Experimental and Computer Simulation Studies of the Adsorption of

different models for MCM-41 with different degrees of surface heterogeneity. Model 1 has a nearly homogeneous pore surface while model 2, which is der...
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Experimental and Computer Simulation Studies of the Adsorption of Ethane, Carbon Dioxide, and Their Binary Mixtures in MCM-41 Yufeng He and Nigel A. Seaton* Institute for Materials and Processes, School of Engineering and Electronics, University of Edinburgh, Kenneth Denbigh Building, King’s Buildings, Mayfield Road, Edinburgh EH9 3JL, U.K. Received June 13, 2003. In Final Form: September 1, 2003 The adsorption of pure ethane and carbon dioxide, and binary mixtures of these components, in MCM-41 has been studied experimentally and by grand canonical Monte Carlo (GCMC) simulation, at temperatures between 264 and 303 K and pressures up to 3 MPa. The experimental isotherms were measured using a bench-scale, open-flow adsorption/desorption apparatus. The simulations were carried out using three different models for MCM-41 with different degrees of surface heterogeneity. Model 1 has a nearly homogeneous pore surface while model 2, which is derived from a matrix of crystalline R-quartz, has a heterogeneous but nevertheless regular surface. These two models give generally good predictions of the adsorption of ethane in MCM-41, except at low pressures where the surface heterogeneity of MCM-41 dominates the adsorption. Model 3 has an amorphous structure, generated by an energy-minimization procedure; this model gives better predictions for ethane adsorption, especially at low pressures, suggesting that it incorporates a good representation of the heterogeneity of the real MCM-41 material. Excellent predictions of the adsorption of pure carbon dioxide and binary mixtures of ethane and carbon dioxide in MCM-41 are obtained with model 3, further confirming the realism of this model. Long-ranged electrostatic interactions are included for the simulation of carbon dioxide; these interactions, which play an important role, are treated by a simple one-dimensional summation method, which gives an accurate calculation of the potential.

1. Introduction MCM-41 consists of a hexagonal array of long, unconnected cylindrical pores with diameters that can be tailored within the range 15-200 Å.1,2 This regular, and geometrically simple, pore structure allows us to use MCM41 as a model adsorbent to test our understanding of adsorption at the molecular level and to evaluate methods for the prediction of multicomponent adsorption equilibrium.3 Atomistic simulations of adsorption in MCM-41 materials have been carried out for a number of adsorptives, such as pure nitrogen,4,5 and binary mixtures of methane and carbon dioxide,6 dichloromethane and nitrogen,7 and methane and ethane.3 Different models have been proposed for MCM-41, from the simplest, one-dimensional potential which is only a function of the distance of the adsorptive molecule from the center of the pore, to more complex models generated by a simulation of the MCM41 matrix. Maddox and Gubbins4 used a one-dimensional potential, in which the adsorbent is completely homogeneous, to simulate the adsorption of nitrogen in MCM-41. * To whom correspondence should be addressed. (1) Kresge, C. T.; Leonowicz, M. E.; Roth, W. J.; Vartuli, J. C.; Beck, J. S. Nature 1992, 359, 710. (2) Beck, J. S.; Vartuli, J. C.; Roth, W. J.; Leonowicz, M. E.; Kresge, C. T.; Schmitt, K. D.; Chu, C. T.-W.; Olsen, D. H.; Sheppard, E. W.; McCullen, S. B.; Higgins, J. B.; Schlenker, J. L. J. Am. Chem. Soc. 1992, 114, 10834. (3) Yun, J.-H.; Duren, T.; Keil, F. J.; Seaton, N. A. Langmuir 2002, 18, 2693. (4) Maddox, M. W.; Gubbins, K. E. Int. J. Thermophys. 1994, 15 (6), 1115. (5) Maddox, M. W.; Gubbins, K. E. Langmuir 1997, 13, 1737. (6) Koh, C. A.; Montanari, T.; Nooney, R. I.; Tahir, S. F.; Westacott, R. E. Langmuir 1999, 15, 6043. (7) Koh, C. A.; Westacott, R. E.; Nooney, V. B.; Tahir, S. F.; Tricarico, V. Mol. Phys. 2002, 100 (13), 2087.

Maddox et al.5 subsequently introduced a heterogeneous pore model, in which the MCM-41 structure was modeled as an amorphous array of oxygen atoms, each one interacting with adsorptive molecules via the LennardJones potential. In their work, the pore wall was divided into eight equal sectors, and the oxygen-nitrogen interactions for all the oxygen atoms in each of the sectors were given a different Lennard-Jones energy. Koh et al. proposed a method to generate an MCM-41 model to study the binary mixtures of carbon dioxide and methane,6 and dichloromethane and nitrogen:7 silicon and oxygen atoms were inserted at random into a unit cell of a size determined by X-ray diffraction until the correct density of atoms was obtained. Two criteria were used to decide if each randomly generated position was acceptable: that the position was neither within the free volume of the pore nor within 3 Å of any the other atoms. Yun et al. used a regular array of oxygen atoms arranged on a rectangular grid of three concentric cylinders to study the adsorption of methane-ethane binary mixtures in MCM-41.3 The work reported here has two aims: (i) to study the influence of the surface heterogeneity of MCM-41 on the adsorption of gas mixtures containing components of different polarity, and on the adsorption of the corresponding pure components, and (ii) to evaluate the performance of MCM-41 models of differing complexity, combined with Monte Carlo simulation of adsorption, in predicting adsorption. The heterogeneity of an adsorbent can be broken down into two aspects:8 energetic (or surface) heterogeneity and structural heterogeneity. Structural heterogeneity is caused by the presence of pores of different sizes, shapes, and connectivities,9 while energetic heterogeneity results (8) Nicholson, D. Langmuir 1999, 15, 2508. (9) Kruk, M.; Jaroniec, M.; Sayari, A. Langmuir 1999, 15, 5683.

10.1021/la035047n CCC: $25.00 © 2003 American Chemical Society Published on Web 10/30/2003

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Figure 1. Three models for MCM-41 used in this study: red, oxygen; blue, silicon.

from surface irregularities as well as from the presence of functional groups and impurities. There is essentially no structural heterogeneity for MCM-41 materials, since the pore channels in MCM-41 are almost identical to each other and are unconnected.1,2 Thus, in studying MCM-41 materials we are dealing only with energetic heterogeneity. Three different models of MCM-41 materials with different forms and extents of energetic heterogeneity are considered in this study. Two adsorptivessethane and carbon dioxidesare used as pure gases and as binary mixtures of different compositions. Ethane is essentially nonpolar and probes the physical structure of the pore. Carbon dioxide has a strong quadrupole moment and is therefore sensitive to electrostatic interactions with the adsorbent. As both adsorptives are relatively low molecular weight gases, not much larger than the oxygen atoms on the pore wall, both should be sensitive to surface roughness. 2. Experimental Section Pure-silica MCM-41 samples were supplied by Chonnam National University, Korea. Standard nitrogen adsorption measurements at 77 K gave a BET specific surface area and BJH average pore diameter for this sample of 1013.7 m2/g and 26.96 Å, respectively. The ethane and carbon dioxide gases were supplied by BOC with a purity of 99.99%. The experimental isotherms were measured using a bench-scale, open-flow adsorption/desorption apparatus that allows both the static volumetric measurement of pure-component isotherms and the measurement of mixture adsorption using a flow-through technique. Puregas adsorption experiments were carried out at temperatures from 264.6 to 303.2 K and pressures up to 3 MPa. Binary mixture experiments were carried out at 264.6 K, with gas-phase mole fractions of carbon dioxide of 12.45%, 47.06%, 58.71%, and 89.51%, and at pressures up to 2 MPa. Full details of the operating procedure can be found in ref 3. The uncertainty in the amounts adsorbed in the pure-component and binary experiments is less than 0.2% and 1.5%, respectively.

3. Monte Carlo Simulations. I. Model Development for MCM-41 Three models of MCM-41, all based on a one-dimensional channel, with different degrees of surface heterogeneity and complexity, were used in this study. A graphical representation of the three models is shown in Figure 1. Model 1 is created by the method of Yun et al.,3 in which a pore with a homogeneous structure at the atomic scale is generated by forming three concentric cylinders of oxygen atoms (which are arranged in a regular array) with a layer of silicon atoms between each layer of oxygen atoms; the innermost (i.e. surface) layer is of oxygen atoms. This model does not reproduce the structure of real amorphous silica but rather places the silicon and oxygen atoms in a simple geometrical arrangement. The skeletal density of the model pore is set to be 2.2 g/cm3, corresponding to the density of amorphous silica, which

one would expect to apply also to the MCM-41 matrix. Fourteen rows of oxygen atoms are generated in the z direction, which gives a pore length of 40.8 Å; for dispersion interactions this is sufficiently large, with the use of periodic boundary conditions, to eliminate the influence of finite system size. Model 2 is based on the R-quartz crystal structure with a skeletal density of 2.66 g/cm3: the value for the R-quartz crystal at room temperature, which is higher than the density of amorphous silica. A block of R-quartz is generated, and then a series of model pores is created by removing the oxygen and silicon atoms whose centers are within the volume of a set of cylinders (whose radius is slightly smaller than the effective pore size, taking into account the size of the atoms removed near the surface of the cylinder). Then those silicon atoms at the pore surface that are bound to fewer than four oxygen atoms are saturated by oxygen atoms. Oxygen atoms with fewer than two silicon atoms attached to them are then saturated by hydrogen atoms, with an oxygen-hydrogen bond of length of 0.96 Å placed in the direction of the removed silicon atom. The pore length is 39.5 Å in model 2; since the skeletal density of this model is 2.66 g/cm3, higher than the density of amorphous silica, the number of oxygen atoms is higher than that in model 1. In model 3 an amorphous silica surface is generated using a stochastic simulation of the silicon and oxygen atoms forming the matrix. Oxygen and silicon atoms in a ratio of 2:1 are first randomly generated in a cylindrical simulation box with the restrictions that (1) at most four oxygen atoms are within 1.65 Å (the approximate length of a silicon-oxygen bond) of a silicon atom and (2) at most two silicon atoms are within 1.65 Å of an oxygen atom. The atoms are then allowed to move around in the simulation box according to an energy minimization algorithm with the potential of the whole system calculated using the BKS equation,10,11 keeping the coordination numbers of silicon and oxygen atoms at the physically correct values of 4 and 2, respectively. The BKS potential consists of a long-ranged Coulomb term and short-ranged repulsion and dispersion interactions:

Φij ) qiqj/rij + Aij exp(-bijrij) - cij/rij6

(1)

Values for the parameters Aij, bij, and cij and the atomic charges for the application of the BKS potential to silica can be found in ref 10. Periodic boundary conditions are applied in the z direction of the cylinder, parallel to the pore wall. The pore length is set to be 40 Å. The system is equilibrated for 5 000 000 moves before a model pore is cut following the same procedure as that in model 2. (10) Beest, B. W. H. van; Kramer, G. J.; Santen, R. A. van Phys. Rev. Lett. 1990, 64 (16), 1955. (11) Mischler, C.; Kob, W.; Binder, K. Comput. Phys. Commun. 2002, 147, 222.

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Table 1. Summary of the Properties of the Three MCM-41 Models model 1

model 2

model 3

1764 882 2.20 16.38 40.81

2852 1426 2.66 17.11 39.50

1816 908 2.20 18.27 40.00

no. of oxygen atoms no. of silicon atoms skeletal density, g/cm3 pore radius, Å pore length, Å

Table 2. Potential Parameters for MCM-41 (ref 14) and Ethane Used in GCMC Simulations O in MCM-41 Si in MCM-41 C2H615

/kB, K

σ, Å

q, e

185.0 (ref 3)

2.708 (ref 6)

-0.09 +0.18

139.8

3.512

lE-E, Å

2.353

The pore-wall thickness in all the three models is set to be between 8 and 10 Å, a value typical of MCM-41 materials,12 which corresponds approximately to the width of three layers of oxygen atoms. The pore size was determined using the method of Yun et al.,3 in which it is adjusted to fit the pore-filling transition in a particular adsorption isotherm, ideally at the lowest experimental temperature. The pore size for each of the three models was optimized by carrying out simulations of the adsorption of ethane at 264.6 K, with different values of the pore radius, choosing the radius that best fitted the experimental isotherm. The properties of the three models are listed in Table 1. 4. Monte Carlo Simulations. II. Potentials and Long-Ranged Interactions The oxygen atoms in the MCM-41 matrix are represented by single spherical Lennard-Jones sites with negative partial charges. Positive partial charges are applied to the silicon atoms in the matrix to make the whole model pore structure electrically neutral. The hydrogen atoms have a small effect on adsorption and are ignored in the potential calculation for both the adsorptives. (In effect, the contribution of surface hydrogens is subsumed into the oxygen-adsorptive interaction.) The ethane molecule is represented by two uncharged Lennard-Jones sites. The interaction between the sites in the ethane molecule and the oxygen atoms in the MCM41 matrix is given by a truncated Lennard-Jones potential. The silicon atoms in the matrix are ignored, since their low polarizability results in a negligible dispersion interaction.13 In the simulations, the Lennard-Jones potential was truncated at 19.05 Å in all three models. The potential parameters for ethane and the MCM-41 model pore are summarized in Table 2. Carbon dioxide was represented by the EPM model,16 since this model is able to accurately reproduce the experimental densities of coexisting bulk liquid and vapor phases and the saturation pressure, and it should thus be capable of giving a good representation of both high-density and low-density adsorbed phases. In the EPM model, the carbon and oxygen atoms are represented by LennardJones sites, which also have partial charges. (The setting of the values of the partial charges on the oxygen and (12) Ciesla, U.; Schuth, F. Microporous Mesoporous Mater. 1999, 27, 131. (13) Bezus, A. G.; Kiselev, A. V.; Lopatkin, A. A.; Pham Quang Du. J. Chem. Soc., Faraday Trans. 2 1978, 74, 367. (14) Burchart, E. D.; Vandegraaf, B.; Vogt, E. T. C. J. Chem. Soc., Faraday Trans. 1992, 88, 2761. (15) Fischer, J.; Heinbuch, U.; Wendland, M. Mol. Phys. 1987, 61, 953. (16) Harris, J. G.; Yung, K. H. J. Phys. Chem. 1995, 99, 12021.

silicon atoms is addressed in section 5.) The potential parameters for the EPM model can be found in ref 16. The interactions among the various sites in the carbon dioxide and ethane molecules, and the atoms in the MCM41 matrix are given by the sum of a truncated LennardJones potential and an electrostatic contribution:

{

Uij(r) )

[( ) ( ) ]

4ij

σij

12

-

r

σij r

l

qiqj

k)-l

4π0|r˜ + k˜ L|

∑

6

qiqj

l

+

∑ ˜ + k˜ L| k)-l 4π |r

r e rcut

0

(2) r > rcut

Here r is the distance between the centers of two interacting sites of type i and j; rcut is the cutoff distance; q is the partial charge applied to each site; l is the number of images of the main simulation box in the +z and -z directions; L is the length of the simulation box; and 0 is the vacuum permittivity (8.854 19 × 10-12 C2 J-1 m-1). k˜ is a vector in the z direction with |k˜ | ) k. The LennardJones parameters for the unlike interactions are calculated using the Lorenz-Berthelot rules. Note that the only contribution of the silicon atoms is via electrostatic interactions with the sites in the carbon dioxide molecules. The electrostatic interactions are long-ranged, and the summation over all the molecules involved (in the main simulation cell and replica cells) is in principle only conditionally convergent. The Ewald summation17 is a convergent series and is widely used for the treatment of long-ranged interactions in the simulation of bulk systems. For simulations in confined systems with two periodic dimensions, such as simulations of adsorption in slitshaped pores, several methods have been used.18-20 However, none of these methods are suitable for the treatment of long-ranged electrostatic interactions in the one-dimensional pores of MCM-41, and an alternative technique must be used. In this work, we have used a simple summation over replica systems in the z direction which, for the interactions involved here (in effect, quadrupole-quadrupole and quadrupole-charge interactions, though the quadrupole on the carbon dioxide is represented by point charges), turns out to be rapidly convergent. In this system, the most slowly converging electrostatic interaction is between a carbon dioxide molecule and a charged atom in the matrix. The summation procedure was assessed by calculating this interaction over different numbers of replica systems in the z direction. The potential between a carbon dioxide molecule at a randomly chosen position and an oxygen atom on the surface of the pore is calculated first in the main simulation cell (l ) 0 in eq 2), then with two additional images (l ) 1), and so on. The results, together with corresponding results for the interaction between carbon dioxide molecules, are shown in Table 3. Since the potential for l ) 100 of the main simulation cell is identical, to seven significant figures, to the value for l ) 1000, we treat this as the exact result in calculating the error. (The rate of convergence of the summation is insensitive to the choice of locations of the carbon dioxide molecules and the oxygen atom.) (17) Jorge, M.; Seaton, N. A. Mol. Phys. 2002, 100 (13), 2017. (18) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1989. (19) Rhee, Y. J.; Halley, J. W.; Hautman, J.; Rahman, A. Phys. Rev. B 1989, 40 (1), 36. (20) Lekner, J. Physica A 1991, 176, 485.

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Table 3. Convergence of the Summation for the Electrostatic Interaction in Eq 2

l

surface oxygen cation/CO2, 1 × 10-22 J

0 1 2 3 4 5 6 7 10 100 1000

2.635 311 2.646 565 2.648 815 2.648 406 2.648 201 2.647 998 2.647 997 2.647 895 2.647 792 2.647 588 2.647 588

error, % -0.52 -0.12 -0.05 -0.03 -0.02 -0.01 -0.01 -0.01 0.00

CO2/CO2, 1 × 10-22 J -6.584 186 -6.523 214 -6.521 168 -6.520 759 -6.520 759 -6.520 759 -6.520 759 -6.520 759 -6.520 759 -6.520 759 -6.520 759

error, % 0.97 0.04 0.01 0.00 0.00 0.00 0.00 0.00 0.00

The potential between an oxygen atom in the MCM-41 model matrix and a carbon dioxide molecule (the potential between a point charge and a quadrupole) and the potential between two carbon dioxide molecules (the potential between two quadrupoles) converge over just a few images of the simulation cell. It is worth noting that the errors without any long-range correction (0.52% and 0.97% for the two types of interaction) are already small, though not negligible. These errors are reduced essentially to zero for l ) 10. For speed of execution, we used l ) 5, which introduces an error of no more than 0.01%. This summation thus provides a straightforward and accurate way to calculate the long-ranged electrostatic interaction in one-dimensional systems. The initial configuration for the GCMC simulations was generated by randomly placing 10 molecules in the model pore, the system was equilibrated for 1 000 000 GCMC steps, and then data were collected for another 1 000 000 GCMC steps to get the average amount adsorbed. The standard GCMC algorithm was used. The simulated results (which are in terms of absolute adsorption) were converted into their experiment counterpart (excess adsorption) following the procedure given in ref 3.

Figure 2. Solid density profile for the three models.

5. Results and Discussion I. Solid Density Profile in the Three PoreStructure Models. Figure 2 shows the solid density profile for the three models. We define the interfacial range of the model pores to be the range of the radial coordinate for which the pore bulk skeletal density is significantly greater than zero and has not yet attained the bulk density for that model (2.2 g/cm3 in the case of models 1 and 3 and 2.66 g/cm3 for model 2). Model 1 has a regular and highly homogeneous surface, and the interfacial range is essentially zero. The interfacial range in models 2 and 3 is substantial, roughly from 16 to 19 Å in both cases, although as the matrix is crystalline in model 2 and amorphous in model 3, the profiles are otherwise distinct. II. Adsorption of Ethane. GCMC simulations of ethane in the three pore-structure models were carried out at 264.6 K; the results are plotted along with the experimental data in Figure 3. The simulation results for ethane in all three models fit the experimental isotherm quite well in the high-pressure range, and they all predict the pore-filling transition in the adsorption isotherms between about 0.6 and 1.2 MPa. (The statistical error in the simulated amount adsorbed is, at low and moderate pressure, similar in size to the symbols in this and other figures; above the pore-filling pressure the error is about twice as large.) The simulation results for models 1 and 3 accurately fit the experimental isotherm at moderate pressures, while those for model 2 overpredict the experimental adsorption. This overprediction is due to an

Figure 3. Adsorption isotherms for ethane in MCM-41 at 264.6 K.

unrealistically high skeletal density in model 2 (2.66 g/cm3, compared with 2.2 g/cm3, corresponding to amorphous silica, in models 1 and 3). Figure 4 shows a plot of the simulated adsorption isotherms of ethane in the three models and the experimental isotherm, at low pressure. On these axes, Henry’s law is a horizontal line. While none of the sets of data conform precisely to Henry’s law over this pressure range, the simulation data for model 1 (with a completely homogeneous surface) show only a small deviation from Henry’s law. Model 2 (with a heterogeneous but regular surface) is a little further from Henry’s law, while both the experimental data and model 3 (with a heterogeneous and amorphous surface) show large deviations from Henry’s law. Comparing the simulation and experimental data, models 1 and 2 greatly underestimate the experimental adsorption (except for model 2 at the highest pressure, where there is a small overprediction). Model 3 gives the best agreement with experiment, with a very similar isotherm shape and only small quantitative differences, showing that this model, with a relatively high degree of surface heterogeneity and a substantial interfacial range, is a realistic representation of the real

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Figure 4. Adsorption of ethane in MCM-41 at 264.6 K at low pressure.

Figure 5. Adsorption isotherms for ethane in model 3 at the temperatures 264.6, 273.2, and 303.2 K.

MCM-41 material. At least as far as this set of models is concerned, the more amorphous the pore surface, the higher the degree of energetic heterogeneity and the more accurate the simulation results. Figure 5 shows the experimental and GCMC simulation results (using model 3) for the adsorption and desorption of ethane at 264.6 K and for the adsorption of ethane at 273.2 and 303.2 K. With the exception of the simulation results at the lowest temperature, the simulated isotherms are predictions rather than fits. The predictions are in good agreement with the experimental data over the whole pressure range and over the three different temperatures. There is no hysteresis either in the experiments or in the simulation at the lowest temperature, 264.6 K, further supporting the realism of the model and confirming that the adsorption of ethane in MCM-41 pores of this size, at these temperatures, is supercritical. The excess adsorption density of ethane as a function of radial distance is plotted in Figure 6 for the three porestructure models. The adsorption of ethane in models 1 and 2 first occurs at a distance about 3 Å from the surface layer of oxygen atoms, with the second and third layers building up progressively. There is thus a layering effect in the mechanism of adsorption of ethane in models 1 and

He and Seaton

Figure 6. Density profile for ethane in the three models at 264.6 K. The excess densities for models 2 and 3 are shifted upward by 3.0 and 6.0 mmol/cm3, respectively.

Figure 7. Adsorption isotherms for carbon dioxide in model 3 at 264.6 K with different values of point charge on the oxygen atoms in the MCM-41 matrix.

2. The adsorption of ethane in model 3 first occurs in the interfacial region of the MCM-41 matrix, with no evidence of layering. This is a strong indication that there is no layering effect in adsorption in real MCM-41 materials; this is supported by experimental studies of adsorption of Ar condensed into a porous glass.21 III. Adsorption of Carbon Dioxide. GCMC simulation of the adsorption of carbon dioxide in MCM-41 was carried out only in model 3, since this model gives the best results for ethane adsorption. A charged model of carbon dioxide was used by Koh et al.6 to investigate the adsorption behavior of the methane-carbon dioxide mixture in MCM-41. The value of the point charge on the silicon atoms in the MCM-41 matrix was 0.36e in their study. We used this value to simulate the adsorption of pure carbon dioxide in MCM-41 at 264.6 K and found that the simulation results overestimated the adsorption of pure carbon dioxide at low and moderate pressures, as shown in Figure 7. We reduced the charge to get the best fit between simulation and experiment, giving a value of 0.18e. If the point charge for the silicon atom is reduced (21) Huber, P.; Knorr, K. Phys. Rev. B 1999, 60 (18), 12657.

Adsorption in MCM-41

Figure 8. Adsorption isotherms for CO2 in model 3 at 264.6 K for the 3CLJ model, and EPM model with different numbers of images of the simulation box in the axial direction.

further, the simulation results give a poor fit to the experimental isotherm across the pressure range. Therefore, the partial point charge of 0.18e for the silicon atoms and the corresponding value of -0.09e for oxygen atoms are used in this study (see Table 2). Figure 8 shows the effect of different approaches on the calculation of the electrostatic interaction. Simulations of the adsorption of carbon dioxide in model 3 were carried out with different values of the parameter l in eq 2, corresponding to different numbers of images of the main simulation cell. l ) 0 means that the potential was calculated in the main simulation cell only and without any correction for the long-ranged electrostatic interaction but with a large cutoff distance (19.05 Å). If the partial point charges on the EPM model of carbon dioxide are omitted, the potential becomes a three-center LennardJones (3CLJ) model for carbon dioxide; the adsorption results for this model are also shown in Figure 8. The 3CLJ model greatly underpredicts the amount adsorbed of carbon dioxide in MCM-41 at 264.6 K across the whole pressure range, demonstrating the importance of the quadrupolar interaction in this system. The result for the EPM model with l ) 0 greatly overestimates the adsorption of carbon dioxide across the whole pressure range, especially at low and moderate pressures, confirming the importance of properly accounting for the electrostatic interaction. The simulated isotherms from l ) 5 and l ) 6 are within the error bars of each other, supporting the conclusion of section 4 that l ) 5 is adequate, and also within the error bars of the experimental data, demonstrating that model 3 also works well for a quadrupolar adsorptive in MCM-41. Figure 9 shows the simulated adsorption isotherms for carbon dioxide at 264.6, 273.2, and 303.2 K, together with the corresponding experimental results. As in the case of ethane adsorption, only the data for the lowest temperature were used to fit the model (the partial charges in this case), so the simulation results at the other temperatures are strictly predictions. The predictions of the experimental data are excellent, even at low pressure, providing further support for the type of heterogeneity incorporated in model 3. Model 3 is thus capable of giving accurate predictions for the adsorption of both ethane and carbon dioxide across the whole experimental temperature and pressure ranges.

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Figure 9. Adsorption isotherms of CO2 in model 3 at the temperatures 264.6, 273.2, and 303.2 K.

Figure 10. Adsorption of binary ethane/CO2 mixtures at 264.6 K (constant gas composition path): (a) yCO2 ) 0.1245; (b) yCO2 ) 0.471.

IV. Adsorption of Binary Mixtures of Ethane and Carbon Dioxide. Figure 10 shows experimental and GCMC predictions for the adsorption of ethane and carbon dioxide as a function of pressure, at 264.6 K and at two fixed compositions. Figure 11, in turn, shows experimental and GCMC predictions for this system as a function of composition, at 264.6 K and two fixed pressures. The good agreement demonstrates that GCMC simulation can predict the binary adsorption of ethane and carbon dioxide

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Figure 12. Adsorbate density profile for a binary ethane/CO2 mixture with yCO2 ) 0.471.

Figure 11. Adsorption of binary ethane/CO2 mixtures at 264.6 K (constant pressure path): (a) pressure ) 151.45 kPa; (b) pressure ) 1488.28 kPa.

in MCM-41 across the pressure range, especially at the lower of the two pressures. In an earlier paper,22 ideal adsorbed solution theory was applied to study the same system. Rather poor results were obtained using this approach, showing that ethane-carbon dioxide mixtures behave nonideally in MCM-41, presumably due to the effect on competitive adsorption of the differing polarity of the two adsorptives. GCMC simulation, in contrast, captures this nonideal behavior. The adsorbate density profile for the adsorption of ethane and carbon dioxide from a mixture of bulk gas with 47.1% carbon dioxide is plotted in Figure 12. Compared with the density profile for the adsorption of pure ethane, shown in Figure 6, it seems that ethane molecules are squeezed out from the interfacial region by the carbon dioxide molecules. This displacement effect reflects the importance of the electrostatic interactions between the carbon dioxide molecules and the atoms in the matrix, for adsorptive molecules close to the heterogeneous MCM-41 surface.

ethane, carbon dioxide, and binary mixtures of these components. Model 1 gives a good account of the adsorption of ethane at moderate and high pressures, but it underestimates the amount adsorbed at low pressures, because of the inadequate description of the surface structure in this model. Model 2 overestimates the amount of the adsorption of ethane in MCM-41 at moderate pressures, due to the unrealistically high skeletal density of this model. Model 3, which has an amorphous surface giving a higher degree of surface heterogeneity, gives the most accurate results for the adsorption of ethane in MCM-41 across the whole pressure range. Model 3 also gives good results for the adsorption of carbon dioxide and ethane-carbon dioxide mixtures, where electrostatic interactions are important. The different character of the interactions between the ethane and the surface, and the carbon dioxide and the surface, gives rise to significant nonideality, captured accurately by our GCMC simulation of adsorption in this model. The competitive adsorption between ethane and carbon dioxide in the mixture is of particular interest. The ethane molecules are squeezed out of the interfacial region of the model pore, since the carbon dioxide molecule is smaller and has a stronger interaction with the wall because of the large quadrupole moment. The one-dimensional direct summation of the electrostatic interactions between the carbon dioxide molecules and the charged sites on the surface, and among the carbon dioxide molecules, is accurate and efficient for this system. We expect this method to be useful in handling long-ranged interactions in other systems which are large in only one dimension.

Three different pore-structure models for MCM-41, with different degrees of complexity and surface heterogeneity, have been used in a GCMC study of the adsorption of

Acknowledgment. The authors are grateful to Prof. G. Seo (Chonnam National University, Korea) for providing MCM-41 samples. The financial support of the U.K. Engineering and Physical Sciences Research Council, and an ORS award from Universities U.K., is gratefully acknowledged.

(22) Yun, J.-H.; He, Y.; Otero, M.; Du¨ren, T.; Seaton, N. A. Charact. Porous Solids VI 2002, 144, 685.

LA035047N

6. Conclusions