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Prediction of Gas Mixture Adsorption on Activated Carbon Using Molecular Simulations V. Yu. Gusev‡ and James A. O’Brien*,† Department of Chemical Engineering Yale University, New Haven, Connecticut 06520-8286 Received May 1, 1998. In Final Form: August 12, 1998
Introduction Reliable methods for adsorption characterization of activated carbons1 and predicting single- and multicomponent adsorption equilibria are important for the correct design of industrial separation equipment and heterogeneous chemical reactors.2,3 These tasks are strongly interrelated, since the surfaces of a vast majority of adsorbents are heterogeneous.4 Due to their preparation process, activated carbons are often chemically and geometrically heterogeneous and lack crystalline structure. Therefore, they cannot be characterized using X-ray scattering techniques. The recent trend in adsorption science is to use microscopic molecular theory and simulation methods to characterize the adsorption properties of real adsorbents.5-12 In contrast with traditional thermodynamic and empirical methods,1 the microscopic approach is based on direct consideration of the intermolecular forces, which are likely to be a key factor in the highly inhomogeneous environments of industrial adsorbents. The Monte Carlo simulation approach9-12 is especially attractive in this regard, since, unlike density functional theory,5-7 it is exact in principle for a given set of intermolecular potentials.13 Currently, Monte Carlo-based methods can provide a consistent view of single-component adsorption on activated carbons9-12,14 based on limited experimental data. For the treatment of mixture adsorption on real adsorbents, however, phenomenological methods, e.g., the ‡ Present address: CuraGen Corp., 555 Long Wharf Drive, New Haven, Connecticut 06511. † Present address: PTT, Inc., 305 Madison Ave., Suite 1425, New York, New York 10017. E-mail:
[email protected]. * To whom correspondence should be addressed.
(1) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Academic Press: London, 1982. (2) Yang, R. T. Gas Separation by Adsorption Processes; Butterworths: London, 1987. (3) Doraiswamy, L. K. Catalytic Reactions and Reactors: A Surface Science Approach; Pergamon Press: Oxford, U.K., 1991. (4) Rudzinski, W.; Everett, D. H. Adsorption of Gases on Heterogeneous Surfaces; Academic Press: London, 1992. (5) Seaton, N. A.; Walton, J. P. R. B.; Quirke, N. Carbon 1989, 27, 853. (6) Lastoskie, C.; Gubbins, K. E.; Quirke, N. J. Phys. Chem. 1993, 97, 4786. (7) Olivier, J. P.; Conklin, W. B.; v. Szombathely, M. In Characterization of Porous Solids III; Rouquerol, J., Rodriquez-Reinoso, F., Sing, K. S. W., Unger, K. K., Eds.; Elsevier: Amsterdam, 1994; p 81. (8) Quirke N.; Tennison, S. Proc. Carbon ′94, 1995, 242. (9) Gusev V.; Seaton N.; O’Brien J. Langmuir 1997, 13, 10, 28152821. (10) Gusev V.; O’Brien J. Langmuir 1997, 13, 10, 2822-2824. (11) Stubos A. K.; Kanellopoulos, N. K.; Cracknell, R. F.; Papadoupoulos, G. K.; Nicholson D. Langmuir 1997, 13, 10, 2795-2802. (12) Lopez-Ramon, M. V.; Jagiello J.; Bandosz T. J.; Seaton N. A. Langmuir 1997, 13, 4435-4445. (13) Nicholson, D.; Parsonage, N. G. Computer Simulation and the Statistical Mechanics of Adsorption; Academic Press: London, 1982. (14) Kaneko K.; Cracknell R. F.; Nicholson D. Langmuir 1994, 10, 4606.
ideal adsorption solution theory (IAST)15 and derived approaches,16-19 are the only tools available. In IAST, the mixture adsorption equilibrium is calculated on the basis of single-component adsorption data and the assumption of a uniform adsorbed phase. However, IAST predictions may exhibit dramatic discrepancies with experiment,18 possibly due to IAST’s lack of explicit consideration of the heterogeneity of the fluid-solid interactions.20-22 The multispace adsorption model (MSAM)18,19 appears to be successful at correlating experimental data on heterogeneous activated carbons. Currently, the MSAM approach requires an adsorbent structure parameter to be estimated using limited mixture information; it is, therefore, only semipredictive. Microscopic Monte Carlo-based methods are widely used to study mixture adsorption in crystalline solids23-27 and idealized confinements,28-38 although no attempt has been made to use these methods for predicting adsorption on heterogeneous activated carbons. In this Note, grand canonical Monte Carlo (GCMC) simulations13 are used to predict mixture adsorption on activated carbon, based on a pore size distribution determined independently using a combination of molecular simulations and a single experimental methane adsorption isotherm.9 We compare the results of these computer simulations of mixture adsorption both with our experimental measurements and with IAST predictions. Experimental Section A volumetric custom-built apparatus was used to measure single-component and mixture adsorption at temperatures of 308.2-373.2 K and pressures from about 0.003 to 3 MPa. (15) Myers, A. L.; Prausnitz, J. M. A.I.Ch.E.J. 1965, 11, 121. (16) Valenzuela, D. P.; Myers, A. L.; Talu, O.; Zwiebel, I. A.I.Ch.E.J. 1988, 34, 3, 397-402. (17) Hu, X.; Do, D. A.I.Ch.E.J. 1995, 41, 1585. (18) Gusev V.; O’Brien J.; Jensen C.; Seaton N. A. A.I.Ch.E.J. 1996, 42, 10, 2773. (19) Jensen, C. R. C.; Seaton, N. A.; Gusev, V. O′Brien, J. A. Langmuir 1997, 13, 1205. (20) Myers, A. L. Proceedings of the International Conference on Fundamentals of Adsorption; Engineering Foundation: New York, 1984; p 365. (21) O’Brien, J. A.; Myers, A. L. Proceedings of the International Conference on Fundamentals of Adsorption; Engineering Foundation: New York, 1987; p 451. (22) Sircar, S. A.I.Ch.E.J. 1995, 41, 1135. (23) Woods, G. B.; Rowlinson, J. S. J. Chem. Soc., Faraday Trans. 2 1989, 85, 756. (24) Razmus, D.; Hall, C. A.I.Ch.E.J. 1991, 37, 5, 769. (25) Cracknell, R. F.; Gubbins, K. E. Langmuir 1993, 9, 824. (26) Maddox, M. W.; Gubbins, K. E. Int. J. Thermophys. 1994, 15, 6. (27) Dunne J.; Myers, A.; Kofke, D. A. Adsorption 1996, 2, 41-50. (28) MacElroy, J. M. D.; Suh, S.-H. Mol. Phys. 1987, 60, 475. (29) Tan Z.; Gubbins K. E. J. Phys. Chem. 1990, 94, 6061. (30) Kierlik, E.; Rosinberg, M. L.; Finn, J. E.; Monson P. A. Mol. Phys. 1992, 75, 1435. (31) Tan, Z.; Gubbins, K. E. J. Phys. Chem. 1992, 96, 845. (32) Cracknell, R. F.; Nicholson D.; Quirke N. Mol. Phys. 1993, 80, 885-897. (33) Cracknell, R. F.; Nicholson D.; Quirke N. Mol. Sim. 1994, 13, 161-173. (34) Kierlik, E.; Rosinberg, M. L.; Fan, Y.; Monson P. A. J. Chem. Phys. 1994, 101, 12, 10947. (35) Kaminsky, R. D.; Monson, P. A. Langmuir 1994, 10, 2, 530. (36) Nicholson, D.; Gubbins, K. E. J. Chem. Phys. 1996, 104, 20, 8126. (37) Gusev, V.; O’Brien, J.; Gomez, A.; Jensen, C. R. C.; Papadopoulos, G.; Seaton, N. Procedings of the Adsorption; LeVan, M. D., Ed.; Engineering Foundation: New York, 1996; p 337. (38) Cracknell, R. F.; Nicholson, D.; Tennison, S. R.; Bromhead. J. Adsorption 1996, 2, 193.
S0743-7463(98)00510-1 CCC: $15.00 © 1998 American Chemical Society Published on Web 09/22/1998
Notes
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Table 1. Molecular Center-center Lennard-Jones Interaction Parameters CH4 C2H6 CH4/C2H6
σff, nm
ff/kB, K
0.381 0.3512 0.3661
148.1 139.8 146.0
l, nm
ref
σsf, nm
sf/kB, K
0.2353
39 40 L-B
3.605 3.456
64.4 62.57
Pressures were measured by either of two MKS Baratron capacitance manometers and a digital MKS read-out having an accuracy of 0.15% of reading. The temperature was controlled by a set of Omega 100W platinum resistance thermometers, PID controllers and heat exchangers. In the mixture adsorption measurements, a flow-through technique enabled the gas-phase bulk mole fraction to be held constant over a range of temperatures and pressures. The control of gas flow rate, pressure, and composition was carried out using the MKS setup. Gas mixture composition was measured using an HP 5880A gas chromatograph. The accuracy of the adsorption measurements was about 1% and 3% of loading in the case of the singlecomponent and binary adsorption measurements, respectively. Further details of the experimental procedure are available elsewhere.18 The sample of activated carbon BPL 6 × 16 (Calgon Carbon Corp., Pittsburgh, PA) used earlier9,10,18 was outgassed at 10-2 mmHg pressure and 373 K for 24 h prior to measurements. The methane and ethane (National Compressed Gases, Inc.) had a quoted purity of better than 99.97% and were both used as received. GCMC Method. Methane and ethane molecules were modeled as one-center and rigid two-center species correspondingly. The interactions between the centers were described by truncated Lennard-Jones (LJ) potentials:
uff(r) )
{
[( ) ( ) ]
4ff 0,
σff r
12
-
σff r
6
r < Rc
,
(1)
r > Rc
The LJ fluid parameters used in the simulation were taken from fits to bulk second-virial-coefficient data39,40 (see Table 1). Methane-ethane LJ parameters were calculated using LorentzBerthelot combination rules. Each wall of the model graphitic slit pore was represented by a series of stacked planes of LJ atoms. The interaction energy between an atomic center of the fluid molecule and a single pore wall at a distance z (measured between the centers of the fluid atom and the atoms in the outer layer of the solid) was described by Steele’s 10-4-3 potential:39
usf(z) ) 2πFssfσsf2∆
[(
) ( )
2 σsf 5 z
10
-
σsf z
4
-
σsf4
]
3∆(0.61∆ + z)3
(2)
where ∆ ) 0.335 nm is the (center-to-center) separation between graphite layers and Fs ) 114 nm-3 is the graphite number density of carbon atoms. σsf and sf are solid-fluid LJ collision and welldepth parameters. The interaction energy of a molecule center with slit-shaped pore walls usf(z) is modeled as the interaction with two such planar surfaces placed a distance H (also measured between centers of the corresponding atoms) apart:
upore ) usf(z) + usf(H - z)
(3)
The unlike solid-fluid interaction parameters σsf and sf were obtained using the Lorentz-Berthelot combination rules. The estimated values reproduced experimental Henry’s law constants in the case of methane on graphitized carbon blacks.41-43 (39) Steele, W. A. The Interactions of Gases with Solid Surfaces; Pergamon: Oxford, U.K., 1974. (40) Fischer, J.; Lustig, R.; Breitenfelder-Manske, H.; Lemming, W. Mol. Phys. 1984, 52, 485-497. (41) Specovius, J.; Findenegg, G. H. Ber. Bunsen-Ges. Phys. Chem. 1978, 82, 174-180. (42) Stacy, T. D.; Hough, E. W.; McCain, W. D. Jr. J. Chem. Eng. Data. 1968, 13, 74. (43) Sams, J. R. J. Chem. Phys. 1965, 43, 7, 2243.
Estimates of the initial isosteric heat of ethane adsorption on the open surface at 300 K using Monte Carlo integration also produced corroborating values within the experimental range of 16.0-19.7kJ/mol.44 The scheme for generating grand canonical ensemble45 Markov chains included trials of four types:32 moving a particle, creating a particle, deleting a particle, and changing the particle identity. The probability of the trial was determined according to one of the following equations:
Pmove ) min{1, exp[-∆Ec (r)/kBT]}
(4)
Pcreate ) min{1, (N + 1)-1 exp[-∆Ec(r)/kBT + B]}
(5)
Pdelete ) min{1, N exp[-∆Ec(r)/kBT + B]}
(6)
Pchange ) min{1, Nj/(Ni + 1) exp[-∆Ec(r)/kBT + Bi - Bj]} (7) where ∆Ec(r) is the configurational energy change associated with the move, kB is the Boltzmann constant, B t µ′/kBT + ln〈N〉 ) ln(fV/kBT) is Adams’ constant, µ′ is the excess chemical potential, relative to an ideal gas having the same density, 〈N〉 is the mean number of particles, V is the volume of the system, and f is the bulk gas-phase fugacity, determined from the PengRobinson equation of state for each component in the methaneethane mixture.46 Equation 7 applies to an attempt to change a j-type molecule into an i-type molecule and derives from the ratio of the eq 5 and 6. The initial type of the species in each trial was chosen randomly with equal probability. In the case of the ethane model, the molecule moves consisted of either rotation or translation, the type of move being chosen randomly with equal probability. The orientation of the ethane molecule was specified by two Euler angles φ and θ, and the random change in the orientation was done via the values of φ and cos(θ) in order to keep the acceptance probability expressions identical for each component.47 The scales of translation and rotation moves were adjusted independently throughout the runs so that, on average, 50% of all trials were accepted. The use of the identity-swapping trials did not affect the GCMC averages; however, as was expected,31,32 it improved convergence, considerably reducing the magnitude of standard deviations. To optimize the number of particles while satisfying the competing requirements of microscopic reversibility9 and computational speed, the size of the simulation cell was automatically adjusted during the equilibration part of each simulation run within the range of 10σm to 150σm (the latter corresponding to the lowest adsorbate densities). The potential cutoff Rc was kept constant at 5σm. The accuracy of our GCMC code was checked against the results of other methane-ethane mixture simulations at 296.2 K in a single pore 2.5σm wide.38
Results and Discussion The model pore structure used in this work is the independent structureless slit pores model (ISSPM). The ISSPM pore size distribution of the activated carbon BPL-6 was determined earlier by fitting the 308.2 K experimental methane adsorption isotherm to a “kernel” set of 40 simulated model adsorption isotherms.9 Each of the model isotherms was determined by the GCMC method in carbonaceous slit pores 0.63 to 5.72 nm (1.65σm to 15σm) wide.9 The SVDNNLS fitting procedure used both nonnegativity constraints and singular value decomposition to control unphysical negative pore volumes in ISSPM (44) Lal, M.; Spenser, D. J. Chem. Soc., Faraday Trans. 2 1973, 70, 910. (45) Norman G. E.; Filinov V. S. Teplofizika Vysokikh Temperatur. 1969, 7, 2, 233-240. (46) Sandler S. Chemical and Engineering Thermodynamics; 2nd ed.; Wiley: New York, 1989, Vol. 182, p 314. (47) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, U.K., 1992; p 131.
6330 Langmuir, Vol. 14, No. 21, 1998
Figure 1. Gibbs excess mixture adsorption of methane and ethane on BPL-6 activated carbon at 308.2 K vs bulk pressure: (filled symbols) experiment; (empty symbols) mixture GCMC prediction using ISSPM; (squares) ethane; (circles) methane; (Lines) IAST prediction based on single-component GCMC prediction using ISSPM: (dotted line) ethane; (solid line) methane. Bulk methane composition y ) 0.48.
and linear dependence of GCMC adsorption isotherms, respectively. The consistency of this method was established by quantitatively predicting single-component methane9 and ethane adsorption10 within wide pressure ranges and different temperatures on the same sample of the activated carbon. The resulting pore size distribution retained only 5 of the original 40 pore sizes.10 In this work the methane-ethane binary mixture adsorption was calculated in 20 slit pores in the same pore width range. The densities of adsorbate determined in GCMC simulations were then added at each pressure (with weights corresponding to the BPL-6 ISSPM pore size distribution) to yield a prediction of the total adsorption for each component. Mixture predictions were done at three temperatures (308.2 K, 333.2 K, 373.2 K) and two bulk mixture methane mole fractions (y ) 0.48, y ) 0.75). Adsorption of both components was also predicted by applying IAST to the single-component adsorption isotherms. It should be noted that IAST applied to experimental singlecomponent isotherms and GCMC and ISSPM-based single-component isotherms9,10 were in close agreement. The remainder of this discussion will refer to the results obtained at 308.2 K and composition y ) 0.48 (Figure 1); however, it is also applicable to the rest of the conditions. Three features of the plots shown in Figure 1 should be noted. (a) All of the predictive methods show good agreement with experiment in the low-pressure limit. This suggests that the GCMC model and ISSPM may represent correctly the features of the solid-fluid interactions in the real activated carbon when the effects of fluid-fluid interactions or smallest. This is hardly surprising, since the single-component GCMC adsorption predictions were successful at low pressures.9,10 It should be pointed out that in contrast to thermodynamic predictive approaches, such as, e.g., IAST, GCMC simulations require the adsorption isotherm of only one component in the case presented here. (b) As pressure increases, theoretical methods begin to fail. The prediction of ethane adsorption is better than that of methane. Theoretical values are in agreement with experiment at pressures up to 1 MPa in the case of ethane and up to 0.1 MPa in the case of methane.
Notes
Figure 2. Selectivities S21 for methane and ethane mixture adsorption on BPL-6 activated carbon at 308.2 K: (filled circles) experiment; (lines) GCMC (each marked with the corresponding pore width in units of σsf). Bulk methane composition y ) 0.48.
(c) The GCMC method displays agreement with IAST. This corroborates previous comparisons of the IAST with the results of GCMC simulations of binary methaneethane adsorption with ethane modeled both as a single LJ atom37 and as a two-center LJ molecule.38 To gain a better insight into the high-pressure discrepancies between simulations and experiment, we analyze the pressure dependence of the selectivity S21 predicted for the BPL-6 ISSPM and single pores. The selectivity is defined as
S21 )
x2/y2 x1/y1
(8)
where x and y are the compositions of the adsorbed and bulk binary phases, respectively. At low pressures the selectivity predicted using GCMC (Figure 2) is largest in the narrowest pore (H ) 1.9σm) and is a decreasing function of the pore width. As pressure increases, this behavior can reverse. At sufficiently high pressures, the selectivity decreases with pressure in all of the pores studied in our GCMC simulations. However, within the micropore range (H < 4σm), its value does not become as small as the minimum experimental selectivity of the BPL activated carbon, observed at high pressures. Since it is well established from single-component measurements that BPL-6 is a primarily microporous adsorbent,9,10,48,49 Figures 1 and 2 suggest that some important properties of the BPL-activated carbon affecting mixture adsorption are missing in the ISSPM approximation. The model of independent slit-shaped pores is most likely a considerable simplification of the real pore structure of the activated carbon, since it assumes the wall potential to be a function of a single intrapore coordinate. The results shown in Figures 1 and 2 suggest that the correct description of the mixture adsorption requires a more sophisticated model pore structure (at least at the level of secondary or interpore structure; the individual pore is probably adequately modeled). The most important missing feature is the topology of the adsorption centers.4 (48) Reich, R.; Ziegler, W. T.; Rogers, K. A. Ind. Eng. Chem. Proc. Dev. Des. 1980, 19, 336. (49) Sosin K. A.; Quinn D. F. J. Porous Mater. 1995, 1, 111.
Notes
Langmuir, Vol. 14, No. 21, 1998 6331
interactions between the adsorbate components would have a similar effect in the context of the present study. Using the unphysically large value me ) 180kT instead of the one supplied by the Berthelot rule brings methane adsorption into closer agreement with experiment at higher pressures, leaving ethane adsorption essentially unaffected (Figure 3). At low pressures this change had no effect on the amounts adsorbed, suggesting that, as long as the interactions between components do not play a considerable role, mixture adsorption can be wellpredicted within the ISSPM framework. When these interactions do come into play (at high adsorbate densities), the ISSPM is no longer adequate for mixture predictions. Conversely, one can speculate that GCMC mixture adsorption predictions using the ISSPM approximation for the activated carbon would be better when ideal solution behavior is observed in the real physical experiment. Figure 3. Gibbs excess mixture adsorption of methane and ethane on BPL-6 activated carbon at 308.2 K. The methaneethane LJ interaction parameter me ) 180kT is artificially increased compared to the value supplied by the Berthelot rule me ) 143.9kT. Key: (filled symbols) experiment; (solid lines with empty symbols) GCMC-based prediction using ISSPM; (squares) ethane; (diamonds) methane. Bulk methane composition y ) 0.48.
GCMC mixture predictions used within the ISSPM approximation of the structure of the BPL activated carbon are found to be in agreement with IAST. However, experimental data show negative deviations from both of these approaches in the Raoult’s law sense. It has been noted that heterogeneity of the adsorbent surface always introduces negative deviations from ideal adsorbed solution behavior.16,21,50 Furthermore, it was shown for a simple model that an artificial increase in activity coefficients of the mixture components adsorbed on a homogeneous surface has an effect similar to that of a heterogeneous surface.21,50 Therefore, it was instructive to check whether an artificial increase in the fluid-fluid (50) Myers, A. L. A.I.Ch.E.J. 1983, 29, 691.
Conclusions GCMC simulation can be used for low-pressure mixture adsorption predictions on real activated carbons. At high adsorbate densities, mixture adsorption appears to be more sensitive to the real heterogeneity and structure of the activated carbon than does the single-component adsorption. Even though we have used a heterogeneous model to describe the activated carbon, the GCMC predictions are in agreement with ideal adsorbed solution theory. Accordingly, the attempt to predict the mixture adsorption of methane and ethane was less productive at pressures above 0.1MPa, where fluid-fluid interactions become important. We interpret this as the inability of a set of structureless independent slit pores to account completely for activated carbon heterogeneity in all carbons, although the approach may be useful in some carbons. Acknowledgment. This work is supported in part by the U.S. National Science Foundation through Grant No. CTS-9215604. LA980510V
