© Copyright 1999 by the American Chemical Society
VOLUME 103, NUMBER 2, JANUARY 14, 1999
LETTERS Computer Simulations of Hydrogen Adsorption on Graphite Nanofibers Qinyu Wang and J. Karl Johnson* Department of Chemical and Petroleum Engineering, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15261 ReceiVed: September 30, 1998; In Final Form: NoVember 9, 1998
Adsorption of hydrogen on graphitic nanofibers has been computed from Grand Canonical Monte Carlo simulations. The graphite platelet spacing has been optimized to maximize the weight fraction of hydrogen adsorbed. Comparison of experimental data of Rodriguez and co-workers (Chambers, A; Park, C.; Baker, R. T. K.; Rodriguez, N. M. J. Phys. Chem. B 1998, 102, 4253) with adsorption isotherms from simulations indicate that the phenomenal uptake observed from experiments cannot be explained in terms of reasonable solid-fluid potentials. We have varied the strength and range of the solid-fluid potential in order to reproduce the experimental excess adsorption. If the form of the potential is held constant, the potential well depth must be increased by a factor of about 150 in order to reach the experimental data. If the range of the attractive well is allowed to increase from r-6 to r-4, the potential well depth must be increased by about a factor of 30 to match experimental data. Given the magnitude of the well depths, we conclude that no physically realistic graphite-hydrogen potential can account for the adsorption reported by Rodriguez et al.
Hydrogen storage by physisorption has been the subject of numerous experimental studies in recent years.1 The motivation stems from the need to store hydrogen safely and economically for applications such as fuel-cell vehicles.1 Many experimental groups have focused on hydrogen adsorption on graphitic sorbents. These include activated carbons,2,3 carbon nanotubes,4 and graphitic nanofibers.5,6 By far the most striking experimental results reported have been hydrogen uptake on graphitic nanofibers (GNFs).5 GNFs are new carbon materials produced by catalyzed decomposition of carbon-containing compounds.6,7 They consist of very small graphitic platelets, 30-500 Å on a side, and stacked in layers forming fibers many micrometers in length. Rodriguez and co-workers have reported that some samples of these nanofibers can adsorb phenomenal amounts of hydrogen at room temperature.5 Excess adsorption of up to 2 kg of H2/kg of carbon has been reported at an initial pressure of 112 atm and 298 K.5 In this paper we seek to answer the question of whether standard physisorption models can account for this high hydrogen uptake in GNFs.
We have performed Grand Canonical Monte Carlo (GCMC) simulations of hydrogen adsorption on a model of GNFs. The GNFs are modeled by single graphite platelets with a pore width H. A sample snapshot of a simulation cell is shown in Figure 1. The pore width H is defined as the distance between graphite platelets, as measured from the carbon centers. Adsorption is allowed within the pores and on the external surface (edges) of the platelets. The graphite platelet is a planar hexagonal lattice of carbon sites, held rigidly in place throughout the simulation. The carbon atoms at the edge of the platelet were treated as if all bonds were saturated (i.e., no dangling bonds), but terminating atoms were not explicitly accounted for in the hydrogennanofiber potential. GNFs consist of parallel stacks of graphite platelets that are oriented parallel, perpendicular, or at an angle with respect to the fiber axis. These structures are termed tubular, platelet, and herringbone, respectively.5 Our model is a firstorder approximation to the platelet structure of GNFs because the platelets are oriented perpendicular to the fiber axis. In this study, hydrogen molecules are treated as classical
10.1021/jp9839100 CCC: $18.00 © 1999 American Chemical Society Published on Web 12/19/1998
278 J. Phys. Chem. B, Vol. 103, No. 2, 1999
Letters
φMCB(r,θ) )
[(
) ( )
σsf 33/2 CB 2 r
Figure 1. Snapshot of a simulation cell used to model platelet graphite nanofibers. The pore width is 9 Å. The filled circles are carbon atoms, and the open circles represent hydrogen molecules.
spherical particles. The hydrogen-hydrogen interaction is modeled by the Silvera-Goldman potential,8 which has previously been shown to accurately model the properties of fluid hydrogen.9 We have used the Crowell-Brown (CB) potential10 and a modified version of the Crowell-Brown (MCB) potential for the hydrogen-carbon interactions. The Crowell-Brown potential was chosen because the anisotropic polarizability of the graphite sheet is explicitly taken into account, which should provide a better description of the adsorption on the edge of the graphite sheet than the isotropic potentials. The CrowellBrown and Silvera-Goldman potentials have been used previously to model hydrogen adsorption on graphite, graphitic slit pores, and carbon nanotubes11,12 and have been shown to be accurate for reproducing experimental adsorption isotherms for H2 on graphite.11 The Crowell-Brown potential is given by
φCB(r,θ) )
[(
4CB
]
) ( )
σsf r
12
-
σsf 6 3(P| - P⊥)cos2 θ + (P| + 5P⊥) (1) r 4P| + 2P⊥
where r is the distance from the hydrogen molecule to the carbon atom, θ is the angle between the axis normal to the graphite sheet and a line connecting the hydrogen and carbon atoms, σsf is the solid-fluid Lennard-Jones size parameter, σff is the fluid-fluid Lennard-Jones size parameter, and CB is the well depth at θ ) 0, written in terms of atomic parameters as
CB )
EHECPH(4P| + 2P⊥) (EH + EC)σ6ff
(2)
The parameters are given elsewhere.10 The CB potential accounts for the difference in the polarizability of the graphite sheet parallel (P|) and perpendicular (P⊥) to the graphite plane. The range of the solid-fluid potential can have a significant effect on adsorption. We have modified the standard CB potential to make it longer-ranged by making the attractive term vary as r-4 instead of r-6. The r-4 term can represent a dipolequadrupole interaction. This form of the potential can be rationalized by noting that heteroatom or geometric defects in the graphite platelet could give rise to local dipoles. These dipoles would interact with the quadrupole on hydrogen to give a potential that scales as r-4. The modified CB potential for hydrogen-carbon interaction is given by
12
]
σsf 4 3(P| - P⊥)cos2 θ + (P| + 5P⊥) (3) r 4P| + 2P⊥
The MCB potential gives the same well depth and crosses zero at the same value of r as the CB potential for θ ) 0. The total solid-fluid potential for the CB potential is computed by explicitly summing interactions with carbon atoms on three platelets above and below the hydrogen molecule. The MCB potential is longer-ranged, and so five platelets above and below a given hydrogen molecule are included in the solid-fluid potential. The error due to truncation of the range of the potential was found to be less than 1 K at the potential minimum. Figure 2 shows the hydrogen-nanofiber potentials from the CB and MCB potentials in a GNF platelet model with a pore width of H ) 30 Å. The hydrogen-nanofiber potential in the center of the pore is -33 K for the MCB potential but only -2.43 K for the CB potential, with the difference being due to the longrange character of the MCB potential. A cutoff of 15 Å has been used for the fluid-fluid interactions. The number of pores used in the primary simulation cell was always consistent with the fluid-fluid cutoff, so that four slit pores were used for H ) 9 Å, two for H ) 15 Å, and one for H g 30 Å. We have simulated infinitely long nanofibers by applying a periodic boundary condition in the z direction. The platelets are centered in the simulation cell with respect to the x and y directions in order to mimic an isolated nanofiber. The simulations employed a lateral box length of Lx ) Ly ) 60 Å, except for the MCB potential with g 30CB, for which Lx ) Ly ) 120 Å was used. Some simulations were repeated with larger values of the lateral dimension; the results were in agreement with the smaller cell sizes within statistical uncertainty. Periodic boundary conditions were used in all three directions, but the minimum image convention was not used to compute solid-fluid interactions in the x and y directions (i.e., the nanofiber was isolated, rather than in a periodic array of nanofibers). The area of each of the graphite platelets is about 500 Å2, making them somewhat smaller than the smallest of the experimentally observed nanofibers. The smaller surface area should not affect the physics of adsorption. Adsorption is allowed on the external surface of the GNFs to account for the edge-on adsorption. The GCMC simulations were performed by holding the platelet spacing fixed for a given simulation. In previous studies of hydrogen adsorption, we have explicitly accounted for quantum effects.11,12 Inclusion of quantum corrections will decrease the amount of hydrogen adsorbed at a given temperature and pressure. Quantum effects are expected to be quite small for the temperatures and pressures of interest in this study. The excess adsorption was computed as a function of the platelet spacing. The excess adsorption is defined as the difference between the amount of hydrogen in the vessel with the adsorbent and the amount present in the same vessel without the adsorbent. Note that the definition of excess adsorption used here and by Rodriguez et al.5 is different from that in standard use.3 We first consider the excess adsorption in GNF platelets using the standard CB potential. We have calculated the adsorption isotherm for the GNF platelet with a pore width of H ) 9 Å from the standard CB potential. We have chosen H ) 9 Å because our previous study12 has shown that at 298 K and 100 atm, the idealized slit pore of width H ) 9 Å gives the largest excess adsorption. Although all edge effects were ignored in our previous calculations, we do not expect this to dramatically affect the optimum pore width. This has been confirmed by comparing the simulation results of GNF platelets with pore
Letters
Figure 2. Adsorption potentials for hydrogen in a platelet GNF model with a pore width of H ) 30 Å. The solid line is the standard CrowellBrown potential, and the dashed line is the modified Crowell-Brown potential with an attractive term varying inversely as the fourth power of the distance between the molecules.
Figure 3. Excess weight fractions of hydrogen adsorbed on platelet GNFs as a function of pore width from the CB potential with different well depths at 298 K and 112 atm. Dashed lines denote the range of experimental data.5
widths of H ) 9, 15, 30, and 60 Å (Figure 3), where it was found that the H ) 9 Å pore gives the highest excess weight fraction. We compare the maximum adsorption from simulations with the experimental data of Rodriguez et al.5 The experiments show that the GNF platelets give weight fractions of hydrogen uptake from 45% to 53% at 298 K and an initial pressure of 112 atm. The weight fraction of hydrogen is defined as WH2/ (WH2 + Wcarbon), where WH2 is the excess weight of hydrogen and Wcarbon is the weight of carbon. In the GCMC simulations, the chemical potential is held fixed throughout the simulation. This does not correspond exactly to the experimental setup where the pressure drops as gas adsorbs, but it is easy to see that simulations with the pressures held constant at the maximum experimental pressure will provide an upper-bound estimate of the amount that can adsorb when the pressure is allowed to drop. The simulation results for the H ) 9 Å GNF platelet at 298 K and 112 atm gives a weight fraction of 0.46%, which is a factor of 100 less than that reported experimentally.5 The excess adsorption isotherm (not shown) goes through a maximum at about 50 atm, where the largest weight fraction is only 1.6%. Experimental measurement of the spacing between the graphite platelets in GNFs before adsorption gives a value of 3.4 Å, similar to the spacing between layers of turbostratic graphite. We note that it is not possible for hydrogen to adsorb into a graphitic pore of width 3.4 Å because the pore width is the distance between the carbon centers, so that a carbon pore
J. Phys. Chem. B, Vol. 103, No. 2, 1999 279
Figure 4. Excess weight fractions of hydrogen adsorbed in platelet GNFs as a function of pore width from the MCB potential with different well depths at 298 K and 112 atm. Dashed lines denote the range of experimental data.5
of width 3.4 Å has virtually no space available for adsorption. This indicates that the platelet spacing must increase dramatically to allow large amounts of hydrogen to adsorb. However, the platelet spacing has not been measured experimentally in the presence of the adsorbate, so the in situ spacing is not known. The platelet spacing is held constant in the simulations, so we cannot directly compare our simulations with the nanofiber experiments. We therefore performed simulations for GNF platelets with three additional pore widths, H ) 15, 30, and 60 Å, at 298 K and 112 atm. It is important to point out that the equilibrium values of adsorption do not depend on the details of approach to equilibrium. In other words, the fact that our platelets do not expand during the course of a simulation will not change the equilibrium loading for a given spacing. Thus, the expansion of the platelets can be reliably modeled by performing a series of equilibrium simulations with different values of the fixed platelet spacing. For GNF platelets with pore width larger than H ) 9 Å, the weight fraction decreases with pore width and eventually goes to a constant. This is because the standard CB potential is very weak in the center of large pores and, therefore, has a negligible effect on the gas density near the center of the pore given the fact that no capillary condensation occurs. We note that nonparallel graphite platelets can produce a strong solid-fluid interaction in corners where platelets meet.13 Although there is no experimental evidence for the presence of nonparallel plates in the nanofiber samples, if such defects were present, the enhanced solid-fluid interaction in the corners would facilitate the adsorption. However, we believe that adsorption at the corners would constitute only a small fraction of the total amount adsorbed since the surface area of the corners would be small. The densities in the center of the large pores are identical to the bulk gas density, so that increasing the pore width to larger values will not increase the excess adsorption in the pore. Our simulations indicate that the very large values of adsorption reported in the experiments5 cannot be explained by the standard solid-fluid potential models for hydrogen-carbon interactions. It appears that a much stronger and perhaps longer-ranged solid-fluid potential is needed to reproduce the experimentally observed hydrogen uptake. We have performed simulations with stronger solid-fluid potentials by simply scaling the well depth of the CB potential. This shows the effect of the strength of the solid-fluid potential on adsorption. Figure 4 shows the excess weight fraction as a function of wall spacing H for potentials with seven different well depths, ) 1, 5, 10, 20, 50, 100, and 150CB at 298 K and
280 J. Phys. Chem. B, Vol. 103, No. 2, 1999
Figure 5. Density profiles for hydrogen inside GNF platelets with a pore width of H ) 30 Å. The density profile from the CB potential with ) 150CB is given in part a, and the MCB potential with ) 30CB density profile is given in part b.
112 atm, where is the well depth of the potential used in the simulation. The dashed lines in the plot denote the range of experimental data. Not surprisingly, the weight fraction of hydrogen increases with the strength of the solid-fluid potential. The range of the experimental data can be reached by increasing the potential strength but only for ≈ 150CB for a pore of H g 15 Å. A value of ) 150CB corresponds to a binding energy of 3507 K (0.30 eV) for a hydrogen molecule interacting with a single carbon atom (at θ ) 0). This value is far below the C-H bond enthalpy of 4.3 eV.14 However, the hydrogen-pore binding energy for a nanofiber with a pore width of H ) 30 Å turns out to be 76 500 K (6.6 eV), which is over an order of magnitude larger than the largest binding energies for a single adatom physisorbed onto a surface.15 The experimental values of the isosteric heat of adsorption for hydrogen on basal plane graphite at zero coverage range from 500 to 650 K.16-18 The 6.6 eV binding energy corresponds to very strong chemisorption. There are no known physisorption potentials with such large binding energies. We therefore conclude that the potential well depths required to reproduce the experimental data are unphysical. Some fraction of the hydrogen adsorbed on the nanofibers may be chemisorbed, as indicated by Rodriguez et al.5 However, it is inconceivable that chemisorption on carbon could account for more than four H atoms per carbon (i.e., methane). The experimentally observed hydrogen uptake corresponds to 1014 H atoms per carbon. On the other hand, it may be possible that some metals capable of dissociatively absorbing hydrogen are dispersed in the nanofibers as a result of the process used to remove the metal catalyst particles.6 These metals could be responsible for some fraction of the hydrogen uptake. The density profiles for hydrogen adsorbed in a H ) 30 Å pore at ) 150CB are presented in Figure 5a. The density profile shows a very high peak for the first-layer adsorption. This indicates that the extremely strong solid-fluid forces cause the hydrogen molecules to pack much closer than what is traditionally thought of as close packing. The average nearestneighbor spacing between hydrogen molecules in the first layer is 2.2 Å, compared to the 3.51 Å nearest-neighbor spacing for monolayer completion of para-H2 on graphite.15 Three layers of hydrogen form on each wall of the pore, as
Letters opposed to one layer for the standard CB potential. The density in the center of the pore is equal to the bulk density, even for ) 150CB, because of the short-ranged nature of the potential. The excess adsorption exhibits a maximum for a pore width of about H ) 30 Å. Recall that the maximum of excess adsorption occurs at H ) 9 Å for the regular potential. The excess weight fraction for the MCB potential is shown as a function of pore width and in Figure 4. For ) 30CB, the GNF platelets with pore widths H g 15 Å give weight fractions falling into the experimental data range. A value of ) 30CB for the MCB potential in a H ) 30 Å pore gives a binding energy of 46 200 K (4.0 eV), which is well in the chemisorption range. The well depth required to achieve experimental loadings with the MCB potential is considerably less attractive than for the CB potential. The difference can be explained in terms of the effect that the range of the potential has on the density profiles away from the platelet surface. Due to the longer range of the MCB potential, the density of H2 in the center of a H ) 30 Å pore, shown in Figure 5b, is substantially higher than the bulk gas density. The density of H2 away from the platelets constitutes a substantial fraction of the excess adsorption for the MCB potential. In contrast, excess adsorption beyond the first three adsorbed layers for the CB potential is essentially negligible, as can be seen by comparing Figure 5a and 5b. The average H2 nearest-neighbor spacing in the first layer is 2.6 Å for Figure 5b. This is larger than the spacing for the CB potential with ) 150CB, but still considerably more densely packed than graphite monolayer coverage.15 We have computed the adsorption isotherm (not shown) for the H ) 30 Å pore using the MCB potential with ) 30CB. It was found that the filling of the first three layers on each wall of the pore is a continuous process. The formation of the dense fluid in the center of the pore is also continuous. This indicates that no capillary condensation occurs at 298 K, even with a very strong and long-ranged solid-fluid potential. This is not surprising because 298 K is well above the critical temperature of hydrogen (33 K). The excess adsorption isotherm exhibits maximum at a pressure of 210 atm. In this study we have attempted to model the salient physics of hydrogen adsorption on graphitic nanofibers. We have used the best available graphite-hydrogen potential and have modeled the experimental geometry with a fair amount of detail. We conclude that the experimental results are not consistent with any reasonable physisorption model. Assuming that the solid-fluid potential is not very seriously in error, our results indicate that no slit pore geometries are capable of adsorbing the amount of H2 reported by Rodriguez et al.5 Unrealistically strong solid-fluid potentials are needed to reproduce experimental data, even if the potential is long-ranged. Given our results, there is a need for independent experimental verification of the data of Rodriguez and co-workers. Confirmation of the experiments would necessitate a substantial revision of our understanding of the physics of adsorption for this system. Acknowledgment. Support from the National Science Foundation through CAREER Grant No. CTS-9702239 to J.K.J. is acknowledged. Sandia National Laboratory and the donors of the Petroleum Research Fund, administered by the American Chemical Society, are acknowledged for partial support of this work. References and Notes (1) Hynek, S.; Fuller, W.; Bentley, J. Int. J. Hydrogen Energy 1997, 22 (6), 601.
Letters (2) Amankwah, K. A. G.; Noh, J. S.; Schwarz, J. A. Int. J. Hydrogen Energy 1989, 14, 437. (3) Chahine, R.; Bose, T. K. Int. J. Hydrogen Energy 1994, 19, 161. (4) Dillon, A. C.; Jones, K. M.; Bekkedahl, T. A.; Kiang, C. H.; Bethune, D. S.; Heben, M. J. Nature 1997, 386, 377. (5) Chambers, A.; Park, C.; Baker, R. T. K.; Rodriguez, N. M. J. Phys. Chem. B 1998, 102, 4253. (6) Rodriguez, N. M. et al. U.S. Patent 5653951, 1997. (7) Krishnankutty, N.; Rodriguez, N. M.; Baker, R. T. K. Catal. Today 1997, 37, 295. (8) Silvera, I. F.; Goldman, V. V. J. Chem. Phys. 1978, 69, 4209. (9) Wang, Q.; Johnson, J. K.; Broughton, J. Q. Mol. Phys. 1996, 89, 1105.
J. Phys. Chem. B, Vol. 103, No. 2, 1999 281 (10) Crowell, A. D.; Brown, J. S. Surf. Sci. 1982, 123, 296. (11) Wang, Q.; Johnson, J. K. Mol. Phys. 1998, 95, 299. (12) Wang, Q.; Johnson, J. K. J. Chem. Phys. 1999, 110, 577. (13) Bojan, M. J.; van Slooten, R.; Steele, W. A. Sep. Sci. Technol. 1992, 27, 1837. (14) Atkins, P. W. Physical Chemistry; W. H. Freeman and Co.: New York, 1990. (15) Bruch, L. W.; Cole, M. W.; Zaremba, E. Physical Adsorption: Forces and Phenomena; Clarendon Press: Oxford, 1997; p 2. (16) Pace, E. L.; Siebert, A. R. J. Phys. Chem. 1959, 63, 1398. (17) Constabaris, G.; Sams, J. R., Jr.; Halsey, G. D., Jr. J. Phys. Chem. 1961, 65, 367. (18) Dericbourg, J. Surf. Sci. 1976, 59, 565.
