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Langmuir 1997, 13, 2822-2824
Can Molecular Simulations Be Used To Predict Adsorption on Activated Carbons? Vladimir Yu. Gusev and James A. O’Brien* Department of Chemical Engineering, Yale University, New Haven, Connecticut 06520-8286 Received May 8, 1996. In Final Form: March 11, 1997X We demonstrate that the adsorption of ethane on an industrial activated carbon may be predicted quantitatively using molecular simulations of a two-center model of ethane and a pore size distribution for the micropores of the active carbon. The pore size distribution was determined from the adsorption of methane on the same carbon at a single temperature. No adjustable solid-fluid parameters were used. A less realistic spherical model of ethane was not adequate to predict ethane adsorption.
Introduction Developments in molecular simulation and the theory of fluid adsorption have driven considerable progress in the characterization of porous solids using adsorption. The pore structure of heterogeneous activated carbons, which, unlike that of e.g., zeolites, is irregular, can now be characterized more reliably down to molecular length scales.1-3 Although most efforts have been concentrated on the use of subcritical (typically nitrogen) gas adsorption,2,3 supercritical characterization has attractive advantages.1 Although not all of the difficulties of adsorptionbased characterization have been worked out (e.g., the ill-posed nature of the pore size distribution inversion problem1,4), it appears that it may already be possible to apply theory and simulation to predict adsorption on irregular porous solids.1,5 We report in the following the results of a study aimed at developing computer simulation-based methods for the prediction of adsorption on activated carbon. On the basis of the carbon pore-size distribution (PSD) previously determined using a combination of methane experimental isotherm data and simulations of methane adsorption, we predict the adsorption of a different adsorbate (ethane) on the activated carbon at a series of temperatures, using no additional adjustable parameters. Methods The experimental Gibbs excess adsorption isotherms used in this study were measured using our own custom-built volumetric apparatus; our procedures are described in detail elsewhere.1 Ethane adsorption was measured at three temperatures (308.2, 333.2, and 373.2 K) and over a range of pressures from 0.001 to 3 MPa; the amount adsorbed was measured to within 1%. * Author to whom correspondence should be addressed. Current address: PTT, Inc., 630 Third Ave., New York, NY 10017. X Abstract published in Advance ACS Abstracts, May 1, 1997. (1) Gusev, V. Yu., O’Brien, J. A.; Seaton, N. A. A Self-Consistent Method for Characterization of Activated Carbons Using Supercritical Adsorption and Grand Canonical Monte-Carlo Simulations. Langmuir 1997, 13, 2815. (2) Lastoskie, C.; Gubbins, K. E.; Quirke, N. Pore Size Distribution Analysis of Microporous Carbons: A Density Functional Theory Approach. J. Phys. Chem. 1993, 97, 4786. (3) Seaton, N. A.; Walton, J. P. R. B.; Quirke, N. A New Analysis Method for the Determination of the Pore Size Distribution of Porous Carbons From Nitrogen Adsorption Measurements. Carbon 1989, 27, 853. (4) Mamleev, V. Sh.; Bekturov, E. A. Improved method for Analysis of Energetic Heterogeneity of Surfaces from Adsorption Isotherms. Langmuir 1996, 12, 441-449. (5) Quirke, N.; Tennison, S. R. The Interpretation of Pore Size Distributions of Microporous Carbons. Carbon 1996, 34, 1281. (6) Fischer, J.; Lustig, R.; Breitenfelder-Manske, H.; Lemming, W. Influence of Intermolecular Potential Parameters on Orthobaric Properties of Fluids Consisting of Spherical and Linear Molecules. Mol. Phys. 1984, 52, 485-497.
S0743-7463(96)00456-8 CCC: $14.00
Table 1. Molecular Interaction Parameters Used in GCMC and NLDFT Calculations ethane model
σff, nm
ff/kB, K
l, nm
ref
one LJ center two LJ centers
0.395 0.3512
243.0 139.81
0.2353
7 6
The activated carbon used was Pittsburgh BPL 6 × 16 from Calgon Carbon Corporation. Ethane (purity > 99.98%, National Compressed Gases, Inc.) was used as received. Our approach uses grand canonical Monte Carlo (GCMC) molecular simulations. We have discussed the technique more extensively elsewhere.1 The usual GCMC trials were included: attempts to move, create, and destroy molecules. Fluid-fluid interactions were described by truncated LennardJones (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 second-virial-coefficient data and are summarized in Table 1. In the case of the two-center model of ethane, molecule movements consisted of an equal number of rotation and translation attempts. The extents of the attempted translations and rotations were adjusted during the simulations to satisfy the usual criterion that approximately half of all rotations and half of all translations be accepted. The minimum size of the simulation cell (in the directions parallel to the pore wall) was chosen as 10σff, while all potentials were truncated at 5σff. The interaction energy between a fluid atom 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:7 2 usf(z) ) 2πFssfσsf ∆
[( ) ( ) 2 σsf 5 z
10
-
σsf z
4 σsf
4
-
]
3∆(0.61∆ + z)3
(2)
where ∆ ) 0.335 nm is the separation between graphite layers and Fs ) 114 nm-3 is the surface number density of carbon atoms in a graphite layer. The solid-fluid LJ collision and well-depth parameters σsf and sf, as in our study of methane,1 were determined using the Lorentz-Berthelot combination rules. We estimated the low-pressure isosteric heat of ethane adsorption on an open (i.e., nonporous) carbon surface at 300 K using Monte Carlo integration to be between 18 and 18.6 kJ/mol, which falls within the experimental range of 16.0-19.7 kJ/mol8 and agrees with other Monte Carlo estimates.9 The interaction of an adsorbate molecule with a slit-shaped pore is modeled as the interaction energy, usf(z), with two such planar surfaces placed at a distance H (measured between the centers of the surface atoms in the opposing pore walls) apart: (7) Steele, W. A. The Interactions of Gases with Solid Surfaces; Pergamon: Oxford, 1974.
© 1997 American Chemical Society
Adsorption on Activated Carbons
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Table 2. Pore Size Distribution for the Activated Carbon, Determined from Methane Adsorption at a Single Temperature1 pore no.
H,a nm
V, cm3/g
1 2 3 4 5
0.7239 0.8763 0.9906 1.1049 1.524
0.029 0.053 0.118 0.033 0.298
a Center-to-center distances between carbon atoms in opposing pore walls.
Table 3. Solid-Fluid Potential Parameters Used in the Simulations of Both Models of Ethane Computed Using the Lorentz-Berthelot Combining Rules ethane model
σsf, nm
sf/kB, K
one LJ center two LJ centers
0.3675 0.3456
82.49 62.57
upore ) usf(z) + usf(H - z) GCMC simulations were run for 2 × 106 to 2 × 107 configurations at each isotherm point, on a Hewlett-Packard 9000/735 workstation. The bulk thermodynamic properties of methane were computed throughout using a virial-type equation of state.10 The reproducibility of our calculations was checked against literature data.9 Isotherms were simulated for the five pore sizes (Table 2) which represent the carbon PSD determined earlier.1 The solid-fluid parameters used in the simulations are shown in Table 3.
Results Parts a and b of Figure 1 show the adsorption isotherms of two-center and single-center ethane, respectively, at 308.2 K in the five different sizes of pore, plotted as number of molecules per cubic nanometer. The elongated twocenter model has a significant effect on the adsorption in all pores studied, by comparison to the one-center model. These differences were discussed in some detail by Cracknell et al.9 In order to calculate the adsorbate excess density,1 we determined by trial the smallest pore in which adsorption of model ethane molecules was still possible. For the twocenter model of ethane, this was a pore of width 0.587 nm, while for the one-center model it was 0.625 nm. These values were then used to estimate the excluded pore width1 for the adsorbed ethane molecules by subtracting one fluid atom diameter from the center-to-center width of the smallest pore; this gave 0.236 and 0.229 nm for the twoand one-atom models, respectively. The excess density of the adsorbate was determined as the number of molecules per unit accessible pore volume, less the density of the bulk phase. The pore size distribution of BPL-6 activated carbon shown in Table 2 was extracted, using a SVDNNLS technique, from a combination of (a) the experimental methane 308 K adsorption isotherm at pressures from subatmospheric to 3 MPa and (b) a set of GCMC-simulated isotherms for 40 independent infinite slit carbon pores under the same conditions.1 No adjustable parameters were used in the methane simulations. Figure 2 shows the predictions generated by integrating the GCMC single-pore ethane isotherms over the PSD (8) Lal, M.; Spenser, D. Interactions of Alkanes with Graphite. J. Chem. Soc., Faraday Trans. 2, 1973, 70, 910. (9) Cracknell, R. F.; Nicholson, D.; Quirke, N. A Grand Canonical Monte-Carlo Study of Lennard Jones Mixtures in Slit Pores; 2: Mixtures of Two Center Ethane with Methane. Mol. Simul. 1994, 13, 161-175. (10) Sychev, V. V.; Vasserman, A. A.; Kozlov, A. D.; Zagoruchenko, V. A.; Spiridonov, G. A.; Tsymarny, V. A. Thermodynamic Properties of Ethane; National Standard Reference Data Service of the USSR: 1987.
Figure 1. Adsorbed (absolute) densities of ethane (symbols) computed using GCMC molecular simulation in slit-shaped pores at 308.2 K: (a) two-LJ-center molecular model of ethane; (b) one-LJ-center molecular model of ethane. Pore widths are as follows: 0.7239 nm, circles; 0.8763 nm, inverted triangles; 0.9906 nm, squares; 1.1049 nm, diamonds; 1.524 nm, triangles. The lines are drawn to guide the eye.
Figure 2. Gibbs excess adsorption of ethane on BPL-6 activated carbon: filled symbols, experiment; solid lines, GCMC-based prediction using the two-LJ-center molecular model of ethane; dotted lines, GCMC-based prediction using the one-LJ-center model of ethane. Data are shown for the following temperatures: 308.2 K, diamonds; 333.2 K, inverted triangles; 373.2 K, squares.
(solid lines) and the experimental ethane adsorption isotherms (symbols) on BPL-6 activated carbon at 308.2, 333.2, and 373.2 K. The GCMC prediction based on the two-center model of the ethane molecule is quantitative for most of the pressure range. At high pressures (above 1 MPa), where the experimental isotherms flatten, the two-center model underestimates adsorption at 308.2 and 333.2 K and overestimates it at 373.2 K. This is essentially a failure to predict the behavior of high-density adsorbate,
2824 Langmuir, Vol. 13, No. 10, 1997
which leads to an inaccurate predicted saturation capacity for the activated carbon. We see two possible explanations for this: (i) We ignored the quadrupole of the ethane molecule. Inclusion of this property into our model could alter the configurations9 and, hence, the density of the adsorbed phase at high density. (ii) The method employed to assess the pore size distribution is insensitive to pores wider than 2.29 nm.1 If wider pores do exist in the activated carbon sample, they might provide better ways to arrange the high-density ethane at lower temperatures, while at higher temperatures slightly larger pores would adsorb considerably fewer molecules. In general, it should be noted that we obtain better predictions at higher temperature, indicating that adsorption becomes less sensitive to the actual structure of the adsorbent material at high temperature. For comparison, we also show in Figure 2 the predictions (dotted lines) of the one-center model. This model was not capable of quantitative prediction at any temperature. Here again, the biggest discrepancy between prediction and experiment is found at high loadings. However, unlike the two-center model, this model consistently overestimates the amount adsorbed at high pressure. This is because spherical particles can be packed to a higher density than elongated two-center ethane. It is interesting to note that, at lower pressures, an increase in temperature improves this model’s predictive abilities (at 373.2 K the simpler model is close to quantitative below 0.2 MPa).
Gusev and O’Brien
Once again, this demonstrates that a detailed description is less important at high temperatures. Conclusions This study demonstrates the potential for quantitatively predicting adsorption isotherms in industrially-relevant adsorbents using a combination of (a) molecular simulation and (b) a relatively simple description of the adsorbent material’s microstructure. Taking into account all the assumptions used, the method described here performs remarkably well for this “real-world” system. We note that no adjustable solid-fluid interaction parameters were used for either methane or ethane; only a single methane adsorption isotherm, along with the (independently available) molecular properties of the bulk solid and fluids, was required. Future work will seek to refine our method on several complementary fronts: (i) the use of a larger set of pores and a larger pressure range in compiling the initial kernel of the GCMC data, in order to increase the precision of the initial pore size distribution determination;1 (ii) the use of more sophisticated models of the adsorbate and the adsorbent pores, as well as testing with more complicated adsorbate species. Acknowledgment. This work is supported in part by the U.S. National Science Foundation through Grant No. CTS-9215604. LA960456N
