Three-Site Lattice Gas Model for Adsorption of Binary Aromatic

Langmuir 2001, 17, 61-68

61

Three-Site Lattice Gas Model for Adsorption of Binary Aromatic Mixtures in Silicalite P. Szabelski* and J. Narkiewicz-Michałek Department of Theoretical Chemistry, Faculty of Chemistry, Maria Curie-Skłodowska University, M. Curie-Skłodowska Sq. 3, Lublin, 20-031 Poland Received May 31, 2000. In Final Form: October 16, 2000 Adsorption of the binary benzene/p-xylene mixture in silicalite is studied by means of a generalized version of the homogeneous three-site lattice gas model. The energy parameters found during fitting of single-component experimental isotherms are used as the input data for the mixed adsorption data fitting procedure. The obtained results include single and mixed adsorption isotherms, isothermal-isobaric phase diagrams, and partial isotherms of benzene and p-xylene adsorption in silicalite. Theoretical predictions of the lattice gas model are compared with the experimental data reported by Li and Talu.

Introduction The discovery of intermediate-pore zeolites such as ZSM-5 and ZSM-11 based on the 10-membered oxygen rings stimulated a considerable increase in the use of synthetic zeolites in modern separative, adsorptive, and shape-selective catalytic processes. These processes rely on the microporous zeolite architecture which confines molecules to specific orientations or paths within the framework, giving the solid the property of shape selectivity. ZSM-5 zeolites are one of the most versatile and valuable adsorbents in modern petrochemical and hydrocarbon processing. Having a pore diameter comparable with the sizes of typical aromatic molecules (benzene, xylenes, or toluene), ZSM-5, or its aluminum-free analogue silicalite became an effective tool for isomerization and separation of multicomponent aromatic gas mixtures. For example, xylene isomerization catalyzed by ZSM-5 is biased toward the production of the most valuable isomer p-xylene, because the diffusivity of p-xylene in ZSM-5 is much greater than that of m-xylene or o-xylene, thus allowing the para product to diffuse selectively out of the crystal.1 Virtually, all industrial applications of ZSM-5 involve multicomponent adsorption. Therefore, the prediction of mixed adsorption equilibria as well as transport mechanism of aromatics in these zeolites plays a key role in improvement of current applications and development of new ones based on a shape selectivity. The main question concerning mixed adsorption of aromatics in ZSM-5 zeolites is estimation of selectivity for a certain type of molecules. The selectivity originates in many cases not only from differences in size and shape of the adsorbed molecules but also from energetic and entropic effects. So far, no rigorous theoretical description has been proposed for such complicated multicomponent and multiphase systems. Much experimental work has been carried out on the adsorption characteristics of single aromatics in ZSM-5 zeolites. Researchers have made use of both macroscopic measurements (e.g., adsorption isotherms,1-7 heats of * To whom correspondence should be addressed: FAX, tel (48)(81) 537-56-85; E-mail [email protected]. (1) Wu, P.; Debebe, A.; Ma, Y. H. Zeolites 1983, 3, 118. (2) Lohse, U.; Fahlke, B. Chem. Technol. (Leipzig) 1983, 35, 350. (3) Richards, R. E.; Rees, L. V. C. Zeolites 1988, 8, 35. (4) Guo, C. J.; Talu, O.; Hayhurst, D. T. AIChE J. 1989, 35, 573.

adsorption6-9) and microscopic techniques such as neutron scattering,10 X-ray diffraction,11-14 and NMR15-17 to probe the processes occurring within the zeolite framework. In contrast, however, the field of multicomponent adsorption is still poorly examined. Here, an exception are the works by Gladden et al.17-19 and Hung,20 who used 2H NMR and FT-Raman spectroscopy to probe the adsorption of the binary mixture of benzene and p-xylene in silicalite-1. To our knowledge, the only equilibrium data on the benzene + p-xylene vapor mixture adsorption in silicalite published up until now are those of Li and Talu.21 These authors reported pure component and mixed adsorption isotherms of benzene and p-xylene in silicalite measured at 70 °C along with the corresponding phase diagram. The total pressure of the mixture was fixed at pressure levels about 1.20 and 2.53 kPa, respectively. At 70 °C the pure benzene isotherm was essentially of type I with the maximum capacity equal to about four molecules per unit cell while p-xylene isotherm displayed type IV with the first plateau at about four molecules per unit cell and the maximum capacity at about six molecules per unit cell. The obtained dependence of the total adsorption on the benzene mole fraction in the gas phase showed very unusual behavior. (5) Talu, O.; Guo, C. J.; Hayhurst, D. T. J. Phys. Chem. 1989, 93, 7294. (6) Lee, C. K.; Chiang, A. S. T. J. Chem. Soc., Faraday Trans. 1996, 92, 3445. (7) Pope, C. G. J. Phys. Chem. 1986, 90, 835. (8) Thamm, H. Zeolites 1987, 7, 341. (9) Thamm, H. J. Phys. Chem. 1987, 91, 8. (10) Jobic, H.; Bee, M.; Dianoux, A. J. J. Chem. Soc., Faraday Trans. 1989, 85, 2525. (11) van Koningsveld, H.; Tunistra, F. Acta Crystallogr. 1989, B45, 423. (12) van Koningsveld, H.; Jansen, J. C.; Van Bekkum, H. Acta Crystallogr. 1996, B52, 140. (13) Sacerdote, M.; Bosselet, F.; Mentzen, B. F. Mater. Res. Bull. 1990, 25, 539. (14) Mentzen, B. F.; Vigne -Maeder, F. Mater. Res. Bul. 1987, 22, 309. (15) Kustanovich, I.; Vieth, H. M.; Luz, Z.; Vega, S. J. Phys. Chem. 1989, 93, 7427. (16) Portsmouth, R. L.; Gladden, L. F. J. Chem. Soc., Chem. Commun. 1992, 512. (17) Portsmouth, R. L.; Duer, M. J.; Gladden, L. F. J. Chem. Soc., Faraday Trans. 1995, 91, 559. (18) Portsmouth, R. L.; Gladden, L. F. J. Chem. Soc., Faraday Trans. 1995, 91, 963. (19) Ashtekar, S.; Hastings, J. J.; Gladden, L. F. J. Chem. Soc., Faraday Trans. 1998, 94, 1157. (20) Huang, Y. J. Am. Chem. Soc. 1996, 118, 7233. (21) Li, J.; Talu, O. Chem. Eng. Sci. 1994, 49, 189.

10.1021/la0007630 CCC: $20.00 © 2001 American Chemical Society Published on Web 12/12/2000

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A rapid change in the total amount adsorbed occurred at intermediate mole fractions. Total isotherms at the two pressures changed from concave to convex as the benzene mole fraction increased. The phase diagram indicated preferential adsorption of p-xylene in a wide range of benzene mole fraction in the gas phase. Additionally, the selectivity toward p-xylene at high pressure was higher than at low pressure in a certain composition range. The steps observed on the isotherms indicate that the lateral interactions play a very important role in the adsorbed phase behavior. Li and Talu21 applied the heterogeneous ideal adsorbed solution (HIAS) theory to fit the experimental data of mixed benzene/p-xylene adsorption in silicalite. That approach involved an extension of standard IAS theory to heterogeneous surfaces. The structural heterogeneity of silicalite was represented by the pure component twopatch vdW model. With such a model, despite a highly complicated nature of the system, Li and Talu were able to reproduce the experimental data with satisfactory accuracy. However, this approach gives no insight into the mechanism of the binary adsorption process on a microscopic level. Information of this kind can be obtained by means of microscopic techniques or computer simulations. The majority of computer simulations of mixed gas adsorption in zeolites focused mainly on adsorption of small molecules in large cagelike structures. The adsorption of small molecules including Xe, Ar, and CH4 and their binary mixtures in zeolite NaA was simulated by Van Tessel et al.22 Heuchel and co-workers23 reported phase diagrams for adsorption of binary mixtures of CH4 and CF4 in silicalite at different total pressures and gasphase compositions. Configuration-bias Monte Carlo simulations of adsorption isotherms for mixtures of linear and branched alkanes in silicalite were performed by Vlugt et al.24 and by Macedonia and Maginn.25,26 Leonidas et al.27 carried out molecular dynamics simulations for the n-butane-methane mixture in silicalite determining energy distributions for the sorbate-sorbate interactions and for the total energy felt by a single molecule adsorbed in different pores. Atomistic Monte Carlo simulations were also used to calculate adsorption isotherms and differential heats of adsorption of single aromatics in ZSM-5 zeolites.28-33 However, such simulations are computationally intensive, requiring access to a supercomputer or fast dedicated workstations, and what is more important, the results obtained so far do not fit precisely the experimental data. Difficulties in predicting adsorption isotherms and diffusivities for tight-fitting molecules were often attributed to uncertainties in the zeolite structure determination29,32 and/or to the rigid lattice assumption.31 Li (22) Van Tassel, P. R.; Davis, H. T.; McCormick, A. V. Langmuir 1994, 10, 1257. (23) Heuchel, M.; Snurr, R. Q.; Buss, E. Langmuir 1997, 13, 6795. (24) Vlugt, T. J. H.; Krishna, R.; Smit, B. J. Phys. Chem. 1999, 103, 1102. (25) Macedonia, M. D.; Maginn, E. J. Mol. Phys. 1999, 96, 1375. (26) Macedonia, M. D.; Maginn, E. J. Fluid Phase Equilib. 1999, 158-160, 19. (27) Gergidis, L. N.; Theodorou, D. N. J. Phys. Chem. 1999, 103, 3380. (28) Grauter, B.; Fiedler, K. Adsorpt. Sci. Technol. 1989, 6, 191. (29) Li, J.; Talu, O. J. Chem. Soc., Faraday Trans. 1993, 89, 1683. (30) Snurr, R. Q.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1993, 97, 13742. (31) Snurr, R. Q.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1994, 98, 5111. (32) Clark, L. A.; Snurr, R. Q. Chem. Phys. Lett. 1999, 308, 155. (33) Klemm, E.; Wang, J.; Emig, G. Microporous Mesoporous Mater. 1998, 26, 11.

Szabelski and Narkiewicz-Michałek

and Talu29 performed Monte Carlo simulations of benzene in the Olson and Taylor structures and found differences of up to 40% in the predicted Henry’s constants. Snurr et al.31 calculated full adsorption isotherms for benzene in the Olson silicalite structure and the PARA silicalite structure of van Koningsveld et al.11 They reported qualitative differences in the simulated isotherms. The siting of adsorbates within the pores and the heats of adsorption for the two structures were also markedly different. The selection of a proper potential used to represent zeolite/sorbate and sorbate/sorbate interactions in tight-fitting systems is also of crucial importance. Klemm et al.33 probe various potential models to simulate the behavior of benzene in silicalite and found great differences in the predicted Henry’s constants. As atomistic GCMC simulations confirmed the existence of distinct adsorption sites for benzene in silicalite, Snurr et al.31 proposed a hierarchical approach that combines the predictive capability of an atomistic simulation and the computational efficiency of a lattice model. First, short atomistic simulations are used to obtain parameters for the lattice model. The parameters describe the free energy in various adsorption sites due to the interactions between the adsorbed molecule and the zeolite, as well as to the interactions between neighboring adsorbed molecules. These energies are then inputs to a lattice model from which the adsorption equilibrium properties of the system are determined. This methodology was applied by Snurr et al.31 to calculate the adsorption of benzene in silicalite. The theoretical isotherms calculated by their hierarchical lattice model were compared with GCMC simulations but were not fitted to the experimental adsorption isotherms. Although calculations were performed for several temperatures, the corresponding heats of adsorption were not calculated. Heats of adsorption were estimated by these authors only by using the GCMC simulations for the changing zeolite structure, but the results of their simulations were not able to reproduce the experimental data well. As generally known, the behavior of isosteric heats of adsorption is a much stronger test for theory than the behavior of adsorption isotherms. Lattice models have been used for many years to describe localized adsorption in zeolites. The method is best suited for zeolites having discrete adsorption sites or cages connected by narrow windows. For localized adsorption in zeolites without cages such as ZSM-5 the adsorption sites are often taken to be minimum-energy locations within the zeolite. Starting with the partition function for the system, an expression for the adsorption isotherm can be derived, and the physical meaning can be ascribed to the parameters appearing in the final expression. This approach was used by Lee et al.34,35 in their study of benzene and p-xylene adsorption in silicalite. Discrete sites in the straight channels (S), zigzag channels (Z), and channel intersections (I) were assumed. When sorbate interactions were considered only for the nearestneighbor sites, the grand partition function describing the system could be transformed to a two-dimensional Ising model, and an exact solution for the occupancy density was determined. To extend the model to include sorbate interactions between next-neighbor sites, the mean-field theory was applied to obtain the fractional occupancy of each site. As with other lattice models, the model of Lee et al. includes adjustable parameters that were fitted to the experimental data to obtain a reasonable agreement. (34) Lee, C. K.; Chiang, A. S. T.; Wu, F. Y. AIChE J. 1992, 39, 128. (35) Lee, C. K.; Chiang, A. S. T. Proc. Sep. Topic Conf. AIChE, Miami 1992, 365.

Binary Aromatic Mixtures in Silicalite

Langmuir, Vol. 17, No. 1, 2001 63

As the reported computer simulations provide a strong support for the three-site lattice model of adsorption sites for aromatics in silicalite, in our previous publications36-39 we proposed an extended version of the lattice model proposed by Lee et al. to describe the adsorption of benzene and p-xylene in silicalite. Following the X-ray diffraction data concerning the location of benzene molecules in MFI zeolites and computer-simulated guest-host interactions reported by Mentzen et al.,13 we assumed that there exist two equally probable orientations of benzene molecules in the channel intersections which are characterized by different values of the adsorption energy. These forms were assumed to compete for occupying channel intersections. The second assumption was that the energy of adsorption of molecules on the same kind of sites may differ due to structure defects. In our model we neglected a possible phase transition in the zeolite structure and kept all the energies of adsorption constant throughout the whole loading range. These additional assumptions led us to predict simultaneously the two steps observed by Lee et al. on the experimental adsorption isotherm of benzene in silicalite at 303 K, as well as the differential heats of adsorption of benzene and p-xylene in silicalite measured by Thamm.9 We also showed that our extended lattice model was able to reproduce well the temperature dependence of adsorption isotherms of benzene and p-xylene in silicalite. Thus, encouraged by the success of our three-site lattice gas (TSLG) model in predicting pure component adsorption equilibria in silicalite, we decided to test whether the model is able to describe the adsorption mechanism of benzene + p-xylene mixture in silicalite.

Figure 1. Channel structure of silicalite and the corresponding lattice of adsorption sites used in the TSLG model.

component adsorption isotherms in silicalite can be found with the homogeneous TSLG model by application of the mean-field theory. The appropriate set of equations describing adsorption of a single gas on different types of sites inside the silicalite takes the form

pxKxj exp

Theory In the homogeneous three-site lattice gas model (TSLG), proposed by us for modeling adsorption of aromatics in silicalite, the silicalite internal structure is mapped as a regular two-dimensional lattice of adsorption sites shown in Figure 1. The sites are divided into three types S, Z, and I corresponding to three possible locations of aromatic molecules inside silicalite (straight channel, zigzag channel, and channel intersection, respectively). In accordance with the recent experimental finding of Mentzen,13 additional possibility of two different spatial configurations (denoted by i1 and i2) of a single aromatic molecule adsorbed in the channel intersection is also taken into account. All the types of sites including i1 and i2 locations are characterized by different values of the nonconfigurational free energy of adsorption Exj,

Exj ) xj + kT ln fxj

{∑ } {∑ } x ωxx jl θl

(1)

where xj is the potential energy of sorbate-sorbent interaction and fxj is the molecular partition function of the admolecule x occupying the site j (j ) s, z, i1, i2). The next set of parameters which is involved in our model are the energies of lateral interactions ωxx ij between two molecules of the same type x adsorbed on the adjacent adsorption sites i and j (i, j ) s, z, i1 i2). The single(36) Rudzin˜ski, W.; Narkiewicz-Michałek, J.; Szabelski, P.; Chiang, A. S. T. Langmuir 1997, 13, 1095. (37) Chiang, A. S. T.; Lee, C. K.; Rudzin˜ski, W.; Narkiewicz-Michałek, J.; Szabelski, P. In Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces, Studies in Surface Sciences and Catalysis; Rudzin˜ski, W., Steele, W. A., Zgrablich, G., Eds.; Elsevier: Amsterdam, The Netherlands, 1997; Vol. 104, p 519. (38) Narkiewicz-Michałek, J.; Szabelski, P.; Rudzin˜ski, W.; Chiang, A. S. T. Langmuir 1999, 15, 6091. (39) Szabelski, P.; Narkiewicz-Michałek, J. Annales UMCS, Section AA 1999/2000, LIV/LV, 341.

θxj

kT

l

)

for j ) s, z

x ωxx jl θl

1 + pxKxj exp

(2)

kT

l

and

{∑ } {∑ } {∑ } x ωxx jl θl

pxKxj exp

θxj

l

)

xx x ωi1l θl

1 + pxKxi1 exp

l

kT

kT

+ pxKxi2 exp

xx x ωi2l θl

kT l for j ) i1, i2 (3)

where px is the pressure in the gas phase and the constants Kxj (j ) s, z, i1, i2) are defined as follows:

(

Kxj ) exp

)

Exj + µox kT

(4)

Above µox is the standard chemical potential of the adsorbate x in the gas phase. The detailed derivation of equation system (2)-(3) can be found elsewhere.36 The unit cell of silicalite contains four intersection sites, four sites in straight pores, and four in the sinusoidal ones. Thus, theoretically 12 molecules can be accommodated per unit cell, and the overall relative coverage of adsorption sites in silicalite will be given by

θxt )

1

∑j θxj

3

where j ) s, z, i1, i2

(5)

64



The equation system (2)-(3) can be easily generalized to describe adsorption of any aromatic binary mixture (x + y) in silicalite. The contributions θxj to the partial adsorption isotherm of the component x coming from the adsorption on different types of sites take the following form:

∑j (ωxxsj θxj + ωxysj θyj )/kT}

pxKxs exp{ θxs ) 1+

∑ paKas exp{∑j

x (ωax sj θj

+

(6)

y ωay sj θj )/kT}

a)x,y

pxKxz exp{ θxz ) 1+

∑j (ωxxzj θxj + ωxyzj θyj )/kT}

∑ paKaz exp{∑j

x (ωax zj θj

+

(7)

y ωay zj θj )/kT}

a)x,y

∑j (ωi1jxxθxj + ωi1jxyθyj )/kT}

pxKxi1 exp{ x ) θi1

1+

∑ ∑

∑j (ωaxkj θxj + ωaykj θyj )/kT}

paKak exp{

a)x,yk) i1,i2

(8)

∑j (ωi2jxxθxj + ωi2jxyθyj )/kT}

pxKxi2 exp{ x ) θi2

1+

Figure 2. Comparison of the experimental isotherm of benzene adsorption in silicalite measured by Li and Talu at 343 K, with the theoretical one, calculated from eqs 2 and 3 by using the parameters collected in Table 1. Contributions to the total isotherm coming from adsorption on different types of sites are also shown. Table 1. Parameters Found during Fitting the Single-Component Experimental Isotherms of Benzene and p-Xylene Adsorption in Silicalite at 343 K with the TSLG Modela x

x ay y paKak exp{∑(ωax ∑ ∑ kj θj + ωkj θj )/kT} a)x,yk) i1,i2 j

benzene p-xylene

(9)

Analogous set of equations can be obtained for the adsorption of the second component (y) in silicalite. In this case one should replace the index x by y (and vice versa) in the above expressions. The overall mixed adsorption isotherm θt is further defined as

θt )

θxt

+

θyt

(10)

where

θxt )

1

∑θxj 3 j

and θyt )

1

∑j θyj

3

(10a)

denote now the partial adsorption isotherm of the components x and y, respectively, and j ) s, z, i1, i2. The parameters ωxy ij appearing in eqs 6-9 denote energies of lateral interactions between molecules of different type (x and y) adsorbed on the adjacent sites i and j (i, j ) s, z, i1 i2). Theoretical description of the binary benzene + p-xylene adsorption in silicalite can be then easily obtained with the TSLG model by assuming that x ) benzene (B) and y ) p-xylene (P). Results and Discussion To test the predictive possibilities of the TSLG model, we focused our attention on the experimental data for vapor benzene + p-xylene mixture adsorption on silicalite at 343 K published by Li and Talu21 and discussed briefly in the introductory section. As these authors reported also the single-component adsorption isotherms measured at the same temperature, the strategy of our calculations was the following. First, we fitted the experimental singlecomponent adsorption isotherms with the smallest possible number of energy and interaction parameters. Next we used these parameters to fit the binary data. The

Kxi1 (Pa-1) 10-3

1.08 × 1.49 × 10-2

Kxi2 (Pa-1) 6.21 × 10-3

Kxs (Pa-1) 9.04 × 10-4

x

Kxz (Pa1-)

xx ωi1i1 (kJ/mol)

xx ωsi1 (kJ/mol)

benzene p-xylene

11.00 9.00

-6.00

8.82 × 10-3

x

xx ωzi1 (kJ/mol)

xx ωzi2 (kJ/mol)

ωxx zz (kJ/mol)

benzene p-xylene

-12.00

-6.00

16.50

a

The Henry’s constant Kxj is defined as exp{(Exj + µox)/kT}.

PB Table 2. Cross-Interaction Parameters ωBP ij ) ωij Found during Fitting Simultaneously the Experimental Benzene/p-Xylene Phase Diagram and the Total Amount Adsorbed in Silicalite at 343 K BP ωi1z (kJ/mol)

ωBP sz (kJ/mol)

BP ωsi1 (kJ/mol)

BP ωsi2 (kJ/mol)

BP ωi1i1 (kJ/mol)

-14.27

-1.86

-14.27

-5.71

10.00

additional parameters to be found while fitting best mixed adsorption isotherms were the lateral interaction energies between the molecule x adsorbed on the site i and the molecule y adsorbed on the site j, ωxy ij . The results of our calculations are shown in Figures 2-8, and the energy parameters found by computer are listed in Tables 1 and 2. Let us first consider single-component adsorption isotherms. Figures 2 and 3 show the comparison of the experimental adsorption isotherms of benzene and pxylene with the theoretical ones calculated by using the parameters collected in Table 1. In addition to the composite isotherms, the component isotherms coming from adsorption on different types of sites are also depicted in these figures. From Figure 2 it follows clearly that the adsorption of benzene in silicalite at 343 K starts in the channel intersections (I). The adsorbed benzene molecules fill rapidly all accessible sites I in the state denoted here by i1. This prediction is in agreement with the experimental evidence,13,18,19 and the results of computer


Figure 3. Comparison of the experimental isotherm of p-xylene adsorption in silicalite measured by Li and Talu at 343 K, with the theoretical one, calculated from eqs 2 and 3 by using the parameters collected in Table 1. Contributions to the total isotherm coming from adsorption on different types of sites are also shown.

simulations29-31 showing that at low loadings the preferential adsorption sites for benzene are the spacious channel intersections. Together with the intersections the channels are filled continuously with benzene molecules. Because of the symmetry of our equations for adsorption on sites S and Z, it is impossible to judge which of them are filled along with I sites until some additional information is available. Mentzen et al.13 have suggested that at the highest loadings benzene molecules fill the straight channels and the channel intersections forming a long polymer chain. Also, the results of 2H NMR studies reported by Portsmouth et al.18 confirm that in this loading regime benzene molecules may be located mainly inside the straight channels and the channel intersections. A similar conclusion of enhanced adsorption in the straight channels comes from the FT-Raman measurements.19 Thus, it seems reasonable to accept that the final state predicted by our model and corresponding to a maximum coverage of about 5 M/u.c. consists of benzene molecules adsorbed in the channel intersections (I) and the straight channels (S). This siting is in agreement with our earlier predictions obtained with the TSLG model for benzene adsorption at 298 K.36-38 There is, however, an important difference between adsorption at low and high temperatures. The isotherm at 70 °C exhibits no sudden jump at a loading of about four molecules per unit cell, contrary to what was observed at lower temperatures.5-7 At higher temperatures, accessibility of possible adsorption sites inside the silicalite structure is probably strongly limited by enhanced network vibrations, as well as by intensified vibrations and rotations of the adsorbing molecules. On the other hand, the mechanism of p-xylene adsorption in silicalite at 343 K is more complex than that referring to benzene. Looking at Figure 3, one can see that the isotherm displays a sudden jump at a loading above 4 M/u.c., as at lower temperatures.5-7 At loadings lower than 4 M/u.c. adsorption of p-xylene takes place mainly in the channel intersections in state i1. A further increase in pressure causes redistribution of the molecules adsorbed on sites I combined with very rapid filling of zigzag channels (Z). Then the total isotherm reaches its maximum value corresponding to about 6 M/u.c. Moreover, the observed sudden drop of the i1 partial isotherm is accompanied by appearance of the isotherm corresponding to occupation of sites I in state i2. Interchange of forms

Langmuir, Vol. 17, No. 1, 2001 65

Figure 4. Comparison of the experimental isothermal-isobaric phase diagrams measured by Li and Talu at 343 K at two different total pressures, with the predictions of the TSLG model. The theoretical curves are calculated from eqs 6-9 by using the parameters collected in Tables 1 and 2.

Figure 5. Selectivities of p-xylene at 343 K measured by Li and Talu and predictions by the TSLG model (solid lines) and two-patch MvdW model of Li and Talu (b, 1.2 kPa; O, 2.53 kPa).

i1 and i2 denotes that the adsorbed molecules alter their spatial configuration to enable a much more efficient packing of molecules inside the zeolite structure. Indeed, when the adsorbed amount of p-xylene increases, the molecules become more and more densly packed. This forces p-xylene molecules to adsorb in a more restricted orientation. Thus, at the highest loadings p-xylene fills mainly zigzag channels and channel intersections. The predicted pore filling sequence for p-xylene is in good agreement with the experimental data coming from different measurements.10,11,16-19 Figure 4 shows the comparison of the experimental phase diagrams for benzene + p-xylene mixture in silicalite and the results obtained by us with the TSLG model. As can be seen from Figure 4, the calculated curves corresponding to the total pressures of 1.2 and 2.53 kPa differ only slightly. This result is in accordance with the experimental data. Both diagrams correspond to high preferential adsorption of p-xylene over the whole range of benzene mole fractions in the gas phase. A much more stringent test of a model is calculation of the selectivity. As shown in Figure 5, our model predicts the experimental selectivities with similar accuracy to the HIAS approach used by Li and Talu (compare Fig. 6 in ref 21), whereas

66


Figure 6. Comparison of the experimental total adsorbed amount measured by Li and Talu at 343 K at two different total pressures, with the predictions of the TSLG model. The theoretical curves are calculated from eqs 6-9 by using the parameters collected in Tables 1 and 2.

the multicomponent van der Waals approach (MvdW) using the two-patch pure component representation gives the values unrealistically high. Despite a relatively good quality of the fit obtained for the phase diagrams and selectivities, the pronounced discrepancies are observed between the experimentally found and theoretically predicted total adsorbed amounts shown in Figure 6. One can see that at the two total pressures our model overestimates the total amount adsorbed at the low benzene mole fractions and underestimates it at the high benzene mole fractions in the gas phase. At the same time the position of a steep change in the adsorbed amount observed in the experiment at both total pressures is predicted correctly. At low mole fractions of benzene in the gas phase, almost pure p-xylene adsorbs in the silicalite. Thus, the reason why the origin of the calculated isobaric mixed isotherms is placed too high in comparison with the experimental data lies in the accuracy with which the pure p-xylene adsorption at pressures of 1.2 and 2.53 kPa is predicted. As the pure p-xylene isotherm was measured only up to 1.2 kPa, the theoretical isotherm obtained while fitting best the experimental data may not predict well the adsorbed amount at higher pressures. Indeed, the calculated isotherm in Figure 3 displays a slightly increasing tendency, and as the p-xylene pressure reaches 2.53 kPa, the predicted loading becomes equal to about 7 M/u.c. In consequence, the calculated values of the total amount adsorbed at low benzene mole fractions are too high. In Figure 7 we have shown the changes in occupation of different types of sites for the benzene + p-xylene mixture adsorption in silicalite at 1.2 kPa. As follows from Figure 7, two different regions can be distinguished. The first region corresponds to the benzene mole fraction up to about 0.5, at which a sudden drop of the adsorbed amount occurs. The second one corresponds to the remaining 0.5-1 interval. In the first region the total loading is almost exclusively affected by the p-xylene adsorption. The molecules of p-xylene stay mainly in the zigzag channels and also partially in the channel intersections in states i1 and i2. All the zigzag channels remain occupied until the benzene mole fraction exceeds 0.5. On the other hand, for the forms i1 and i2 we observe a slight decline of the corresponding curves. Here, the relative order of the curves corresponding to the p-xylene adsorption on different types of sites is the same as for pure


Figure 7. Contributions to the total amount adsorbed at 343 K and at 1.2 kPa, coming from adsorption of benzene and p-xylene on different types of sites. The filled squares denote the experimental total amount adsorbed.

p-xylene adsorbed at higher pressures (compare Figure 3). Besides the dominating adsorption of p-xylene, in the first region we also observe a slow increase in the number of benzene molecules adsorbed in the straight channels. However, adsorption in the straight channels drops suddenly at the benzene mole fraction equal to about 0.5. At this value rapid changes in occupation of different sites occur. Thus, we observe a very sharp decrease in adsorption of p-xylene in the zigzag channels and a simultaneous increase in the number of molecules occupying sites i1. The p-xylene i2 form diminishes at this point. The adsorption of benzene in the straight channels is replaced by the form i1. In the second part of the benzene mole fraction interval we observe continuous displacement of the adsorbed p-xylene molecules by the molecules of benzene. Both types of competing molecules adsorb in the channel intersections in the form i1. Additionally, the decrease in adsorption of p-xylene in the zigzag channels present in the second part is connected with increasing occupation of straight channels by benzene molecules. According to Figure 7, the mixed adsorption process can be described as follows. At sufficiently low values of the benzene mole fraction in the gas phase almost only p-xylene adsorbs in silicalite from the mixture. It occupies mainly the sinusoidal channels as well as most of the channel intersections. This siting is in accordance with the results obtained for pure p-xylene at 1.2 kPa. With the increasing mole fraction of benzene, the sparse incoming benzene molecules occupy the sites in the straight channels forcing the p-xylene molecules to leave the intersections. As the number of benzene molecules in the unit cell increases, the structure of the adsorbate becomes less packed. (Larger p-xylene molecules are replaced by smaller benzene molecules.) When the free space inside the channels is sufficiently large and the chemical potential of p-xylene in the gaseous phase sufficiently low, the adsorbed molecules undergo a sudden redistribution. The molecules of p-xylene leave the sinusoidal channels and fill the channel intersections. At the same time, due to increasing benzene pressure, the benzene molecules start to compete with p-xylene molecules in occupying the channel intersections. Both types of competing molecules tend to reach the most entropically favorable sites. At 343 K the adsorption of benzene from the mixture takes place on only one type of sites (I). On the other hand, the shape of the curve corresponding to the total amount adsorbed results exclusively from an


Figure 8. Comparison of the experimental partial amounts adsorbed of benzene and p-xylene measured by Li and Talu at 343 K and 1.2 kPa, with the predictions of the TSLG model.

abrupt change in the adsorbed amount of p-xylene. These conclusions are in agreement with the theoretical predictions of the two-patch model proposed by Li and Talu.21 Figure 8 presents the comparison of the calculated individual isotherms of benzene and p-xylene with the experimental data. One can see that the adsorption of p-xylene exhibits a sudden drop in the vicinity of equimolar composition in the gas phase, whereas no abrupt change is observed on the benzene adsorption isotherm. Now, let us discuss the values of the parameters obtained in the calculations while fitting the experimental data best. First of all, the values of the Henry’s constants show that preferential adsorption sites for the benzene and p-xylene molecules are the channel intersections. The sites that are occupied next, however, are different. The benzene molecules prefer to locate in the straight channels, whereas the p-xylene molecules adsorb in the zigzag channels. Thus, at low benzene mole fraction in the mixture the most of channel intersections are occupied by p-xylene molecules. The incoming benzene molecules are forced to locate in the sites (S). However, the situation in which two adjacent sites (I) and (S) are occupied by the p-xylene and benzene molecules, respectively, is energetically unfavorable as indicated by a large negative value PB ) -14.27. This is why of the interaction parameter ωi1s the adsorption of benzene from the mixture with p-xylene is hindered at low benzene mole fractions. The repulsion between two benzene molecules adsorbed on the adjacent BB ) -6.0), and thus sites (I) and (S) is much smaller (ωi1s the occupation of these sites in adsorption from pure benzene is much easier. Somewhat surprising may be a strong attraction between p-xylene molecules adsorbed on sites (Z) (large positive value of ωPP zz ) and, at the same time, a strong repulsion between p-xylene molecules occupying the adjacent sites (I) and (Z) (large negative PP ) predicted by our model. This value of the parameter ωi1z may result from the fact that the adsorption of p-xylene molecules in the zigzag channels is accompanied by the change of the zeolite structure from the ortho to para form confirmed experimentally.28 The computer simulations of benzene adsorption in both these forms of silicalite performed by Snurr et al.30 have shown that the free energy of adsorption in the zigzag channels is higher for the para structure. As our lattice model does not take explicitly into account the possible change of the zeolite structure upon adsorption, it is greatly probable that highly cooperative adsorption on sites (Z) simulates an increase

Langmuir, Vol. 17, No. 1, 2001 67

of the free energy of adsorption on these sites caused by a phase transition. From the analysis of the sorbate-sorbate energy values collected in Tables 1 and 2, a general conclusion can be drawn that a repulsion occurs between the molecules occupying the nearest-neighbor sites (I-Z, I-S) and an attraction between the molecules occupying next-nearestneighbor sites (I-I, Z-Z). Similar conclusion was drawn by Czaplewski and Snurr,40 who used the atomistic Monte Carlo simulations to calculate the free energies for sulfur hexafluoride and neopentane molecules adsorbed in silicalite. For larger neopentane molecules they found the free energies between the two occupied adjacent sites to be very repulsive, along with all the free energies of triplets. For smaller SF6 molecules all the two-body interactions except the I-S interaction were attractive. Having these free energies, they used a lattice model to calculate the equilibrium loading of single adsorbates and their mixture. The results agreed well with the full GCMC simulations. Unfortunately, the authors did not compare their results with the appropriate experimental data. They only stated that for sulfur hexafluoride both the lattice and the GCMC models overpredict the Henry’s constant and underpredict the saturation loading with the parameters used in their calculations. Thus, the comparison of the predictive capability of their lattice model and the model proposed by us cannot be made. Large positive values of the parameters ωi1i1 collected in Tables 1 and 2 suggest the presence of strong attractive interactions between the molecules adsorbed in the adjacent channel intersections. Furthermore, these attractive interactions seem to be weakly influenced by the type of interacting molecules. This prediction is somewhat inconsistent with the conclusions drawn from the experimental data.8,9 The differential heat of adsorption of benzene in silicalite measured by Thamm at 301 K remains constant at loadings below four molecules per unit cell, thus indicating that the benzene molecules adsorbed in the channel intersections do not interact with each other. The minima and maxima observed at higher loadings were interpreted as a signature of strong guest-guest interactions. The similar behavior of the differential heats of adsorption was observed for toluene and ethylbenzene adsorption in silicalite at low loadings. However, for p-xylene in silicalite the gradually increasing differential heat of adsorption was obtained at loadings below four molecules per unit cell. It was interpreted by Thamm as being a result of attractive interactions between the adsorbed p-xylene molecules. The constant heats of adsorption at low loadings do not necessarily indicate the lack of interaction between the adsorbed molecules. In our previous publication,38 we have shown that the assumption of energetically nonequivalent lattice sites of the same kind in silicalite combined with the strong guest-guest interactions leads to a quantitative agreement between the experimental and theoretically predicted differential heats of adsorption of benzene in silicalite in the whole range of loadings. As generally known, the energetic heterogeneity of adsorption sites leads to a decrease of the differential energy of adsorption with coverage, whereas the attractive adsorbate-adsorbate interactions have an opposite effect. When adsorption goes on an energetically heterogeneous lattice of sites, the ultimate calorimetric effect of adsorption will be a result of interplay between these two effects. Some confirmation of the possibility of attractive guest-guest interactions at low loadings comes also from the coverage (40) Czaplewski, K. F.; Snurr, R. Q. AIChE J. 1999, 45, 2223.

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dependence of the experimental corrected diffusivities for aromatics in ZSM-5 zeolites.41 Conclusions The three-site lattice model developed for adsorption of single aromatics in ZSM-5 zeolites has been generalized to describe the adsorption from binary mixture. The equations for the individual adsorption isotherms and the total adsorption isotherm were derived and used to describe the experimental equilibrium data for benzenep-xylene mixture in silicalite. The parameters involved in the model were found by fitting best the single component and binary adsorption isotherms. It was shown that our model is able to reproduce semiquantitatively the phase diagrams of benzene adsorbed from the mixture with p-xylene at constant total pressure. The sudden drop of the total adsorbed amount appearing at the intermediate mole fraction of benzene in the mixture is also well reproduced. (41) Shah, D. B.; Guo, C. J.; Hayhurst, D. T. J. Chem. Soc., Faraday Trans. 1995, 91, 1143.


The main conclusion that can be drawn from our calculations is that, when coadsorbed, benzene and p-xylene are both able to access the respective sites for adsorption favored during the single-component adsorption processes. Benzene occupies the straight channels (S) and channel intersections (I) whereas p-xylene locates in the channel intersections (I) and the sinusoidal channels (Z). At a sufficiently low mole fraction of p-xylene in the mixture a sudden decrease of p-xylene adsorbed in sites (Z) is observed. Simultaneously, the number of p-xylene molecules occupying the channel intersections increases. As a result, the total adsorbed amount suddenly decreases. With the increasing mole fraction of benzene in the mixture, benzene starts to displace p-xylene from the channel intersections which are preferential adsorption sites for both species. In the whole mole fraction range the adsorption process is associated with significant sorbate-sorbate interactions. Acknowledgment. This research was supported by KBN Research Grant 3 T09A 015 14. LA0007630

Three-Site Lattice Gas Model for Adsorption of Binary Aromatic

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