon
radial distribution
sorbed in sodium-Y zeolite at 375 K.
function for xenon ad-
Volume 177,number I
CHEMICALPHYSICS LETTERS
o.4,
-03r I 5
IL
0.2
I
0.1
-1:,:
012345
N
Fig. 4. Distribution of occupancies, F(N), for the large cavity at a temperature of 375 K.
for both zero- and one-occupancy. However, the difference is not surprising in view of the relatively large size of the supercage as a consequence of using the spherically averaged potential. The distribution function shows that there exist cages with a high occupancy of rive, even at the low loading of one xenon/cage.
4. Dynamics The cage residence time, site residence time and the site-site migration time have been calculated. The cage residence time, z,, was determined using a distance criterion to decide whether a given molecule belonged to a specific cage. A molecule within a distance of 5.9 A of a cage is said to reside in the cage in question. The value reported here, 9.9 ps, is found to be about an order of magnitude larger than that found for methane near 300 K [ 14 1. The difference can be attributed to the large mass of xenon compared to that of methane. This decreases the mobility of xenon significantly compared to that of methane. This is also supported by the velocity autocorrelation function discussed below. In the calculation of the site residence time (r$), an energy cutoff of - 13 kJ/mol has been employed. The calculated site residence time is 0.59 ps, which is again significantly greater than the value obtained for methane. The site-site migration time (r,) is the average time the particle spends between two visits to a site. It is found to be 1.3 ps, which is in agree-
8 February 1991
ment with the energy distribution function shown in fig. I. The calculated diffusion coefficient was also found to be much smaller than that of methane in Nay. Fig. 5 shows the velocity autocorrelation function for the motion of xenon in Nay. The striking feature of the velocity autocorrelation function here is the slow decay of the correlation as compared with those reported in the literature for other atoms or molecules such as methane adsorbed in faujasite [ 3,5,14]. This is primarily due to the exceptionally high mass of xenon, We have also calculated the velocity autocorrelation function for the velocity component parallel and perpendicular to the surface of the zeolite cage,
c,(~)=(~,(O)~fi,(t))
3
(3)
where i(t) is the unit vector from the centre of the cage to the centre-of-mass of the xenon atom. Thus, ii,,(t) is the velocity component parallel to the surface whereas z?*(t) is the velocity component perpendicular to the surface. The behaviour of the C,,(I) and C, ( f ) is shown in the inset of fig. 5. We are not aware of any experimental studies related to the dy-
_o.toO 0.0
2
6
4
8
t,ps
Fig. 5. Xenon velocity autocorrelation function for xenonin zeolite NaY at 375 K. The inset shows (a) thevelocity autocorrelation function for the velocity component perpendicular to the zeolite surface, and (b) the velocity component parallel to the zeolite surface.
57
Volume 177,number I
CHEMICALPHYSICSLETTERS
namics of xenon in faujasite. The velocity autocorrelation function, C, (l), crosses the x-axis below 1 ps, thereby indicating the high-frequency motion being performed by the xenon atom in the direction perpendicular to the surface. In contrast, along the direction parallel to the surface the motion is of relatively lower frequency, as indicated by C,,(t). The calculated diffusion coefficient at this loading and temperature was found to be 2.4~ low8 m2 s-‘. It should be possible to measure the diffusion coefflcient by ‘29Xe pulsed-field-gradient NMR. We have described a molecular dynamics calculation of a realistic model of xenon adsorbed in zeolite NaY. The results are generally in good agreement with the grand canonical and partition function calculations of Rowlinson and co-workers using a spherical potential but differ in some details. The decay of the correlation is slow as compared to other organic molecules adsorbed in faujasite. We are presently investigating several other small molecules adsorbed in faujasite.
8 February 1991
References [ 1 ] J.S. Rowlinson, Proc. Roy. Sot. 402 (I 985) 67. [ 21 G.B. Woods,A.Z. Panagiotopoulosand J.S. Rowlinson,Mol. Phys. 63 (1988) 49. [3] P. Demo&, E.S. Fois, G.B. Suffritti and S. Quatieri, preprint. [4] S. Yashonath, J.M. Thomas, A.K. Nowak and A.K. Cheetham, Nature 331 (1988) 601. [ 51 P. Demontis, S. Yashonath and M.L. Klein, J. Phys. Chem. 93 (1969) 5016. [6] D.H. Olsen, J. Phys. Chem. 72 (1968) 4366. [ 71 G.R. Eulenberger,D.P. Schoemaker and J.G. Keil, J. Phys. Chem.71 (1967) 1812. [8] A.N. Fitch, H. Jobic and A. Renouprez, J. Phys. Chem. 90 (1986) 1311. [9] A.V. Kiselev and P.Q. Du, J. Chem. Sot. Faraday Trans II 77 (1981) I. [lo] A.G. Bezus, A.V. Kiselev, A.A. Lopatkin and P.Q. Du, J. Chem. Sot. Faraday Trans. II 74 (1978) 367. [ 1I ] J.O. Hirschfelder, C.F. Curtiss and R.B. Bird, Molecular theory of gases and liquids (Wiley. New York, 1964). [ 121G. Ciccotti and J.P. Ryckeart,Comput. Phys. Rept. 4 (1986) 345. [ 131H. Stach, U. Lohse, H. Thamm and W. Schirmer, Zeolites 6 (1986) 74. [ 141S. Yashonath, P. Demontis and M.L. Klein, Chem. Phys. Letters I53 (1988) 551.
I
CHEMICAL PHYSICS LETTERS
8 February 1991
Adsorption of xenon in zeolite Y: a molecular dynamics study * S. Yashonath Solid State andStructural Chemistry Unit, Indian Institute of Science, Bangalore, 560 012, India Received 13 March 1990; in final form I9 November 1990
A molecular dynamics calculation of a realistic model of xenon adsorprion in sodium-Y zeolite is reported. The equilibrium properties such as the energy distribution function, the centre-of-cage-centre-of-mass radial distribution function, and the cageoccupancy distribution function are obtained. The results are in reasonable agreement with those of earlier calculations. The dynamics is significantly slower than that observed for other small organic molecules. Xenon exhibits anisotropic motion in the large cavity.
and computational details. The results and discussion are presented in section 3.
1. Introduction Adsorption in zeolites has attracted much attention in recent times. The problem is complicated by the large number of factors influencing the adsorption in the channels and cages of the zeolites. Among these, geometrical as well as the chemical state of the zeolite determined by the %/Al ratio and the nature of the extraframework cations play important roles in determining the adsorption characteristics. Adsorption of xenon in faujasites has been studied by Rowlinson and co-workers by direct calculation of partition functions, and by a grand canonical Monte Carlo method [ 1,2]. These results have yielded interesting insights into the structure of the adsorbed fluid, distribution of occupancies and thermodynamic behaviour. Recently, some work on adsorption of small organic molecules in faujasites has also been reported [ 3-51. Here, we report a molecular dynamics calculation of xenon adsorbed in faujasite. Our interest is to study the equilibrium and the dynamical behaviour of the adsorbed xenon in faujasite and to compare our results with those of earlier calculations. In section 2, we discuss the details of the intermolecular potential
* Contribution istry Unit.
54
No. 691 from Solid State and Structural Chem-
0009-2614/91/$
2. The details of calculation The crystal structure of faujasite has been determined by several workers [ 6-8 1. The space group is Fd3m. In the present calculation, the atomic coordinates and the lattice parameter a=24.85 8, reported by Fitch et al. have been used [ 81. The zeolite lattice was kept rigid and only the xenon coordinates were included in the integration. The number of extraframework sodium cations were 48 per unit cell corresponding to a Si/AI ratio of 3.0. Of the 48 cations, 16 are in Si sites and the remaining 32 occupy S,, sites [ 4,8]. In the present calculation, we have adopted the model of Kiselev and co-workers [ 91 for the zeolite-xenon interaction. The interaction between the adsorbed xenon and the zeolite is confined to the oxygens and the sodiums. This is a reasonable assumption in view of the fact that the silicon and the aluminium are buried within the oxygen lattice, thus preventing the close approach of the xenon to these atoms. The xenon-(oxygen, sodium) interaction was taken to be of the LennardJones form [ 91,
@ik=-A$+$,i=Xe,k=O,Na. 03.50 0 1991 - Elsevier Science Publishers B.V. (North-Holland)
Volume 177,number 1
Table I Potential parameters for xenon-Nay zeolite at T= 375 K Atom
Xe
8 February 199I
CHEMICALPHYSICS LETTERS
A ( IO'kJ mol-’ A6)
B ( lo6 kJ mol-’ A’*)
0
Na
0
Na
8.2793
2.9143
Il.1345
7.9079
The dispersion parameters Aik were obtained from the Kirkwood-Muller expression and the repulsion parameters Blk by imposition of the constraint that the force should be zero at the equilibrium distance. The details are given in ref. [ lo]. The polarization energy is taken into account in the present calculation since this is a many-body term and would result in a considerable increase in the computational time. The xenon-xenon interaction was modelled by a Lennard-Jones potential,
(2) with a=4.10 8, and e/k=221 K [lo]. Molecular dynamics calculations were performed in the microcanonical ensemble with periodic boundary conditions. The system consisted of one unit cell of faujasite consisting of 384 oxygen, 48 sodium and eight xenon atoms. The xenon atoms were uniformly distributed at the start of the simulation in the large cavities or the supercages. A time step of 1.0 fs was employed for the integration. Equilibration was performed over a period of about 20 ps and averages accumulated over a fairly long period of 0.1 ns. A shifted potential with a potential truncation of IO A has been employed. Integration was carried out by means of a simple Verlet scheme [ 121.
and the calculated value of 17.25 kJ/mol obtained by Kiselev and Du [ 91 in view of the fact that the Si/Al ratio employed by us here is higher and qs,decreases with an increase in the Si/Al ratio [ 13 1. Part of the discrepancy is due to the neglect of the polarization interaction. It is difftcult to compare our results to those of Woods et al. due to the spherical potential approximation employed by them which does not correspond to any specific Si/Al ratio. Fig. 1 shows the interaction-energy distribution function, N(U). The curve shows a main peak near - 12 kJ/mol and a shoulder near - 15 kJ/mol. The shoulder arises from the xenon near the minimum energy or the adsorption site. The xenon atoms which are not near the adsorption site contribute to the higher-energy region comprising the main peak and the high-energy tail. This may be compared with the adsorption of methane in faujasite which showed a characteristic bimodal distribution. A similar bimodal distribution was also observed in the case of benzene [ 51. In contrast to these, the present results show an almost unimodal distribution with only a barely visible shoulder which seems to suggest the absence of two or more markedly distinct regions in the supercage for the case of xenon. Therefore, it is expected that a spherically averaged potential should be more appropriate for xenon adsorbed in faujasite than for methane and benzene for which there appear to exist several significantly different regions in the supercage. The higher-energy region, namely the region above - 8 kJ/mol, was initially thought to be
c
3. Results and discussion
O.lO2
The average temperature of the system is 375.9 K. The total interaction energy of a xenon atom is ( U) = ( U,) + ( Ugh), where ( V,) is the guestguest and ( Ugh) is the guest-host contribution. We have obtained a value of - 12.33 kJ/mol for ( U) . The guest-guest contribution to the total interaction energy was found to be small. The isosteric heat of adsorption, qa, is 15.46 kJ/mol. This compares reasonably with the experimentalvalue of 180.0 kJ/mol
z
0.00
- 20.0
-40
-12 0 U.kJ/mol
Fig. 1. Energy distribution function for xenon in zeolite NaY at a concentration of one atom per large cavity and a temperattire of 375 K.
55
Volume177,number I
CHEMICALPHYSICSLETTERS
due to xenon migrating from one large cavity to another. Closer examination, however, revealed that this is not so. The region with U> - 8 kJ/mol seems to be due to xenon in the proximity of the cage centre. The distribution of the methane in the supercage is shown in fig. 2. Here, the centre-of-cage-centre-ofmass (cot-corn) radial distribution function (rdf ) is plotted as a function of the distance of methane from the centre of the supercage. The cot-corn rdf shows a main peak near 4 A and a smaller one near 1 A. The main peak in the rdf suggests that the xenon atoms spend a large fraction of their time near the walls of the supercage. This is similar to the behaviour shown by methane and other molecules [ 5,141. This type of cot-corn rdf seems to be a characteristic feature of X,Y-type of zeolites. The shape of the coccorn rdf and the position of the peaks are strongly influenced by two factors: One is the nature of the interaction and the other is the geometry of the cage. The comparison with the results of Rowlinson and co-workers [ 21, who employed a spherically averaged potential, is worthwhile. The present results show a broader spread of the main peak extending to much smaller r values and a small peak near 1 A absent in the earlier study [2]. This means that the molecules are, in fact, able to stray significantly more often towards the centre of the cage than suggested by a spherically averaged potential. This view is in accordance with the fact that the sites in the large cavity are localized regions near the cage wall, and it is only in these regions that molecules spend a fairly large amount of time, thus contributing to the main 6
8 February1991
peak in the cot-corn rdf. Thus, if P(r, 0, 4) is the probability of finding a xenon atom at a point given by (r, 8, $), where r, 0, 9 are the polar coordinates of points within the large cavity, then it is evident that P( r, 19,4) varies as a function of i3and # as well as of r. This suggests that the potential function has strong angular dependence. It is not known if these anisotropies are also tetrahedral in symmetry reflecting the cage symmetry, since the potential felt by the guest atom arises not only from just the atoms comprising the inner walls of the large cavity but also from those beyond it. The tail near 6 A arises from the diffusion of xenon from one large cavity to another. This tail is likely to become increasingly prominent with increase in temperature. Fig. 3 shows the xenon-xenon radial distribution function. The main peak near 4.5 A corresponding to the minimum in the Xe-Xe interaction potential (0=4.10 A) suggests the existence of a significant population of dimer, even at this low concentration of one xenon per supercage. Such dimer formation has been observed for a one-site model of methane adsorbed in ZSM-5 [ 31. For a noble gas fluid, the second peak in the g(r) should appear at approximately $ r, where rl is the position of the first peak. It is interesting to note the second peak in the xenon-xenon rdf appears only beyond I 1 A. It is therefore, apparent that the zeolite influences the fluid structure strongly, at least at low loadings. The cage distribution function is shown in fig. 4. It is seen that the fraction of cages with zero-occupancy is 0.33 which is less than the fraction of cages with an occupancy of one. This is in contrast to a value of 0.37 obtained by Rowlinson and co-workers
/f-l
/
\
I
Fig. 2. Centre-of-cage-centre-of-mass radial distribution function for xenon in sodium-Y zeolite at a temperature of 375 K. 56
Fig. 3. Xenon-xenon
radial distribution
sorbed in sodium-Y zeolite at 375 K.
function for xenon ad-
Volume 177,number I
CHEMICALPHYSICS LETTERS
o.4,
-03r I 5
IL
0.2
I
0.1
-1:,:
012345
N
Fig. 4. Distribution of occupancies, F(N), for the large cavity at a temperature of 375 K.
for both zero- and one-occupancy. However, the difference is not surprising in view of the relatively large size of the supercage as a consequence of using the spherically averaged potential. The distribution function shows that there exist cages with a high occupancy of rive, even at the low loading of one xenon/cage.
4. Dynamics The cage residence time, site residence time and the site-site migration time have been calculated. The cage residence time, z,, was determined using a distance criterion to decide whether a given molecule belonged to a specific cage. A molecule within a distance of 5.9 A of a cage is said to reside in the cage in question. The value reported here, 9.9 ps, is found to be about an order of magnitude larger than that found for methane near 300 K [ 14 1. The difference can be attributed to the large mass of xenon compared to that of methane. This decreases the mobility of xenon significantly compared to that of methane. This is also supported by the velocity autocorrelation function discussed below. In the calculation of the site residence time (r$), an energy cutoff of - 13 kJ/mol has been employed. The calculated site residence time is 0.59 ps, which is again significantly greater than the value obtained for methane. The site-site migration time (r,) is the average time the particle spends between two visits to a site. It is found to be 1.3 ps, which is in agree-
8 February 1991
ment with the energy distribution function shown in fig. I. The calculated diffusion coefficient was also found to be much smaller than that of methane in Nay. Fig. 5 shows the velocity autocorrelation function for the motion of xenon in Nay. The striking feature of the velocity autocorrelation function here is the slow decay of the correlation as compared with those reported in the literature for other atoms or molecules such as methane adsorbed in faujasite [ 3,5,14]. This is primarily due to the exceptionally high mass of xenon, We have also calculated the velocity autocorrelation function for the velocity component parallel and perpendicular to the surface of the zeolite cage,
c,(~)=(~,(O)~fi,(t))
3
(3)
where i(t) is the unit vector from the centre of the cage to the centre-of-mass of the xenon atom. Thus, ii,,(t) is the velocity component parallel to the surface whereas z?*(t) is the velocity component perpendicular to the surface. The behaviour of the C,,(I) and C, ( f ) is shown in the inset of fig. 5. We are not aware of any experimental studies related to the dy-
_o.toO 0.0
2
6
4
8
t,ps
Fig. 5. Xenon velocity autocorrelation function for xenonin zeolite NaY at 375 K. The inset shows (a) thevelocity autocorrelation function for the velocity component perpendicular to the zeolite surface, and (b) the velocity component parallel to the zeolite surface.
57
Volume 177,number I
CHEMICALPHYSICSLETTERS
namics of xenon in faujasite. The velocity autocorrelation function, C, (l), crosses the x-axis below 1 ps, thereby indicating the high-frequency motion being performed by the xenon atom in the direction perpendicular to the surface. In contrast, along the direction parallel to the surface the motion is of relatively lower frequency, as indicated by C,,(t). The calculated diffusion coefficient at this loading and temperature was found to be 2.4~ low8 m2 s-‘. It should be possible to measure the diffusion coefflcient by ‘29Xe pulsed-field-gradient NMR. We have described a molecular dynamics calculation of a realistic model of xenon adsorbed in zeolite NaY. The results are generally in good agreement with the grand canonical and partition function calculations of Rowlinson and co-workers using a spherical potential but differ in some details. The decay of the correlation is slow as compared to other organic molecules adsorbed in faujasite. We are presently investigating several other small molecules adsorbed in faujasite.
8 February 1991
References [ 1 ] J.S. Rowlinson, Proc. Roy. Sot. 402 (I 985) 67. [ 21 G.B. Woods,A.Z. Panagiotopoulosand J.S. Rowlinson,Mol. Phys. 63 (1988) 49. [3] P. Demo&, E.S. Fois, G.B. Suffritti and S. Quatieri, preprint. [4] S. Yashonath, J.M. Thomas, A.K. Nowak and A.K. Cheetham, Nature 331 (1988) 601. [ 51 P. Demontis, S. Yashonath and M.L. Klein, J. Phys. Chem. 93 (1969) 5016. [6] D.H. Olsen, J. Phys. Chem. 72 (1968) 4366. [ 71 G.R. Eulenberger,D.P. Schoemaker and J.G. Keil, J. Phys. Chem.71 (1967) 1812. [8] A.N. Fitch, H. Jobic and A. Renouprez, J. Phys. Chem. 90 (1986) 1311. [9] A.V. Kiselev and P.Q. Du, J. Chem. Sot. Faraday Trans II 77 (1981) I. [lo] A.G. Bezus, A.V. Kiselev, A.A. Lopatkin and P.Q. Du, J. Chem. Sot. Faraday Trans. II 74 (1978) 367. [ 1I ] J.O. Hirschfelder, C.F. Curtiss and R.B. Bird, Molecular theory of gases and liquids (Wiley. New York, 1964). [ 121G. Ciccotti and J.P. Ryckeart,Comput. Phys. Rept. 4 (1986) 345. [ 131H. Stach, U. Lohse, H. Thamm and W. Schirmer, Zeolites 6 (1986) 74. [ 141S. Yashonath, P. Demontis and M.L. Klein, Chem. Phys. Letters I53 (1988) 551.