Molecular Simulations of Hydrogen Storage in Carbon Nanotube Arrays

Grand canonical ensemble Monte Carlo (GCEMC) molecular simulations of hydrogen storage at ..... of Bath for provision of a University Research Student...
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Langmuir 2000, 16, 10521-10527

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Molecular Simulations of Hydrogen Storage in Carbon Nanotube Arrays You Fa Yin,†,‡ Tim Mays,*,§ and Brian McEnaney‡ Materials Research Centre, Department of Engineering and Applied Science, University of Bath, Bath BA2 7AY, United Kingdom, and Department of Chemical Engineering, University of Bath, Bath BA2 7AY, United Kingdom Received June 27, 2000 Grand canonical ensemble Monte Carlo (GCEMC) molecular simulations of hydrogen storage at 298 and 77 K in triangular arrays of single wall carbon nanotubes (SWCNT) and in slit pores (modeling activated carbons) were performed. At 298 K the US DOE target gravimetric hydrogen storage capacity (6.5 wt %) is reached at 160 bar for optimally configured arrays of open SWCNT of wide diameter, but the equivalent volumetric capacity is ∼40% of the DOE target [695 (STP) v/v]. For slit pores at 298 K the optimal volumetric capacity is ∼20% of the target. Simulations for 77 K and 70 bar indicate that triangular arrays of open and closed SWCNT of various diameters in a wide range of configurations exceed the DOE gravimetric target. A capacity of 33 wt % is found for arrays of narrow, open, or closed SWCNT that are widely spaced. Here, adsorption occurs entirely in the interstitial space between the nanotubes. Volumetric capacities close to the DOE target are found for arrays of narrow, open or closed SWCNT with a range of interstitial spacings. The maximum volumetric capacities for simulations with slit pores at 77 K and 70 bar are ∼73% of the DOE target for a range of pore widths. Capacities from simulations for nanotubes and slit pores at 298 and 77 K are in reasonable agreement with experimentally measured capacities. It is concluded that the potential of carbon nanotubes for storage of hydrogen is superior to that of activated carbons.

Introduction Hydrogen is an attractive energy vector because of its low environmental impact,1 but a critical problem is its low energy density. For example, the US Department of Energy (DOE) hydrogen plan for fuel cell powered vehicles requires a gravimetric density of 6.5 wt %. This is equivalent to a volumetric density of 62 kg H2 m-3,2 or 695 (STP) v/v. There are several hydrogen storage methods,1,3 including compressed gas, liquefaction, metal hydrides, and physisorption, but, at present, none of these technologies achieves the DOE target. Although physisorption has been claimed to be the most promising hydrogen storage technology4 and activated carbons the best adsorbent,5,6 the highest volumetric storage capacity of commercially available activated carbons is around 32 kg H2 m-3 at 77 K and 50 bar, equivalent to 359 (STP) v/v. Recently, there has been a resurgence of interest in the potential of carbon materials as hydrogen storage media following claims that single wall carbon nanotubes (SWCNT),2 and certain types of vapor grown carbon fibers7 may have high hydrogen storage capacities at room * To whom correspondence should be addressed. Telephone: +44 (0)1225 826528. Fax: +44 (0)1225 826894. E-mail: t.j.mays@ bath.ac.uk. † Present address: Institute of Polymer Technology and Materials Engineering, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom. ‡ Materials Research Centre. § Department of Chemical Engineering. (1) Ter-Gazarian, A. Energy Storage for Power Systems; Institution of Electrical Engineers: London, 1994. (2) Dillon, A. C.; Jones, K. M.; Bekkedahl, T. A.; Kiang, C. H.; Bethune, D. S.; Heben, M. J. Nature 1997, 386, 377. (3) Amankwah, A. G.; Noh, J. S.; Schwarz, J. A. Int. J. Hydrogen Energy 1989, 14, 437. (4) Hynek, S.; Fuller, W.; Bentley, J. Int. J. Hydrogen Energy 1997, 22, 601. (5) Chahine, R.; Bose, T. K. Int. J. Hydrogen Energy 1994, 19, 161. (6) Carpetis, C.; Peschka, W. Int. J. Hydrogen Energy 1980, 5, 539. (7) Chambers, A.; Park, C.; Baker, R. T. K.; Rodriguez, N. M. J. Phys. Chem. 1998, 102, 4253.

temperature. On the basis of temperature programmed desorption experiments Dillon et al.2 postulated that triangular arrays of SWCNT with diameters of 20 Å have a volumetric storage capacity for hydrogen of about 560 (STP) v/v. Theoretical calculations of hydrogen adsorbed in carbon nanotubes by Stan and Cole8 indicated that nanotubes are good adsorbents for hydrogen and that quantum effects are not important for adsorption at temperatures above 50 K. Also, Monte Carlo molecular simulations of hydrogen adsorption at 293 K and up to 100 bar by Darkrim and Levesque9 indicate that SWCNT are good adsorbents for hydrogen. Molecular simulations of nitrogen adsorption in carbon nanotubes10,11 also suggest that they might be good adsorbents. On the other hand, Wang and Johnson12 and Rzepka et al. 13 performed molecular simulations on hydrogen storage in both activated carbons and carbon nanotubes. They found that the hydrogen storage capacity of both systems is low and that carbon nanotubes adsorb more hydrogen than activated carbons only at very low pressures. Wang and Johnson12 concluded that nanotubes are not suitable sorbents for achieving the DOE targets for vehicular hydrogen storage at ambient temperature. In addition, experimental results of nitrogen adsorption in carbon nanotube materials published so far14-17 seem to (8) Stan, G.; Cole, M. W. J. Low Temp. Phys. 1998, 110, 539. (9) Darkrim, F.; Levesque, D. J. Chem. Phys. 1998, 109, 4981. (10) Maddox, M. W.; Gubbins, K. E. Langmuir 1995, 11, 3988. (11) Maddox, M. W.; Ulberg, D.; Gubbins, K. E. Fluid Phase Equilibria 1995, 104, 145. (12) Wang, Q.; Johnson, J. K. J. Chem. Phys. 1999, 110, 577. (13) Rzepka, M.; Lamp, P.; de la Casa-Lillo, M. A. J. Phys. Chem. B 1998, 102, 10 894. (14) Gaucher, H.; Pellenq, R. J. M.; Grillet, Y.; Bonnamy, S.; Beguin, F. Carbon ‘97, Penn State: PA, 1997; p 388. (15) Mackie, E. B.; Wolfson, R. A.; Arnold, L. M.; Lafdi, K.; Migone, A. D. Langmuir 1997, 13, 7197. (16) Tsang, S. C.; Harris, P. J. F.; Green, M. L. H. Nature 1993, 362, 520. (17) Alain, E.; McEnaney, B.; Mays, T. J. Carbon ‘99; Charleston, SC, 1999; p 88.

10.1021/la000900t CCC: $19.00 © 2000 American Chemical Society Published on Web 11/23/2000

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Figure 1. Cross-sectional view of model triangular nanotube array. The shaded area denotes the cross sections of the simulation cell.

confirm these simulation results. Experimental BET surface areas for nitrogen at 77 K for nanotubes range from 15 m2 g-1 to 300 m2 g-1, which are much lower than those of commonly available activated carbons. In our previous studies of nitrogen adsorption in isolated carbon nanotubes and slit pores,18-21 we found that nitrogen is more strongly adsorbed in nanotubes than in carbon slits and exohedral adsorption (adsorption on the outside of tubes) might be more important than endohedral adsorption (adsorption inside tubes) in some applications. The study reported here was designed to consider hydrogen storage in single wall carbon nanotube arrays with varying nanotube diameters and nanotube separations using grand canonical ensemble Monte Carlo (GCEMC) molecular simulations. The main purpose of this study was to find the optimal configurational parameters of SWCNT arrays for hydrogen storage. The effects of storage pressures are considered and comparisons with activated carbons and experimental measurements of hydrogen adsorption in nanotubes are also made. Models and Simulations The Model Array. In the arrays used in this work, Figure 1, SWCNT of diameter D are placed at the corners of equilateral parallelogram with sides of (D+G). Repeating this unit cell leads to an hexagonal array of nanotubes. The diameter, D, is defined as the internuclear distance between diametrically opposed carbon atoms in a nanotube; and nanotube separation, G, is defined as the minimum internuclear distance between two adjacent nanotube walls. The SWCNT are assumed to be aligned with their axes parallel to each other. Values of D and G were varied from 6 to 120 Å and from 4 to 30 Å respectively. The ends of the nanotubes can be either open or closed. If the nanotubes are open, then both endohedral and exohedral adsorption may occur, while only exohedral adsorption can take place in arrays of closed nanotubes. An alternative model adsorption space is a square array, which we used earlier for simulation studies of adsorption of nitrogen in SWCNT arrays.21 The packing density of nanotubes for square arrays is lower than for triangular arrays and, for given values of D and G, the interstitial spaces are larger. Consequently, a square array has a higher adsorption capacity than the equivalent triangular array. (18) Yin, Y. F.; Mays, T. J.; McEnaney, B. Carbon ‘97; Penn State, PA, 1997; p 66. (19) Yin, Y. F.; Mays, T. J. Carbon ‘98; Strasbourg, France, 1998; p 831. (20) Yin, Y. F.; Mays, T. J.; McEnaney, B. Fundamentals of Adsorption 6, Meunier, F., Ed.; Elsevier: Paris, 1998; p. 261. (21) Yin, Y. F.; Mays, T. J.; McEnaney, B. Langmuir 1999, 15, 8714.

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Simulations. The commonly used method22,23 of GCEMC molecular simulations (constant chemical potential, volume, and temperature) was used to simulate the adsorption of hydrogen over a range of pressures at 298 and 77 K. While there are explicit potentials both for interactions between hydrogen molecules and carbon atoms (e.g., the Crowell-Brown potential, which accounts for the polarizability of carbon atoms12), and for hydrogenhydrogen interactions (e.g., the Sillvera-Goldman potential, which includes three body terms12), we used a generic single site Lennard-Jones (LJ) 12:6 pair potential for carbon-hydrogen and hydrogen-hydrogen interactions.9,13 The LJ potential yields the same essential features as more complex potentials, but at a lower cost computationally. In the gas phase the LJ potential was truncated at a distance of 5σgg, where σgg is the LJ length parameter for hydrogen-hydrogen (gas-gas) interactions. Adsorption potentials for gas-solid interactions which can be applied to both endohedral and exohedral adsorption in isolated SWCNT were derived by integration of the single-site LJ 12:6 pair potential for carbon-hydrogen interaction over a single nanotube wall, assuming that the nanotube is infinitely long and the surface density of carbon atoms in the tubes Fa ) 0.3818 atom Å-2 (the same as a perfect graphite layer plane).19 These potentials were then adapted to model the interactions in SWCNT arrays and the contribution of nanotubes and molecules adsorbed in neighboring cells to the total interaction was considered. The simulation cell is centered on the interstitial space between the nanotubes, Figure 1. The length of the simulation cell parallel to the nanotube axes was normally set to 10σgg, but was on occasion increased to increase the number of molecules in the cell, and hence reduce statistical errors. Periodic boundary conditions were applied to all the directions, i.e., the pattern shown in Figure 1 is imaged to fill all the space. Values used for LJ energy and distance parameters,  and σ, for gas-gas (gg) and gas-solid (gs) interactions are24,25 gg/kB ) 41.5 K, σgg ) 2.96 Å, and gs/kB ) 34.1 K, σgs ) 3.18 Å, where kB is Boltzmann’s constant. The Peng-Robinson equation of state26 was used to calculate the chemical potential of bulk hydrogen gas; the parameters used in the PengRobinson equation are critical pressure pc ) 12.80 bar, critical temperature Tc ) 33.20 K, and acentric factor ω ) -0.22. The main output of the simulations is the average number of molecules adsorbed in the simulation cell Ncell as a function of bulk gas-phase pressure and system temperature. For the purpose of comparison, hydrogen storage in activated carbons was also simulated using a gas-solid interaction potential function that was derived earlier23 and the same LJ parameters as used for the simulations in SWCNT arrays. Micropores in activated carbons were modeled as slits formed between walls consisting of single perfect graphite layer plans (Fa ) 0.3818 atom Å-2) to maximize both the volumetric and gravimetric capacities. Delivered Capacities. The amount of usable gas in a gas storage system can be expressed as the delivered volumetric capacity, VDEL, i.e., the amount of gas stored (22) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, UK, 1987. (23) Mays, T. J. Fundamentals of Adsorption; LeVan, M. D., Ed.; Kluwer Academic Publishers: Boston, MA, 1996; p 603. (24) Steele, W. A. The Interaction of Gases with Solid Surface; Pergamon Press: Oxford, UK, 1974. (25) Kihara, T. Intermolecular Forces; John Wiley & Sons: New York, 1978. (26) Peng, D. Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1976, 15, 59.

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Figure 3. Storage volumetric hydrogen capacities of singlewalled carbon slit pores at 298 K as a function of storage pressure and pore width, H. The dotted line shows the storage capacity of compressed hydrogen gas at the same temperature.

Figure 2. Hydrogen capacities (at 1 bar) of triangular arrays of open SWCNT at 298 K as functions of storage pressure, nanotube diameter D, and nanotube separation G. (a) Delivered volumetric capacities. The delivered capacity of compressed hydrogen gas is also shown. (b) Delivered gravimetric capacities.

at the higher (storage) pressure less the amount retained in the container at the lower (delivery) pressure. The amount stored at any pressure, VP, can be determined from Ncell by the following equation:

VP )

NcellVmol NAVcell

(1)

where Vmol is the molar volume of the gas at STP, NA is Avogadro’s number, and Vcell is the volume of the simulation cell which is equal to the volume occupied by both the solid and the adsorbed molecules. Thus, VDEL is obtained from the difference between values of VP at the storage and delivery pressures. In this study, storage and delivery pressures were normally 70 and 1 bar, respectively. For studies of the effects of storage pressure, the storage pressure was varied from 1 to 200 bar. Another important storage parameter is the gravimetric capacity, VG, which is defined as the percentage weight of the stored hydrogen over the weight of the storage medium; VG can be calculated from simulation results using the following equation:

VG )

Ncell × 100 6πDLFa

(2)

where L is the length of the simulation cell and Fa ) 0.3818 Å-2 is the number of carbon atoms per unit area in the nanotube wall. Results and Discussion Storage in Triangular Arrays of Open SWCNT arrays at 298 K. Figure 2(a) shows delivered volumetric

hydrogen capacities of some triangular arrays of open SWCNT with different values of D and G as functions of storage pressure at 298 K. Also shown is the effect of storage pressure on the delivered capacity of compressed hydrogen gas. Uptake is negligible in arrays of the smallest nanotubes, D ) 6 Å, with the smallest separation, G ) 3.2 Å, because hydrogen molecules are excluded from the interior of the nanotubes and the interstices between them. With the other arrays delivered volumetric capacities increase with storage pressure, although the differences in capacities between the different arrays are rather small. Even at the highest storage pressure studied (200 bar), the maximum capacity is less than half of the DOE target value (695 (STP) v/v) and the enhancement of volumetric capacity of hydrogen in arrays of SWCNT over that of compressed gas is modest. From this point of view, triangular arrays of SWCNT are not promising for hydrogen storage at ambient temperatures. The ability of the triangular nanotube arrays to deliver hydrogen looks more promising when expressed on a gravimetric basis, Figure 2(b). The maximum delivered hydrogen capacity from the array with D ) 60 Å and G ) 10 Å exceeds the DOE target of 6.5 wt % at a storage pressure of ∼160 bar. The reason the volumetric target is more difficult to reach than the gravimetric target is that the volume of the simulation cell increases rapidly, as ∼(D+G)2, whereas the weight of the simulation cell increases more slowly with increases in nanotube diameter, as ∼D, and is independent of changes in G. Comparisons of Storage in Open Nanotube Arrays and in Slit Pores. Figure 3 shows the volumetric storage capacities for hydrogen at 298 K in some slit pores formed between single carbon layer planes as functions of storage pressure and slit width, H, defined as the internuclear separation of carbon atoms in opposite pore walls. The slit-shaped pores may be taken as models for micropores in activated carbons. In the examples chosen, hydrogen capacities are not very sensitive to pore width and they are not much greater than those for compressed gas. This indicates that activated carbons are unlikely to be useful adsorbents for storage of hydrogen at ambient temperatures. A more detailed exploration of the effect of storage pressure and pore width on hydrogen capacities in slit pores, Figure 4, shows that delivered volumetric hydrogen capacity reaches a maximum at H ) 6.7 Å and it is about twice that of compressed gas. The maximum delivered capacities at 70 bar and 298 K in single wall carbon nanotube arrays and in single wall carbon slit pores are similar (cf., Figures 2 and 4). However, for slit pores the capacity decreases sharply as pore widths depart from

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Figure 4. Hydrogen capacities of single-walled carbon slit pores at 298 K as functions of pore width, H; storage pressure 70 bar, delivery pressure 1 bar. The dotted line shows the delivered capacity of compressed hydrogen gas at 1 bar at the same temperature and storage pressure.

the optimal value. In practice this means that pore widths in activated carbons must be controlled to within a few Å to achieve a capacity close to the optimal value. In the case of nanotubes, all arrays studied give similar capacities, except with the smallest nanotubes, indicating that the control of nanotube spacings to achieve useful capacities may not be so critical. It is interesting to note that the smallest slit-shaped pore, H ) 6 Å, has a significant volumetric hydrogen capacity, Figure 4, whereas arrays of nanotubes with D ) 6 Å (and G ) 3.2 Å) have nearly zero capacity, Figure 2. Thus, hydrogen molecules can enter slit pores with a width of 6 Å, but they are excluded from nanotubes with D ) 6 Å. This is because in such small pores the repulsive component of the interaction potential between adsorbate molecules and the pore wall is more strongly enhanced in nanotubes than in slits.18,20 Storage in Triangular Arrays of Closed SWCNT at 77 K. As expected, stored hydrogen capacities at 77 K and 70 bar in triangular arrays of closed SWCNT increase with increasing G at constant D, Figure 5(a), as the interstitial space available to hydrogen increases. However, except at the smallest nanotube separation, G ) 4 Å, the capacities decrease progressively with increasing D. This is so because with increasing D the volume of the simulation cell increases rapidly as ∼(D + G)2, whereas the interstitial space available to the hydrogen molecules increases at a lesser rate. For the smallest nanotube separations, G ) 4 Å and D < 40 Å, the storage capacity oscillates with changing D, Figure 5(a). These oscillations are associated with orderdisorder transitions in the packing of hydrogen molecules in the narrow interstitial spaces. The peaks in storage capacity at D ) 10 and 20 Å, Figure 5, are related to the development of ordered packing of hydrogen molecules in the narrow interstices of the triangular array. A molecular snapshot of the triangular array with G ) 4 Å, Figure 6(a), shows that at D ) 10 Å each intersticial space between the nanotubes is just wide enough to accommodate a single column of tightly packed hydrogen molecules. For D ) 20 Å each intersticial is just wide enough to hold three columns of tightly packed hydrogen molecules, Figure 6(b). For intermediate nanotube diameters the packing of the hydrogen molecules is less well ordered. The gravimetric hydrogen storage capacities in triangular arrays of closed SWCNT at 70 bar and 77 K, Figure 5(b), increase progressively with increasing nanotube separation, G. The DOE target capacity, 6.5 wt %, is met

Figure 5. Hydrogen capacities at 77 K and 70 bar of triangular arrays of closed SWCNT with different nanotube separations, G, as functions of nanotube diameter, D. (a) Storage volumetric capacities. The lines in the graph are plotted according to eq 4. (b) Storage gravimetric capacities.

or exceeded for all nanotube separations greater than 7 Å over the whole range of nanotube diameters. Thus, as at ambient temperatures, the gravimetric target is more easily met than the volumetric target. The optimal gravimetric capacity in this study is substantial (33 wt %) and is found for arrays of small nanotubes, D ) 6 Å, with large separations, G ) 30 Å. Packing of Hydrogen Molecules in Interstitial Spaces. Simple geometric arguments show that the volume available to hydrogen molecules in unit volume of triangular arrays of closed SWCNT, Vav, is:

Vav ) 1 -

π(D + σcc)2 2 x3(D + G)2

(3)

where σcc is the LJ diameter of carbon atoms. If geometric aspects dominate storage capacities, then the storage capacity, VS, will be proportional to the volume available,

VS ) CfVav

(4)

where C is a conversion factor to standard temperature and pressure (C ) 2739 (STP) v/v in the case of hydrogen) and f is the packing factor that describes the proportion of the available volume occupied by hydrogen molecules. Except for the smallest nanotube separation, G ) 4 Å, the curves in Figure 5(a) show that eq 4 is a good fit to the simulation results for triangular arrays of closed SWCNT. This indicates that the interstitial volume available to hydrogen molecules mainly determines the storage capacity, because the adsorption potential is generally high over the whole of the interstitial space.

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Figure 8. Delivered hydrogen volumetric capacities of triangular arrays of closed SWCNT at 77 K and 1 bar as a function of storage pressure. Also shown are the delivered capacities of compressed hydrogen gas at 77 K and 1 bar and the enhancement of capacity of the adsorbed gas over compressed gas. The DOE target capacity is also shown.

Figure 6. Molecular snapshots from simulations of adsorption in triangular arrays of closed SWCNT at 77 K and 70 bar with G ) 4 Å. (a) D ) 10 Å, showing single columns of hydrogen molecules in the interstices; (b) D ) 20 Å, showing three columns of hydrogen molecules in the interstices.

Figure 7. Packing factor, f, from eq 4 as a function of nanotube separation, G, for adsorbed hydrogen molecules in triangular arrays of closed SWCNT at 77 K and 70 bar. The error bars are plus and minus one standard deviation. The packing factor of liquid hydrogen is estimated from the bulk density at 20 K and the LJ diameter.

Equation 4 slightly overestimates storage capacity at large tube diameters, Figure 5, because, the adsorption potential at the center of the interstices becomes rather weak at large D. The variation of packing factor, f, with D, Figure 7, is similar to that found for packing of nitrogen in square arrays of closed SWCNT,21 but the values of f for hydrogen are smaller. The values of f are less than that for closely packed hard spheres, f ) 0.74, and most are higher than that of liquid hydrogen, which was calculated from the liquid density at 20 K and the LJ distance parameter, σgg.

The maximum f at G ) 7 Å corresponds to formation of ordered monolayers between nanotubes, similar to those found for nitrogen.21 The low packing factor for G ) 4 Å is due to the low dimensionality of the adsorbate at this nanotube separation, illustrated in Figure 6. Effects of Increasing Storage Pressure. Figure 8 shows the delivered capacities, VDEL, of hydrogen at 77 K in a triangular array of closed SWCNT as a function of storage pressure from 1 to 200 bar. The triangular array used in Figure 8 is the optimal one for delivered capacity of hydrogen stored at 70 bar, D ) 6 Å, G ) 15 Å. Also shown is the delivered capacity for compressed hydrogen gas at the same temperature and the DOE target delivered capacity. In both cases delivered capacity increases with storage pressure, but, for the nanotube array, the DOE target value is reached at ∼70 bar, whereas compressed gas requires a pressure of almost 200 bar. Figure 8 also shows that the enhancement in delivered capacity of adsorbed gas over compressed gas decays progressively from a maximum at low pressure, reaching ∼300% at 70 bar. For pressures over ∼100 bar the increase in delivered capacity from the nanotube array is not very great, while the capacity from compressed gas continues to increase almost linearly. Thus, the enhancement in capacity from the nanotube array over compressed gas becomes less efficient when the storage pressure is over ∼100 bar. Storage in Open Triangular SWCNT Arrays at 77 K. Figure 9 shows delivered volumetric hydrogen capacities at 77 K and 70 bar of open triangular arrays of SWCNT as functions of D and G. Comparison with delivered volumetric hydrogen capacities of closed triangular arrays under the same conditions, Figure 10, shows that open nanotubes have significantly higher delivered capacities at large D values, reflecting the contribution of endohedral adsorption. By contrast, the capacities of arrays of open and closed nanotubes of the smallest diameter are similar, indicating that exohedral adsorption dominates capacity in both cases. This is also shown in Figure 11 in which the exohedral contributions to the delivered capacities in open nanotube arrays are plotted as a function of D and G. For arrays with the smallest nanotube diameters, D ) 6 Å, the exohedral contribution to capacity is close to 100% for all nanotube separations, except G ) 4 Å. With the same exception, the exohedral contribution decreases progressively with increasing D. Thus, optimal delivered hydrogen capacities, approaching the DOE target value, are found for open or closed

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Figure 9. Delivered volumetric hydrogen capacities at 77 K for triangular arrays of open SWCNT with different nanotube separations, G, as a function of nanotube diameters, D. Storage pressure 70 bar, delivery pressure 1 bar.

Figure 10. Delivered volumetric hydrogen capacities at 77 K for triangular arrays of closed SWCNT with different nanotube separations, G, as a function of nanotube diameters, D. Storage pressure 70 bar, delivery pressure 1 bar.

Figure 11. Exohedral contributions to delivered hydrogen capacities at 77 K for triangular arrays of open SWCNT with different nanotube separations, G, as a function of nanotube diameter, D. Storage pressure 70 bar, delivery pressure 1 bar.

arrays with D ) 6 Å and G ranging from 13 to 30 Å. In practice this means that for arrays of narrow SWCNT it is not necessary to open the nanotubes, since the important adsorption space is the interstices between the tubes and the optimal capacity is not very sensitive to the spacing between the tubes in the range studied. It is also likely

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Figure 12. Hydrogen capacities of single walled carbon slit pores at 77 K as functions of pore width, H. Storage pressure 70 bar, delivery pressure 1 bar. Also shown are the delivered capacity of compressed hydrogen gas under the same conditions and the DOE target capacity.

that diffusion of hydrogen molecules in to and out of this space will be faster than diffusion in to and out of the endohedral space in narrow nanotubes. Comparison of Capacities in Nanotube Arrays and Slit Pores at 77 K. Figure 12 shows the volumetric storage capacities at 77 K for hydrogen in slit-shaped carbon pores at 70 and 1 bar and the delivered capacities as a function of pore width, H. Also shown are the DOE target capacity and the delivered capacity of compressed hydrogen gas at 70 bar. Storage capacities are around the DOE target value for all of the pore widths studied. Optimal storage capacities of ∼750 (STP) v/v. are found in slits with widths of ∼9 and ∼12 Å, where two and three layers respectively of adsorbed hydrogen molecules are formed. However, in small pores delivered capacities are much lower than storage capacities because large amounts of hydrogen are retained on depressurization to 1 bar. For pore widths less than about 9 Å, delivered capacities are lower than that of compressed gas. The optimal delivered capacity of 550 (STP) v/v is found for pores with H ∼15 Å where about four layers of hydrogen molecules are adsorbed in the pore. These results suggest that activated carbons with wide micropores are likely to be better for storage of hydrogen at 77 K than highly microporous carbons with pore sizes less than ∼10 Å. Comparisons between Simulations and Experimental Measurements. In the case of slit-shaped carbon pores, volumetric capacities VP and gravimetric capacities VG are related by VG ) 1.169 × 10-3HVP. Thus, the volumetric delivered capacities at 298 K and 70 bar for slit-shaped carbon pores shown in Figure 4 correspond to gravimetric capacities that range from 0.5 wt % in the smallest pores to a maximum value of ∼1.9 wt % in the largest pores studied, H ) 20 Å. The gravimetric capacity of pores with H ∼7 Å is ∼1 wt %. The gravimetric hydrogen capacity of 0.6 wt % measured on an activated carbon at 298 K and 60 bar,5 Table 1, is within this range. Considering that the experimental measurements were at a lower pressure and that there is a distribution of pore sizes in the activated carbon, the agreement between experiment and simulations is reasonable. A similar conclusion is reached from a comparison of the experimentally measured adsorption capacity for hydrogen at 77 K and 60 bar on an activated carbon (4.7 wt %)27 and simulations of hydrogen storage capacities in slit pores at 77 K and 70 bar (4.2-15.3 wt %) Table 1.

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Table 1. Comparisons of Gravimetric Hydrogen Storage Capacities from Experiments and Molecular Simulations system

T/K

P/bar

H2/wt %

ref

activated carbon (E)a slit pores (S)a activated carbon (E)a slit pores (S)a SWCNT, 50% purity (E)a triangular array open SWCNT (S)a SWCNT, High purity (E)a triangular array open SWCNT (S)a

298 298 77 77 300 298 80 77

60 70 60 70 101 100 72 70

0.6 0.5-1.9 4.7 4.2-15.3 4.2 4.7 maxb 8.25 33 maxc

5 d 27 d 28 d 29 d

a (E) Experiment. (S) Simulation. b D ) 60 Å, G ) 10 Å. c D) 6 Å, G ) 30 Å. d This work.

In the case of nanotubes, comparisons between experimental and simulated gravimetric hydrogen capacities are complicated because experimental hydrogen capacities have been measured on nanotube samples that have different purities and that have not been ordered into arrays. Also, the simulated gravimetric capacities depend on the geometry of the array, ranging from very low values to maximum values for the geometries studied. An experimental study of hydrogen adsorption by SWCNT of 50 wt % purity at ambient temperatures and ∼101 bar gave a capacity of 4.2 wt %, Table 1,28 This is in reasonable agreement with the hydrogen capacity at similar temperatures and pressures (4.7 wt %) obtained from simulations on triangular arrays of open SWCNT with D ) 60 Å, G ) 10 Å. Molecular simulations of hydrogen storage at 77 K and 70 bar on triangular arrays of open SWCNT with D ) 6 Å, G ) 30 Å, produce a very high capacity (33 wt %, Table 1). This may be compared with an experimental measurement made on high purity SWCNT at similar temperatures and pressures (8.25 wt %, Table 1).29 The data for nanotubes and activated carbons in Table 1 also show that the potential of SWCNT to store hydrogen (27) Noh, J. S.; Agarwal, R. K.; Schwartz. J. A. Int. J. Hydrogen Energy 1987, 12, 693. (28) Liu, C.; Fan, Y. Y.; Liu, M.; Cong, H. T.; Cheng, H. M.; Dresselhaus, M. S. Science 1999, 286, 1649. (29) Ye, Y.; Ahn, C. C.; Witham, C.; Fultz, B.; Liu, J.; Rinzler, A. G.; Colbert, D.; Smith, K. A.; Smalley, R. E. Appl. Phys. Lett. 1999, 74, 2307.

is superior to that of activated carbons at both ambient and liquid nitrogen temperatures. Conclusions Molecular simulations of the storage of hydrogen in optimally configured triangular arrays of open SWCNT at ambient temperatures indicate that the US DOE target gravimetric capacity can be achieved at ∼160 bar. However, optimal volumetric capacities at the same pressure are less than 40% of the DOE target volumetric capacity. For slit pores formed between single carbon layer planes (modeling activated carbons) the optimum delivered volumetric capacity is ∼20% of the DOE target value. Thus the potential of SWCNT to store hydrogen at ambient temperatures is superior to that of activated carbon, but DOE target capacities will be difficult to achieve at reasonable storage pressures. Molecular simulations of hydrogen storage at 77 K and 70 bar in triangular arrays of open and closed SWCNT indicate that the DOE gravimetric targets are exceeded for a wide range of nanotube configurations. A substantial hydrogen storage capacity of 33 wt % is found for an array of narrow nanotubes (D ) 6 Å) that are widely separated (G ) 30 Å). Here, hydrogen adsorption occurs entirely in the interstitial spaces in the array (exohedral adsorption) and similar capacities are found for open and closed nanotubes. Delivered volumetric capacities close to the DOE target are found for arrays of narrow, open, or closed SWCNT of the same diameter and with a range of spacings (G ) 13-30 Å). The maximum delivered volumetric hydrogen capacity for slit pores at 77 K and 70 bar is ∼73% of the target value for range of pore widths (H ) 12-20 Å). The simulations of hydrogen capacities for activated carbons and SWCNT at ambient temperatures and at 77 K are in reasonable agreement with experimentally measured capacities. Acknowledgment. You Fa Yin thanks the University of Bath for provision of a University Research Studentship. LA000900T