J. Phys. Chem. 1994,98, 5709-5713
5709
High-pressure Adsorption of Methane and Ethane in Activated Carbon and Carbon Fibers Shroyi Jiang, John A. Zollweg,' and Keith E. Gubbins School of Chemical Engineering, Cornell University, Zthaca, New York,14853 Received: September 2, 1993; In Final Form: February 8, 1994"
W e present experimental results for adsorption of methane and ethane in activated carbon (AC6 10) and activated carbon fibers (KF1500 and A10) a t pressures up to 10 MPa and temperatures between 313.15 and 373.15 K from a modified direct weighing densimeter. The general features of high-pressure adsorption in these carbons are discussed. We also report grand canonical Monte Carlo simulations and nonlocal density functional theory calculations to model methane adsorption in carbons. By combining these calculated results with the pore size distribution calculated from previously obtained data, we are able to compare our simulation and theoretical results with those of our experiments.
Introduction
Experiment
Adsorption in porous materials offers the possibility of storing methane at high density while maintaining moderate physical conditions for the bulk phase. The search for a suitable material is currently an active area of research. Using density functional theory, Tan and Gubbinsl determined that an optimal carbon slit pore would have a width of about 11.4 A. Matranga et al.2 later determined that a slit width of 11.4 A is optimal for a system with a storage pressure of 3.5 MPa and an exhaustion pressure of 0.1 MPa at ambient temperature using molecular simulations. Their model assumes that adjacent slits are divided by a single layer of graphite, so it represents a theoretical upper limit for slit pores. Even such an ideal material would yield only one-fourth of the heat of combustion of gasoline for a fixed volume. Cracknell et ~ 1carried . ~ out similar calculations for both slit carbon pores and for cylindrical zeolite pores. Their calculations show that the best model zeolite will yield only one-tenth of the heat of combustion of gasoline for a fixed volume for a storage pressure of 3.5 MPa and an exhaustion pressure of 0.1 MPa at 274 K. The amount of methane stored could be increased by increasing micropore volume and/or surface area. Recently developed activated carbon fibers (ACF's) are highly microporous solids of large micropore volume and great surface area. The ACF's are composed of small graphite crystals instead of infinite graphite surfaces. Kaneko et ~ 1have . estimated ~ that surface areas up to 6000 m2/g are theoretically possible with such structures for pores separated by a single carbon layer. Such surface areas are much higher than the theoretical upper limit of 2630 m2/g for pores formed by infinite single graphite layers. ACF's of 3000 m2/g surface area can be commercially supplied. They are attractive candidates for use as storage media of natural gas. In this work, we measured adsorption isotherms of methane and ethane in activated carbon (AC610) and activated carbon fibers (KF1500 and A10) a t pressures up to 10 MPa and temperatures between 3 13.15 and 373.15 K. The adsorption isotherms of nitrogen in AC610 at 77.5 K have been measured by Seaton et al.5 and Rhykerd et a1.6 The pore size distribution (PSD) of AC610 has been analyzed with the aid of local and nonlocal density functional theories (DFT) by Seaton et aL5and Lastoskie et al.' By assuming the previously calculated PSD, we are able to compare our simulation and theoretical results with those of our experiments in AC610. Such a comparison provides a good test of the model used in the theory and simulation and of the PSD. Kaneko et a1.8 measured an adsorption isotherm of methane in A10 at pressures up to 5 MPa at 303.15 K. We have also compared our results with theirs.
Apparatus. The direct weighing densimeter was first built by Millerg and then modified by Deitrick.Io It had been used to measure accurate pressure-temperature-volume data a t elevated temperatures and pressures. It was further modified in this work to measure the adsorption isotherms of fluids in microporous materials at elevated pressures. Figure 1 shows a schematic representation of the apparatus. A high-pressure vessel filled with a carbon adsorbent is suspended from an electronic balance. A stable temperature environment for the pressure vessel is provided by a surrounding oven, which provides temperature control to within about 0.005 K. A capillary tubing is used to connect the freely hanging vessel with the gas source, pressure measurement, and vacuum system. The electronic balance is housed in a temperature-controlled cabinet to ensure maximum mass measurement accuracy. The temperature and pressure of fluid in the vessel are measured using a calibrated platinum RTD (Minco SlO55-2) and a calibrated pressure transducer (THydronics TH-2V3 with O. 15% accuracy), respectively. The electronic balance used is an Arbor Model 2007, with a mass capacity of 2000 g and a resolution of 1 mg. Computer-controlled data acquisition was installed so that temperature and pressure data were taken periodically and plotted on the computer screen. hocedures. The volume of the high-pressure vessel is first calibrated by a reference gas whose specific volume is known. In this work, nitrogen is chosen. The volume of the vessel is determined to be 86.689 cm3. The adsorbent (approximately 5-35 g) is then sealed in the vessel and heated at 383 K for a minimum of 24 h under vacuum. The weight of adsorbent is obtained by subtracting that without adsorbent from that with adsorbent under vacuum. The dead space of the adsorbent (between particles and inside pores) is determined by high-pressure helium measurement at 373.15 Kon the assumption that no helium is adsorbed. After the calibration with helium, the adsorbent is again evacuated thoroughly. Adsorption isotherms are measured as pressure increases from 0.1 to 10 MPa at constant temperature. Equilibrium for each condition is achieved in less than 1 h. A few points on desorption isotherms are measured for all the samples. No hysteresis is found. The Gibbs (excess) adsorption isotherms reported are obtained by subtracting the amount of adsorbate in the bulk from the total amount of adsorbate in the system. The excess adsorption per unit volume, rv, is given by
* Author to whom correspondence should be addressed. 0
Abstract published in Aduunce ACS Absrrucrs, April 1, 1994.
0022-3654/94/2098-5709$04.50/0
r"= P , - & where pp and Pb are the overall density in the pore and bulk density, respectively. The amount of adsorbate in the bulk is calculated from the calibrated dead volume and standard PVT data. The standard PVT data for nitrogen, helium, methane, and ethane are from Vargaftik.11 0 1994 American Chemical Society
Jiang et al.
5710 The Journal of Physical Chemistry, Vol. 98, No. 22. 1994
Screw Pump
............................ .........................
I R
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inell Outer Oven Inner Oven yy
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,.
Figure 1. Schematic diagram of apparatus. The solid lines represent tubing and dashed lines electrical wiring. Symbols of a pressure valve, a cross-product, and a gauge denote high pressure valve, low pressure valve, and pressure gauge, respectively.
Materials. The activated carbon used is AC610 (Sutcliffe Speakman Carbons Ltd.) with a BET surface area6of 486 m2/g. The activated carbon fibers used are KF1500 (cellulose-based ACF, Toyobo Co.) and A10 (pitch-based ACF, Osaka Gas Co.) with BET surface areadz of 1500 and 1000 mz/g, respectively. Gaseous hydrocarbons used as adsorbate aremethane (Matheson Gas Co.) and ethane (Matheson Gas Co.) with purities higher than 99.99% and 99.0% respectively.
movement of a particle, taken in the usual Metropolis Monte Carlomanner,andtheneitheranattempteddeletionofarandomly chosen particleortheattempted insertion ofa particleata random position. For slit pores, periodic boundary conditions were imposed only in thexand y directions. Simulations werecarried out at a fixed slit width H, temperature T, and configurational chemical potential 140" defined as pan
Model Simulation, and Theory Model. The Lennard-Jones (LJ) potential is used in this work to represent the interactions between adsorbent molecules,
where p is the total chemical potential of the system and A is the thermal de Broglie wavelength. A correction for nonideaiity of the bulkgas phase wascalculated from thesecondvirial coefficient A-' exp(p/kT) = p / k T
with rthe interparticledistance, offthepoint at whichthe potential is zero, and elf the well depth. The methane parameters are u = 3.81 .&and c/k = 148.1 K taken from Steele." The potential is truncated, but not shifted at r, = 3 . 5 0 ~for both GCMC simulations and DFT calculations to make comparisons. In the production of adsorption isotherms using DFT, the numerical integrations were done to sufficiently large distance so that it is numerically equivalent to infinity (the full potential). The asdorbent-adsorbate interactions are represented by the 10-4-3 solid-fluid potential"
where A = 2np,e,p:fA, A is the separation between graphite lattice planes, p . is the solid density, and and u,f are the crossparameters for adsorbent-adsorbate interaction, which are calculated using a geometric mean for cSf and an arithmetic mean for o,f. z is the distance between an adsorbate molecule and the adsorbent surface. The graphite parameters are taken from Steelell and are uss= 0.340 nm, es/k = 28.0 K and A = 0.335 nm. For a given slit width H, the external potential @&) experienced by a fluid molecule at z is calculated as the superposition of 6 %for ~ the two walls @w(z) = %r(Z)
+ 4r(H- Z)
(4)
Simulation. We use the grand canonical Monte Carlo method of Adams." Each stepofthesimulation consists ofan attempted
(5)
=p-3kTln(A/o)
+ 2B2(p/kT)'
(6)
The pressure can be determined from the above equation. The secondvirialcoefficient ofmethaneis-37.0cm3/mol (B* = B/ul = -1.1107) at 313.15 K taken from Dymond and Smith.15 Theory. We use the nonlocal DFT due to Kierlik and Rosinberg,I6 which follows the general formalism of the density functional theories.17 It is based on the usual separation of fluidfluid potential into attractive and repulsive contributions. According to Weeks, Chandler, and Andersen,I8 the fluid-fluid potential can be split at the minimum r.in = 2'I6un into an attractive and a repulsive potential. The attractive contribution is estimated from the mean-field approximation. The repulsive part is modeled by a reference hard-sphere potential. The equivalent hard-sphere diameter is taken to be simply un, the hard core diameter for fluid-fluid interactions. Therefore, the grand potential functional of a system is given by
R = Fh" + i J J d r dr' p(r)
p(r')
@'"(lr
-
1')
+
where P i s the free energy of a hard-sphere reference fluid, p(r) the number density at position I, the attractive part of the fluid-fluid potential, p ' ( r ) the external potential, and p the chemical potential. For theexcesscontribution to the freeenergy functional of the reference hard-spheres fluid, Kierlik and RosinbergI6 follow PercusI9 and Rosenfeld20 in writing
Gcus = k T J dr W ( 0 1
(8)
where kTJ. is the Helmholtz free energy density of the uniform
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Figure 2. Gibbs adsorption isotherms for methane in three adsorbents-AC610 (0),KF1500 (A),and A10 (+) at (a) 313.15 K, (b) 333.15 K, (c) 353.15 K, and (d) 373.15 K.
hard-sphere fluid for some "smoothed" or weighted density pa(r) and p,(r) = Jdr' p(r')
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where &) (a = 1-4) are weighting functions. $ is taken from the scaled particle theory,*l and d a )are scalars that are simply related to the Heaviside step function and its derivatives and, hence, are independent of density. The introduction of the four density-independent weight functions is the main difference from the other nonlocal approximations proposed in the current literature. This is a great simplification. On the other hand, by construction, this functional generates the Percus-Yevick pair direct correlation function in the uniform limit and also predicts good values for higher order correlation functions. Therefore, this version of nonlocal DFT has several advantages over the others, especially for application to mixtures. The pressure of the bulk gas phase is calculated from the equation of state of the homogeneous fluid, which is composed of a hard-sphere pressure and a mean-field attractive contribution,
Results and Discussion The objective of this work is to study the adsorption behavior of methane and ethane in various microporous materials at near ambient temperatures and moderate pressures. Therefore, we study the adsorption of methane and ethane in three different carbon adsorbents at pressures up to 10 MPa and at temperatures between 3 13.1 5 and 373.1 5 K. Gibbs adsorption isotherms for methaneandethaneinAC610, KF1500, and AlOat four different temperatures are given in Figures 2 and 3. For methane adsorption as shown in Figure 2, the AC610 has the greatest adsorption, followed by KF1500 and A10 while for ethane adsorption, as shown in Figure 3, the order of decreasing adsorption is still AC610, KF1500, and A10 except a t 313.15 K. Even though the surface area of AC610 is lower than that of KF1500 and A10, AC610 has a larger micropore volume and contains some portion of smaller pores. Therefore, the amount of methane and ethane adsorbed in AC610 grows faster than that in KF1500 and A10 in the lower pressure region and is also greater in the higher pressure region. As shown in Figures 2 and 3, most of the adsorption isotherms show a maximum. It is important to point out that it is the Gibbs adsorption that is being measured. The total adsorption is still increasing after the maximum, but now the rate of increase in the density of the adsorbed phase is not
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Figure 4. Comparison of adsorption isotherms for methane in A10. The solid line represents our result at 313.15 K and the dashed line that of Kaneko et a1.* at 303.15 K.
as great as that of the gas phase. For all three carbon adsorbents, ethane adsorption isotherms rise sharply to their maxima around 2-3 MPa, while methane adsorption isotherms increasegradually to their maxima at higher pressure between 6 and 10 MPa. This is due to the stronger interaction potential between ethane molecules and the substrate. The activated carbon fibers KF1500 and A10 do not show larger adsorption capacities as expected, but instead are usually lower. The structures and thus properties of activated carbon fibers are more complicated than those of nonfibrous activated carbons and are not known well at present. In our continuing studies, we plan to investigate other types of activated carbons with higher specific surface areas using similar experimental methods, and to model the activated carbon fibers using molecular simulation techniques. With these studies, we hope to have a better understanding of structures and properties of materials of this type. Figure 4 shows a comparison of an adsorption isotherm of methane in A10 measured by Kaneko et al.* and by us. Their measurements were made a t 303.15 K while ours are at 3 13.15 K. However, the methaneadsorption from their isotherm is even lower than that from ours. We repeated our experiments for the calibration of dead volume using helium and for the measurement of the methane adsorption isotherm. The reproducibility was excellent. Weused5.377gofAlOinourexperimentwhileKaneko et a[.* used less than 100 mg. The discrepancy could be due to the small amount of adsorbent used and the fact that there is substantial variety of properties within samples. A direct use of the above results can be made by plotting versus pressure the storage density of methane in the vessel filled with
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Figure 7. Comparison of adsorption isotherms for methane in slit pores with H* = 5.0 at 313.15 K from G C M C simulation (solid line) and nonlocal DFT (dashed line).
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Figure 5. Storage densities of methane in the vessel filled with AC610 (0)and in the bulk (A) plotted against pressures at (a) 313.15 K, (b) 333.15 K, (c) 353.15 K, and (d) 373.15 K.
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H' Figure 8. Adsorption isobars (dashed lines) for methane in slit p r e s at 3 13.1 5 K for pore widths H* from 1.9 to 4.0 from nonlocal DFT. The surface drawn through the dashed lines shows the adsorption-pressurepore width relation.
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Figure 6. Same as Figure 5, but for ethane.
adsorbent and in the bulk.22 The amount of methane stored includes that adsorbed and that in the dead volume (between particles and inside pores). This approach is arbitrary because the values strongly depend on the packing of adsorbent. Here we give only the plots of storage density versus pressure for methane (Figure 5) and ethane (Figure 6) in AC610, since the determination of packing volume for carbon fibers is much more arbitrary than that of AC610. It can be seen from Figure 5a that to store the same amount of methane at 3.5 MPa using AC610 would require a pressure of 7 MPa as a compressed gas. Alternatively, storage capacity of methane as a compressed gas is only 40% of that stored using AC610 at the same pressure of 3.5 MPa. As shown in Figure 6, the effect of AC610 on ethane storage is greater t h a n on methane. The PSD of AC610 was determined by Seaton et al.5 and also by Lastoskie et al.' By using the calculated PSD of Lastoskie et al.,' we are able to compare our simulation and theoretical prediction with our experiment. The comparison provides a test of the model used in the theory and simulation and also of the PSD. A molecular simulation approach has the advantage that statistical mechanical equations are solved exactly for the prescribed model. The principal disadvantage is cost. Nonlocal DFT is quite accurate under a wide range of conditions and computationally much faster than the simulation technique. We carried out some GCMC simulations to determine adsorption isotherms and compared them with those predicted from nonlocal DFT. One example is given in Figure 7, where the amount of
methane STPCC (cubic centimeters at standard temperature and pressure) adsorbed per unit micropore volume is plotted against pressure. It shows good agreement between the simulation and theoretical prediction. Therefore, nonlocal DFT was used to generate the adsorption isobars for methane in slit pores at T = 313.15 K for H* = 1.9-40. Here H* = H / u where H i s pore width and u is hard core diameter of methane molecules. The results for H* = 1.9-4.0 are shown in Figure 8. The isobars decay with the pore width and approach the bulk value as the pore separation becomes large. By applying the PSD of AC610 to each isobar, we can obtain the amount of methane adsorbed a t a fixed pressure. The Gibbs adsorption isotherm so obtained is given in Figure 9, together with the adsorption isotherm from our experiment. The agreement is only fair. There are several possible sources of error in the theoretical prediction of the adsorption isotherm: (1) the assumption of slit pores with parallel walls and an infinite graphite layer neglects the inhomogeneity of the materials, (2) pore blocking and networking effects (neglected in the model) may be significant, (3) swelling of the carbon pores could occur a t the high pressures used here, and is neglected in the model, and (4) there could be errors due to the use of the DFT. In view of existing evidence of the swelling of these carbon pores on adsorption,23 it seems likely that this may well be an important factor in producing the discrepancy in Figure 9. Conclusions
Adsorption isotherms of methane and ethanein activated carbon (AC610) and activated carbon fibers (KF1500 and A10) have been measured at pressures up to 10 MPa and temperatures between 313.15 and 373.15 K by a modified direct weighing
The Journal of Physical Chemistry, Vol. 98, No. 22, 1994 5713
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for providing the computer program for the nonlocal density functional theory. We acknowledge financial support of this work from a grant from the National Science Foundation (No. CTS9 122460).
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References and Notes
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Figure 9. Comparison of adsorption isotherms from our experiment (solid line) and theoretical prediction (dashed line) for methane in AC610 at 313.15 K.
densimeter. The order of decreasing adsorption is AC610, KFl500, and A10 for methane and ethane adsorption, except for ethane adsorption at 313.15 K. On a volume basis, AC610 is found to have 2.5 times higher methane uptakes than bulk compressed methane at a storage pressure of 3.5 MPa near room temperature. KFl500 and A10 do not show adsorption capacities larger than AC610. Further efforts are needed to have a better understanding of the structures and properties of the activated carbon fibers. The nonlocal DFT due to Kierlik and Rosinberg is shown to give adsorption isotherms in good agreement with molecular simulation at these temperatures and pressures. It is useful for the generation of adsorption isotherms over a wide range of conditions, because it is computationally much faster than the simulation. The adsorption-isotherm of methane in AC6 10 predicted by combining the nonlocal DFT predictions and a previously obtained PSD iS in Only fair agreement with experiment. TOimprove the theoretical prediction, several factors and pore (e'g*inhomogeneity Of the be taken into account.
Acknowledgment. It is a pleasure to thank N. Quirke, K. Kaneko, and T. Suzuki for providing several carbon samples and reprints prior to publication, and E. Kierlikand M. L. Rosinberg
(1) Tan, Z.; Gubbins, K. E. J . Phys. Chem. 1990, 94, 6061. (2) Matranga, K. R.; Myers, A. L.; Glandt, E. D. Chem. Eng. Sci. 1991, 47, 1569. (3) Cracknell, R. F.; Gordon, P.; Gubbins, K. E. J . Phys. Chem. 1993, 97, 494. (4) Kaneko, K.; Ishii, C.; Ruike, M.; Kuwabara, H. Carbon 1992, 30, 1075. (5) Seaton, N. A.; Walton, J. R. P. B.; Quirke, N. Carbon 1989,27,853. Jessop, C. A.; Roddiford, S. M.; Seaton, N. A.; Walton, J. R. P. B.; Quirke, N. In Characterization of Porous Solids II; Rodriguez-Reinoso, F., Ed.; Elsevier: Amsterdam, 1991. (6) Rhykerd, C. L.; Went, G. T.; Gubbins, K. E.; Duncan, T. M. Manuscripfin preparation. (7) Lastoskie, C.; Gubbins, K. E.; Quirke, N. J . Phys. Chem. 1993, 97, 4786. ( 8 ) Kaneko, K.; Murata, K.; Shimizu, K.; Camara, S.; Suzuki, T. Langmuir, 1993, 9, 1165. (9) Miller, J. F. M.S. Thesis, Cornell University, 1984. (10) Deitrick, B. E. M.S. Thesis, Cornell University, 1986. (1 1) Vargaftik, N. B. Handbook of Physical Properties of Liquids and Gases, 2nd ed.;Hemisphere: Washington, 1983. (12) Suzuki, T. Private communication, 1993. (1 3) Steele, W. A. Surf.Sci. 1973,36,3 17. Steele, W. A. The Interaction of Gases with Solid Surfaces; Pergamon: Oxford, 1974. (14) Adams, D. J. Mol. Phys. 1974,28, 1241. Adams, D. J. Mol. Phys. 1975, 29, 307. Adams, D. J. Mol. Phys. 1979, 32, 647. (15) Dymond, J. H.; Smith, E. B. The Virial Coefficients of Pure Gases and Mixtures: Clarendon: Oxford. 1980. (16). Kierlik, E.; Rosinberg, M.L. Phys. Reu. 1990, A42, 3382. Kierlik, E.; Roslnb%%M. L.PhYS. Reo. 19917 A441 5025. (17) Evans, R. In Inhomogeneous Fluids; Henderson, D., Ed.; Dekker: New York, 1992. (18) Weeks, J. D.; Chandler, D.; Anderson, H. L. J. Chem. Phys. 1971, 543'5237. (19) Percus, J. J . Stat. Phys. 1988,52, 1157. (20) Rosenfeld, Y Phys.Reu. Lett. 1989,63,980. Rosenfeld, Y.; Levesque, D.; Weis, J. J. J . Chem. Phys. 1990,92,6918. Rosenfeld, Y. Phys. Rev. 1990, A42, 5978. Rosenfeld, Y. J . Chem. Phys. 1990,93,4305. (21) Reiss, H.; Frisch, H.; Lebowitz, J. L. J . Chem. Phys. 1959,31,369. Helfand, E.; Frisch, H. L,; Lehwitz, J. L. J , Chem. phys. 1961, 34, 1037. (22) Barton, S.S.; Dacey, J. R.; Quinn, D. F. In Proceedings of the First International Conference on the Fundamentals of Adsorption; Myers. A. L., 1984. Ed.; EngineeringFoundation: New (23) Kaneko, K.; Suzuki, T.; Fujiwara, Y.; Nishikawa, K. In Characterization of Porous Solids It; Rodriguez-Reinoso, F., Ed.; Elsevier: Amsterdam, 1991. I
