Langmuir 1994,10, 1257-1267
1257
Adsorption Simulations of Small Molecules and Their Mixtures in a Zeolite Micropore Paul R. Van Tassel, H. Ted Davis, and Alon V. McCormick' Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 Received August 20, 1993. I n Final Form: January 24, 1994" We simulate the adsorption of small molecules (Xe, Ar, CHI) and their binary mixtures in zeolite NaA using the grand canonical ensemble Monte Carlo method. We report the isotherm, energy, entropy, and adsorbate density distribution. The effects of nonideal mixing in the pore are assessed by comparing the simulated binary isotherms to those predicted by a pore filling model (Ruthven, D. M. Nut. Phys. Sci. 1971,232,70. Ruthven, D. M.; Loughlin, K. F.; Holborow, K. A. Chem. Eng. Sci. 1973,2%,701). At low pore loadings, we observe strong selectivity for a more polarizable molecule, but at higher pore loadings, a smaller, less polarizable molecule can adsorb selectively. This occurs at significantly lower pressures in our simulations than would be predicted by the pore filling model. This increased selectivity for the smaller molecule occurs because of differences in the two component's ability to pack efficiently in the pore beyond that accounted for by the pore filling model.
Introduction Separation processes using zeolites rely on the selective adsorption of one component of a mixture, where the selectivity may be due to differences in either adsorption rates or the adsorption equilibria. While kinetic selectivity is often due to molecular sieving effects, equilibrium selectivity (where both components can fit in the pore) is due to differences in the complex energetic and entropic interactions between the adsorbates and the pore. This is poorly understood, particularly at high poor occupancy. It is frequently assumed that equilibrium selectivity can be predicted by assuming ideal mixing. However, since the placement of adsorbates and their interactions are complex, nonideal mixing can be encountered even for simple adsorbates. For instance, Talu and Zwiebel have observed highly nonideal mixtures of COZ,HzS, and C3Hs in H-mordenite: Santili et al. have reported "antimolecular sieving" effects to explain trends in catalytic behavior of zeolites: and Somers et al. have reported sorption selectivity which oscillates with the width of a slit pore.6 We expect nonideal mixing to become especiallyimportant at higher pore loadings, where the energy and entropy of adsorption may become highly coverage dependent. To investigate features of micropore sorption selectivity over a wide range of pore loading, we propose the use of molecular simulation techniques. Molecular simulations have been used to determine equilibrium"" and dynamiclwl properties of pure fluids
* To whom correspondence should be addressed.
Abstract Dublished in Advance ACS Abstracts, March 15,1994. (1) Ruthved, D. M. Not. Phys. Sci. 1971,232,70. . (2) Ruthven, D. M.; Loughlin, K. F.; Holborow, K. A. Chem. Eng. Sci. 1973,28,701. (3) Talu, 0.;Zwiebel, I. AlChE J. 1986, 32, 1263. (4) Santilli, D. 5.;Harris, T. V.; Zones, 5.I. Microporoua Mater., in 0
press.
(5) Somers, S. A.; McCormick, A. V.; Davis, H. T. J. Chem. Phys., in
press.
(6) Stroud, H. J. F.; Richards, E.; Limcharoen, P.; Parsonage, N. G. J. Chem. SOC.,Faraday Trans. 1 1976, 72,942. (7) Kretschmer, R. G.; Fielder, K. 2.Phys. Chem. 1977,258,1045. (8) Soto, J. L.; Myers, A. L. Mol. Phys. 1981,42, 971. (9) Kono, H.; Takaaaka, A. J. Phys. Chem. 1986, 91, 4044. (10) Woods, G. B.; Panagiotopouloe, A. Z.;Rowlinson, J. S. Mol. Phys. ~~
1988, 63, 49. (11) Woods,G. B.; Rowlimn, J. 5.J. Chem. SOC.,Faraday Trans 2 1989,85,766. (12) Razmus, D. M.; Hall, C. K. AlChE J. 1991,37,769.
adsorbed in zeolite micropores. They have been particularly useful to us in determining how the zeolite crystal imposes structure on the adsorbed phase and how this structure influences adsorption thermodynamics and dynamics.13J6J7 In the case of a binary adsorbed phase, we expect simulation to be valuable in monitoring the competition between the components of the mixture for pore space. Relatively few studies have probed the behavior of mixtures in zeolites,lZJ6 and they have primarily reported only low-coverage data, where the mixing tends to be ideal. Here, we report grand canonical ensemble Monte Carlo simulations of single-component and binary mixtures of small molecules (xenon, argon, and methane) adsorbed in zeolite NaA over a wide range of coverages. In addition, we compare the simulated results with those expected from an ideal mixing model based on (13) Van Tassel, P. R.; Davis, H. T.; McCormick, A. V. Mol. Phys. 1991, 73,1107. (14) Snurr, R. Q.; June, R. L.; Bell, A. T.; and Theodorou, D. N. Mol. Simul. 1991,8, 73. (15) Karavias, F.; Myers, A. L. Langmuir 1991, 7, 3118. (16) Van Tassel, P. R.; Davis, H. T.; McCormick, A. V. Mol. Phys. 1992, 76, 411. (17) Van Tassel, P. R.; Davis, H. T.; McCormick,A. V. J. Chem. Phys. 1993,98,8919.
(18)Yashonath, S.; Thomas, J. M.; Nowak, A. K.; Cheetham, A. K. Nature 1988,331,601. (19) Leherte, L.; Lie, G. C.; Swamy, K. N.; Clementi, E.; Derouane, E. G.; Andre, J. M. Chem. Phys. Lett. 1988,145, 237. (20) Yashonath, S.; Demontis, P.; Klein, M. Chem. Phys. Lett. 1988, 153, 551. (21) Cohen De Lara, E.; Kahn, R.; Goulay, A. M. J. Chem. Phys. 1989, 90,7482. (22) Leherte, L.; Andre, J. M.; Vercauteran, D. P.; Derouane, E. G. J. Mol. Catal. 1989,54,426. (23) Demontis, P.; Yashonath, S.; Klein, M. J. Phys. Chem. 1989,93, 5016. (24) Fritzsche, S.; Haberlandt, R.; Kaerger, J.; Pfeifer, H. Chem. Phys. Lett. 1990,171, 109. (25) Pickett, S. D.; Nowak, A. K.; Thomas, J. M.; Peterson, B. K.;
Swift, J. F. P.; Cheetham, A. K.; den Ouden, C. J. J.; Smit, B.; Poet, M. F. M. J.Phys. Chem. 1990,94,1233. (26) June, R. L.: Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1990,
94,8232. (27) Yashonath, S. J. Phys. Chem. 1991,95, 5877. (28) Yashonath, S.; Demontis, P.; Klein, M. J. Phys. Chem. 1991,95, 5881. (29) Fritzache, S.; Haberlandt, R.; Karger, J.; Pfeifer, H.; Heinzinger, K. Chem. Phys. Lett. 1992,198, 283. (30) Nicholas, J. B.; Trouw, F. R.; Mertz, J. E.; Iton, L. E.; H o p f i e r , A. J. J. Phys. Chem. 1993,97,4149. (31) Maginn, E. J.; Bell, A. T.;Theodorou, D. N. J.Phys. Chem. 1993, 97, 4173.
0743-7463/94/2410-1257$04.50/00 1994 American Chemical Society
1258 Langmuir, Vol. 10, No. 4, 1994
Van Tassel et al.
w Figure 2. A 2 X 2 X 2 system of CY cages connected together by shared eight-membered rings to form a repeating crystal.
U
- *
--•
Ul m
'
Figure 1. CY cage representing a single pseudocell of NaA. The vertices represent either silicon or aluminum atoms which are connected by oxygen atoms residing near the centers of the line segments. Sodium ions, represented by spheres, are located in the centers of the six- and eight-membered rings in cation-rich NaA (a) and in the six-memberedrings only in cation-poor NaA (b).
pore volume filling. Our specific goal is to learn whether and when mixing in the pore deviates from ideal mixing and to rationalize this behavior on the basis of the arrangement of the adsorbates. We illustrate striking contrasts in adsorption selectivity depending on whether equilibrium is most strongly influenced by (1)molecular polarizability, which determines the energetic interaction between the adsorbate and the zeolite, or (2) molecular size, which dictates how well adsorbates "pack" inside the zeolite pore. We will show that selectivity due to molecular size can occur at a much lower pressure than is predicted by the pore volume filling adsorption model.
Adsorbent and Adsorbates Zeolite NaA is a crystalline aluminosilicatewhose largest cavity, the a! cage (diameter -11.8 A), may house small adsorbed molecules. The a cage, shown in Figure 1,is a single unit cell of NaA. Shaped roughly like a truncated cuboctahedron, it is connected to other a! cages through shared eight-membered rings to form a cubic crystal (Figure 2). The NaA system is chosen because of its industrial use in certain separation processes32and because its simple structure offers the hope that principles illustrated here will be generalizable to other adsorbent/ adsorbate systems with similarly confined fluids. A single unit cell of dehydrated NaA has the chemical formula Na&i12Al120@. Lattice positions are available from the l i t e r a t ~ r e .First, ~ ~ we consider a "cation-rich" model NaA with sodium ions in the centers of the six- and (32) Ruthven, D. M.; Derrah, R. I. J. Chem. SOC.,Faraday Trans. 1 1975, 71, 2031.
eight-memberedrings (11total per unit cell whose positions are illustrated in Figure la). (Crystallographically, the sodium ion in an eight-membered ring has been shown to occupy one of four degenerate positions, each slightly off center. The choice of placement in the center, then, represents an average of these degenerate positions.) To investigate the effect of framework dealumination or ion exchange, we later consider a "cation-poor" NaA which contains sodium ions only in the center of the sixmembered rings (Figure lb). This placement of cations is similar to CaA, but the use of sodium allows us to examine the effects of structure without introducing the poorly modeled polarization effect of a divalent cation. Xenon, argon, and methane are chosen as adsorbates both because they represent a range of sizes and adsorption strengths and because, being simple nonpolar molecules, they are computationally convenient. Molecules containing permanent electric poles (such as N2) are neglected in this initial study because (1)the energetic interactions of polar molecules are less accurately modeled than those of nonpolar molecules and (2) the effects of adsorbate size and pore filling are best first investigated if only nonpolar adsorbates are used. The potential energy is calculated atomistically34 and is assumed to be the sum of pairwise interactions. Separate terms in the potential account for sorbate-framework repulsion, dispersion, and sorbate-framework induced dipole-static electric field interactions. Sorbate-sorbate interactions are modeled with a 6-12 Lennard-Jones potential, where methane is considered a spherical particle. The form of the potential has been discussed elsewhere for one-component simulations.13 Potential parameters are taken from the and are given in Tables 1 and 2. The interaction strengths and sizes of the adsorbates are evident from the interaction potential for like pairs of adsorbates (Figure 3). Lorentz-Barthelot mixing rules, which are successful for bulk are used to determine the Lennard-Jones parameters between two different species: bij = (ai + ~ j ) / 2and cij = (cicj)'/2.
Theory i. Grand Canonical Ensemble. For the grand canonical ensemble (a collection of states of a thermodynamic system, each with the same chemical potential, volume, and temperature), the partition function and thermody(33) Yanagida,R. Y.; Amaro,A. A.; Seff, K. J. Phys. Chem. 1973,77, 805. (34) Bezus, A. G.; Kisilev, A. V.; Lopatkin, A. A.; Du, P. Q.J. Chem. SOC.,Faraday Trans. 2 1977, 74,367. (35) Kiselev,A. V.; Du, P. Q.Dokl. Akad. Nauk SSSR 1978,238,384, 241,386. Faraday Trans. 2 1981, (36) Kiselev, A. V.; Du, P. Q. J. Chem. SOC., 77, 1. (37) Shukla, K. P.; Haile, J. M. Mol. Phys. 1987,62,617.
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Langmuir, Vol. 10,No. 4, 1994 1259
Sorbate-Sorbate Potential
2
:I
the adsorbates, and
-Xe-Xe
: I
I
N=
.
CN~
(5)
i=l
In eq 4, h is Planck's constant and mi is the adsorbate mass. The multicomponent isotherm is given by the ensemble average occupancy of each component:
-2 2
3
4
5
6
7
8
9
10
rih
Figure3. Lennard-Jonespotential energyof interactionbetween like adsorbates versus separation. Table 1. Parameters Used To Determine the Energetic Interaction between the Zeolite Framework and the Adsorbates.
O(CR) O(CP) Na Xe
1.4p 1.25" 0.3094 4.01" 2.6W 1.63"
CHI
Ar
10.P 9.9"
5.6" 45.5" 16.W 19.46"
1.52" 1.52" 0.98" 2.18" 2.0060 1.92"
1.101 0.8005 4.803
a a = polarizability, x = diamagnetic susceptibility, m w = van der Waals radii, and q1= electric charge. The form of the potential is atomistic and is discussed elsewhere.18
Table 2. Lennard-Jones Parameters for the Potential Energy of Interaction among the Adsorbate@ atom
U/A
(clkYK
Xe
4.1 3.82 3.4
221 148 120
CHI
Ar
namics characteristic of single-component adsorption in the grand canonical ensemble have been discussed prev i o ~ s l y The . ~ ~ grand canonicalensemble partition function for an I-component mixture is defined as38
ii. Canonical Ensemble. In order to explain trends in the entropy revealed by grand canonical ensemble simulations, it will be helpful to consider separately the contributions to the entropy of the adsorbed phase from (1)the adsorbate mass and (2) translational freedom. In order to do this conveniently, we can calculate the entropy of a single adsorbate in the canonical ensemble (note that now the number of molecules, not the chemical potential, is fixed):39
where ( @ ) I is the average potential energy of a single adsorbed molecule and Q1 is the partition function for a single adsorbate, from which a volume (V,) accessible to an adsorbate may be defined by
Substituting into eq 7, the entropy for a single adsorbate is
(S),= k ln((2~mkT)~/'V,lh~) + (3/2)kT
(9)
9 is the potential energy as a function of the position of
We further assume that this result, strictly true for a closed system at N = 1,is approximately true for an open system at (N) = 1. Equation 9gives the well-known contribution to the entropy from the adsorbate mass as well as the contribution from the accessiblevolume. Physically,these represent contributions to the adsorbate's translational freedom from accessible volume on one hand and translational momentum on the other. iii. Pore Filling Model. To determine how the mixture isotherm deviates from an expected mixture isotherm, an "ideal" mixture model is needed. We choose here a theoretical treatment similar to the straightforward statistical model proposed by Ruthven.lI2 This model accounts both for energetic and entropic interactions between an adsorbate and the micropore and for a decrease in available pore space as the pore fills. This model assumes, though, that the interactions do not change with loading (i.e., they may be predicted by the Henry's law portion of the single-component isotherms) and that adsorbates interact with each other only by excluding pore volume. However, because (i) we wish to isolate volume filling aspects of this model and (ii) single-component simulations show sorbate-sorbate attractive interactions to be small compared to sorbate-zeolite interactions,le we have modified the original form so as to neglect sorbatesorbate attraction.
(38) Hill, T. L. An Introduction to Statistical Thermodynamics; Addison-Wesley: Reading, 1960.
(39) Davis, H. T. Equilibrium Statistical Mechanics: Phases, Interfaces, and Thin Films; V C H Weinheim, 1993.
where Ni is the number of adsorbates of component i, N is the I-component vector of Nis, p is the I-component vector of chemical potentials, k is the Boltzmann constant, V is the system volume, T is the temperature, and Q(N, V, T ) is the canonical ensemble partition function for an I-component mixture:
where
is the classical configuration integral for a composition N, hi is the thermal de Broglie wavelength of species i (which accounts for kinetic energy), Ai = h / ( 2 ~ m ~ k T ) ~ / '
(4)
Van Tassel et al.
1260 Langmuir, Vol. 10,No. 4,1994 Table 3. P a r a m e t e r s Used in the P o r e Volume Filling Model Isotherm of Eq 15. zeolite
CR
CP
adsorbate Xe Ar CHI Xe Ar
CHI
Z1/(lO-B m3) 226.1 1.525 4.143 296.3 2.271 1.548
Vi/v 1/14 1/19 1/14 1/17 1/21 1/17
(I 2 1 is calculated numerically via eq 14,and Vi is chosen such that Vi/ V = 1 at a loading of one adsorbate per cage beyond the singlecomponent simulation isotherm plateau.
The partition function is of the form
where V is the volume of the pore, Vi is the molecular volume in the pore of the ith component, q ( x ) is the heaviside function ( ~ ( x =) 1for x I0, ~ ( x =) 0 otherwise), and Zl,i is the one-body classical configuration integral for a single molecule of the ith species:
more favorable than that predicted from the low-loading single-component isotherm.
Simulation We use the grand canonical ensemble Monte Carlo to determine both single-component (GCMC) and binary isotherms of small molecules in zeolite NaA. The equilibrium stateof a system of adsorbates in a zeolite micropore a t constant temperature, volume, and chemical V, p ) is simulated as a Markov potential of each species (T, chain of states, each of which is generated by a random "step" from a previous state. These steps and their probabilities of acceptance are of the following types. (1)Translations: an adsorbate is chosen at random and translated a random distance in the x , y,and z directions. The new state is accepted with probability
where A@ is the difference in the potential energy of the system between the old and new states. (2) Insertions: an adsorbate of a randomly chosen component is inserted at a random position within the cage. The insertion is accepted with probability
(11) where cPi(r)is the potential energy of a molecule of the ith species at position 1: in the pore. The configuration integrals are evaluated numerically, and the volume occupied by each adsorbate is determined by observing the pore occupancy at the simulated single-component isotherm plateau. Specifically, the Vi's are chosen such that, in the single-component isotherm (I= l),the free volume term (in parentheses in eq 10) is zero when the loading exceeds saturation. Values for these parameters appear in Table 3. The isotherm can then be calculated from eq 6 using the partition function from eq 10. Strictly speaking, ideal mixing implies that the energy is independent of composition and that the components compete on an equal footingfor volume. Sucha convention makes little sense, though, in a confined environment where total volume is fixed and it is taken for granted that the energy of interaction with the zeolite must differ for the two components. Instead, we use the above model as an "expected" mixture isotherm. The difference between the expected and simulated isotherm determines the effects on mixture equilibria arising from (1)changes in the interactions of the adsorbates with the pore architecture a t higher loading and (2) the interactions between the adsorbates themselves. We will show below that even for the simple adsorbates studied here, pronounced differences exist between the expected and simulated isotherms. Assuming the above model provides an "idealistic" mixture, we define an excess amount adsorbed as the difference between the amount adsorbed in the simulation and the amount adsorbed as predicted by the pore filling model, i.e.,
where N:'" is the amount of species i present in an I-component mixture simulation andNimdelisthe amount of component i adsorbed that is predicted by the model. A positive value of Nies implies that the net interaction of component i with the pore wall and other components is
where Vis the volume of the accessible pore space in the zeolite. Insertion attempts of the various Components occur with equal probability. (3)Deletions: a randomly chosen adsorbate is removed from the system. The deletion is accepted with probability
The frequency of deletion attempts must be the same for all components, regardless of the occupancy distribution in the system in order to maintain an equal a priori probability of insertion and deletion. (4) Exchanges: the identity of a random adsorbate of species i is changed to species j , and the new state is accepted with probability
Exchange steps are not a part of standard GCMC, nor are they needed to obtain equilibrium. Their inclusion, though, has been shown to decrease the number of simulation steps required to achieve equilibration.42 In systems with large potential energy barriers (such as crowded zeolite pores), exchange steps are especially helpful. The acceptance probabilities reflect the ratio of the grand canonical ensemble partition function (eq 1)before and after the step is applied. Note that these probability rules can be used with any number of components.
Results i. Single-Component Adsorption in NaA. Before examining mixtures, it is instructive to compare single(40)Norman, G.E.;Filinov, V. 5.High Temp. (USSR) 1969,7,216. (41)Allen, M.P.;Tildealey, D. J. Computer Simulation of Liquids; Clarendon: Oxford, 1989. (42)Kofke, D.A. Mol. Simul. 1991, 7,285.
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3
-1
f $1 8
c
-85.0
I
-45.0
-25.0
p
-5.0
15.0
I kJ1mol
Figure 4. Adsorption isotherm for xenon, methane, and argon versus chemical potential in cation-rich NaA at 300 K. The uncertainty of the data in this and subsequent graphs is smaller than the size of the data points themselves. Experimental data for methane are from Ruthven,u and those for argon are from LindeP component adsorption of xenon, methane, and argon in NaA. The isotherms, shown in Figure 4, are reported as the number of adsorbed molecules per unit cell (i.e., per a! cage) as a function of chemical potential. The conversion between pressure and chemical potential is straightforward and involves only integration of the Gibbs-Duhem equation (dp = p-l dp). Thus, at low pressures, the chemical potential of an ideal gas is38
p"(P,T) = kT ln(PA3/kT) = pref(T)+ kT In P (17) where the reference chemical potential is pref(T) = kT ln(A3/kT) and A is determined from eq 4. A LennardJones equation of state is used to integrate eq 10when the density is greater than that of an i d e a l g a ~ Experimental .~~ isotherm dataw7 are converted in this manner. Consideringthat experimentalsamples may contain crystalline impurities and that the potential energy function is only an approximation to the real sorbate-zeolite interaction, the isotherms agree reasonably well with the limited amount of available experimental data (Figure 4). At low chemical potential, the number of xenon atoms in the pore is greatest, followed by argon, and finally methane (Xe > Ar > CH4). This order deviates from the order of polarizability and adsorption energy (Figure 5), which is Xe > CH4 > Ar. Argon adsorbs more than does methane in this regime because of an entropic advantage; argon enjoys more translational freedom because of its small size (Figure 6). At a higher chemical potential, though, the order becomes Ar > CH4 > Xe-the reverse of the order of adsorbate size. For both xenon and methane, an isotherm plateau occurs at aloading of 13adsorbates per cage, which corresponds to the filling of adsorption sites (Figure 7a) as discussed earlier.le The argon isotherm, on the other hand, fails to exhibit a strong plateau. Owing to ita small (43)Nicolas, J. J.; Gubbina, K. E.; Streett, W. B.; Tildesley,D. J. Mol. Phys. 1979,37,1429. (44)Yucel, H.; Ruthven, D. M. J. Chem. SOC.,Faraday Trans. 1 1980, 7 :m .1-, _-. (45)Argon on 4A (NaA) Pellets. Linde Date, ref H, graph 2.021. (46)Jameson, C.J.; Jameson, A. K.; Gerald, R., II; de Dim, A. C. J. Chem. Phys. 1985,83,2663. (47)Argon on 5A (CaA)Pellets. Linde Data: ref H, graph 2.031. (48) Dorfman, Y. G. Diamagnetism i Khimicheskaya suajaz; Gostfumatizdat: Moskva, 1961. (49)Pauling, L.TheNature of the ChemicaZBond;CornellUniversity Press: New York, 1945. (60)Hirachfelder, J. 0.; Curtis, C. F.; Bird, R. B.Molecular Theory of Gases and Liquids; Wiley: New York, 1964.
0.0 2.0
I
4.0
I
6.0
I
8.0
I
10.0
I
120
I
14.0
I
16.0
per cage
Figure 5. Adsorption energy for xenon, methane, and argon versus average pore loading in cation-rich NaA at 300 K.
0.0 2.0
4.0
6.0
8.0
10.0
120
14.0
16.0
per cage
Figure 6. Adsorption entropy for xenon, methane, and argon versus average pore loading in cation-rich NaA at 300 K. size, argon is less strictly confined to localizedsites (Figure 7b) than either xenon or methane. Figure 5 shows that xenon adsorbs the most exothermally, but that ita large size causes the onset of repulsion to occur at a lower loading than for either methane or argon. The small size of argon allows it to continue to adsorb up to a high loading without the onset of crowding. Although an isotherm plateau appears for methane, no repulsion is observed over the chemical potential range studied. Apparently, methane is small enough to fill the number of available adsorption sites (13) without appreciable crowding; it is large enough, though, that any additional adsorption beyond 13 would cause extreme crowding. At low loadings, the entropy (Figure 6)is greatest for xenon even though the volume accessibleto argon is greater than for xenon. The reason is given in eq 9: the entropy varies with both the accessiblevolume and adsorbate mass, and xenon is much heavier than argon. At higher loadings, where adsorbed xenon becomes quite localized due to crowding, the translational freedom enjoyed by the smaller argon atoms provides them with the highest entropy. The entropy of methane remains lower than that of xenon or argon a t all loadings since it is too large to enjoy as much freedom as argon and is lighter than xenon and argon. ii. Binary Adsorption of Xenon and Argon in NaA. Simulated isotherms of a xenon/argon mixture at 300 K are shown in Figure 8a, where the chemical potentials of both components are kept equal. At low chemical potential, xenon adsorbs much more strongly than argon because xenon has a greater adsorption energy. In fact, the xenon in the mixture behaves almost identically to the single-component xenon, indicating that the coadsorbed argon offers little opposition to xenon adsorption. Argon, in effect, is able to keep out of the way of xenon.
Van Tassel et al.
1262 Langmuir, Vol. 10, No. 4, 1994
Figure 7. Simulation snapshota of a canonical ensemble simulation of (a, left) 12 xenon atoms and (b, right) 12 argon atoms in a single NaA a cage.
Excess .........Excess ..............Xe... Ar 0 0
-65.0
45.0
-25.0
pxe= pk
-5.0
15.0
/ kJ/mol
-65.0
45.0
-25.0
p%= pk
-5.0
16.0
/ kJ/mol
Figure 9. Excess amount adsorbed of xenon and argon as calculated from eq 17versus the chemical potential of each species in cation-rich NaA at 300 K.
9
a
w-2
-65.0
45.0
-25.0
-6.0
15.0
36.0
pxe= pk / kJ/mol Figure 8. Simulated binary and single-component isotherms for xenon and argon and (b, bottom) the isotherm calculated from the pore volume filling model of eq 15 versus the chemical potential of each species in cation-rich NaA at 300 K.
As the chemical potentials of both species are increased together, argon begins to enter the pore and, finally, displaces some of the adsorbed xenon. A t the highest chemical potential, argon dominates the pore composition. To determine whether this competitive adsorption can be predicted by a simple pore volume filling model, we compare the simulated mixture isotherm to an isotherm calculated using eq 10. Figure 8b shows that the preferential adsorption of xenon at low chemical potential and
of argon at high chemical potential is in fact qualitatively predicted by the model. However, the chemical potential a t which argon begins to displace xenon from the pore is much lower than predicted by the pore filling model. The implication is that argon can more easily enter the pore than can be accounted for by simple pore fillingarguments. The advantage argon enjoys over xenon is further evidenced by the excess amount defined by eq 14. The excess xenon is always negative, and the excess argon is always positive (Figure 9). The selectivity in NaA can be attributed to the arrangement of adsorbates in the pore. We attribute the preferential filling of argon to its ability to pack into the void space in the pore created by the pore architecture and the coadsorbed xenon. The density distribution of a xenon/argon mixture shows that, at an intermediate chemical potential, the most likely locations of the adsorbates in the pore are near the four-membered rings (Figure lo), a finding consistent with the density distribution found earlier for xenon.13 At a high chemical potential, the argon density distribution (dark gray) shows that additional pore volume is occupied, while the xenon density distribution (white) suggests that no new sites are formed. Simulation snapshots (Figure 11)verify that the argon atoms are indeed more delocalized and have access to regions of the pore unoccupied by xenon. This ability to
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Langmuir, Vol. 10, No. 4, 1994 1263
Figure 10. Density distribution of a binary mixture of xenon (white) and argon (dark gray) in cation-rich NaA a t 300 K at c(xs = C(AU = -15 kJ/mol (left) and pxe = p h = 0 (right).
Figure 11. Simulation snapshots of a grand canonical ensemble simulation a t pxe = p h = 0 with (a, left) 4 xenon and 11 argon atom and (b, right) 7 xenon and 8 argon atoms in a single NaA CY cage.
occupyadditional spacewithin the pore interiorgives argon a “packing” advantage over xenon at high loadings. This will be discussed further below. iii. Binary Adsorption of Xenon and Methane. Simulationsof a xenon/methane binary isotherm (Figure 12a)at 300 K show that, as observed above, xenon adsorbs more strongly in the low-loading regime. Although methane begins to adsorb at higher chemical potentials, it is unable to displace xenon the way argon did. The xenon plateau in the binary isotherm corresponds to the amount of single-componentxenon that will adsorb prior to the onset of crowding (Figure 5). Being slightlysmaller, methane can fill the adsorption sites left unoccupied by xenon without encountering repulsion, but methane is unable to fill any additional pore volume in the way that the very small argon could. The successful adsorption of methane in the mixture a t high chemical potential is not predicted by the model isotherm (Figure 12b). Xenon andmethane have thesame maximum loading (13 adsorbates per cage) due to the fact that they both fill the same adsorption sites. Hence, in
this model, methane has neither an energetic nor a volume filling advantage. In the simulation, though, the slightly smaller size of methane allows it to fill sites which, if filled by xenon, would be accompanied by repulsion. The density distribution of the xenon/methane mixture (Figure 13) shows again that the most likely location of the adsorbatesin the pore is near the four-membered rings. However, because methane is larger than argon, no additional sites form at high chemical potential. Xenon now has a competitive advantage at all loadings due to a greater polarizability than methane. iv. Adsorption in Dealuminated NaA. The selectivity observed above in NaA is attributed in part to the smaller molecules’ (argon and methane) ability to pack efficiently inside the pore space. To determine the sensitivity of this packing effect to pore architecture, we alter the structure of the zeolite by removing the sodium ions in the eight-membered rings to form a dealuminated or cation-poor NaA (Figure lb). Although this is only a small structural modification, it has been reported pre-
Van Tassel et al.
1264 Langmuir, Vol. 10, No. 4, 1994 9
The xenon/argon mixture simulation appears in Figure 17,and the xenon/methane mixture simulation appears in Figure 18. The results show that the selectivity observed in the cation-rich NaA also occurs in cation-poor NaA. To determine if the preference for argon in the xenon/ argon mixture is due to entropic effects, we calculate the xenon/argon binary isotherm at a higher temperature (400 K) in the cation-poor system. Although qualitativelythe features of the isotherm (Figure 19)are similar to those at 300 K, the argon is able to displace even more xenon a t high loadings at 400 K! This indicates that entropic effects are present and so the efficient packing of argon produces benefits both energetically and entropically.
1
-65.0
45.0
15.0
-5.0
-25.0
pxe= pa,
/ kJ/mol
Xe Simulation 9 Xe Model
[email protected] CHA..Model ............... ......... 0
**&"6"-A
,." ,
-0'
-65.0
45.0
-25.0
pb = pa.
-5.0
I
15.0
.... 35.0
/ kJ/mol
Figure 12. (a, top) Simulated binary and single-component isotherms for xenon and methane and (b, bottom) the isotherm calculatedfrom the pore volume filling model of eq 15 versus the chemical potential of each species in cation-rich NaA at 300 K.
viously that the structure of the adsorbed phase changes significantly with cation removal.16 Figures 14-16 show the cation-poor single-component isotherm, energy, and entropy for xenon, argon, and methane. The removal of the sodium ions has increased the capacity of the system: 16 xenon and methane molecules may adsorb per cage, as compared to 13for the cation-rich system. Other differencesin single-component adsorptionin cation-rich versus cation-poor NaA have been discussed previ0us1y.l~
Discussion The single-component simulationspresented here show the adsorption isotherms in zeolites are clearly correlated to the adsorbate size and polarizability. Larger adsorbates (such as xenon and methane) occupy well-defined polyhedral adsorption sites, the saturation of which is accompanied by an isotherm plateau. Smaller adsorbates (such as argon) fill the pore in a less regular fashion and thus exhibit no obvious plateaus in the isotherm. Mixing, however, is trickier. The xenon/argon mixture is an example of a binary system where one component is larger and more polarizable than the other. We observe that, at a low chemical potential, the more polarizable component is adsorbed preferentially, in agreement with a pore volume filling model. A similar observation has recently been made experimentally for a binary mixture of hydrocarbons adsorbed in a ~ e o l i t e . ~At a higher chemicalpotential,the smaller,less polarizable component begins to adsorb and to displace the larger molecule from the pore space. The pore volume filling model predicts this "comeback", but only at a much higher chemical potential than we observe here (corresponding to a difference of many decades of pressure). This failure of the theory is due to neglect of molecular packing effects that are more subtle than simple excluded volume. Packing effects are further evidenced by the simulation snapshots of a xenon/argon mixture in NaA (Figure 13). Xenon, being large and polarizable, is restricted to adsorption sitesnear the four-memberedrings, while argon, being small and less polarizable, is able to fit into crevices in the a cage between the xenon atoms and thus more
Figure 13. Density distribution of a binary mixture of xenon (white) and methane (dark gray) in cation-rich NaA at 300 K at C(XI = mH4 = -15 kJ/mol (left) and pxe = C(CH4 = 0 (right).
Adsorption Simulations of Small Molecules
Langmuir, Vol. 10, No. 4, 1994 1265
8 -65.0
45.0
-5.0
-25.0
15.0
p I kJ1mol Figure 14. Adsorption isotherm for xenon, methane, and argon versus chemical potential in cation-poor NaA at 300 K. Experimental data for xenon are from Jameson,m and those for argon
are from Linde."
-45.0
, -25.0
I
-5.0
15.0
pLxs = pAr I kJ1mol
Xe Simulation Xe Model ............................... r Simulation .................................... A t r Model 0
9
'1 4
0
...JW -65.0
Xenon
fe.,-
8-
jeL 3
-65.0
0 0.0
4.0
8.0
12.0
16.0
20.0
UP per cage Figure 15. Adsorption energy for xenon, methane, and argon versus average pore loading in cation-poor NaA at 300 K.
0.0
*.
4.0
8.0
120
16.0
20.0
UP per cage Figure 16. Adsorption entropy for xenon, methane, and argon versus average pore loading in cation-poor NaA at 300 K. efficiently fill the pore space. The filling is entropically favored since the argon atoms tend to be more delocalized than the xenon atoms. Neither size nor polarizability alone could account for this packing advantage, for it is both the delocalization of argon due to a smaller energetic interaction with the pore and its small size relative to xenon which allow it to pack efficiently. Methane, being close in size to xenon, does not enjoy the packing ability exhibited by argon. The binary density distribution shows that methane competes only for the same sites as xenon over the entire loading range. Unable to form additional sites, methane has neither an energetic nor a packing advantage, and thus cannot displace any xenon from the pore. Methane does, however, enter the pore at high chemical potentials, a feature not predicted by the volume filling model. This is because although xenon and methane compete for the same sites in the
I
-45.0
-25.0
-6.0
15.0
35.0
pxe= pAr I kJ1mol Figure 17. (a, top) Simulated binary and single-component isotherms for xenon and argon and (b, bottom) the isotherm calculated from the pore volume filling model of eq 15versus the chemical potential of each species in cation-poor NaA at 300 K.
zeolite, only methane can saturate the sites without the onset of repulsive energy. The physical effects responsible for observed selectivity at both low and high chemical potentials is shown schematically in Figure 20. At low loading, competition is based principally upon the relative interaction energies of the adsorbates, with the order being Xe > CH4 > Ar. At high loading, competition is based primarily on packing ability. Argon (diameter 3.84A), due to its small size, is able to pack more efficiently inside the pore than is xenon (d = 4.36 A). Methane (d = 4.00 A), although smaller than xenon, is unable to pack in a more efficient manner. There must then exist a critical ratio of molecular sizes in a binary mixture above which this packing advantage exists. This ratio must depend on the pore structure insofar as the volume available for adsorption depends on the potential energy surface in the pore, which in turn depends on the pore architecture. Increasing the temperature confirms that the packing ability of argon produces advantages that are both entropic (dueto greater translational and configurational freedom) and energetic (due to the lesser degree of crowding associated with addition to the pore). Single-component simulations show that xenon is favored energetically and entropically at low loadings (where mixing effects may be neglected). Thus, an increase in the argon concentration in the pore may only be brought about a t high loadings. Although only nonpolar adsorbates are studied here, it is surprising that moving from cation-rich to cation-poor NaA has little effect on the qualitative form of the mixture isotherm. It has been shown that the cation content has a greater affect on the adsorbate arrangement than on the energetic interaction with the pore wal1,la so one would
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1266 Langmuir, Vol. 10, No. 4, 1994
9
0
-66.0
-46.0
-6.0
-26.0
16.0
.................... Ar
.....
-66.0
.....
*.
46.0
-6.0
16.0
ulation ........ I
....................................
.*.*'
Z
-26.0
pxs= pAr / kJ/mol
............... ...........
L
-46.0
-66.0
pxe= pm, / kJ/mol
-26.0
pxe= pa,
-6.0
16.0
36.0
/ kJ/mol
Figure 18. (a, top) Simulated binary and single-component isotherms for xenon and methane and (b, bottom) the isotherm calculated from the pore volume filling model of eq 15 versus the chemical potential of each species in cation-poorNaA at 300 K. expect that the degree of separation observed at high loadings (due to the "packing effects") would be sensitive to pore structure. Instead, we observe that the separation is quite insensitive to changes in pore structure, suggesting that the trend for smaller, less polarizable molecules to pack more efficiently a t high loadings may be a general feature which applies to other pore structures. Of course, for binary adsorption where one molecule possesses a permanent dipole moment, changes in cation content could have a more pronounced effect on mixture equilibria. The selective adsorption investigated here is especially interesting since all of the species are small enough to diffuse through the pore space. This offers hope for the development of selective adsorbents for situqtions where none of the components in a mixture are sterically excluded (molecular sievingeffect), so the intracrystalline diffusion of the selectively adsorbed species may be quite large. Although we have investigated adsorption of only simple spherieal molecules, the principles described here may also apply to separations of larger molecules. For instance, the competition between size and polarizability may be used to predict the equilibrium distribution of large and small hydrocarbons adsorbed in a zeolite pore. It has recently been observed experimentally that a branched hydrocarbon adsorbs preferentially to an unbranched one in a zeolite at low loading? consistent with the results presented here. For more complex adsorbates, a competition for pore space figures to hinge on differences in size, polarizability, shape, and perhaps deformability. On the basis of the results presented here, we expect the mixing of more complex adsorbates to be highly nonideal. Only by determining and quantifying each of these factors will
0
*.k ...................................
*.a
d
I
-76.0
-66.0
-36.0
I
I
-16.0
6.0
I
26.0
pxs= pk / kJ/mol
Figure 19. (a, top) Simulated binary and single-component isotherms for xenon and argon and (b,bottom) the isotherm calculated from the pore volume f i g model of eq 16 versus the chemical potential of each species in cation-poor NaA at 400 K.
Figure 20. A schematic of (a) relative energies of interaction of xenon, methane, and argon with the zeolitepore wall and (b) the packing abilities of these adsorbates. we be able to predict complex mixture equilibria such as the product distribution from catalytic cracking processes.
Conclusions The adsorption isotherms for xenon, methane, argon, and their mixtures in zeolite NaA and dealuminated NaA are reported. The single-component isotherms show an order of preference of Xe > Ar > C& at low pore loadings
Adsorption Simulations of Small Molecules
where energetic factors are dominant. At higher pore loadings, the order is Ar > CHI > Xe due to the differing sizes of the adsorbates. The binary isotherm indicates that xenon, due to ita high interaction energy with the pore wall, is preferentially adsorbed over methane and argon a t low to intermediate pore loadings, in agreement with a simple pore volume fiiing model. At higher loadings, argon displaces xenon at a much lower chemical potential than predicted by the model due to ita ability to pack efficiently into regions of the pore inaccessible to xenon. Methane, being nearly as large as xenon, is unable to occupy this additional pore space, so it cannot displace xenon from the pore. The selective adsorption of mixtures of small molecules observed here may have implications in separations of long and short hydrocarbons in pores large enoughto easily
Langmuir, Vol. 10, No. 4, 1994 1267
diffuse through. Our resulta are limited to mixtures of nonpolar molecules. We expect that the behavior of polar mixtures can be even more complex.
Acknowledgment. We wish to thank S. A. Somers and M. C. Mitchell for helpful discussions regarding this work, the Minnesota Supercomputer Institute for use of a Silicon Graphics IRIS workstation and agrant on a Cray X-MP EA supercomputer, M. Hughes for assistance with the graphics, and the Center for Interfacial Engineering. This work was funded in part by the National Science Foundation (Grant CTS-9058387),the American Chemical Society Petroleum Research Fund, the Dow Chemical Co., the Mobil Oil Co., and a University of Minnesota Doctoral Dissertation Fellowship for P.R.V.T.
