Adsorption of CH4− CF4 Mixtures in Silicalite: Simulation, Experiment

Langmuir 1997, 13, 6795-6804

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Adsorption of CH4-CF4 Mixtures in Silicalite: Simulation, Experiment, and Theory Matthias Heuchel,*,† Randall Q. Snurr,‡ and Eckhard Buss§ Institute of Physical and Theoretical Chemistry and Institute of Technical Chemistry, University of Leipzig, D-04103 Leipzig, Germany, and Department of Chemical Engineering, Northwestern University, Evanston, Illinois 60208 Received July 17, 1997. In Final Form: October 2, 1997X Grand canonical Monte Carlo (GCMC) simulations of binary Lennard-Jones mixtures in the zeolite silicalite have been used to predict the adsorption of CH4 and CF4 mixtures as a function of gas phase composition, total pressure, and temperature. For single components and mixtures, predictions of adsorption isotherms and isosteric heats are in good agreement with experiment at room temperature. Within the experimental pressure range of 0 to 17 bar, the mixtures are well described by the ideal adsorbed solution (IAS) theory. For very high loading, deviations from IAS theory appear. The configurations generated in the simulation were used to calculate sorbate-zeolite interaction energy distributions for different types of siting locations within the zeolite pores. These distributions display a pore shape related energetic heterogeneity in different regions of silicalite. Near saturation at a total loading of 12 molecules per unit cell, the shape of the observed energy distribution is relatively independent of the composition in the pore. Nevertheless, the energetic heterogeneity is responsible for a mild segregation in the adsorbed mixtures, with methane adsorbed preferentially in the silicalite zigzag channels and CF4 preferentially in the straight channels.

Introduction Physical adsorption of gas mixtures in microporous materials such as activated carbons and zeolites has attracted a great deal of attention in recent years. A main reason for this is that the separation of gases by selective adsorption of one species is an attractive alternative to the more common liquification/distillation procedures. In addition adsorption offers the possibility to develop separations with improved selectivity. Mixture adsorption in micropores is also of fundamental importance in heterogeneous catalytic processes. The application of computer simulation methods,1,2 for instance molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) simulation, to mixture adsorption in pores allows one to make predictions for real systems. Also the simulated data provide an unambiguous means to test theories of adsorption. GCMC simulations allow a direct determination of the individual adsorbed amounts at conditions of interest and therefore of the selectivity for the selective adsorption of one mixture component. Further, molecular simulations have proven extremely useful in elucidating the role of molecular-level interactions in micropore adsorption and diffusion. Over the last decade, several simulation studies of mixture adsorption have been made. Initially the nature of phase equilibria, especially capillary condensation in active carbons, was studied, usually with Lennard-Jones (LJ) mixtures in pores of idealized geometry, such as slitlike and cylindrical structures.3-8 While most of these † Institute of Physical and Theoretical Chemistry, University of Leipzig. ‡ Department of Chemical Engineering, Northwestern University. § Institute of Technical Chemistry, University of Leipzig. X Abstract published in Advance ACS Abstracts, November 15, 1997.

(1) Nicholson, D.; Parsonage, N. G. Computer Simulation and the Statistical Mechanics of Adsorption; Academic Press: New York, 1982. (2) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1987. (3) Tan, Z.; Van Swol, F.; Gubbins, K. E. Mol. Phys. 1987, 62, 1213. (4) Heffelfinger, G. S.; Tan, Z.; Gubbins, K. E.; Marconi, U. M. B.; Van Swol, F. Mol. Simul. 1989, 2, 393. (5) Sokolowski, S.; Fischer, J. Mol. Phys. 1987, 71, 393.

S0743-7463(97)00803-2 CCC: $14.00

studies have considered noble/inert gases, like Ar and Kr, mixtures of spherical LJ particles were also applied to describe, e.g., the adsorption of butane and carbon dioxide in a slitlike pore at supercritical conditions.9 The extension to nonspherical model mixtures has been performed, e.g., by Cracknell et al.,10,11 who studied CH4-C2H6 mixtures in a carbonaceous slit pore, where ethane was modeled as two LJ sites separated by a fixed bond length and methane as a simple LJ sphere. An interesting observation was the behavior of the ethane selectivity. Initially, it increases with pressure to a maximum value, and then it decreases. Later, Cracknell et al.12 studied the adsorption of CH4CO2 in the same slit-shaped carbonaceous micropores. Again, methane was modeled as a spherical LJ particle. Analogous to C2H6, carbon dioxide was modeled as a LJ dumbell, but with three point charges and therefore with a quadrupole moment. In contrast to the results for the hydrocarbon mixture, the selectivity of CO2 increases monotonically with pressure. This example showed clearly that, in addition to a difference in molecular shape, the chemical nature can be expected to have a significant influence on the properties of the adsorbed mixture. The behavior of mixture adsorption in zeolites has been investigated by molecular simulation in only a few studies. GCMC simulations of N2-O2 mixtures in zeolite 5A have been reported by Razmus and Hall.13 Their model included point quadrupole moments of the O2 and N2 molecules, as well as LJ sites for the atoms. Over a coverage range where the mixing tends to be ideal, selectivities for the binary mixtures were calculated. In the same year, Karavias and Myers14 reported simulations for three binary systems (C2H4-CO2, CH4-CO2, and i-C4H10-C2H4) (6) Finn, J. E.; Monson, P. A. Mol. Phys. 1991, 72, 661. (7) Cracknell, R. F.; Nicholson, D.; Quirke, N. Mol. Phys. 1993, 80, 885. (8) Piotrovskaya, E. M.; Brodskaya E. N. Langmuir 1993, 9, 3548. (9) Okayama, T.; Yoneya, J.; Nitta, T. Fluid Phase Equilib. 1995, 104, 305. (10) Cracknell, R. F.; Nicholson, D.; Quirke, N. Mol. Sim. 1994, 13, 161. (11) Cracknell, R. F.; Nicholson, D. Adsorption 1995, 1, 7. (12) Cracknell, R. F.; Nicholson, D.; Tennison, S. R.; Bromhead, J. Adsorption 1996, 2, 193. (13) Razmus, D. M.; Hall, C. K. AIChE J. 1991, 37, 769. (14) Karavias, F.; Myers, A. L. Mol. Simul. 1991, 8, 51.

© 1997 American Chemical Society

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in a model zeolite X cavity. The adsorbate molecules were modeled as LJ interaction sites with point multipole moments. Because the oxygen ions that form the walls of the large cavities in zeolite X lie roughly in a spherical shell, the zeolite was modeled as a collection of identical, nearly spherical cavities. Sorbate-solid electrostatic interactions resulting from sodium ions in the zeolite crystal were taken into account. Phase diagrams and total coverage were calculated, and good agreement with experiments at room temperature was found, except for the system i-C4H10-C2H4. Later, the same model of a spherical cavity was used by Dunne and Myers15 in GCMC simulations to study specifically the size effect on adsorption of a simple LJ mixture in zeolite 13X. For these nonpolar adsorbates, the zeolite provides an energetically homogeneous surface. The ratio of molecular diameters was 1.34, which is equivalent to a molecular volume ratio of 2.42. The authors found at high pore filling a moderate negative deviation from ideal mixing. This was explained with a partial exclusion of the larger molecules from portions of the micropore volume. A negative deviation from Raoult’s law in the adsorbed mixture was also found in a simulation of adsorption of liquid N2 and O2 in a model NaX zeolite cavity at 77.5 K.16 Adsorption of an equimolar gas mixture of nitrogen and methane in zeolite Y was studied by Maddox and Rowlinson,17 who used a two-site LJ model for nitrogen and a five-site LJ model for methane. They found that methane is adsorbed preferentially and that selectivity was almost independent of the pressure. Thus the authors claimed that the IAS theory is “reliable for mixtures of this kind”. The adsorption of mixtures of small molecules (Xe, Ar, and CH4 ) on zeolite NaA was simulated with GCMC over a wide range of pressures by Van Tassel et al.18 All molecules were represented by LJ spheres, and the mixture composition was fixed at equal chemical potential of both components. The potential energy was calculated atomistically. Separate terms in the potential account for sorbate-framework repulsion, dispersion, and sorbate-framework induced dipole-static electric field interaction. The selectivity dependence on pressure in both Xe-Ar and Xe-CH4 mixtures was studied in a later work.19 At low pressure Xe is selectively adsorbed due to its greater energetic interaction with the zeolite. At high pressure a reversal in selectivity appears, because the smaller component “packs” in the pore with greater efficiency as compared to the bulk. A further GCMC study of Xe-Ar mixtures in NaA was carried out by Jameson et al.20 in the framework of an extended NMR study. So far, all simulation studies of mixture adsorption in zeolites that we are aware of have considered zeolite A or faujasite, both of which have micropores consisting of roughly spherical cavities. Another important micropore shape is a channel system, as can be found, e.g., in silicalite, the pure silica form of the ZSM-5 (MFI) zeolites. Silicalite has been used in many experimental and theoretical studies. Its well-defined structure and chemically simple nature suggest that this would be another ideal reference material for attempts to gain a better molecular understanding of mixture adsorption in microporous materials.

To provide verification of the simulation results, we performed extensive adsorption measurements.25 The binary gas mixtures were produced with a mixing apparatus using the pure gases. The adsorption equilibria were measured for both pure gases and binary gas mixtures using a Sartorius high-pressure microbalance, Model S3D-P. Details of the apparatus are shown in ref 25, where further information about the experimental procedure may be found. The pressure measurements in the range of 0-17 bar were carried out with an accuracy of 0.15%. The temperature was kept constant within (0.02 K. The primary data were the mass excess mσ of the adsorbed phase compared with the gas phase. In order to obtain the absolute mass adsorbed, m, the primary data were corrected by addition of the corresponding mass in the gas phase, i.e., the product of the micropore volume vMiPo and the gas density. The micropore volume was determined using the t-plot of the N2 adsorption isotherm at 77 K. Gas densities were calculated using the virial equation of state truncated after the second virial coefficient.

(15) Dunne, J. A.; Myers, A. L. Chem. Eng. Sci. 1994, 49, 2941. (16) Dunne, J. A.; Myers, A. L.; Kofke, D. Adsorption 1996, 2, 41. (17) Maddox, M. W.; Rowlinson, J. S. J. Chem. Soc., Faraday Trans. 1993, 89, 3619. (18) Van Tassel, P. R.; Davis, H. T.; McCormick, A. V. Langmuir 1994, 10, 1257. (19) Van Tassel, P. R.; Davis, H. T.; McCormick, A. V. Mol. Simul. 1996, 17, 239. (20) Jameson, C. J.; Jameson, A. K.; Lim, H.-M. J. Chem. Phys. 1996, 104, 1709.

(21) Snurr, R. Q.; Ka¨rger, J. J. Phys. Chem. B 1997, 101, 6469. (22) Ka¨rger, J.; Ruthven, D. M. Diffusion in Zeolites and Other Microporous Solids; Wiley-Interscience: New York, 1992. (23) Chen, N. Y.; Degnan, T. F., Jr.; Smith, C. M. Molecular Transport and Reaction in Zeolites; VCH: New York, 1994. (24) Theodorou, D. N.; Snurr, R. Q.; Bell, A. T. In Comprehensive Supramolecular Chemistry; Alberti, G., Bein, T., Eds.; Pergamon: Oxford, 1996; Vol. 7, pp 507-548. (25) Buss, E.; Heuchel, M. J. Chem. Soc., Faraday Trans. 1997, 93, 1621.

With respect to the work for zeolites having cavities, it would be of interest to see how mixture behavior depends on the geometry of the pore system. Within an extended investigation of adsorption and diffusion of simple mixtures in silicalite we have chosen the binary mixture of methane and tetrafluoromethane (CF4) for our studies. This is a simple mixture of molecules with approximately spherical shape, which can be well represented by a LJ mixture. The ratio of molecular diameters is about 1.25, which is equivalent to a molecular volume ratio of 1.95. Therefore, a comparison with the work of Dunne and Myers15 can be made. A further motivation for this system comes from our interest in diffusion in the channel system of silicalite. In other work21 MD simulation was used to investigate the selfdiffusion of binary mixtures of CH4 and CF4 in the zeolite silicalite. Given the complexities of single-component diffusion in zeolites,22-24 simulations studies may play a key role in understanding multicomponent diffusion. For such studies, knowing the thermodynamic equilibrium of the pore/gas system is a necessity. In the remainder of this paper we first review our adsorption measurements for CH4-CF4 mixtures on silicalite. Then we show briefly how the adsorbed amounts of the individual species were determined from the gravimetrically-measured total adsorbed mass of the mixture. These experimental results are used for comparison with our GCMC results. Further sections describe the model and the simulation details. The results section compares experimental and simulated data. Calculated results for local composition and several interaction energies are used to understand in more detail the adsorption behavior of CH4-CF4 in silicalite. Adsorption Measurements

Adsorption of CH4-CF4 Mixtures in Silicalite

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Equilibrium Compositions from Gravimetric Measurements Van Ness26 suggested an iterative method to determine the partial adsorbed amounts n1 ) x1n and n2 ) x2n, from binary mixture adsorption equilibria, for which m, the total mass adsorbed per unit mass of adsorbent, was determined. n is the total number of adsorbed moles, and xi is the mole fraction of component i in the adsorbed phase. The original method assumes an equilibrium between an ideal gas phase and a two-dimensional adsorbed phase. For a micropore system, it is more correct to treat the adsorbed phase as a three-dimensional system. Cracknell and Nicholson11 derived for the case of a planar surface in slit pores the analogue to the Gibbs adsorption isotherm with separate terms involving the bulk pressure and the surface tension or spreading pressure. Although this decomposition is not really possible for silicalite, this model was used in ref 25. Recently, Vuong and Monson27 showed that in fact the decomposition is not necessary for a fully consistent thermodynamic treatment. Although there will be no difference to the calculated partial loading in ref 25, we present here an improved derivation of the basic formula. We formulate now the fundamental equation for the internal energy of an adsorbed mixture in a inert porous solid phase of fixed total volume

du ) T ds + Φ dv + µ1 dn1 + µ2 dn2

It should be mentioned that the application of eq 3 requires absolute adsorption quantities. For a real gas mixture the chemical potential µig of the component i can be written as

(4)

where µiog(T) is the standard chemical potential depending on temperature T and R is the universal gas constant. The fugacity fig of component i is defined as

fig ) φiyiP

(5)

where P is the total gas pressure of the mixture, φi is the fugacity coefficient, and yi is the mole fraction of component i in the gas mixture. At constant temperature the change of the chemical potential of component i in the gas phase follows as

[ ( )]

dµig ) RT Zi d ln P + RT

∂ ln φi 1 + yi ∂yi

dyi (6)

T,P

where Zi is the partial molar compressibility factor of component i in the gas phase. At equilibrium between (26) Van Ness, H. C. Ind. Eng. Chem. 1969, 8, 464. (27) Vuong, T.; Monson, P. A. Langmuir 1996, 12, 5425.

( )

1 ∂Ω* y1(1 - y1) n ∂y1 T,P x1 ) y1 ∂ ln φ1 1 + y1 ∂y1 T,P

( )

(8)

where Ω* ) Φv/(RT) is the reduced grand potential. If the gas composition yi is held constant in eq 6, one can obtain an equation to calculate Ω* for a binary adsorbed phase of constant pore volume v

∫0Pn[x1Z1 + (1 - x1)Z2] d ln P

(9)

Furthermore, the total number of adsorbed moles n in the last two equations can be substituted by

n)

m m ) M x1M1 + (1 - x1)M2

(10)

(2)

(3)

µig ) µiog(T) + RT ln fig

(7)

and, thus dµi in eq 3 can be substituted by eq 6. The resulting relationship can be restricted to constant pressure as well as to constant gas composition in order to derive equations for the calculation of the adsorbed phase composition. The ln φi values of the binary gas mixture must conform the Gibbs-Duhem relation, and with application of (y1 d ln φ1 + y2 d ln φ2 ) 0) one obtains at constant pressure for the mole fraction of, e.g., component 1 in the adsorbed phase

Ω* ) -

which for constant temperature yields the Gibbs adsorption isotherm

v dΦ + n(x1 dµ1 + x2 dµ2) ) 0

dµig ) dµi

(1)

where s and and v are entropy and volume of the fluid mixture in the porous material. Φ ) Ω/v is the grand potential density. This quantity is -P for a bulk fluid. µi is the chemical potential of component i in the adsorbed phase. The fundamental eq 1 implies a Gibbs-Duhem relation

s dT + v dΦ + n1 dµ1 + n2 dµ2 ) 0

the gas phase and the adsorbed phase, for every component i

where m is the mass adsorbed per unit mass of adsorbent and M is an averaged molecular weight of the adsorbed mixture calculated from the molecular weights M1 and M2 of the pure components. For a set of gravimetric pure gas and mixture isotherms, eqs 8-10 can be solved by simultaneous iteration to determine the unknown equilibrium composition of the adsorbed phase in the case of mixture adsorption. The numerical procedure applied here, using the virial equation to take into account the real gas behavior, is described in ref 25. Model Representation For the simulation, methane and CF4 molecules were modeled as single interaction sites. Sorbates were assumed to interact with one another and with the zeolite by a pairwise-additive Lennard-Jones potential between interaction sites. Interactions with the zeolite silicon atoms were neglected as in much of the previous work in this field. The oxygen atoms of the zeolite lattice were assumed to be fixed at the crystallographic coordinates determined from X-ray diffraction studies of the orthorhombic phase.28 Silicalite has two sets of interconnected pores, about 5.5 Å in diameter. A set of straight (S) channels is directed along the y crystallographic axis, while a set of zigzag (Z) channels is directed along the x axis. These channels meet in a somewhat larger channel intersection (I). CH4-CH4 and CH4-oxygen LJ parameters were identical to those used by others.29,30 CF4(28) Olson, D. H.; Kokotailo, G. T.; Lawton, S. L.; Meier, W. M. J. Phys. Chem. 1981, 85, 2238. (29) Goodbody, S. J.; Watanabe, K.; MacGowan, D.; Walton, J. P. R. B.; Quirke, N. J. Chem. Soc., Faraday Trans. 1991, 87, 1951. (30) Maginn, E. J.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1993, 97, 4173.

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Table 1. Lennard-Jones Parameters internaction

σ (Å)

/k (K)

interaction

σ (Å)

/k (K)

CH4-CH4 CF4-CF4 CH4-CF4

3.73 4.66 4.19

147.9 134.0 140.8

CH4-O CF4-O O in silicalite

3.21 3.73 2.81

133.3 109.6 89.6

CF4 parameters were taken from the literature.31 Using the silicalite oxygen parameters of June et al.,32 LorentzBerthelot combining rules were applied to obtain parameters for the CF4-oxygen interactions.2 Table 1 lists the parameters used. They are identical to those used in our MD simulations of diffusion in these systems, which yielded self-diffusivities in good agreement with measurements by pulsed field gradient NMR.21 GCMC Simulations The GCMC simulations used the energy-bias GCMC algorithm of Snurr et al.33 As in standard GCMC, there are three types of moves used to sample the grand canonical ensemble: (1) particle displacements, (2) attempts to insert an additional molecule into the system at a randomly-chosen position, and (3) attempts to remove one of the existing molecules. In the energy-bias scheme, one exploits the knowledge of the structure of the zeolite and the known energetics experienced by sorbates at different locations within the zeolite lattice to bias insertion moves so that they are attempted more often in the energetically more favorable regions of the zeolite. Details are given in ref 33. The energy-bias algorithm substantially improves the efficiency of the simulation. For simulations of mixtures, an additional move, a particle exchange, was introduced. A particle exchange move consists of randomly choosing a molecule of each species and attempting to interchange their positions (or equivalently their chemical identities). The change in potential energy ∆U is calculated and the move is accepted with probability

p ) min{1, exp(-∆U/kT)}

(11)

The particle exchange moves are similar to those used by Van Tassel et al.,18 but our moves involve two particles rather than switching the identity of just one molecule. These kinds of moves are introduced to decrease the number of simulation steps needed to achieve equilibration. All simulations used a system of 27 unit cells. The production runs were typically 4 × 106 Monte Carlo steps long, but for the higher densities at T ) 200 K and P ) 1 bar 8 × 106 steps were used. The first one million steps were used for equilibration and not included in the averaging. Each Monte Carlo step consisted of a translation attempt, followed by either an insertion or deletion attempt (with 50% probability of each) and, for mixtures, a particle exchange. The statistical uncertainties in the results were estimated by dividing each simulation run into 10 blocks and calculating the standard deviation of the block averages. Runs of a mixture with about 12 particles per unit cell took about 10 h on an IBM RISC 6000. The fugacity of the gas in the fluid outside the silicalite was related to its pressure by a virial equation of state. This equation was used for simulation and experimental data up to 10 bar with only second virial coefficients. For (31) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. (32) June, R. L.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1990, 94, 8232; 1991, 95, 1014. (33) Snurr, R. Q.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1993, 97, 13742.

Figure 1. Adsorption isotherms of single components from experiment (open symbols with line) and simulation (closed symbols) at 300 K.

higher pressures fugacities have been calculated on the basis of the virial expansion up to the fourth virial coefficient. The coefficients determined experimentally by Doulsin et al.34 were used. Results Single Component Adsorption. Before trying to simulate adsorption of CH4-CF4 mixtures, it was necessary to verify that the molecular model was capable of reproducing single-component behavior for these species. The methane parameters had been used in the past by other authors29,30 and shown to yield isotherms in good agreement with experiment. Our calculated and measured adsorption isotherms for the single components in silicalite at 300 K are shown, as a function of pressure, in Figure 1. At lower pressures the simulated isotherms are in excellent agreement with the experimental ones. As can be seen, CF4 is more strongly adsorbed than CH4, but the adsorption isotherms intersect at higher pressure. When the adsorption approaches the saturation loading, more of the smaller methane molecules can fill the pore volume of silicalite. The limitations of the model can be seen in the higher pressure range; the intersection point for the model mixture is at about 8 bar, whereas the experimental value is around 13 bar. We have fitted our simulated and experimental isotherms by a new semiempirical isotherm equation, proposed by Jensen and Seaton35

[ (

n(P) ) KP 1 +

)]

KP a(1 + κP)

c -1/c

(12)

where n(P) is the adsorbed amount, K is Henry’s law constant, a is a measure of capacity, and κ represents an adsorbed phase compressibility. The parameter c determines the curvature of the isotherm. At low pressure the isotherm follows Henry’s law asymptote. For κ ) 0 eq 12 reduces to the Toth equation. If in addition c ) 1, the Langmuir isotherm appears. Table 2 shows the determined values for the parameters. Especially in the highpressure region, the new isotherm shows a significant improvement over the Toth equation, which is frequently used to represent adsorption isotherms on zeolites analytically. In general, the accuracy was increased by a factor of 2, and experimental and simulated isotherms can be fitted by eq 12 with an accuracy of about 1%. We notice that the c parameter is close to 1. For the simulated isotherms, we find that the capacity value a for CF4 in silicalite is around 12 molecules per unit cell. For methane (34) Doulsin, D. R.; Harrison, R. H.; Moore, R. T. J. Phys. Chem. 1967, 71, 3477. (35) Jensen, C. R. C.; Seaton, N. A. Langmuir 1996, 12, 2866. (36) Karavias, F.; Myers, A. L. Mol. Simul. 1991, 8, 23.

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Table 2. Parameters for the Semiempirical Isotherm Equation of Jensen and Seaton35 for Adsorption of Single Components in Silicalite molecule CH4 expt 300 K CH4 GCMC 300 K CH4 GCMC 200 K CF4 expt 300 K CF4 GCMC 300 K CF4 GCMC 200 K

a (/unit K (/unit cell) cell/bar) 13.9 16.8 16.9 11.6 11.5 11.7

4.60 4.23 153 17.1 20.2 3210

κ (10-3/ bar)

c

1.08 5.83 0.99 0.729 1.11 17.5 1.12 8.46 1.08 2.22 1.19 168

accuracy (%) 0.4 0.4 0.5 1.4 1.6 1.5

Figure 2. Isosteric heats of adsorption for CF4 and CH4 on silicalite. Open symbols with lines represent experimental results derived from single component isotherms at 273, 298, and 325 K. Closed symbols are GCMC results.

the value is close to 17. While for CF4 the capacity a from experiment gives a similar value (11.6 molecules per unit cell), for CH4 the fitted experimental value is lower (13.9 molecules per unit cell). The numerical fit of the single component isotherms with the modified Toth isotherm, eq 12, is needed for the thermodynamic calculations below. Isosteric heats of adsorption qst of the pure gases obtained from both simulation and experiment are shown in Figure 2. The experimental data have been obtained by differentiating the pressure data in the experimental isotherms at 273, 298, and 323 K (see ref 25) with respect to temperature at constant loading.

ln P [∂ ∂T ]

qst ) Z RT2

(13)

n

where Z is the compressibility factor of the pure component. The simulation result has been calculated from the loading dependence of the mean potential energy per molecule 〈U〉 using the definition of the isosteric heat,27 as the difference of the partial molar enthalpy of the sorbate in the gas phase and the partial molar internal energy in adsorbed phase (see also refs 32, 14, and 37). We have fitted 〈U〉 with a polynomial in density and calculated the isosteric heat with the following formula

( )

qstMC ) HR + RT - 〈U〉 - 〈N〉

∂〈U〉 ∂〈N〉

(14) T,v

where HR is the the molar residual enthalpy of the pure component in the real gas state. The isosteric heats of both adsorbates show only a very small slope with increasing loading. For methane the experimental heat curve remains nearly constant up to about 7 molecules per unit cell. The mean value is 20.4 (37) Snurr, R. Q.; June, R. L.; Bell, A. T.; Theodorou, D. N. Mol. Simul. 1991, 8, 73. (38) Dunne, J.; Mariwala, R.; Rao, M.; Sircar, S.; Gorte, R. J.; Myers, A. L. Langmuir 1996, 12, 5888.

Figure 3. Phase diagrams for adsorption of binary mixtures of CF4 and CH4 on silicalite at 300 K and constant pressures P ) 1 bar and P ) 10 bar. Open symbols represent results derived from gravimetric measurements using Van Ness’s method. Closed symbols are GCMC results.

kJ/mol. This value and the constancy over a high coverage range are in very good agreement with recent calorimetric measurements of Dunne et al.38 An experimental value of 20 kJ/mol was determined by Smit39 from data in literature. A somewhat lower value was found with microcalorimetry at 77 K.40 Also the simulated isosteric heats remain constant with loading. The calculated mean value is 18.1 kJ/mol. Recently, the same value was reported by Talu et al.41 This is not surprising, because the authors used for their GCMC simulations a very similar atomistic model. Further Monte Carlo results for methane in silicalite for various models may be found in the work of Smit.39 For CF4, the simulation predicts an isosteric heat at zero loading of about 25.0 kJ/mol. The limiting value at zero loading from experiment is about 26.5 kJ/mol. Simulation and experiment show a slight increase with loading up to 10 molecules per unit cell, and then a clearly visible decrease. The positive slope can be explained by enhanced attractive interactions between the CF4 molecules, and at high loading, a slight repulsion can be detected. Neither simulation nor experiment detect a significant decrease in the isosteric heat with increasing loading at low coverage. Mixture Adsorption. Equilibrium diagrams at T ) 300 K are presented in Figure 3 for gas pressures of P ) 1 bar and P ) 10 bar. In good agreement, experiment and simulation show a preferred adsorption of CF4 for all mole fractions of the gas mixture. The simulated equilibrium diagrams obtained for pressures above the experimental range (P g 17 bar) will be discussed below. First we focus on a further comparison of experimental and simulated (39) Smit, B. J. Phys. Chem. 1995, 99, 5597. (40) Llewellyn, P. L.; Coulomb, J.-P.; Grillet, Y.; Patarin, J.; Lauter, H.; Reichert, H.; Rouquerol, J. Langmuir 1993, 9, 1846. (41) Talu, O.; Myers, A. L. In Fundamentals of Adsorption; LeVan, M. D., Ed.; Kluwer: Boston, MA, 1996; p 945.

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Figure 5. Selectivity for CF4 versus gas phase composition at P ) 1 bar (diamonds) and P ) 10 bar (squares) from experimental data (open symbols) and GCMC simulation (closed symbols).

Figure 4. Adsorption for CF4 and CH4 and their binary mixtures on silicalite at different gas phase compositions at 300 K and constant pressures P ) 1 bar and P ) 10 bar. Dotted lines with open symbols represent results derived from gravimetric measurements. Closed symbols are GCMC results. Full lines are the predictions from simulated data for the pure components with IAS theory.

results. Figure 4 shows individual and total amounts adsorbed vs gas phase composition. For both gas phase pressures, P ) 1 bar and P ) 10 bar, experimental and GCMC values are in qualitative agreement. The deviation is about 5% of the saturation loading. At P ) 1 bar, the total loading is changing from about 3.5 molecules per unit cell for pure methane to about 7.5 molecules for pure CF4. For the gas pressure of 10 bar the total number of adsorbed particles is relatively constant (about 11-12 molecules/unit cell). The average potential energy experienced by the molecules in the zeolite pores is related to the heat of adsorption. This energy can be considered as arising from two sources: zeolite-sorbate and sorbate-sorbate interactions, both of which vary with loading for singlecomponent adsorption.37 For the pure components and the mixtures of Figure 4 the sorbate-sorbate interactions contribute less than 5% to the total potential energy 〈U〉 of a sorbed molecule. So, the molecules are really dominated by the sorbate-zeolite energy. Interestingly, for the mixtures of Figure 4, the zeolite-sorbate interactions for methane and CF4 are remarkably constant with varying composition, taking values of about -15.7 and -22.8 kJ/mol for methane and CF4, respectively. This is somewhat surprising, since as we discuss later, the molecules are segregated into different portions of the zeolite at different compositions and the different channels are known to have different adsorption energies.32 Below, we investigate further the connection between sorbate siting and energetics. The most sensitive parameter with respect to mixture separation is the selectivity. For CF4 it is defined as

SCF4 )

xCF4yCH4 xCH4yCF4

(15)

Figure 6. Temperature dependence of sorbed amounts (above) and interaction energies (below) of CF4 and CH4 for the adsorption of an equal molar gas mixture at P ) 1 bar.

Figure 5 shows for both experiment and simulation that the separation factor SCF4 is small (between 3 and 5), and, at constant T and P, it always decreases slightly with increasing mole fraction of CF4 in the gas phase. Simulation and experiment are in acceptable agreement. In the pressure range, P e 20 bar, the selectivity decreases with increasing pressure. The good correlation of simulated and experimental results allows one to draw the conclusion that our model describes at least qualitatively the real system. In the following we want to obtain further insight into the behavior of the system from additional simulation results. The effect of temperature on mixture adsorption is shown in Figure 6 for an equimolar mixture at 1 bar. In the temperature range from 200 to 325 K, the loading of CF4 changes from 12 to 4 molecules per unit cell, while the methane loading changes only from about 3 to 1 molecule per unit cell. Once more, the mean zeolite-sorbate interactions for methane and CF4 are remarkably constant

Adsorption of CH4-CF4 Mixtures in Silicalite

Langmuir, Vol. 13, No. 25, 1997 6801 Table 3. Local Minima in kJ/mol of Zeolite-Sorbate Interaction in Different Regions of the Channel System: Intersections (I), Straight Channels (S), and Zigzag Channels (Z)

Figure 7. Adsorption for CF4 and CH4 and their binary mixtures on silicalite for different gas phase composition at 300 K and 20 bar (above) and 200 K and 1 bar (below). Closed symbols are GCMC results. Lines are the predictions from simulated data for the pure components with IAS theory.

for the different equilibrium compositions belonging to different temperatures. In ref 25 it was shown that the experimental mixture data can be well represented by the ideal adsorbed solution (IAS) theory.42 This was a strong argument for a more or less ideal behavior of the adsorbed phase. To confirm this assumption, we calculated from our simulated adsorption isotherms of both pure components the mixture behavior under the assumptions of the IAS theory. Simulation results for the individual and total loading at T ) 300 K and gas pressures of 1 and 10 bar are compared with the IAS theory in Figure 4. The agreement is quantitative. For a higher pressure than the experiments (P ) 20 bar, Figure 7 above), where the average loading is 12-14 molecules per unit cell, the IAS predictions start to underestimate slightly the average occupancy of both CH4 and CF4. For still higher coverages (between 14 and 16 molecules per unit cell) as they appear at lower temperature of T ) 200 K and P ) 1 bar, the difference between simulation and IAS is more pronounced (negative deviation from ideal mixing) as can be seen in Figure 7 below. The IAS range in silicalite, up to about 12 molecules per unit cell, corresponds to reduced densities (F* ) Nσ3/ vMiPo) of about 0.37 (pure methane) to 0.71 (pure CF4). These values are significantly higher than the reduced densities of about 0.23 to 0.31 in the spherical cavity of the NaX model used by Dunne and Myers,15 where a mixture of similar size difference showed already a substantial negative deviation from ideality. It appears that differences in zeolite structure have an important effect on the applicability of the IAS theory. In silicalite the pores are so narrow that a molecule in a channel interacts with at most only two other sorbate molecules, while in faujasite many molecules are in close contact in a single cage. Moreover, the partial exclusion of the larger (42) Myers, A. L.; Prausnitz, J. M. AIChE J. 1965, 11, 121.

molecule

I

S

Z

CF4 CH4

-22.2 -16.7, -15.9

-25.9 -18.4

-26.7 -24.6 -18.6, -18.4, -18.3, -18.1

molecule from parts of the micropore space, the argument in ref 15 for the nonideal mixing behavior, is probably less important for the narrow channel system of silicalite, and and resulting the IAS theory is more adequate. Energetic Heterogeneity from Structure. The pore walls in silicalite consist only of oxygen atoms and are therefore chemically homogeneous. However the varying shape of different pore sections creates locally different regions. The influence of this structure effect on loading, composition, and energetics will be now investigated in more detail. To see the extent of this structural heterogeneity and for calculating where the molecules adsorb within the pore system, we divided the intracrystalline space into intersection (I), straight (S), and zigzag (Z) regions as described by June et al.43 using the methanesilicalite potential energy surface. The three regions have relative sizes of 14.2%, 38.4%, and 47.4%, respectively. Table 3 presents the local minima of the zeolite-sorbate interaction in the different regions. A further tool for the characterization of energetic heterogeneity is the adsorption energy distribution (AED) function, F(U). The AED function for a microporous solid represents the normalized probability density of volume elements in the pore space with a zeolite-sorbate interaction energy between U and U + dU. This distribution provides information of global energetic heterogeneity of a solid, which arises from both structural and surface (chemical) heterogeneity. It is a fingerprint for the interaction of a specific adsorbate with the solid adsorbent. The AED function is usually evaluated by inverting the general integral equation for gas adsorption on heterogeneous solids:44,45

θt(P,T) )

∫θl(P,T,U) F(U) dU

(16)

∆

where θt(P,T) denotes the overall adsorption isotherm measured experimentally and ∆ is the range of the adsorption energy. The AED F(U) is usually found with advanced numerical methods on the basis of an a priori assumed model for the energy-dependent local adsorption isotherm θl(P,T,U), and U is the adsorption energy on an interaction site. Any independent calculation of the AED may be helpful to select or develop “correct” local adsorption isotherms, which can be used later for a determination of AEDs from experimental data. This is the motivation for the following discussion. Further information about the whole concept of AED functions, including methods for evaluating the AED from experimental data, can be found in, e.g., refs 44 and 45. The total AED functions for CH4 and CF4 in silicalite and their parts assigned to the three channel segments have been calculated from the three-dimensional particlezeolite interaction potential. They are shown in Figures 8 and 9. Because the pore walls in silicalite consist completely of oxygen atoms, the AED characterizes only an energetic heterogeneity due to the different geometrical (43) June, R. L.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1991, 95, 8866. (44) Jaroniec, M.; Mady R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988. (45) Rudzinski, W.; Everett, D. H. Adsorption of Gases on Heterogeneous Surfaces; Academic Press: New York, 1992.

6802 Langmuir, Vol. 13, No. 25, 1997

Figure 8. AED of CH4/silicalite potential energies among the different zeolite channel regions: intersection, straight channel, and zigzag channels. The three distributions add up to the total distribution.

Heuchel et al.

Figure 10. Distribution of observed adsorbate-silicalite potential energies for pure CH4 (1) and pure CF4 (2) at T ) 300 K and P ) 10 bar from GCMC for the three channel regions: intersection (I), straight channel (S), and zigzag channels (Z).

Figure 9. AED of CF4/silicalite potential energies among the different zeolite channel regions (see Figure 8).

Figure 11. Probability of adsorbate-silicalite potential energies (adsorbate energy distribution) for CH4 (1) and CF4 (2) in an approximately equal-molar adsorbate mixture (xCF4 ) 0.52) at T ) 300 K, P ) 10 bar, and yCF4 ) 0.25 from GCMC for the three-channel regions.

structure of the channel segments. For both molecules, CH4 and CF4, the energy range with significant number of adsorption sites in the pore space is only about 10 kJ/ mol. The difference of energy minima between S and Z channels in comparison to the intersections (I region) is only about 2 kJ/mol (CH4) and 4-5 kJ/mol (CF4). Therefore, for both components, we might expect a slightly preferred adsorption in the S and Z regions of the channel system with respect to the intersections based on energetics. Of course, entropic effects must also be taken into account. Also, if we compare, e.g., for CH4, the local AED for S and Z regions, we see that both regions have nearly the same local adsorption energy minimum (see also Table 3), but the Z region contains more of these preferred locations. Therefore, we would expect more molecules to reside in the Z regions based on the size of the regions. At very high temperature a single molecule would occupy every volume element of the accessible pore space with the same probability, nearly independent of the local adsorption energy. In that case the frequency of adsorption energies observed in a simulation run would agree approximately with the AED. However, under normal circumstances, this observed energy distribution of the adsorbate will deviate from the AED, because pore space elements with more favorable adsorption energies will be occupied preferentially, and if more than one molecule is in the system, they may disturb each other in finding the preferred adsorption sites. In Figure 10 we show distributions of the adsorbate-zeolite energies experienced by individual molecules during the GCMC simulation for pure CH4 and pure CF4 at T ) 300 K and P ) 10 bar. In both cases there are about 12 molecules per unit cell (see Figure 4). The comparison of the distributions for methane in Figure 10 with the AED for methane (Figure 8) shows a significantly higher frequency of adsorbate energies for

S and Z segments in the range of the first frequency maximum (-16 to -18 kJ/mol) in Figure 10 than in the respective AED function. The second AED maximum (-12 to -13 kJ/mol) is much less occupied in the actual distribution of Figure 10 than in Figure 8. The corresponding is true for pure CF4 as a comparison of Figures 10 and 9 shows. Next we consider the situation in an approximately equal molar mixture (about 6 CH4 and 6 CF4 per unit cell). The distributions of the interaction energies in Figure 11 show no significant shifting with respect to the functions for the pure components. This means the adsorption energies of CH4 are not seriously changed in comparison to the situation for pure CH4 through the presence of CF4 molecules. This is also expressed in the mean values of the adsorption energies in the different pore regions, shown in Table 4. This last analysis of energy distributions is a further argument for the ideal behavior of the mixture at this total loading. To summarize, the energetic differences in the pore regions are small, and therefore, the effect of this structure-related energetic heterogeneity will be small. We think this explains the relative constancy of many mean values, for example, of the potential energy 〈U〉, and also contributes toward the successful representation of mixture data by the IAS theory at a total loading of up to 12 molecules per unit cell. It should be mentioned that at T ) 200 K and P ) 1 bar, where mean packing in the pore is still higher, more pronounced shifts in the distributions of the adsorbate energies from pure components to mixtures can be observed. Figure 12 shows for pure CH4 (15.9 molecules per unit cell) and pure CF4 (14.0 molecules per unit cell) the distributions for the adsorbate energies during the simulation. For the gas phase composition yCF4 ) 0.1 the average mixture in the pore consists of about 7.8 methanes and 7.2 CF4 per unit cell. The respective frequencies of

Adsorption of CH4-CF4 Mixtures in Silicalite

Langmuir, Vol. 13, No. 25, 1997 6803

Table 4. Mean Energies (kJ/mol) of Zeolite-Sorbate Interaction for the Total Unit Cell and for Different Regions of the Channel System: Intersections (I), Straight Channels (S), and Zigzag Channels (Z) for Adsorbate Mixtures at T ) 300 K and P ) 10 bar CH4

CF4

yCF4

xCF4

mean

I

S

Z

0.00 0.10 0.25 0.50 0.75 0.90 1.00

0.00 0.28 0.52 0.75 0.90 0.96 1.00

-15.7 -15.7 -15.7 -15.7 -15.7 -15.8

-14.4 -14.5 -14.6 -14.7 -14.7 -14.8

-15.8 -15.9 -15.9 -15.8 -15.8 -15.8

-15.9 -16.0 -16.1 -16.2 -16.2 -16.3

mean

I

S

Z

-23.0 -22.9 -22.8 -22.7 -22.7 -22.7

-20.6 -20.6 -20.6 -20.6 -20.6 -20.5

-23.7 -23.8 -23.8 -23.8 -23.8 -23.8

-23.0 -22.9 -22.8 -22.8 -22.7 -22.7

Figure 12. Distribution of observed adsorbate-silicalite potential energies for pure CH4 (1) and pure CF4 at T ) 200 K and P ) 1 bar from GCMC for the three channel regions: intersection (I), straight channel (S), and zigzag channels (Z).

Figure 13. Probability of adsorbate-silicalite potential energies (adsorbate energy distribution) for CH4 (1) and CF4 (2) in an approximately equal-molar adsorbate mixture (xCF4 ) 0.48) at T ) 200 K, P ) 1 bar, and yCF4 ) 0.10 from GCMC for the three-channel regions.

adsorbate-zeolite energies are shown in Figure 13. The comparison of Figures 12 and 13 shows for methane, when going from pure adsorbate to an approximately equal molar mixture, a clear decrease of frequencies of adsorbate-zeolite energies in the straight channels, a clear increase in the intersections, and a slight increase for more favorable energies in the Z region. For CF4 we see a slight shift to more favorable energies in the Z region, a clear decrease of frequencies in the intersection, and in the S region an increase in frequencies for less favorable adsorbate-zeolite energies between -19 and -22 kJ/mol. Location of Molecules. For the pure components it has been shown43 that molecules avoid the energetically less favorable channel intersections, especially at low loading or low temperature. The situation for mixture siting is more complicated. An example for various compositions is presented in Figure 14. The segment loadings were determined from GCMC results at 300 K and P ) 10 bar, where the total loading is relatively constant with about 12 molecules per unit cell (see Figure 4). For comparison we show with dashed lines a hypothetical distribution assuming equal density in all volume elements of the channel regions. (Recall that the I, S, and Z regions as we have defined them are not of equal size.) When both components are present, methane is seen to

Figure 14. Distribution of CH4 (circle) and CF4 (triangle) molecules among the different channel regions: Intersection (I), straight (S), and zigzag (Z). The dotted lines represent the hypothetical ideal distribution dictated by the relative volumes of the channel regions. The data represent GCMC results for T ) 300 K and P ) 10 bar. The total loading is about 12 molecules per unit cell.

adsorb preferentially in the Z channels, while CF4 adsorbs more in the S channels. Thus at a nearly equal molar composition of about 5.7 methanes and 6.2 CF4 per unit cell there are on average 2.5 CF4 in the S region but only 1.9 methane molecules, while the Z region contains 3.1 methanes and only 2.9 CF4 molecules. For both pure component systems, the molecules adsorb somewhat preferentially in the Z region of the channel system. These trends can be also expressed as local composition within a particular region. We see, from Figure 14, for example, that at a composition of about 6 methanes and 6 CF4 per unit cell the composition within the S regions is 43% methane and 57% CF4, the composition in the Z regions is 51% methane and 48% CF4, while the overall composition is 48% methane and 52% CF4. This mild segregation of CF4 in the S channels and methane in the Z channels could be anticipated from the mean energies in Table 4 if one assumes (1) sorbate-sorbate interactions are small compared to zeolite-sorbate interactions and (2) the entropy of sorption in S and Z regions is comparable. Table 4 shows that the most favorable region energetically for methane is the zigzag channel and for CF4, the straight channel, and this is the siting preference we observe in Figure 14. The differences of local and mean composition are shown in Figure 15 above. For T ) 200 K and 1 bar the effect

6804 Langmuir, Vol. 13, No. 25, 1997

l Figure 15. Difference of local mole fraction of CF4, xCF , in 4 pore segments and in the whole pore system, xCF4, from GCMC data at conditions of Figure 14 (above) and for T ) 200 K and P ) 1 bar.

is still more pronounced. As can be seen in Figure 15 below, in the S-channel we reach a local deviation in mole fraction of about 0.15 from the mean composition. The implications of different loadings in the channel segments on diffusion are discussed elsewhere21 where the same siting trends have been found from MD simulations. It should be mentioned that in Figures 14 and 15 above the total number of molecules is approximately constant over the whole range of compositions, but in general the total number of molecules adsorbed will change with an isothermal variation of the gas phase composition (as in Figure 15 below). That is also the reason that the dashed lines in Figure 14 are not straight lines. Conclusions The molecular model presented here yields predictions of the adsorption of methane and tetrafluoromethane

Heuchel et al.

mixtures in silicalite in good agreement with experimental data. The mixtures behave ideally, and mixture behavior can be predicted from single-component adsorption using the IAS theory up to pressures of around 17 bar. The internal surface of silicalite is chemically homogeneous, but variations in pore size and shape create an energetic surface heterogeneity. This leads to local deviations in composition for different channel segment types. The extent of this heterogeneity can be expressed through the adsorption energy distribution (AED) function. We have compared the AED with the distribution of energies actually experienced by sorbates during our GCMC simulations. Comparison of the two distributions should be helpful in future development of adsorption theories using the AED to characterize sorbents. It is interesting to compare our results with the simulations of Dunne and Myers.15 They investigated similar mixtures of spherical molecules of different sizes in faujasite zeolites. Their model of faujasite presents a relatively homogeneous surface to the adsorbates, while in silicalite the pore geometry is mildly heterogeneous. However, adsorption of unequally-sized spherical molecules in silicalite obeys IAS theory, while at similar densities adsorption in the homogeneous faujasite model does not. We suggest that this is due to the different pore architectures of the two zeolites. Molecules in faujasite are in close contact with one another in the cages and are subject to partial exclusion effects, where large molecules are excluded from a portion of the micropore volume.15 Such effects seem to be unimportant in the narrow pores of silicalite for small molecules like methane and CF4. Both molecules can access the entire length of all pores, and due to the narrow, one-dimensional nature of a given channel segment, they contact fewer other sorbates and behave as an ideal adsorbed phase. Acknowledgment. The authors thank Professor J. Ka¨rger for helpful discussions. The Alexander von Humboldt Foundation is gratefully acknowledged for a research fellowship to R.Q.S. Part of this work was supported by Deutsche Forschungsgemeinschaft, Graduate College: Physical Chemistry of Interfaces. LA9708039