Adsorption of Liquid-Phase Alkane Mixtures in Silicalite: Simulations

Comparison with experiment gives us increased confidence to use .... The temperature programming of the GC oven was dependent on the mixtures used...
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Langmuir 2004, 20, 150-156

Adsorption of Liquid-Phase Alkane Mixtures in Silicalite: Simulations and Experiment Shaji Chempath,† Joeri F. M. Denayer,‡ Kurt M. A. De Meyer,‡ Gino V. Baron,‡ and Randall Q. Snurr*,† Department of Chemical Engineering and Center for Catalysis and Surface Science, Northwestern University, Evanston, Illinois 60208, and Department of Chemical Engineering, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, Belgium Received July 25, 2003. In Final Form: October 20, 2003 A combination of experimental and computational studies of adsorption from liquid-phase mixtures of linear alkanes in the zeolite silicalite is presented here. Configurational biased grand canonical Monte Carlo simulations combined with identity-swap moves are used to equilibrate the simulations in reasonable times. Interesting trends observed in experiments have been captured quantitatively by simulations. A siting analysis of the simulation data reveals that, during adsorption from a liquid mixture, shorter alkanes prefer the zigzag channels and longer alkanes concentrate in the straight channels of silicalite.

Introduction With increasing computer power and more efficient algorithms, molecular simulation has become an increasingly important tool in the study of adsorption.1 Early simulations examined spherical guest molecules in simple geometries such as slits or cylindrical pores. Today, however, fully atomistic models of complex adsorbents are standard, and flexible adsorbate molecules as long as the alkane C25 have been simulated.2 Grand canonical Monte Carlo (GCMC) has become the standard tool because it readily handles the phase equilibrium problem of interest. GCMC requires the insertion and deletion of new molecules in or out of the system. Completely random insertions are inefficient when much of the simulation cell is occupied by adsorbent atoms or adsorbed molecules. The biasing of insertions3,4 can help to solve this problem. Configurational bias (CB)-GCMC is particularly wellsuited to the simulation of chain molecules. CB-GCMC was originally developed for liquid and polymeric systems5-7 on the basis of the Rosenbluth sampling scheme.8 In this technique, inserted molecules are grown atom by atom in a manner that avoids overlap with other atoms in the system. When applied to adsorbed systems, a molecule can, thus, be threaded through empty pore space in an efficient manner. The adsorption of mixed linear and branched alkanes in zeolites is of interest because separation of these mixtures is important in the petroleum refining industry. Many authors have, therefore, studied the adsorption of * To whom correspondence should be addressed. Fax: 1-847467-1018. Tel.: 1-847-467-2977. E-mail: [email protected]. † Northwestern University. ‡ Vrije Universiteit Brussel. (1) Fuchs, A. H.; Cheetham, A. K. J. Phys. Chem. B 2001, 105, 7375. (2) Maginn, E. J.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1995, 99, 2057. (3) Mezei, M. Mol. Phys. 1980, 40, 901. (4) Snurr, R. Q.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1993, 97, 13742. (5) Siepmann, J. I.; Frenkel, D. Mol. Phys. 1992, 75, 59. (6) Frenkel, D.; Mooij, G.; Smit, B. J. Phys.: Condens. Matter 1992, 4, 3053. (7) Laso, M.; de Pablo, J. J.; Suter, U. W. J. Chem. Phys. 1992, 97, 2817. (8) Rosenbluth, M. N.; Rosenbluth, A. W. J. Chem. Phys. 1955, 23, 356.

alkanes by CB-GCMC especially in silicalite. Maginn et al.2 studied the low-occupancy sorption of n-alkanes up to C25 in silicalite using CB-GCMC. It was found that energetically unfavorable configurations, such as an alkane starting in a zigzag channel and ending in a straight channel, are less probable at low temperatures but become increasingly probable with increasing temperature. Macedonia and Maginn9 and Vlugt et al.10 used CB-GCMC to simulate adsorption of linear and branched alkanes in zeolites. Du et al.11 studied the adsorption of mixtures of short alkanes from the gas phase and observed an “adsorption preference reversal” for methane-ethane mixtures in which ethane is preferentially adsorbed at low pressures but methane becomes preferred at higher pressures. Recently, there have been several studies12-14 that dealt with adsorption from mixtures of linear and branched alkanes in silicalite. It should be noted that all of these mixture studies mentioned are done for adsorption from an equimolar mixture in the gas phase and conclusions are drawn on the basis of the observations at the equimolar conditions. In this paper, results are reported for adsorption from the liquid phase with varying mole ratio of adsorbates. Almost all molecular simulations of adsorption to date have been for gas-phase adsorption, and results are compared to gas-phase measurements. For molecules of increasing size, however, liquid-phase processing is more convenient and is widely used in adsorption separations. In principle, CB-GCMC can also be applied to liquid-phase adsorption. The inputs to the simulation are the fluidphase fugacities, which can be obtained if the equation of state for the liquid is known. The insertion and deletion moves, even with configurational biasing, become harder for liquid-phase adsorption, however, because the pores are close to being saturated with molecules. In this work, we implement identity-swap moves in addition to CB (9) Macedonia, M. D.; Maginn, E. J. Mol. Phys. 1999, 96, 1375. (10) Vlugt, T. J. H.; Zhu, W.; Kapteijn, F.; Moulijn, J. A.; Smit, B.; Krishna, R. J. Am. Chem. Soc. 1998, 120, 5599. (11) Du, Z. M.; Manos, G.; Vlugt, T. J. H.; Smit, B. AIChE J. 1998, 44, 1756. (12) Schenk, M.; Vidal, S. L.; Vlugt, T. J. H.; Smit, B.; Krishna, R. Langmuir 2001, 17, 1558. (13) Krishna, R.; Smit, B.; Calero, S. Chem. Soc. Rev. 2002, 31, 185. (14) Vlugt, T. J. H.; Krishna, R.; Smit, B. J. Phys. Chem. B 1999, 103, 1102.

10.1021/la035362+ CCC: $27.50 © 2004 American Chemical Society Published on Web 12/02/2003

Liquid-Phase Alkane Mixtures

moves to converge binary-mixture simulations of nalkanes in silicalite in reasonable times. The isotherms reported here each took only 10 days of computer time on a common 2.2-GHz Pentium-4 processor. Another common problem for molecular simulation is the lack of experimental data for mixtures. Comparison with experiment gives us increased confidence to use simulation as a predictive tool in the future. In this paper, we also report experimental liquid-phase adsorption isotherms for various mixtures of n-alkanes in a nonadsorbing solvent (2,2,4-trimethylpentane, which is commonly known as isooctane). The isotherms were generated for mixtures containing 98% isooctane and 2% adsorbing alkanes in the range of C5 (n-pentane) to C12 (n-dodecane). The ratio of the adsorbing alkanes in the liquid mixture was varied between 0 and 1. Adsorption was directly measured in terms of the number of molecules adsorbed rather than in terms of excess adsorption. Simulation results are used to help understand the experimental findings. Methods Thermodynamic Equilibrium. All simulations were done in the adsorbed phase (zeolite + sorbate), and the liquid phase which is in equilibrium with the adsorbed phase was not simulated. The required equilibrium between the liquid phase and the adsorbed phase was achieved by using the liquid-phase fugacities as inputs to the adsorbed-phase simulations. At equilibrium, the fugacities of all species are equal in all phases. The fugacities corresponding to the liquid-phase compositions were estimated using the PR-EOS. A detailed explanation of the procedure adopted here can be found in ref 15. An example of the calculations is as follows. To calculate the adsorption equilibrium of a mixture containing 98 mol % isooctane, 1.6 mol % n-hexane, and 0.4 mol % n-heptane in the liquid phase, a vapor-liquid equilibrium calculation is done for this mixture using the PengRobinson equation of state (PR-EOS) assuming the gas phase is ideal. The pressure in the gas phase for this mixture at 300 K is calculated to be 7.35 kPa. The mole fractions of isooctane, hexane, and heptane in the gas phase are 94.78, 4.84 and 0.38 mol %, respectively. The partial pressures of hexane and heptane are used as the fugacity inputs for the GCMC code.16 In the GCMC calculations, the gas phase is again assumed to be ideal. Because isooctane is nonadsorbing, it is not part of the GCMC simulations of the adsorbed phase. The nonadsorbing nature of isooctane was verified experimentally, as explained later in this paper. Force Field. All force-field parameters are listed in Table 1. These are exactly the same as the parameters used by Macedonia and Maginn.9 The atomic coordinates of the silicalite atoms are known from the X-ray work of Olson et al.17 The interaction of silicon atoms with the guest molecules was neglected in the force field, as is common. The zeolite framework was considered rigid, and a pretabulated potential map was used for the LennardJones interactions between zeolite oxygen atoms and adsorbed Lennard-Jones centers. Sorbate molecules were modeled using the united atom model for methylene and methyl groups. All intermolecular interactions were truncated at 13.0 Å. The simulation cell used had eight unit cells (two in each direction) of silicalite, and periodic boundary conditions were applied. The sorbate-sorbate interactions were fitted to the vapor-liquid equilibrium of alkanes by Siepmann et al.18 We have checked that these sorbate-sorbate parameters are consistent with the PR-EOS by comparing the specific volumes calculated from the (15) Chempath, S.; Low, J. J.; Snurr, R. Q. Molecular modeling of binary liquid-phase adsorption of aromatics in silicalite. AIChE J, accepted for publication. (16) Gupta, A.; Chempath, S.; Sanborn, M. J.; Clark, L. A.; Snurr, R. Q. Mol. Simul. 2003, 29, 29. (17) Olson, D. H.; Kokotailo, G. T.; Lawton, S. L.; Meier, W. M. J. Phys. Chem. 1981, 85 (15), 2238. (18) Siepmann, J. I.; Martin, M. G.; Mundy, C. J.; Klein, M. L. Mol. Phys. 1997, 90, 687.

Langmuir, Vol. 20, No. 1, 2004 151 Table 1. Force-field Parameters for Zeolite-Sorbate, Sorbate-Sorbate, and Intramolecular Interactionsa nonbonded

/kb, K

σ, Å

CH3-CH3 CH3-CH2 CH2-CH2 CH3-O CH2-O

98.1 67.9 47.0 80.0 58.0

3.77 3.84 3.93 3.60 3.60

bond angle

kθ, kcal rad-2

θ0, deg

CH3-CH2-CH2 CH2-CH2-CH2

62.1 62.1

114 114

torsion

a0/kb, K

a1/kb, K

a2/kb, K

a3/kb, K

CH3-CH2-CH2-CH2 CH2-CH2-CH2-CH2

0.0 0.0

355.0 355.0

-68.2 -68.2

791.3 791.3

a A harmonic potential is used for the bond angle bending V (θ) ) kθ(θ - θ0)2. Torsion angle potentials are treated with the cosine-expansion form V(φ) ) a0 + a1[1 + cos(φ)] + a2[1 - cos(2φ)] + a3[1 + cos(3φ)].

PR-EOS with the specific volumes reported by Siepmann et al.18 for n-heptane. CB-GCMC. CB-GCMC is very effective in simulating the adsorption of long alkanes in the channels of microporous materials. We have followed the methodology as described in ref 9, except that we did not use the high-loading first-atom sampling scheme suggested there. For the mixture simulations, we have also used identity-swap moves, performed as follows. In the case of binary mixtures adsorbed in the zeolite, a random molecule of a randomly chosen adsorbed species is chosen and an attempt is made to convert it to a molecule of the other species. To convert a shorter alkane (with s atoms) to a longer alkane (with l atoms), the last l - s atoms of the longer chain are grown as in a regular CB-GCMC insertion move starting from the s + 1st atom. The moves are accepted with probability

[

Pacc ) min 1,

f2N1 f1(N2 + 1)W

(

exp -

)]

V2 - V1 kT

(1)

where f1 and f2 are the fugacities of short and long alkanes, respectively. N1 is the number of molecules of the shorter alkane before the move, and N2 is the number of molecules of the longer alkane before the move. V1 is the energy of interaction for the shorter alkane molecule before the move. This includes the sorbate-sorbate interaction energy, sorbate-zeolite interaction energy, and intramolecular energy of the molecule. V2 is the energy of the new suggested configuration for the long alkane molecule. W is the Rosenbluth weight for disk sampling9 of the l - s united atom segments. For the reverse move (converting the l-atom long chain to an s-atom short chain), the positions of the first s atoms of the long chain are used as the coordinates for the new short chain and the remaining l - s atoms of the long chain are simply discarded. For this move, the bias, W, for growing the long chain to the current position starting from the s + 1st atom is calculated, and the moves are accepted with acceptance probability

[

Pacc ) min 1,

f1N2W f2(N1 + 1)

(

exp -

)]

V1 - V2 kT

(2)

The total number of CB-GCMC moves used during the simulations was typically 4-10 million steps for each point on the isotherm. Of these moves, 70% were translations or cutand-regrow moves and 30% were insertions, deletions, or identityswap moves. Experiments. The experiments were performed with H-ZSM5, obtained by de-ammoniating a NH4-ZSM-5 zeolite obtained from Zeolyst (CBV8014, SiO2/Al2O3 mole ratio of 80) in a muffle oven in the presence of air. The temperature was kept at 673 K for 40 h. Sorption uptake measurements were obtained by means of batch experiments. Zeolite samples (1 g) were put in 10-mL glass vials. After regeneration overnight (1 K/min from 303 to

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383 K, 1 h at 383 K, then at 1 K/min from 383 to 673 K, 24 h at 673 K), the vials were immediately (at 673 K) sealed with a cap with a septum to avoid the uptake of water and other components from the air and were weighed to determine the regenerated zeolite mass. A mixture of linear alkanes in a nonadsorbing solvent was prepared. All hydrocarbons used were of high purity grade (99%) from Merck and Acros. In most experiments, isooctane (99.5% purity, Acros) was used as the nonadsorbing solvent. A comparative experiment with triisopropylbenzene, a much more bulky molecule, as the solvent gave exactly the same adsorption capacities, confirming the nonadsorbing character of isooctane. Immediately after sealing the cap and weighing the sample, about 10 mL of the mixture was injected through the septum into the zeolite-containing vials, and another 10 mL was added to a vial without zeolite, to be used as a blank sample. Samples were kept at 277 K, to be sure no compounds could evaporate, and stirred frequently. In all measurements, liquid samples were taken after 24 and 48 h, to verify if equilibrium between the adsorbed and the bulk phases was achieved, and analyzed in a gas chromatograph (GC) with a flame ionization detector (FID). The GC was equipped with an HP-5 column (5%-diphenyl-95%-dimethylsiloxane copolymer), with a length of 30 m, film thickness of 0.25 µm, and internal diameter of 320 µm. The temperature programming of the GC oven was dependent on the mixtures used. For each sample (zeolite and blank), three GC analyses were performed and the average was used in further calculations. Typically, the standard error on the GC analysis was between 0.1 and 1.5%. The blank samples were used to obtain calibration lines giving the response of the GC FID to the hydrocarbon concentration for all the tested mixtures. In all cases, straight lines were obtained with a correlation factor R2 of at least 0.999. The amount adsorbed was obtained by calculating the mass balance for the external liquid and the adsorbed phases:

qsorbate )

0 0 + msolvent ) (wt%blank - wt%zeolite)(msorbate 100mzeolite

Figure 1. Experimental adsorption isotherms for octane (C8)/ nonane (C9)/isooctane mixtures in silicalite at 300 K. Open symbols are for experiment 1 (total concentration of octane and nonane ) 8 mol %), and closed symbols are for experiment 2 (total concentration of octane and nonane ) 2 mol %). Circles are for octane loading, and squares are for nonane loading. In some cases, error bars are not visible because they are smaller than the size of the symbols.

(3)

where wt%blank is the concentration of the sorbate in the blank sample (in wt %), wt%zeolite is the equilibrium concentration of 0 the sorbate in the zeolite-containing sample (in wt %), msorbate is the amount of sorbate added to the zeolite-containing vial (in g), 0 msolvent is the amount of nonadsorbing solvent added to the zeolite-containing vial (in g), and mzeolite is the amount of zeolite in the zeolite-containing vial (in g). In these calculations, the correction theoretically needed for the reduction in the total external liquid volume in the zeolite-containing vial as a result of adsorption of the linear alkanes was negligible and not accounted for. To obtain a high sensitivity in the adsorption measurements, the total concentration of the adsorbing components was about 0.20 mL/g zeolite. The concentration of isooctane was close to 98 mol % in most experiments. One experiment was performed with a 4-times-higher concentration of adsorbing components (about 8 mol %) to verify the reproducibility of the method and the effect of the concentration on the amounts adsorbed. Figure 1 compares the octane/nonane isotherms obtained using two different concentrations of the adsorbing components. In this graph, the error bars represent the error in the calculation, obtained by accounting for the standard error on the GC analysis and the experimental errors on the zeolite and liquid mixture weight. For the experiment with the lowest concentration (experiment 2, 2 mol %), the experimental error is very small, as indicated by the error bars. A somewhat larger error is encountered at a higher concentration of the adsorbing components (experiment 1, 8 mol %), with an absolute error up to 0.45 molecules per unit cell. Nevertheless, both experiments give almost exactly the same adsorption isotherms, proving the accuracy and reliability of the used method. Sometimes experimental data for liquid-phase adsorption is given in terms of the excess amount adsorbed rather than the absolute number of molecules adsorbed. Simulations give the absolute number of molecules adsorbed, from which excess adsorption can be calculated. In a previous study,15 we have

Figure 2. Adsorption isotherms from experiments and CBGCMC simulations for pentane (C5)/hexane (C6)/isooctane mixtures in silicalite at 300 K (simulations) and 277 K (experiments). compared the excess adsorption of aromatics from simulations against experimental excess adsorption data from literature. For that system, there were no data of absolute adsorption available. The current experiments on alkanes directly report the absolute number of molecules adsorbed, and all the data reported here are in terms of the absolute amount adsorbed. The use of a nonadsorbing solvent allowed the determination of the absolute adsorption in our experiments.

Results Adsorption isotherms for various n-alkane binary mixtures in silicalite were measured experimentally and calculated by CB-GCMC simulations. The results from the experiment and the simulation are compared in Figures 2-9 for C5/C6, C5/C7, C6/C7, C6/C8, C6/C10, C7/C8, C8/C9, and C8/C12. The concentration of the nonadsorbing solvent (isooctane) in the liquid phase was maintained at 98 mol % in all cases. The shapes of the isotherms vary dramatically among these mixtures. In all cases, there is very good agreement between the simulated and the experimental results. The simulations were performed at 300 K, while the experiments were done at 277 K. To check the effect of this difference in temperature on the adsorption, simulations for one system were also performed at 277 K. Figure 3 includes simulated points at both 277 and 300 K for the C5/C7 system. It can be seen that the results are relatively insensitive to the difference in temperature, justifying the comparison with the experimental results at 277 K in the other figures.

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Langmuir, Vol. 20, No. 1, 2004 153

Figure 3. Adsorption isotherms from experiments and CBGCMC simulations for pentane (C5)/heptane (C7)/isooctane mixtures in silicalite at 300 K (simulations) and 277 K (experiments and simulations).

Figure 6. Adsorption isotherms from experiments and CBGCMC simulations for hexane (C6)/decane (C10)/isooctane mixtures in silicalite at 300 K (simulations) and 277 K (experiments).

Figure 4. Adsorption isotherms from experiments and CBGCMC simulations for hexane (C6)/heptane (C7)/isooctane mixtures in silicalite at 300 K (simulations) and 277 K (experiments).

Figure 7. Adsorption isotherms from experiments and CBGCMC simulations for heptane (C7)/octane (C8)/isooctane mixtures in silicalite at 300 K (simulations) and 277 K (experiments).

Figure 5. Adsorption isotherms from experiments and CBGCMC simulations for hexane (C6)/octane (C8)/isooctane mixtures in silicalite at 300 K (simulations) and 277 K (experiments).

Figure 8. Adsorption isotherms from experiments and CBGCMC simulations for octane (C8)/nonane (C9)/isooctane mixtures in silicalite at 300 K (simulations) and 277 K (experiments).

For equilibrium-based separations (e.g., chromatography), it is important to know the selectivity in the adsorbed phase compared to the liquid phase. The reduced mole fractions (from the simulation) of the longer alkanes in the adsorbed phase are plotted versus the reduced mole fractions in the liquid phase in Figure 10. These reduced mole fractions are defined, neglecting the isooctane solvent, as the ratio of molecules of longer alkane to the total number of adsorbing alkanes (only for Figures 10 and 11). If the mole fraction inside the zeolite is larger than that in the liquid phase, the longer alkane is selectively adsorbed. The mixture of C6/C7 shows selectivity for the shorter alkane over the whole range of compositions. The mixtures of C5/C6, C5/C7, C6/C8, and C6/C10 show

selectivity for shorter alkanes over some concentration range and for the longer one over another range. They, thus, exhibit azeotropy and a reversal in selectivity depending on composition. The mixtures of C7/C8, C8/C9, and C8/C12 show selectivity for the longer alkane over the whole concentration range. A comparison of the experimental and the simulated selectivities is done in Figure 11 for two cases: C6/C7 and C8/C9. It is remarkable that good agreement is obtained even when the data is plotted in this format. This was found to be true for all other cases too (not shown). However, it should be noted that, for the case of C6/C7, simulations do not predict an azeotrope formation, whereas the experimental data, which deviate slightly from the simulation data, predict an azeotrope

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Figure 9. Adsorption isotherms from experiments and CBGCMC simulations for octane (C8)/dodecane (C12)/isooctane mixtures in silicalite at 300 K (simulations) and 277 K (experiments).

Figure 10. Reduced mole fractions of the longer alkane in the zeolite and liquid phase at 300 K for various mixtures predicted by CB-GCMC simulations. These mole fractions are calculated on the basis of the number of molecules of adsorbing alkanes only. For points lying above the dotted line (y ) x), the longer alkane is selectively adsorbed into the zeolite.

Figure 11. Comparison of the experimental (Exp.) and simulation (Sim.) selectivities for C6/C7 and C8/C9 systems. These reduced mole fractions are calculated on the basis of the number of molecules of adsorbing alkanes only. The mole fraction of the longer alkane is plotted here. For points lying above the dotted line (y ) x), the longer alkane is selectively adsorbed into the zeolite.

formation at around a mole fraction of 0.35 in the liquid phase. For adsorption from the gas phase, selectivity for the longer alkane is the expected behavior on the basis of the higher heat of adsorption, but smaller alkanes may pack more efficiently. For adsorption from the liquid phase, the heat of adsorption from a liquid should be considered,

Chempath et al.

Figure 12. Different sections in the channel structure of silicalite. The light-gray sections running along the x direction are the zigzag channels. The dark-gray sections running in the y direction are the straight channels. The black regions are the intersections. The atoms of the zeolite crystal lattice are not shown for clarity. The sites were determined as described previously15 using a probe Lennard-Jones sphere with /k ) 148 K and σ ) 3.73 Å.

which can be approximately obtained as the difference in the gas-phase heat of adsorption and the heat of vaporization. In addition, certain chain lengths fit very nicely in the length of the sinusoidal channels, which affect their packing. Denayer et al.19 explain the observed behavior in terms of these factors. The good agreement shown here between the experimental data and the simulation data should be attributed to the accuracy of the force-field parameters. The zeolitesorbate interaction parameters used here had been optimized for the adsorption of alkanes in silicalite to match the Henry’s law constants and isosteric heats of sorption.14 We suggest as a general result that, if accurate parameters for single-component sorption are available, then binary GCMC can be used to accurately predict mixture adsorption. Thus, binary GCMC can be considered as an alternative to theories such as ideal adsorption solution theory,20 which attempt to predict multicomponent adsorption from single-component adsorption data. The sorbate-sorbate parameters used here were optimized for the vapor-liquid equilibrium of alkanes.18 However, they are not as critical because the sorbatesorbate interaction energies are only typically 5% of the total energy of the system. The zeolite-sorbate parameters are much more important for obtaining accurate results for adsorption thermodynamics. Siting. Silicalite can be divided into three different adsorption regions (sites), as shown in Figure 12. The methodology used to quantitatively define these sites was proposed by June et al.21 and is also described in our recent work.15 Silicalite has straight channels running in the y direction and intersecting zigzag channels running in the x direction. The length of the y direction channel is essentially the length of the unit cell, which is 20 Å. The curvilinear length of the zigzag channel was estimated to be 21.5 Å. Usually, this three-site model is used to describe adsorption in silicalite. However, the region marked as the intersection is rather small. From visualizations of the simulations, we observed that long alkanes (e.g., C12) stretch from one end of the unit cell to the other end in (19) Denayer, J. F. M.; De Meyer, K.; Martens, J. A.; Baron, G. V. Angew. Chem., Int. Ed. 2003, 42 (24), 2774. (20) Myers, A. L.; Prausnitz, J. M. AIChE J. 1965, 11, 121. (21) June, R. L.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1991, 95, 8865.

Liquid-Phase Alkane Mixtures

Figure 13. Adsorption isotherm of the C7/C8 mixture separated for individual adsorption sites. Z represents the zigzag channels and S represents the straight channels.

a zigzag channel without touching the region marked as the intersection. Figure 12 also shows that the zigzag channels run uninterrupted across the unit cell. (This is especially visible in the top zigzag channel of Figure 12.) On the basis of this observation, we reduced the number of sites in silicalite to two: zigzag channels and straight channels. The regions marked as intersections were lumped with the straight channels. This is equivalent to saying that the zigzag channels and straight channels just touch each other in a small region, but neither is cut off by the other. This representation simplifies the analysis of linear alkane adsorption. An alkane is defined to be in a straight channel site if the head and tail of the chain both reside in the straight channel sections. Similarly, if the head and tail are in zigzag channel sections, then the alkane is said to be in the zigzag channel site. This definition works well for alkanes up to C7. From C8 onward, more than 25% of the molecules are found to be in a mixed configuration, where the head is in one site and the tail is in another site. For C12, up to 45-50% of the molecules are found to be in a mixed configuration. The site-based isotherm for the mixtures of C7/C8 is given in Figure 13. Only the molecules in pure zigzag or pure straight channels are considered. The molecules in mixed configurations are not considered in this case. The figure shows that alkanes do not distribute uniformly among the adsorption sites. More C7 molecules are adsorbed in zigzag channels than in straight channels. For C8, more molecules are adsorbed in straight channels than in zigzag channels. This trend that the longer molecule adsorbs preferentially in the straight channels is observed for all of the alkane mixtures simulated. A snapshot of the C5/C7 simulation is shown in Figure 14, where this segregation can be clearly seen. All the pentane molecules are in the zigzag channels (along the x direction), and most of the heptane molecules are in the straight channels (along the y direction). The sorbate-zeolite energies and the intramolecular energies were calculated for molecules in straight channels and zigzag channels separately. The results are plotted in Figure 15. Again, the molecules in mixed configurations are not considered. It can be seen that, in general, the energies of adsorption are lower in the straight channels than in the zigzag channels. Except for C5 and C12, all molecules have lower zeolite-sorbate energies in the straight channels, and for all molecules, the intramolecular energies are lower in the straight channels. This implies that, for any given molecule, the straight channel is preferred. For these linear alkanes, the most stable conformation in the gas phase is the all-trans linear form. Inside the zigzag channels, they are forced to bend by

Langmuir, Vol. 20, No. 1, 2004 155

Figure 14. Snapshot from the C5/C7 mixture simulations at 300 K for liquid-phase concentrations of 1.2% pentane and 0.8% heptane. The thin lines represent the bonds between the silicon and the oxygen atoms of the silicalite lattice. The light-gray spheres represent united atoms of the pentane molecules. Darkgray spheres represent united atoms of the heptane molecules. A united atom approach, where the CH3 or CH2 groups are shown as single spheres, is used here, as in the simulations.

Figure 15. Energies of adsorbed n-alkanes in silicalite. Circles are for the intramolecular energy (marked on the right axis), and squares are for the zeolite-sorbate energy (marked on the left axis). Closed symbols represent energies in straight channels, and open symbols represent energies in zigzag channels. These energies are calculated as averages from all the simulations reported in Figures 2-9.

changing some of the bond-torsion angles from trans to gauche. This leads to an increase in intramolecular energy. The zeolite-sorbate energies are higher in the zigzag channel because even after making one or two trans-togauche turns, the alkane still does not fit as well in the zigzag channel as it fits in the straight channels. Maginn et al.2 also observed that at low temperatures the long alkanes prefer the straight channels on the basis of configurational biased simulations at low occupancy conditions. In the case of decane in straight channels, on average 0.1 bonds are found to be in the gauche position. In the zigzag channels, this number increases to 1.5 bonds. For decane molecules that are in mixed configurations, 2.6 bonds are found to be in the gauche position. Similar trends are observed for C8, C9, C10, and C12. It should be noted that the bending of molecules from one channel to another is very important in filling the channels efficiently.22 If all molecules adsorbed only in straight channels or zigzag channels, much space would be left empty in the zeolite, leading to a much lower loading than is observed experimentally. Our previous studies of single-component sorption22 have shown that alkanes shorter than C6 occupy (22) De Meyer, K. M. A.; Chempath, S.; Denayer, J. F. M.; Martens, J. A.; Snurr, R. Q.; Baron, G. V. J. Phys. Chem. B 2003, 107 (39), 10760.

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spaces between intersections in either straight or zigzag channels, whereas the alkanes from C8 onward position themselves so that their middle carbon atom is near the intersection and the head end and tail end are hanging into the straight or zigzag channels. This is true for multicomponent adsorption also, as verified by looking at the probability distribution of the middle atom of the alkane molecules in the simulations (not shown). Conclusion We have performed CB-GCMC simulations with identity-swap moves for the adsorption of liquid mixtures of n-alkanes in silicalite from C5 to C12. Batch adsorption measurements for the same systems were also carried out. Excellent agreement between the experiments and simulations is observed for all cases. It appears that, if

Chempath et al.

the force-field parameters are optimized for singlecomponent adsorption in microporous materials, they work very well for multicomponent adsorption as well. A sitebased analysis of the adsorption data reveals that, in general, shorter alkanes are pushed into the less favorable zigzag channels while the longer alkanes occupy the straight channels. Both the intramolecular energies and the zeolite-sorbate energies are lower for alkanes adsorbed in straight channels compared to those in zigzag channels. Acknowledgment. This work has been supported by the U.S. National Science Foundation. J.F.M.D is grateful to the F.W.D.-Vlaanderen for a postdoctoral fellowship. LA035362+