Optimization of Carbon Nanotube Arrays for Hydrogen Adsorption

On the basis of these observations, carbon nanotubes do not appear to be useful ... size distribution.5 SWNT “ropes” consist of hundreds of aligne...
3 downloads 0 Views 90KB Size
Download PDF
J. Phys. Chem. B 1999, 103, 4809-4813

4809

Optimization of Carbon Nanotube Arrays for Hydrogen Adsorption Qinyu Wang and J. Karl Johnson* Department of Chemical and Petroleum Engineering, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15261 ReceiVed: January 4, 1999; In Final Form: April 7, 1999

The amount of hydrogen adsorbed in arrays of single-walled carbon nanotubes has been studied as a function of the geometry of the array. The tube lattice spacing has been varied to optimize hydrogen uptake. Two different lattice geometries have been examined, namely, the triangular lattice and the square lattice. None of the geometries studied are capable of achieving adequate hydrogen storage capacity for use in vehicular fuel cells at room temperature. The strength of the solid-fluid interaction potential has been increased in order to identify a combination of potential and geometry that will meet the DOE targets for hydrogen storage for fuel cell vehicles. The DOE target values cannot be reached even by tripling the fluid-wall potential at ambient temperature. However, it is possible to achieve the DOE targets at a temperature of 77 K, but only if the strength of the interaction potential is increased by about a factor of 2 and the lattice spacing of the tubes is optimized. On the basis of these observations, carbon nanotubes do not appear to be useful adsorbents for vehicular hydrogen storage applications.

I. Introduction There has been considerable interest in the past few years in evaluating the ability of single-walled carbon nanotubes (SWNTs) to adsorb molecular hydrogen gas. This interest largely stems from the need to store hydrogen for fuel cell vehicles. Carbon nanotubes were first discovered by Iijima1 in 1991 as nested structures of concentric shells. Subsequently, singlewalled carbon nanotubes have been synthesized by a variety of methods, including carbon-arc vaporization,2 catalytic decomposition of organic vapors,3 and laser vaporization.4 Smalley and co-workers have found that SWNTs self-organize into “ropes” and can be produced with a very narrow size distribution.5 SWNT “ropes” consist of hundreds of aligned SWNTs on a two-dimensional triangular lattice, with an intertube spacing of approximately 3.2 Å, as measured from the center of the tube walls.5,6 The intertube spacing is called the van der Waals gap, because the nanotubes are held together by van der Waals forces. The van der Waals gap is defined as g ) a - D, where g is the van der Waals gap, a is the lattice spacing, and D is the diameter of the nanotube. Hence, g is the distance of closest approach between two tubes, as measured from the center of the tube walls. Recently, Bower et al. have reported a reversible intercalation of SWNT bundles with HNO3 molecules when immersed in a nitric acid solution.7 An expansion of the intertube spacing within the bundles has been experimentally observed by X-ray diffraction and NMR measurement.7 This suggests that g may be considered as an adjustable parameter to some extent, allowing optimization of the lattice spacing with respect to hydrogen uptake. When SWNTs are produced they are naturally capped at each end. Procedures have been devised to remove end caps without destroying the nanotubes,8-10 so that gases can adsorb on the inside surfaces of the nanotubes. Recent experiments report that hydrogen can adsorb in significant amounts on SWNTs.8 Heben and co-workers performed a series of temperature-programmed desorption experiments that indicate that opened SWNTs can adsorb hydrogen * Corresponding author. E-mail: [email protected].

in the range of 5-10 wt % (50-100 kg H/g C) at 133 K.8 These experiments have stimulated many simulation studies on hydrogen adsorption in SWNTs.11-14 Darkrim and Levesque have calculated hydrogen adsorption in a square array of SWNTs at 10 MPa and 298 K. They have considered SWNTs with diameters ranging from 7 to 19.6 Å and an intertube spacing of 3.34 Å. The effect of the intertube spacing on hydrogen adsorption has been studied for tubes of diameter 11.74 Å. It was found that the SWNTs with a diameter of 11.74 Å and an intertube spacing of 7 Å give the highest hydrogen density (10.7 kg H2 m-3) of all the tubes tested at room temperature. Mays et al. have focused their simulations on hydrogen adsorption at 77 K.12 They suggested that the volumetric target value of the DOE hydrogen plan (62 kg H2 m-3) can be achieved with SWNTs of diameter 6 Å and intertube spacings larger than 10 Å. However, the smallest nanotubes produced so far have diameters of approximately 7 Å.2 Rzepka et al. have simulated adsorption of hydrogen inside single SWNTs and compared results with simulations of carbon slit pores.13 Their calculations show that the optimum geometry for hydrogen storage is carbon slit pores with a pore size of 7 Å at room temperature. They note that the nanotube geometry has no advantage over the slit pore geometry except at low pressures.13 Our previous study on hydrogen adsorption in SWNT arrays indicates that the close-packed structure gives relatively low gravimetric and volumetric densities, even though the adsorption potential is quite strong.14 The low values of adsorption are mainly a result of the excluded surface area in the close-packed array of tubes. Most of the external surface area in the tube array is unavailable for adsorption, and adsorption in the interstices constitutes a small fraction of the total amount of hydrogen adsorbed.14 At high pressures and temperatures, hydrogen adsorption in SWNT arrays is dominated by the effective surface area and volume available for adsorption. The observed van der Waals gap of 3.2 Å is obviously not optimum for hydrogen storage. We expect that the gap can be optimized to maximize the amount of H2 adsorbed as a function of temperature and pressure. The objective of this work is to

10.1021/jp9900032 CCC: $18.00 © 1999 American Chemical Society Published on Web 05/18/1999

4810 J. Phys. Chem. B, Vol. 103, No. 23, 1999

Wang and Johnson

determine the maximum amount of H2 that can be stored and delivered when the packing geometry and solid-fluid potential are treated as adjustable parameters. II. Model and Methods A. Potential Models. Hydrogen has been modeled with the Silvera-Goldman potential,15 which has been found to reproduce the thermodynamic properties of fluid hydrogen accurately over a wide range of temperatures and pressures.16 The interaction between a hydrogen molecule with a SWNT is modeled by the Crowell-Brown (CB) potential.17 We chose to use the CB potential because it takes into account the anisotropy of the polarizability of the graphite sheet making up the tube. An effective potential was developed by integrating over the positions of all carbon atoms in a unit cell of the tube. The details of the potential can be found in a previous paper.14 It is important to note that no account has been made for the perturbation of the potential due to curvature-induced strain of the carbon sp2 bonding network or due to the electronic properties of the tube, which depend on chirality. The hydrogennanotube potential can be expressed in cylindrical coordinates (r,θ,z) where r is the distance from the center of the tube to the H2 molecule, θ is the radial angle, and z is the axial distance along the tube. A one-dimensional hydrogen-nanotube potential was obtained by integrating over the θ and z cylindrical coordinates. The averaged fluid-wall potential was fitted to a seventh-order polynomial, 7

V(r) )

( ) R

ai ∑ R-r i)0

i

(1)

where R is the radius of the tube. The interaction potential for hydrogen with the external surface of an isolated tube was computed in a similar fashion. The endohedral and exohedral potentials both have the form given by eq 1, but with different parameters. The solid-fluid potential for a hydrogen molecule in an array of tubes includes the interactions of hydrogen with all the tubes within the cutoff distance,

V(x,y) )

∑i Vi(ri)

(2)

where Vi(ri) is the fluid-wall potential given by eq 1 with ri being the distance from the hydrogen molecule to the center of tube i. The sum is over all nanotubes within the cutoff. Vi(ri) could be either the endohedral or exohedral potential, depending on the position of the hydrogen molecule with respect to tube i. B. Simulation Method. Two array geometries have been studied, namely, triangular and square arrays. The triangular array is modeled by a rhombohedral cell containing four parallel SWNTs on the sites of a triangular lattice, as shown in Figure 1. The square array model consists of a square cell containing four tubes located on the sites of a square lattice, as shown in Figure 2. Periodic boundary conditions were employed in all directions. Three different nanotube sizes have been studied. These are the (9,9) (D ) 12.2 Å), the (12,12) (D ) 16.3 Å), and the (18,18) (D ) 24.4 Å) tubes. The lateral dimensions of the simulation cell are chosen to be Lx ) Ly ) 2a ) 2(g + D), The van der Waals gap g has been varied in order to locate the optimum separation between the tubes for adsorption. The height of the simulation box ranged from 30 to 60 Å, which gave average numbers of molecules between 50 and 2000, depending on the simulation conditions.

Figure 1. Simulation cell of the (9,9) SWNT triangular array with a van der Waals gap of 6 Å.

Figure 2. Simulation cell of the (9,9) SWNT square array with a van der Waals gap of 6 Å.

We have performed classical grand canonical Monte Carlo (GCMC) simulations to calculate the adsorption of hydrogen in tube arrays at 77 and 298 K. Our previous simulations have shown that quantum effects are important for hydrogen adsorption at 77 K and for adsorption in narrow interstices at 298 K.14 However, we do not expect the optimum value of g computed from classical simulations to be substantially different if quantum effects are included. We have opted to perform classical simulations because path integral calculations are considerably more expensive than classical simulations.14,18 At room temperature quantum effects will be essentially negligible for large values of g. Three types of moves are involved in the GCMC method: (i) displacement, (ii) particle creation, and (iii) particle deletion. The probabilities of making a displacement, a creation, and a deletion were set to 0.2, 0.4, and 0.4, respectively. The system was equilibrated for about 5-10 × 105 moves, after which data were collected for 5 × 105 moves. Statistical errors were estimated by dividing the run into a number of subblocks (typically 10) and computing subaverages for each block. The fluid-fluid and solid-fluid cutoff was set to 5σff, where σff is the diameter of the fluid molecule. No longrange corrections was applied. We have repeated calculations at several state points with a larger simulation cell of nine tubes to test the effect of the system size. The size effect was found to be less than 5% on the amount of hydrogen adsorbed. III. Results and Discussion A. Optimum Packing Geometry. We have calculated the amount of hydrogen adsorbed in (9,9), (12,12), and (18,18) tube arrays with different packing geometries at 298 and 77 K. We calculate both the gravimetric (g H2/kg C) and volumetric (kg H2 m-3) densities because both densities are important criteria for evaluating hydrogen storage systems. Figure 3a shows the gravimetric density of hydrogen in tube arrays as a function of van der Waals gap at 298 K and 50 atm. At the smallest tube separation, g ) 3.2 Å, much of the volume and surface area in the tube arrays are unavailable for adsorption because of steric effects in the close-packed structure of the tubes. The tube arrays

Optimization of Carbon Nanotube Arrays

Figure 3. Adsorption of hydrogen as a function of van der Waals gap in tube arrays at 298 K and 50 atm. The open circles, squares, and diamonds represent the (9,9), (12,12), and (18,18) tube arrays, respectively, in a triangular lattice. The filled circles denote the (9,9) tubes in a square lattice. The gravimetric densities are given in panel a, and the volumetric densities are shown in panel b.

with a van der Waals gap of 3.2 Å give the lowest hydrogen uptake of all the packing geometries tested. Increasing the van der Waals gap allows adsorption to take place on the external surface of the nanotubes. The gravimetric densities increase with tube separation. This is due to the larger available volume outside the tubes and the lower ratio of skeletal volume occupied by carbon atoms to the total volume as the van der Waals gap increases. The gravimetric densities increase with tube diameters for the same reasons. The (9,9) tube square array systematically adsorbs more hydrogen on a weight basis than the (9,9) triangular array. This is because the tubes in the square array have more available volume than the triangular array at the same value of g. Figure 3b shows the volumetric density of hydrogen in tube arrays at 298 K and 50 atm. In the high-pressure range the volumetric density is influenced by both the available volume and the solid-fluid potential. As before, the triangular arrays with g ) 3.2 Å give the lowest hydrogen uptake. For a gap of g ) 3.2 Å the volumetric density in the (9,9) tube square array is the highest. This is due to the fact that square array provides a larger available volume than the (9,9) triangular array and a stronger fluid-wall potential than the (12,12) and (18,18) triangular arrays at g ) 3.2 Å. As the van der Waals gap increases, the available volume outside the tube becomes larger but the solid-fluid potential gets weaker, as indicated by the zero pressure isosteric heats of adsorption shown in Figure 4. The isosteric heats of adsorption decrease with the van der Waals gap except that the (9,9) triangular array appears to exhibit a maximum at g ) 5 Å. The estimated statistical uncertainties in the simulations are smaller than the size of the symbols. The (9,9) tube triangular array gives the highest isosteric heats of adsorption over the entire van der Waals gap range. The isosteric heats of adsorption in the (9,9) tube square array are the second highest, except at the largest van der Waals gap, 12 Å. The volumetric density as a function of van der Waals gap exhibits a maximum as a result of the overall effects of the available space and solid-fluid potential. The maximum occurs at about 6-7 Å for the (9,9) and (12,12) tubes. The optimum van der Waals gap is smaller for the (18,18) triangular tube array, occurring at 5 Å. These optimum van der Waals gaps correspond to being able to hold a maximum of one layer of adsorbed

J. Phys. Chem. B, Vol. 103, No. 23, 1999 4811

Figure 4. Isosteric heat of adsorption at zero pressure for hydrogen in SWNT arrays as a function of van der Waals gap at 298 K. The open circles, squares, and diamonds represent the (9,9), (12,12), and (18,18) tube arrays in a triangular lattice, respectively. The filled circles denote the (9,9) tubes in a square lattice.

Figure 5. Adsorption of hydrogen as a function of van der Waals gap in tube arrays at 77 K and 50 atm. The open circles, squares, and diamonds represent the (9,9), (12,12), and (18,18) tube arrays, respectively, in a triangular lattice. The filled circles denote the (9,9) tubes in a square lattice. The gravimetric densities are given in panel a, and the volumetric densities are shown in panel b.

hydrogen between the external surfaces of two nearest-neighbor tubes. In the small van der Waals gap range, the volumetric densities increase with tube diameter. However, this trend is reversed for g larger than about 6 Å. The (9,9) tube triangular array with a van der Waals gap of 6 Å has the highest volumetric density of all the configurations tested. The amount of hydrogen adsorption as a function of van der Waals gap at 77 K and 50 atm is shown in Figure 5. The gravimetric density increases with the van der Waals gap at 77 K, as seen in Figure 5a. Decreasing the temperature from 298 to 77 K shifts the optimum van der Waals gap from 6 to 9 Å for the tubes in the triangular arrays, as shown in Figure 5b. A van der Waals gap of 9 Å corresponds to a maximum of two layers between two nearest 7 tubes, one on the external surface of each tube. This is in agreement with the simulation results of Matranga et al.19 and Cracknell et al.20 for methane storage in idealized carbon slit pores and our previous calculations of hydrogen storage in idealized carbon slit pores at 77 K.14 This indicates that at 77 K the available space outside the tubes plays a more important role than that at 298 K for the triangular lattice. The volumetric densities in the (9,9) tube square array and the (18,18) tube triangular array are fairly constant from g ) 6 Å

4812 J. Phys. Chem. B, Vol. 103, No. 23, 1999

Wang and Johnson

Figure 6. Adsorption isotherms of hydrogen in the (9,9) tube triangular arrays at 298 K. The circles (diamonds) are for g ) 3.2 (6) Å with the regular solid-fluid potential. The squares (triangles) are for arrays with g ) 6 Å and solid-fluid potentials increased by a factor of 2 (3).

Figure 7. Adsorption isotherms of hydrogen in the (9,9) tube triangular arrays at 77 K. The circles (diamonds) are for g ) 3.2 (9) Å with the regular solid-fluid potential. The squares (triangles) are for arrays with g ) 9 Å and solid-fluid potentials increased by a factor of 2 (3).

to g ) 9 Å. The (9,9) tube triangular array with the optimum van der Waals gap of 9 Å gives the highest volumetric density of all the tube and packing geometries tested at 77 K. We have calculated adsorption isotherms for hydrogen in the (9,9) tube triangular arrays with various van der Waals gaps and fluid-wall potentials at 298 and 77 K. We chose to use the (9,9) tube triangular arrays because they give the highest volumetric densities at the optimum van der Waals gap. The simulation results of hydrogen adsorption in the array with the optimum value of g will give the theoretical limit of hydrogen storage in SWNTs. Figure 6 shows the adsorption isotherms of hydrogen in the (9,9) tube triangular arrays with van der Waals gaps of 6 and 3.2 Å at 298 K. Recall that 3.2 Å is the experimentally observed intertube spacing and 6 Å is the optimum van der Waals gap at 298 K and 50 atm. The volumetric densities in the tube arrays with g ) 6 Å are about 50-60% higher than those in the g ) 3.2 Å array over a pressure range from 1 to 100 atm. At 298 K and 100 atm the optimum configuration of SWNT array gives a volumetric density of 10.1 kg H2 m-3 and a gravimetric density of 9.86 g H2/kg C (not shown). The volumetric density is close to, yet a bit lower, than the simulation result of the volumetric density (10.4 kg H2 m-3) in the optimum idealized carbon slit pore with wall spacing equal to 9 Å.14 The gravimetric density in the tube array is only 73% of that in the idealized slit pore. The idealized slit pores give overall better performance for hydrogen storage than SWNT arrays, even with optimum values of g. This indicates that the idealized slit pore is a better geometry for hydrogen adsorption than the SWNT arrays, even though the solid-fluid potential is stronger in the SWNTs. The hydrogen uptake in the optimum (9,9) tube arrays at 298 K is far below the DOE hydrogen plan. The DOE hydrogen plan requires system weight efficiency, of 6.5 wt % 8 (65 g H2/kg C) and volumetric density of 62 kg H2 m-3.8,21 Our simulations indicate that the standard fluid-wall potential model is not capable of producing adsorption densities that approach the DOE storage goals at ambient temperature. B. Effect of the Fluid-Wall Potential. It is important to note that our use of a graphite potential to describe the SWNT potential may introduce errors in the adsorption isotherm. The graphite potential does not account for the differences in the electronic structure of the tube compared with graphite. We have investigated the effect of the solid-fluid potential on the adsorption isotherms by performing simulations with stronger potentials. The stronger potentials are obtained by simply scaling the well depth of the CB potential. Figure 6 shows the adsorption

isotherms in the (9,9) tube array for potentials with well depths increased by a factor of 2 and 3. The optimum value of g for the tripled potential at 298 K was found to be the same as for the unperturbed potential (g ) 6 Å). Presumably, if the strength of the potential was increased further, the optimum value of g would shift to 9 Å. Increasing the strength of the fluid-wall potential greatly enhances the volumetric densities. However, the target values cannot be reached even by tripling the fluidwall potential. Using the tripled solid-fluid potential, the volumetric density is 43 kg H2 m-3 and the gravimetric density (not shown) is 42 g H2/kg C at 298 K and 100 atm. The adsorption isotherms for hydrogen in the (9,9) tube triangular arrays at 77 K for various values of the potential are shown in Figure 7. The optimum van der Waals gap of 9 Å has been used. Decreasing the temperature from 298 to 77 K significantly increases the volumetric densities. Adsorption at 100 atm and 77 K with the regular potential on the most favorable packing geometry, i.e., triangular tube arrays with g ) 9 Å, results in a volumetric density of 60 kg H2 m-3. This is very close to the DOE target of 62 kg H2 m-3. The gravimetric density at this state point is 79 g H2/kg C, which is above the target of 65 g H2/kg C. The volumetric densities in the tube arrays with the optimum intertube separation are 50-80% higher than those in the tube arrays with g ) 3.2 Å at pressures from 3 to 100 atm. At 1 atm where the fluid-wall potential dominates, the tube array with g ) 3.2 Å gives a higher volumetric density than the g ) 9 Å array. It is important to note that no account is made for quantum effects of hydrogen at 77 K. Our previous simulations have shown that at 50 atm the density inside the (9,9) tube from classical simulations is about 17% higher than from quantum simulations.l4 However, even after considering quantum effects, the volumetric density is still not far below the DOE target. Increasing the strength of the fluid-wall potential by a factor of 2 increases the volumetric and gravimetric densities by 87%, 45%, 34%, and 27% at 5, 20, 50, and 100 atm, respectively. When the strength of the fluid-wall potential is increased by a factor of 3, the volumetric and gravimetric densities are increased by 120%, 63%, 46%, and 41% at 5, 20, 50, and 100 atm, respectively. The volumetric and gravimetric densities are 85 kg H2 m-3 and 112.5 g H2/kg C, respectively, at 77 K and 100 atm with a tripled solid-fluid potential. This is well above the DOE target value, even after approximately considering the quantum effects by a discount of 17%. However, quantum effects will certainly be larger than 17% at these high densities. Even so, we expect that adsorption of quantum

Optimization of Carbon Nanotube Arrays

J. Phys. Chem. B, Vol. 103, No. 23, 1999 4813 enhancement of the solid-fluid potential reduces the value of the UCR except at the lowest pressure. This is to be expected because the increased solid-fluid potential results in more hydrogen being “irreversibly” adsorbed on the sorbent at the given discharge pressure. IV. Conclusion

Figure 8. UCRs for the (9,9) SWNT triangular arrays at 298 K. The discharge pressure is 1 atm. The circles (diamonds) are for g ) 3.2 (6) Å with the regular solid-fluid potential. The squares (triangles) are for arrays with g ) 9 Å and solid-fluid potentials increased by a factor of 2 (3).

We have optimized the packing geometry of SWNTs to maximize the amount of H2 adsorbed at both 298 and 77 K. The optimum value of g is a function of temperature, being 6 Å at 298 K and 9 Å at 77 K. We have found that the (9,9) tube triangular arrays with van der Waals gaps of 6 and 9 Å give the highest volumetric densities of all the tube configurations tested at both 298 and 77 K. At ambient temperature with the unperturbed solid-fluid potential, the optimum tube configuration is not capable of achieving the DOE targets and the UCRs are low. At 77 K the (9,9) tube (regular potential) with a van der Waals gap of 9 Å operating at pressures above 50 atm gives gravimetric and volumetric densities very close to the DOE targets and high UCRs. However this temperature is much too low to be of use for vehicular fuel storage. We have investigated the strength of the solid-fluid potential on the adsorption isotherms. Increasing the strength of the solid-fluid potential greatly enhances the volumetric densities and UCRs at 298 K. However, the DOE targets cannot be reached even by tripling the solid-fluid potential in the optimum tube configurations at 298 K. These findings indicate that carbon nanotubes are not good candidates for hydrogen storage for fuel cell vehicles. Acknowledgment. This work was supported by the National Science Foundation through a CAREER award, CTS-9702239, to J.K.J.

Figure 9. UCRs for the (9,9) SWNT triangular arrays at 77 K. The discharge pressure is 1 atm. The circles (diamonds) are for g ) 3.2 (9) Å with the regular solid-fluid potential. The squares (triangles) are for arrays with g ) 9 Å and solid-fluid potentials increased by a factor of 2 (3).

hydrogen would still exceed the DOE targets if the potential is tripled and g ) 9 Å. The DOE targets for volumetric and gravimetric density are not the only measures of adsorption. The usable capacity ratio (UCR) is an important criterion used to judge the performance of an adsorbent.21 It is a measure of the effectiveness of physisorption compared to gas compression at the same pressures. The UCR is defined as the mass of available fuel in a sorbent-loaded vessel divided by the mass of available fuel in a vessel without adsorbent (compressed gas only). The available fuel, in this case hydrogen, is the mass of hydrogen in the vessel at the storage, or working pressure, minus the mass of hydrogen in the vessel at the discharge pressure. UCRs for the (9,9) tube triangular arrays with different van der Waals gaps and solid-fluid potentials are plotted as a function of storage pressure in Figure 8 (298 K) and 9 (77 K). The discharge pressure is 1 atm. At 298 K, the UCR values are around unity or less for the tube array with g ) 3.2 Å. The g ) 6 Å array gives UCRs slightly larger than 1. The UCR values at 298 K increase with the strength of the solid-fluid potential at low pressures. The differences largely disappear at higher pressures. The UCRs at 77 K are much smaller than at 298 K. At 77 K the tube array with g ) 9 Å and the unperturbed solidfluid potential give the highest UCR over the entire pressure range. The (9,9) tubes with g ) 3.2 and 9 Å at increased solidfluid potentials have UCRs less than unity at 100 atm. The

References and Notes (1) Iijima, S. Nature 1991, 354, 56. (2) Iijima, S.; Ichihashi, T. Nature 1993, 363, 603. (3) Bethune, D. S.; Kiang, C. H.; de Vries, M. S.; Gorman, G.; Savoy, R.; Vazquez, J.; Beyers, R. Nature 1993, 363, 605. (4) Amelinckx, S.; Zhang, X. B.; Bernaerts, D.; Zhang, X. F.; Ivanov, V.; Nagy, J. B. Science 1994, 265, 635. (5) Thess, A.; Lee, R.; Nikolaey, P.; Dai, H.; Petit, P.; Robert, J.; Xu, C.; Lee, Y. H.; Kim, S. G.; Rinzler, A. G.; Colbert, D. T.; Scuseria, G. E.; Tomanek, D.; Fischer, J. E.; Smalley, R. E. Science 1996, 273, 483. (6) Fischer, J. E.; Dai, H.; Thess, A.; Lee, R.; Hanjani, N. M.; Dehaas, D. L.; Smalley, R. E. Phys. ReV. B 1997, 55, R4921. (7) Bower, C.; Kleinhammes, A.; Wu, Y.; Zhou, O. Chem. Phys. Lett. 1998, 288, 481. (8) Dillon, A. C.; Jones, K. M.; Bekkedahl, T. A.; Kiang, C. H.; Bethune, D. S.; Heben, M. J. Nature 1997, 386, 377. (9) Sloan, J.; Hammer, J.; Zwiefka-Sibley, M.; Green, M. L. H. Chem. Commun. 1998, 3, 347. (10) Liu, J.; Rinzler, A. G.; Dai, H.; Hafner, J. H.; Bradley, R. K.; Boul, P. J.; Lu, A.; Iverson, T.; Shelimov, K.; Huffman, C. H.; Rodriguez-Macias, F.; Shon, Y-S.; Lee, T. R.; Colbert, D. T.; Smalley, R. E. Science 1998, 280, 1253. (11) Darkrim, F.; Levesque, D. J. Chem. Phys. 1998, 109, 4981. (12) Yin, Y.; McEnaney, B.; Mays, T. Chem. Commun., submitted. (13) Rzepka, M.; Lamp, P.; de la Casa-Lillo, M. A. J. Phys. Chem. B 1998. (14) Wang, Q.; Johnson, J. K. J. Chem. Phys. 1999, 110, 577. (15) Silvera, I. F.; Goldman, V. V. J. Chem. Phys. 1978, 69, 4209. (16) Wang, Q.; Johnson, J. K.; Broughton, J. Q. Mol. Phys. 1996, 89, 1105. (17) Crowell, A. D.; Brown, J. S. Surf. Sci. 1982, 123, 296. (18) Wang, Q.; Johnson, J. K. Mol. Phys. 1998, 95, 299. (19) Matranga, K. R.; Myers, A. L.; Glandt, E. D. Chem. Eng. Sci. 1992, 47, 1569. (20) Cracknell, R. F.; Gordon, P.; Gubbins, K. E. J. Phys. Chem. 1993, 97, 494. (21) Hynek, S.; Fuller, W.; Bentley, J. Int. J. Hydrogen Energy 1997, 22, 601.