Langmuir 1997, 13, 1095-1103
1095
Adsorption of Aromatics in Zeolites ZSM-5: A Thermodynamic-Calorimetric Study Based on the Model of Adsorption on Heterogeneous Adsorption Sites† W. Rudzin´ski,* J. Narkiewicz-Michałek, and P. Szabelski Department of Theoretical Chemistry, Faculty of Chemistry, Maria Curie-Skłodowska University, Lublin 20-031, Poland
A. S. T. Chiang Department of Chemical Engineering, National Central University, Chung-Li, Taiwan, Republic of China 32054 Received March 15, 1996. In Final Form: July 29, 1996X On the basis of new experimental and theoretical findings, a revised version of the three-site model of collective localized adsorption, proposed originally by Lee and Chiang, is presented. Following the new findings, it is assumed, that benzene molecules filling channel intersections may be adsorbed in two different configurational states. That model leads to predicting, for the first time, the two steps observed on the isotherms of benzene adsorption at higher temperatures. The steps are due to cooperative redistributions of molecules adsorbed on various sites. That model allows also obtaining a quantitative simultaneous fit of both adsorption isotherms and the corresponding isosteric heats of adsorption. The estimated parameters of gas-solid interactions on various sites increase in the sequence predicted by computer simulations of one molecule adsorption.
Introduction ZSM-5 is a high silica zeolite with Si/Al ratio varying from a hundred to thousands. The framework of ZSM-5 forms an interconnecting three-dimensional channel structure. There are two types of intersecting channels, both defined by 10-membered oxygen rings, in the framework of ZSM-5. The circular zigzag channels along the a direction have a diameter of about 0.54 nm. The eliptical straight channels along the b direction have a cross section of 0.575 × 0.515 nm.1 (In literature, different dimensions of channels in ZSM-5 can be found.2 Namely, the straight [010] channels are near circular with dimensions 0.54 × 0.56 nm and the sinusoidal [100] channels are elliptical with dimensions 0.51 × 0.55 nm.) The sizes of these channels are comparable to those of aromatic molecules, so these channels can accommodate a molecule as large as 1,3,5-trimethylbenzene, for instance. It has been established that the strength of zeolitic acid sites increases with the Si/Al ratio. Having a rather high Si/Al ratio, ZSM-5 has been known to be a very good acid catalyst. The main benefit of ZSM-5, however, comes from its unique channel structure. The limited channel dimensions allow neither the formation of aromatic compounds with more than 11 carbon atoms inside this zeolite nor the formation of multiple ring precursor that leads to coking. Even if coke does form, the three-directional channel structure makes the diffusional limitation of coke less critical. ZSM-5 is therefore more resistant to the deactivation by coke. Moreover, the interconnected channel structure also reduces the hindrance due to the * The author to whom the correspondence should be addressed. † This paper is submitted for the special issue of Langmuir, devoted to the Second ISSHAC in Poland-Slovakia 1995. Presented at the Second International Symposium on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, held in Poland/ Slovakia, September 4-10, 1995. X Abstract published in Advance ACS Abstracts, February 15, 1997. (1) Flanigen, E. M.; Bennett, J. M.; Grose, R. W.; Cohen, J. P.; Patten, R. L.; Kirchner, R. M.; Smith, J. V. Nature 1978, 271, 512. (2) Meier, W. M.; Olson, D. H. Atlas of Zeolite Structure Types; Juris Druck und Verlag: Zurich, 1978.
S0743-7463(96)00254-5 CCC: $14.00
counterdiffusion of reaction products and reactants, as they may diffuse in and out of the channel system through different pores.3 This has been termed as a “molecular traffic control” mechanism. With these special properties, ZSM-5 zeolite has become one of the most versatile and valuable zeolites in modern petrochemical and hydrocarbon processing. One of the famous applications of ZSM-5 is the MTG (methanol to gasoline) process,4 where a range of low paraffins and small alkylaromatics are produced from methanol. The reforming of naphta is another example. Not only can ZSM-5 selectively crack the n-paraffins, it also alkylates benzene and toluene with the short chain olefins formed by cracking.5 The ability of selective cracking of nparaffins to produce branched paraffins has been utilized in the dewaxing of distillates to reduce the pour point of diesel fuel.6 ZSM-5 zeolite has also been used as an additive in FCC (fluidized catalytic cracking) catalyst to increase the C5-C6 olefinic and paraffinic compounds or the C5-C8 aromatics7 depending on the conditions of that process. Another significant feature of the ZSM-5 zeolite is its shape selectivity, in particular, its selectivity toward parasubstituted aromatics. This selectivity has been very valuable in the processing of BTX (benzene, toluene, xylene). It includes the toluene disproportionation, xylene isomerization, and benzene alkylation processes.8 The high xylene selectivity in the disproportionation reactions is due to the confinement of reaction transition intermediate in the limited pore size.8 The para selectivity is believed to originate from the difference in diffusivities among different isomers.9 A slight change of the crystal (3) Derouane, E. G.; Gabelica Z. J. Catal. 1980, 65, 486. (4) Chang, C. D.; Catal. Rev. Sci. Eng. 1983, 25, 1. (5) Chen, N. Y.; Garwood, W. E.; Heck, P. H. Ind. Eng. Chem. Proc. Des. Dev. 1987, 26, 707. (6) Olson, D. H.; Kokotailo, G. T.; Lawton, S. L.; Meler, W. M. J. Phys. Chem. 1981, 85, 2238. (7) Miller, S. J.; Hsieh, C. R. ACS Symp. Ser. 1991, No. 452, 45. (8) Olson, D. H.; Haag, W. O. ACS Symp. Ser. 1984, No. 248, 275. (9) Ratnasamy, P.; Babu, G. P.; Chandwadkar, A. J.; Kulkarmi, S. B. Zeolites 1986, 6, 98.
© 1997 American Chemical Society
1096 Langmuir, Vol. 13, No. 5, 1997
cell dimension may alter the relative easiness of diffusion and has a large influence on the product distribution.10,11 Again, the comparable size of aromatics and the ZSM-5 channels has been the major reason for the particular selectivity observed in this case. The selectivity of para-substituted aromatics by ZSM-5 zeolite is important in both catalytic processes and in the adsorptive separation of xylene isomers.12-15 The para form of the substituted aromatic can be separated from its other isomers. This separation may be coupled with an isomerization process to convert all isomers to the para form. Furthermore, ZSM-5 zeolite, or its alumina deficient analogue silicalite, is more hydrophobic compared to other zeolites. Therefore, hydrocarbons may be preferentially adsorbed from a humid mixture. This property has been commercially employed in cleaning up VOC, in many cases aromatic vapors, from air.16 In many of the above mentioned applications, the tight fit situation of aromatics in ZSM-5 zeolite is very crucial. Aromatic molecules experience a very strong guest-host interaction in the confined pore space of ZSM-5. The strong interaction leads to the high reactivity, the shape selectivity, and other unusual phenomena. Such a tight fit of the guest-host system is also unique for our fundamental understanding of adsorption in pores. The slight difference in size and shape between the zigzag and straight channels sometimes creates a large difference in the adsorption strength. The three-dimensional interconnected channel structure is much different from the conventional ones familiar to adsorption scientists. It also offers much diversified mechanisms of adsorption phenomena, that can occur. For these reasons, the aromatics/ZSM-5 systems have been studied very extensively in recent years. Various experimental methods have been used, including isotherm measurements,16-27 calorimetry,28-32 gas chromatography,20,21 detailed X-ray35-38 or neutron powder diffraction,39 (10) Chen, N. Y.; Kaeding, W. W.; Dwyer, F. G. J. Am. Chem. Soc. 1979, 101, 6783. (11) Kaeding, W. W.; Chu, C.; Young, L. B.; Butter, S. A. J. Catal. 1981, 69, 392. (12) Maas, R. T.; Visser, R. M. US patent 4,326,092, 1982. (13) Allen, P. T.; Drinkard, US patent 3,698,157 and 3,724,170, 1972. (14) Cattansch, J.; Glassbor, N. J. US patent 3,699,182, 1972. (15) Chiang, A. S. T.; Lin, Z. C.; Lee, M. L. In Fundamentals of Adsorption; Mersmann, A., Ed.; 1990; p 199. (16) Anderson, J. R.; Foger, K.; Mole, T.; Rajadyaksha, R. A.; Snaders, J. V. J. Catal. 1979, 58, 114. (17) Olson, D. H.; Kokotailo, G. T.; Lawton, S. L.; Meier, W. M. J. Phys. Chem. 1981, 85, 2238. (18) Jacobs, P. A.; Beyer, H. K.; Valyon, J. Zeolites 1981, 1, 161. (19) Wu, P.; Debebe, A.; Ma, Y. H. Zeolites 1983, 3, 118. (20) Lohse, U.; Fahlke, B. Chem. Tech. (Leipzig) 1983, 35, 350. (21) Choudhary, V. R.; Srinivasan, K. R. J. Catal. 1986, 102, 328. (22) Stach, H.; Lohse, U.; Thamm, H.; Schrimer, W. Zeolites 1986, 6, 74. (23) Shah, D. B.; Hayhurst, D. T.; Evanina, G.; Guo, C. J. AIChE J. 1988, 34, 1713. (24) Beschmann, K.; Kokotailo, G. T.; Riekert, L. In Characterization of Porous Solids; Unger, K. K., Rouquerol, J., Sing, K. S. W., Kral, H., Eds.; Elsevier: Amsterdam, 1988; p 355. (25) Richards, R. E.; Rees, L. V. C. Zeolites 1988, 8, 35. (26) Guo, C. J.; Talu, O.; Hayhurst, D. T. AIChE J. 1989, 35, 573. (27) Talu, O.; Guo, C. J.; Hayhurst, D. T. J. Phys. Chem. 1989, 93, 7294. (28) Pope, C. G. J. Phys. Chem. 1984, 88, 6312. (29) Pope, C. G. J. Phys. Chem. 1986, 90, 835. (30) Thamm, H. J. Phys. Chem. 1987, 91, 8. (31) Thamm, H. Zeolites 1987, 7, 341. (32) Stach, H.; Thamm, H.; Janchen, J.; Fiedler, K.; Schirmer, W. In Proceedings of the 6th International Conference on Zeolites; Bisio A., Olson, D. H., Eds.; Butterworths: London, 1984; p 225. (33) Lechert, H.; Schweitzer, W. Ibid. p 210. (34) Choudhary, V. R.; Srinivasan, K. R. Chem. Eng. Sci. 1987, 42, 382. (35) Mentzen, B. F. In Zeolites as Catylysts, Sorbents and Detergent Builders; Karge, H. G., Weitkamp, J., Eds.; Elsevier: Amsterdam, 1989; p 477.
Rudzin´ ski et al.
single crystal X-ray diffraction,40 and solid state NMR.41-43 Among these studies, diffraction data furnished information concerning the siting of sorbate molecules and the change of host structure. The results from the solid state NMR provided structure information of the host. Calorimetric and adsorption measurements provided data on the thermodynamics of sorbate-host interactions. Altogether, these results established an impressive body of information about characteristic features of the aromatic/ ZSM-5 systems. However, our understanding of these systems is still lagging behind, and various authors often express contradicting views. There exist statistical theories of adsorption in zeolites with cage and window structures.44-48 A review of the early work using thermodynamic approaches and lattice gas models was given by Ruthven.48 Such theories, however, cannot be applied to the ZSM-5 (or its aluminum deficient analogue silicalite I) zeolite having an interconnecting channel structure. The adsorption of aromatics in ZSM-5 or silicalite exhibits some unique behavior due to their molecular size. Several authors6,26,27,29,31 have reported on various peculiarities of the adsorption of aromatics in ZSM-5 (or silicalite). The isotherm might change from type I to type IV with decreasing temperature. The adsorption heats of several aromatics rise sharply at a loading approaching four molecules per unit cell. A variety of adsorption models has been proposed to describe that very unusual behavior of these systems. Thus, Thamm30 assumed that this might be adsorption of dimers, or a cooperative redistribution of adsorbed molecules, whereas Stach et al.32 saw it as a pore filling with the energy and entropy of different sites determined by Monte Carlo simulations. Talu and co-workers26,27 launched a two-patch model of collective mobile adsorption with surface phase transitions. They argue that in spite of the channel structure of zeolite, the adsorption of aromatics in ZSM-5 cannot be treated in terms of onedimensional systems. The idea to treat the whole adsorption system as a three-dimensional cooperative system has also been accepted by Chiang and co-workers.49 They used a lattice gas model with three kinds of adsorption sites and showed equivalence of their lattice gas model to an Ising model. The authors postulated next that the sharp increase in the adsorption isotherms is due to the phase transition predicted by this model. While considering p-xylene adsorption in ZSM-5, Pan and Mersmann50 have launched a model of localized adsorption on two independent subsystems of sites corresponding to the channel intersections and zigzag channels. Adsorption in the channel intersections is described (36) Sacerdote, M.; Bosselet, F.; Mentzen, B. F. Mater. Res. Bull. 1990, 25, 593. (37) Sacerdote, M.; Bosselet, F.; Mentzen, B. F. C. R. Acad. Sci. 1991, 312(II), 1513. (38) Mentzen, B. F. Mater. Res. Bull. 1992, 27, 831. (39) van Konigsveld, H.; Tuinstra, F.; van Bekkum, H.; Jansen, J. C. Acta Crystallogr. 1989, B45, 423. (40) Sacerdote, M.; Mentzen, B. F. Mater. Res. Bull. 1993, 28, 767. (41) Fyfe, C. A.; Feng, Y.; Grondey, H.; Kennydy, G. K.; Barlow, G. E. J. Am. Chem. Soc. 1988, 110, 3373. (42) Fyfe, C. A.; Feng, Y.; Grondey, H.; Kokotailo, G. T. J. Chem. Soc., Chem. Commun. 1990, 1224. (43) Lefebvre, F.; Sacerdote, M., Mentzen, B. F. C. R. Acad. Sci. 1993, 316 (II), 1549. (44) Riekert, L. Adv. Catal. 1970, 21, 287. (45) Brauer, P.; Lopatkin, A.; Stepanez, G. Ph. Adv. Chem. Ser. 1970, No. 102, 97. (46) Parsonage, N. G. Trans. Faraday Soc. 1970, 66, 723. (47) Woltman, A. W.; Hartwig, W. H. ACS Symp. Ser. 1980, No. 135, 3. (48) Ruthven, D. M. Principles of Adsorption & Adsorption Processes; Wiley: New York, 1984. (49) Lee, C-K.; Chiang, A. S. T.; Wu, F. Y. AIChE J. 1992, 38, 128. (50) Pan, D.; Mersmann, A. B. In Characterization of Porous Solids II; Rodriguez-Reinoso, F., et al., Eds.; Elsevier: Amsterdam, 1991; p 519.
Adsorption of Aromatics in Zeolites
by the Langmuir isotherm, while the adsorption in zigzag channels is modeled by the isotherm corresponding to the quasi-chemical approximation for cooperative adsorption. The interaction between the molecules in neighboring zigzag channels is assumed to be mediated by structural relaxations in the zeolite itself that occur when p-xylene is adsorbed at high loadings in ZSM-5 type zeolites. Pan and Mersmann proposed also a construction of the hysteresis loop for p-xylene on the basis of their model. That construction of the hysteresis loop of p-xylene has, next, been questioned by Snurr et al.51 who launched another model of adsorption in ZSM-5 zeolites. They proposed that the phase change from the ortho to para form of zeolite, which occurs when more than four molecules of p-xylene per unit cell are adsorbed, may also take place in the case of benzene adsorption. Snurr et al. accepted the three-site model launched by Chiang and co-workers but assumed that the phase change in the zeolite structure causes the free energies of adsorption to change on the three kinds of sites. In their model the sharp increase in the adsorption isotherms is essentially due to the change of the zeolite structure. Thus, in spite of the cooperative character of their model, the sharp increase in the adsorption isotherm is due to a cooperative redistribution of adsorbed molecules and not to a phase transition in the phase of the adsorbed molecules. The theoretical isotherms calculated by means of their lattice model were compared with GCMC (grand canonical Monte Carlo) molecular simulations but were not fitted to experimental adsorption isotherms. Although calculations were performed for four temperatures, the corresponding heats of adsorption were not calculated. Heats of adsorption were estimated by these authors only by using GCMC simulations for the changing zeolite structure. As well-known, the behavior of the isosteric heats of adsorption is a stronger test for a theory than the behavior of adsorption isotherms. It should, however, be emphasized that none of the above discussed models can predict appearance of two steps which have been observed experimentally on the isotherm of benzene adsorption in silicalite at higher temperatures. Next, theoretical studies of aromatics adsorption in ZSM-5 focus, almost exclusively, on the comparison of the calculated adsorption isotherms with experimental ones. Although experimental data on the coverage (loading) dependence of the isosteric heats of aromatics adsorption in ZSM-5 were reported as long as a decade ago, they were largely ignored in the theoretical studies. A reliable theory of adsorption should lead to a simultaneous good fit of experimental adsorption isotherms and of the accompanying heats of adsorption. The present paper brings, to our knowledge, a first successful attempt of that kind. Theory Chiang and co-workers49,52,53 have proposed to model the adsorption of aromatics in ZSM-5 as a lattice gas on a square lattice with three types of sites, S (straight channel), Z (zigzag channel), and I (intersection) as indicated in Figure 1. The adsorption energies on these sites are denoted by s, z, and i respectively. There are four sites of each type in a unit cell, while it is found experimentally that only eight molecules of benzene and p-xylene can be adsorbed in a unit cell.26,31 Thus some of these sites must be mutually exclusive. Chiang and co-workers assumed that the neighboring S (51) Snurr, R. Q.; Bell, A. T.; Theodoru, D. N. J. Phys. Chem. 1994, 98, 5111. (52) Lee, C.-K.; Chiang, A. S. T.; Wu, F. Y. Presented at the Fundamentals of Adsorption Conference, Kyoto, 1992. (53) Lee, C-K.; Chiang, A. S. presented at the AIChE Meeting, Miami Beach, FL, 1992.
Langmuir, Vol. 13, No. 5, 1997 1097
Figure 1. (A) Channel structure of silicalite. (B) Schematic model of the three-site lattice structure accepted by Lee and Chiang in their theoretical considerations.
and I sites cannot be simultaneously occupied due to size restrictions. In order to obtain an exact solution for that model, they considered only an attractive interaction Jzi between the molecules occupying the nearest neighbor Z-I pairs. Next, they extended their model by including more interactions between adsorbed molecules. Namely, they assumed attractive interactions Jsz, Jzi, Jss, and Jii for the occupied S-Z, Z-I, S-S, and I-I pairs and a very large repulsive interaction Jsi as a way to account for the mutual exclusion assumption of the occupied S-I pairs. (Since they assumed S and I sites were mutually exclusive, the I (or S ) sites would in fact be next neighbor to each other.) In such a case, only a mean field solution could be obtained52 (see Appendix)
θs )
θz )
θi )
1 1 + (1/λ) exp[-(4Jszθz + 2Jsiθi + 2Jssθs + s)/kT] (1) 1 1 + (1/λ) exp[-(4Jszθs + 2Jziθi + 2Jssθs + z)/kT] (2) 1 1 + (1/λ) exp[-(2Jziθz + 2Jsiθs + 2Jiiθi + i)/kT] (3)
where θj (j ) s, z, i), is the fractional occupancy of jth sites, j is the occupation energy for these sites, and λ is the absolute activity of adsorbate in the system defined as exp(µ/kT). Having all the energy parameters for and J, one can solve these equations for any λ value to obtain the θ values. Chiang and co-workers52,53 used their three-site lattice gas model to fit the experimental isotherms of benzene and p-xylene adsorbed in silicalite. To arrive at the phase transition in the adsorbed phase, they were forced to assume certain values of the parameters s, z, and i and some interrelations of the gas-solid and gas-gas parameters to be fulfilled. However the calculated isosteric heat of adsorption could not be seen as reproducing well the qualitative features of the experimental heats of adsorption reported by Thamm. The estimated energy of adsorption, s, was larger than that for i, which would mean that the sites S are filled first. Meanwhile, the
1098 Langmuir, Vol. 13, No. 5, 1997
Rudzin´ ski et al.
reported atomistic simulations51,54-56 suggest that the channel intersections I are filled first. There are some experimental findings39,42 that seem to support such a view. As the reported simulations already provide a solid support for the three-site model, we have decided to investigate further possibilities of arriving at a consistent theoretical description explaining all the experimental findings. Looking for possible revisions and improvements of the three-site model, we rejected the concept that this is only the phase change in the zeolite structure which might be the source of the step in adsorption isotherms: firstly, because in the case of benzene it is only a hypothesis at present; secondly, because that hypothesis alone does not lead to predicting the two steps in the adsorption isotherm of benzene which have been observed at higher loadings and temperatures. Further, looking to the computer simulations reported by Snurr et al.,51 one can see, that the zeolite phase change should not affect very much the adsorbate-adsorbate interactions. As far as the solid-adsorbate interactions are concerned, these simulations suggest that this zeolite phase change could affect strongly the adsorption on Z sites but should not affect the adsorption on I and S sites much. Thus, we decided to see first which agreement between theory and experiment could be obtained by neglecting the changes in the adsorption parameters which might be caused by the possible phase transition in the zeolite structure. Finally, we focused our attention on the new discovery reported by Mentzen et al.36 Recently they have found that two equally probable orientations of benzene molecules adsorbed in the channel intersection are possible and that these orientations are characterized by different values of the adsorption energy . Thus, we can assume, that these forms denoted herefrom by I1 and I2 compete for occupying channel intersections. In such a case the equation system 1-3 takes the following form,
λ exp{(Es + θs )
∑j ωsjθj)/kT}
1 + λ exp{(Es +
λ exp{(Ez + θz )
∑j
(4)
ωsjθj)/kT}
∑j ωzjθj)/kT}
1 + λ exp{(Ez +
∑j ωzjθj)/kT}
(5)
θi2 ) λ exp{(Ei2 +
λ exp{(Ei1 +
∑ω
i1jθj)/kT}
j
1 + λ exp{(Ei1 +
∑ω j
i1jθj)/kT}
+ λ exp{(Ei2 +
∑ω
i2jθj)/kT}
j
(6)
and (54) Li, J.; Talu, O. J. Chem. Soc., Faraday Trans. 1993, 89, 1683. (55) Snurr, R. Q.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1993, 97, 13742. (56) Grauert, B.; Fiedler, K. Ads. Sci. Technol. 1988, 5, 191.
i2jθj)/kT}
j
1 + λ exp{(Ei1 +
∑ω
i1jθj)/kT}
+ λ exp{(Ei2 +
j
∑ω
i2jθj)/kT}
j
(7)
where Ej ) j + kT ln fj, fj is the molecular partition function of the admolecules occupying the sites of type j, and ωij is the interaction energy of a molecule adsorbed on site i with molecules adsorbed on the nearest sites j. Let us remark that the parameters Ej in the above equations are related to the noncofigurational part of the free energy of adsorption per molecule. The overall adsorption isotherm θ obtained by solving the equation system 4-7 is then given by,
1
∑j θj
θ)
j ) i1, i2, s, z
3
(8)
Theoretically, such an isotherm equation with appropriate interaction parameters ωjm, might show a critical point at temperature Tc such that
() ∂µ ∂θ
( ) ∂2µ ∂θ2
) 0 and
Tc
)0
(9)
Tc
and a nonphysical loop at still lower temperatures. Then, one would have to perform the Maxwell construction to arrive at the physical isotherm, represented by a straight line fulfilling the conditions
∫θθ µ(θ) dθ G
µM )
L
θG - θL
and µM ) µ(θG) ) µ(θL)
(10)
where θG and θL are the surface coverages corresponding to the beginning and the end of the phase transition, respectively. The theoretical isotherms based on the concept of a phase transition in the adsorbed phase will predict a vertical increase in experimental adsorption isotherm at a certain pressure defined in eq 10. Looking more carefully to the behavior of the reported experimental isotherms, one can see indeed a sharp increase which, however, is never perfectly vertical. It seems that this fact has not received enough attention. Then, within the range of the surface concentrations corresponding to the phase transition region, the predicted heat of adsorption is independent of the coverage (loading) and is given by
Q) θi1 )
∑ω
∫θθ Q(θ) dθ
1 θG - θL
G
L
(11)
Let us remark that such constant heats of adsorption have not been observed at higher loadings by adsorbed aromatics, where the phase changes were believed to occur. This must raise serious doubts as to whether the sharp increase(s) in the adsorption isotherms of aromatics are due to phase changes in the adsorbed phase. Now, let us investigate the behavior of the heat of adsorption of aromatics predicted by our eqs 4-7. To that purpose, we rewrite eqs 4-7 as follows,
Fs )
µs - µ kT
) ln
Es +
θs
∑j ωsjθj
1 - θs
kT
- ln λ ) 0 (12)
Adsorption of Aromatics in Zeolites
Fz )
Fi1 )
µz - µ kT
µi1 - µ kT
) ln
) ln
Ez +
θz
Langmuir, Vol. 13, No. 5, 1997 1099
∑j ωzjθj
1 - θz
kT
- ln λ ) 0
∂Gj
∑j ωi jθj
∂µ
m
kT ln λ ) 0 (14)
Fi2 )
µi2 - µ kT
) ln
∑j ωi jθj
Ei2 +
θi2
2
-
Gm j )
kT
Let Qj({θm}) denote the molar differential heat of adsorption on the site of type j, at a certain set of the average surface coverages {θm} (m ) s, z, i1, i2). It is given by,
(
)
∂ µj - µ Qj({θm}) ) -k ∂(1/T) kT
{θm}
(16)
Thus Qj values take the following explicit forms
Qs({θm}) ) Qs° +
∑j ωsjθj
(17)
Qz({θm}) ) Qz° +
∑j ωzjθj
(18)
Qi1({θm}) ) Qi1° +
∑j
ωi1jθj
(19)
Qi2({θm}) ) Qi2° +
∑j ωi jθj
(20)
2
(
)
Ej° + µ° kT d(1/T)
(21)
and µ° in eq 21 is the standard chemical potential of adsorbate molecules in the gaseous phase. An incremental increase in µ, dµ, will result into an incremental increase of θ, dθ, represented by,
∑j
() ∂θj
dµ
∂µ
(22)
That incremental increase will be accompanied by a heat effect dQ,
dQ )
()
∑j Qj
∂θj ∂µ
dµ
(23)
Thus, the overall (measured) differential heat of adsorption Q will be given by
∑Qj( ∂µ ) ∂θj
Q)
∑(
(25)
( ) ∂Gj ∂θm
(26)
∂θm Dm ) ∂µ D
)
∂θj ∂µ
where
(
(27)
Gss Gsz D) s Gi1
Gzs Gzz Giz1
Gis1 Giz1 Gii11
Gis2 Giz2 Gii12
Gis2
Giz2
Gii21
Gii22
)
(28)
and Dm is obtained from D by replacing the mth column of the determinant by the column of constants. From eqs 24 and 27 one will be able to evaluate the heat of adsorption as a function of coverage. Results and Discussion
where
dθ )
)0
The solution of the equation system (25) reads,
ln λ ) 0 (15)
Qj° ) k
∂µ
-
1 - θi1 - θi2
d
∑ m ∂θ
The derivatives (∂θm/∂µ) are found by solving this system of four linear equations. Let Gm j denote the derivative
1
1 - θi1 - θi2
∂Gj ∂θm
) -1 +
(13)
Ei1 +
θi1
Fj multiplied by kT. Thus,
(24)
The derivatives (∂θj/∂µ) can be evaluated from equation system 12-15. It can be done as follows. Let Gj denote
Like in the previous works by Chiang and co-workers, the isosteric heats of adsorption of benzene and p-xylene in silicalite, reported by Thamm30 (Germany), were taken for analysis, along with the adsorption isotherms measured in Chiang’s Laboratory (Taiwan). This fact has to be taken into account while considering the obtained agreement between theory and experiment. The experimental isotherms of benzene and p-xylene in ZSM-5 measured by Chiang and co-workers53 are shown in Figures 2 and 3. One can see that for p-xylene only one plateau at about 4 M/u.c. is observed at all temperatures, followed by a sudden jump to a saturation capacity. In the case of benzene adsorption, two steps are observed: the first is at around 4 M/u.c. and the second one at around 6 M/u.c. The sharp steps in the isotherms of aromatics adsorbed in ZSM-5 silicalite at loadings above 4 M/u.c. have been observed by many authors.6,27,28,32 It seems, however, that it was Chiang and co-workers who first reported on the two steps on the experimental adsorption isotherm of benzene at higher temperatures. At the same time no hysteresis was found in either benzene or p-xylene adsorption isotherms. Such hysteresis was reported earlier by Thamm31 (for benzene) and Richards et al.25 (for p-xylene) using much smaller crystals than these used in Chiang’s experiment. It seems, therefore, that the observed hysteresis was due to desorption from intraparticle pores. While considering the interaction parameters ωmn (m, n ) i1, i2, s, z), we have carried out numerical best-fit calculations, seeking for a minimum number of these parameters that would allow for a reasonably (simultaneous) good fit of experimental adsorption isotherms and heats of adsorption. Table 1 collects the values of the parameters found by computer, while fitting simultaneously an experimental adsorption isotherm and the corresponding isosteric heat of adsorption. Before we comment on the values of the parameters found by computer, we will analyze first the
1100 Langmuir, Vol. 13, No. 5, 1997
Rudzin´ ski et al.
Table 1. Values of Parameters Found by Fitting Simulataneously Our Equations to the Experimental Isotherms and Heats of Adsorption of Benzene and p-Xylene in Silicalite, Measured at 303 Ka benzene p-xylene
benzene p-xylene
benzene p-xylene a
Ki1 (Pa-1)
Ki2 (Pa-1)
Ks (Pa-1)
Kz (Pa-1)
ωzz (kJ/mol)
8.547 × 10-2 3.042 × 10-1
3.873 × 10-3 4.905 × 10-2
2.605 × 10-3 0.0
3.643 × 10-2 3.432 × 10-2
7.60 15.50
ωsz (kJ/mol)
ωsi2 (kJ/mol)
ωzi2 (kJ/mol)
ωsi1 (kJ/mol)
ωzi1 (kJ/mol)
-2.75 0.00
21.00 0.00
-30.30 5.50
-11.00 0.00
-14.00 -4.00
ωi1i1 (kJ/mol)
Qi1° (kJ/mol)
Qi2° (kJ/mol)
Qs° (kJ/mol)
Qz° (kJ/mol)
0.00 8.20
56.00 76.00
105.00 84.00
69.00 0.00
70.00 87.00
The Henry constant Kj is defined as exp{(Ej + µ°)/kT}.
Figure 2. Experimental isotherms of benzene adsorption in ZSM-5 at 273 K (b ), 283 K ([), 293 K (9) and 303 K (2), measured by Chiang and co-workers53.
Figure 3. Experimental isotherms of p-xylene adsorption in ZSM-5 at 273 K (b), 283 K ([), 293 K (9), 303 K (2) and 323 K (+), measured by Chiang and co-workers.53
behavior of our adsorption systems predicted by our equations for those particular sets of parameters. Figure 4 shows graphically the agreement between experimental adsorption isotherm of benzene in ZSM-5 and the theoretical one calculated by using the parameters collected in Table 1. In Figure 7 the comparison between the experimental and theoretical heats of adsorption is presented. Apparently, the number of the parameters is large. If, however, one looks to the complicated shape of the benzene isotherm and heat of adsorption curves and realizes that we fit them simultaneously by using the same set of parameters, one can see a thin margin for an arbitrary choice of these parameters. As a matter of fact, we have performed numerous model calculations which showed,
Figure 4. Comparison of the experimental isotherm of benzene adsorption in silicalite (b) measured by Chiang at 303 K, with the theoretical one (s), calculated from eqs 4-7 by using the parameters collected in Table 1.
Figure 5. Occupation by benzene molecules of various adsorption sites in silicalite, calculated from eqs 4-7, by using the parameters collected in Table 1. The solid line rising sharply at small adsorbate pressures is the occupancy of the I sites by benzene molecules having a certain orientation denoted here by i1 whereas the solid line rising sharply at the highest adsorbate pressures is the occupancy of I sites by benzene molecules having the orientation denoted here by i2. The solid lines denoted by z(s) and s(z) are the occupancies of the sites Z and S, or vice versa. The black circles (b) are the experimental data measured by Chiang.
that the calculated data are very sensitive to a particular choice of these parameters. Meanwhile we would like to draw the reader’s attention to the relatively good fit of the experimental benzene isotherm and the corresponding heat of adsorption. In Figure 5, in addition to the overall theoretical adsorption isotherm, also the contributions are shown, from the
Adsorption of Aromatics in Zeolites
Figure 6. Comparison of the isosteric molar heats of adsorption of benzene in silicalite measured by Thamm30 at 303 K (b) with the theoretical ones calculated by Grauert and Fiedler56 (- - -) and Snurr at al.55 (]) using the Monte Carlo simulations and by Talu et al.54 (s) using the two-patch heterogeneous model with phase transition.
isotherms of adsorption on various adsorption sites. One can see that neither the total theoretical isotherm nor its composite isotherms on a particular kind of site (in a particular configuration), show loops which could be associated with phase transitions. The sharp but not exactly vertical changes in the adsorption isotherm of benzene are due to rapid changes in the occupation of various adsorption sites. We called it the cooperative redistribution of adsorbed molecules. Our theoretical calculations confirm, thus, the long-shared feeling by many scientists, that the adsorption of aromatics in silicalite is governed by a delicate balance between adsorbate-solid and adsorbate-adsorbate interactions. The reason why in Figure 5 we used z(s) and s(z) to denote the occupancy of Z and S sites is following: From a purely theoretical point of view, it is impossible to judge which of the calculated solid lines means the occupancy of Z sites, or S sites alternatively. This is because of the symmetry of eqs 4 and 5. Equation 5 can be obtained from eq 4 by replacing index s by z, and vice versa. The discrimination between the calculated contributions must be made on some rational physical basis. For us that basis is the theoretical and experimental findings reported by Mentzen et al.36 They argue that at the highest loadings of silicalite, the adsorbed molecules form one-dimensional polymers of benzene molecules in the straight channels. The formation of such onedimensional polymers means full occupation of both I and S sites at the highest possible loading. Looking to Figure 5 we can deduce that such occupation could really exist, provided that the solid line s(z) means the occupancy of sites S. The notation s(z) means that this line should, thus, be associated with the occupancy of S sites rather than of the Z sites. The symbol z(s) has a similar meaning. If, however, we interchange the interpretation of these theoretical isotherms, our conclusion that I and Z sites are completely covered at the highest loadings will agree with the conclusion drawn by Snurr et al.51 As we have already mentioned, the behavior of theoretically predicted isosteric heats of adsorption is a much stronger test for the theory than the behavior of theoretical adsorption isotherms. This is because the behavior of the experimental heats of adsorption is much more sensitive to the nature of an experimental adsorption system. Thus, we believe, that special attention should be given to the agreement between theoretical and experimental heats of adsorption. Figure 6 shows the comparison of the experimental heat
Langmuir, Vol. 13, No. 5, 1997 1101
Figure 7. Comparison of the experimental heat of adsorption of benzene molecules adsorbed in silicalite (b) reported by Thamm and the theoretical ones (s), calculated by us, using the parameters collected in Table 1.
Figure 8. Contributions Qcj to the total isosteric heat of adsorption of benzene in silicalite, calculated by us using the parameters collected in Table 1. The solid lines appearing at the smallest and highest surface loadings are the contributions Qci1 and Qci2, respectively, whereas the solid lines z(s) and s(z) correspond to the adsorption on Z and S sites, respectively. The black circles (b) are the experimental data reported by Thamm.
of benzene adsorption in silicalite measured by Thamm30 and the theoretical ones found by Snurr et al.,55 those determined by Grauert and Fiedler56 using Monte Carlo simulations, and those determined by Talu et al.54 using the two-patch heterogeneous model with phase transition. Then, Figure 7 shows the comparison of the experimental heat of benzene adsorption in silicalite measured by Thamm30 and the theoretical one calculated from the equations developed in this paper, using the parameters collected in Table 1. Figure 8 shows the contributions to the total isosteric heat of adsorption of benzene, from the heats of adsorption Qcj generated by the adsorption on various adsorption sites.
( ) ∑( ) Qj
Qcj )
∂θj ∂µ ∂θj ∂µ
(29)
The additional index “c” in Qcj means that this is the “contribution” to the total heat of adsorption, from the molecules occupying sites j. Figure 9 shows the comparison of the experimental isotherm of p-xylene adsorption in silicalite, measured by Chiang, and the theoretical one calculated by us. Figure
1102 Langmuir, Vol. 13, No. 5, 1997
Figure 9. Comparison between the experimental isotherm of p-xylene adsorption in silicalite, measured by Chiang (b), and the theoretical one (s), calculated by using the parameters collected in Table 1.
Figure 10. Occupation by p-xylene molecules of various adsorption sites in silicalite, calculated from eqs 4-7 by using the parameters collected in Table 1. The solid line rising sharply at small adsorbate pressures is the occupancy of the I sites by p-xylene molecules having a certain orientation denoted here by i1 whereas the solid line rising sharply at the highest adsorbate pressures is the occupancy of I sites by benzene molecules having the orientation denoted here by i2. The solid line denoted by z(s) is the occupancy of the sites Z (or S ). The black circles (b) are the experimental data measured by Chiang.
10 shows the contributions from the isotherms of adsorption on various adsorption sites. One can see that, similarly as in the case of benzene adsorption, neither the total theoretical isotherm nor its composite isotherms on a particular kind of site (in a particular adsorbed configuration) show loops which could be associated with phase transitions. The sharp, but not exactly vertical, changes in the adsorption isotherm of p-xylene are due to the cooperative redistribution of adsorbed molecules. Figure 11 shows the comparison between the experimental and theoretical heats of p-xylene adsorption. Figure 12 shows the contributions to the total isosteric heat of adsorption of p-xylene from the heats of adsorption Qcj generated by the adsorption on various adsorption sites. While commenting on Figure 10, we see some differences between the mechanism of benzene and p-xylene adsorption at loading higher than 4 M/u.c. Below that loading the adsorption mechanism is the same. The total adsorption effect is practically due only to the adsorption at channel intersections. Various authors have emphasized various differences in the situation of p-xylene and benzene molecules in silicalite. Thus, Talu and co-workers emphasize more
Rudzin´ ski et al.
Figure 11. Comparison between the experimental heat of p-xylene adsorption in silicalite measured by Thamm (b) and the theoretical one, (s) calculated by using the parameters collected in Table 1.
Figure 12. Contributions Qcj to the total isosteric heat of adsorption of p-xylene in silicalite at 303 K, calculated by us using the parameters collected in Table 1. The solid lines denoted by i1 and i2 appearing at the smallest and highest surface loadings are the contributions Qci1 and Qci2, respectively, whereas the solid line z(s) corresponds to the adsorption on Z (or S ) sites, respectively. The black circles (b) are the experimental data reported by Thamm.
restrictions for rotations of the p-xylene molecule compared to benzene molecules. They did not, however, observe a hysteresis loop in their experiments where big crystals were used. Of course, the interactions between adsorbed molecules must also be different. Then, at the loadings higher that 4 molecules/u.c., the transition takes place from the ortho to para form, induced by adsorbed molecules. We have, however, certain doubts whether this change in the silicalite structure is the main, or the initial, reason for the sharp increase in the isotherm of p-xylene adsorption at the loadings exceeding 4 molecules/ u.c. Looking to Figure 8, one can see that at this “critical” loading a sudden increase of the z(s) and s(z) forms takes place and a sudden disappearance of the form i1. This takes place even in the absence of the phase transition in the zeolite structure assumed so far. We can imagine, however, a situation when this sudden redistribution induces the silicalite phase transition which, in turn, promotes further this sudden rearrangement. Such a view could be supported by the values of the parameters found by computer, and collected in Table 1. One striking property observed there is the high value of the (attraction) parameters ωzz for both benzene and p-xylene adsorption. This would suggest a usually high positive cooperativity
Adsorption of Aromatics in Zeolites
of adsorption of molecules adsorbed on Z sites. That means, the total energy of the molecules adsorbed on Z sites grows rapidly with the number of molecules adsorbed on these sites. However, the calculations show, that adsorption on Z sites starts rapidly only when surface loading exceeds 4 M/u.c, i.e., when the phase transition in the zeolite structure can take place. One may, therefore, assume, that this unusual positive cooperativity simulates, in fact, another factor leading to such a sudden increase of adsorption on Z sites. This may well be a sudden increase of the adsorption energy Ez, induced by the zeolite phase transition. In the case of arguments that for benzene the phase change in the silicalite phase is only a hypothesis at present, we might offer another explanation following the arguments by Pan and Mersmann.50 They believe a strong attraction exists between two molecules on Z sites, transmitted through the solid phase. Finally, a certain compromise between the views expressed by Pan and Mersmann and those launched by Snurr et al. seems to be possible. A still lower value of ωzz for benzene compared to that of p-xylene might be due to the attractions transmitted through the solid phase. To explain, however, the unusually high ωzz value for p-xylene, it seems necessary to assume that it simulates another important factor, enhancing the adsorption on Z sites at loadings higher than 4 M/u.c. This may be the change (increase) of the adsorption energy Ez induced by the change of the zeolite structure, which has been proved to occur for sure. The relatively less successful fit of the experimental data by the theoretical heats of adsorption is probably due to neglecting another physical factor. These are the chemical and geometrical defects in the silicalite structure. Zeolites are usually viewed as very regular crystallographic structures. The common existence of various structure defects has been known for a long time but has not received enough attention. Indeed, such defects should not affect adsorption of small molecules in large cavities and channels. If, however, the dimension of cavities and channels becomes comparable to the values of van der Waals interaction parameters, even small changes in the zeolite local dimensions may result in considerable changes in the gas-solid interactions. This will cause the appearance of a new level of surface heterogeneity, not only different features of the S, Z, and I. The silicalite structure local imperfections will induce an additional dispersion of the adsorption features (nonconfigurational free energies) even for the same kind of adsorption sites. This was Thamm himself who emphasized first that the strongly decreasing heats of aromatics adsorption at small surface coverages must be due to structure imperfections. Similar views were expressed by Talu. This can be seen in Figure 7. Our model assuming that all the sites of a certain type have identical adsorption features is not able to reproduce the decrease in the initial part of the heat of adsorption curve. From the existing literature on the adsorption on heterogeneous surfaces,57,58 it is known that this decrease could be reproduced by assuming a certain dispersion of Ej values on various sites j. We continue the studies along incorporating into our theory that additional level of heterogeneity to see how it may change the interpretation of the mechanism of aromatics adsorption in silicalite. (57) Rudzin´ski, W.; Everett, D. H. Adsorption of Gases on Heterogeneous Surfaces; Academic Press: New York, 1992. (58) Jaroniec, M.; Madey, E. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1989.
Langmuir, Vol. 13, No. 5, 1997 1103
Appendix Mean Field Solution. For a system with N sites of each type, the canonical partition function of the lattice gas can be written as
Ξ(µ, N, T, Jss, Jii, Jsz, Jzi, Jis, s, z, i) )
∑ ∑ ∑
exp[-βH] (A.1)
ns)0,1 nz)0,1 ni)0,1
where Jkl is the pair-interaction energy between two molecules adsorbed on neighboring sites “k” and “l”, and
∑ n2s + Jii ∑ n2i + Jsz ∑ nsnz + Jzi ∑ nzni + Jis ∑ nins + (s + ln λ) ∑ ns + (z + ln λ) ∑ nz + (i + ln λ) ∑ ni
-βH ) Jss
where the activity exp{µ/kT} is written as λ. The summation is over all possible ocupancies, with ni ) 1(0) denoting the site I being occupied (unoccupied). This canonical partition function can be evaluated by using the mean-field approximation. First we write the Helmholtz free energy as a function of H
F ) E - TS ) Tr(FH) + kT Tr (F ln F)
(A.2)
where the entropy S ) -k‚Tr(F ln F) and F is the density matrix. By the mean-field approximation we assume
F)
∏i Fi
(A.3)
where the product is over all sites. We chose the Fi values that minimize F subject to Tr(Fi) ) 1. Following this procedure, we obtain from equation A.1
-
βF ) Jssθ2s + Jiiθ2i + 4Jszθsθz + 2Jziθzθi + N 2Jsiθsθi + (s + ln λ)θs + (z + ln λ)θz + (i + ln λ)θi - [Tr(Fs ln Fs) + Tr(Fz ln Fz) + Tr(Fi ln Fi)] (A.4)
where θj is the fraction of j sites that are occupied, defined as
θj )
∑nj〉 ) 〈nj〉 ) Tr(Fjnj)
1 〈 N
(A.5)
One then finds the Fs, Fz, and Fi that minimize F subject to Tr(Fs) ) Tr(Fz) ) Tr(Fi) ) 1, with Lagrange’s multiplier method. The final result reads as
θs ) Tr(Fsns) ) 1 (A.6) 1 1 + exp[-(2Jssθs + 4Jszθz + 2Jsiθi + s)] λ θz ) Tr(Fznz) )
1 1 1 + exp[-(4Jszθs + 2Jziθi + z)] λ (A.7)
θi ) Tr(Fini) ) 1 (A.8) 1 1 + exp[-(2Jiiθi + 2Jzinz + 2Jsiθs + i)] λ LA960254R
