J. Phys. Chem. B 2005, 109, 8659-8662
8659
Quasi One-Dimensional Nanopores in Single-Wall Carbon Nanohorn Colloids Using Grand Canonical Monte Carlo Simulation Aided Adsorption Technique Tomonori Ohba,† Hirofumi Kanoh,† Masako Yudasaka,‡ Sumio Iijima,‡ and Katsumi Kaneko*,† Department of Chemistry, Faculty of Science, Chiba UniVersity, 1-33 Yayoi, Inage, Chiba 263-8522, Japan, and Japan Science and Technology Agency, NEC Corporation, 34 Miyukigaoka, Tsukuba 305-8501, Japan ReceiVed: January 17, 2005; In Final Form: March 6, 2005
The average interstitial nanopore structure of single-wall carbon nanohorn (SWNH) assemblies was determined using X-ray diffraction and grand canonical Monte Carlo (GCMC) simulation aided N2 adsorption at 77 K. The interstitial nanopores of SWNH assemblies can be regarded as quasi one-dimensional pores due to the partial orientation of the SWNH particles; the average pore width of the interstitial pores is 0.6 nm. Good agreement between the GCMC simulation of a structural model with one-dimensional interstitial nanopores and an experimental adsorption isotherm below P/P0 ) 10-4 is evidence of the quasi one-dimensionality of the interstitial nanopores. A snapshot from the GCMC simulation showed one-dimensional growth of adsorbed N2 molecules.
1. Introduction Investigation of single-wall carbon nanohorns (SWNHs) should help to clarify the adsorption mechanism of methane and hydrogen on carbon nanotubules1-3 because SWNHs have a tube structure similar to that of single-wall carbon nanotubes (SWNTs), although they have much shorter tubes. Sufficient amounts of highly pure SWNH samples are available for adsorption studies.4 The dahlia flower like structure of an assembly of SWNH particles provides only interstitial pores between the particles because the internal pore spaces inherent to SWNH particles are perfectly close. Oxidation treatment of the SWNH donates nanoscale windows on the wall of the SWNH particles, and as a result the internal pore spaces of the oxidized SWNH are available for gas adsorption. We can thus distinguish between gas adsorption in the interstitial and internal nanopores of the SWNH assemblies using as-received and oxidized SWNH samples. Previous grand canonical Monte Carlo (GCMC) simulation aided N2 adsorption showed that the average width of the internal nanopores is 3.2 nm.2 It has been predicted that the interstitial pores of SWNH provide a strong interaction field for molecules, so better characterization of these interstitial pores is essential for designing a nanocarbon adsorbent for methane and hydrogen. X-ray diffraction (XRD) examination indicated that the interparticle spacing of a partially oriented SWNH assembly is 0.4 nm.5 However, since this has not yet been sufficiently established, detailed analysis of the interparticle spacing of SWNH particles is required. Thus, we need to develop a GCMC simulation aided adsorption technique (GSA) to determine the average nanopore geometry. 2. GCMC Simulation and Experiment Transmission electron microscopic images of SWNH particles showed that one end of a single SWNH particle has a cornlike * Corresponding author. Fax 81-43-290-2788. E-mail: kaneko@ pchem2.s.chiba-u.ac.jp. † Chiba University. ‡ NEC Corp.
structure with a tip that has an average angle of π/9 rad. Although the average length of a single SWNH particle has not been precisely evaluated, it is estimated to be about 40 nm. Thus, in the geometric model of an SWNH particle in the GCMC simulation, the lengths of the tube and corn parts were assumed to be 31 and 9 nm, respectively. Furthermore, the wall of a single SWNH particle was approximated to be smooth and a bundled SWNH structure consisting of seven SWNH particles with a hexagonal symmetry was assumed.6-8 The intermolecular interaction between the N2 molecules was approximated by the one-center Lennard-Jones (LJ) potential function, as described by eq 1.
[( ) ( ) ]
Uff ) 4ff
σff r
12
-
σff r
6
(1)
Here, ff is the potential well depth between the N2 molecules and σff is the effective diameter. The LJ parameters used for an N2 molecule were ff/kB ) 104.2 K and σff ) 0.3632 nm. The interaction between a molecule and the carbon wall of the SWNH was approximated by the spinning fishing rod model approximated for the molecule-pore interaction with the SWNH particle.2,8 Here, cc/kB ) 30.14 K and σcc ) 0.3416 nm were used for a carbon atom. The cross parameters of an N2 molecule and a carbon atom were given by the Lorentz-Berthelot rule. The random movement, creation, and removal of a molecule give a new configuration whose total potential energy can be calculated. When this configuration is accepted under the conditions of Metropolis’s sampling scheme, the system reaches equilibrium. The chemical potentials of N2 molecules in the interparticle spacing and gas phase are equal to each other in the grand canonical ensemble. Thus, the adsorption amount at a chemical potential, that is, a pressure, can be calculated. This methodology has been reported previously.9-13 The relationship between the tube diameter at the carbon atom position and the effective pore width of the internal pores, which can be
10.1021/jp0503011 CCC: $30.25 © 2005 American Chemical Society Published on Web 04/05/2005
8660 J. Phys. Chem. B, Vol. 109, No. 18, 2005
Ohba et al.
Figure 1. XRD pattern (a) and radial distribution (b) of SWNH.
determined by gas adsorption, is described by the following equation.14
effective pore width ) tube diameter - 0.30 nm
(2)
Previous work showed that the effective pore width of a single SWNH particle is 2.9 nm, which was determined by comparing experimental and simulated isotherms in an internal pore.2 Therefore, an effective pore width of 2.9 nm was used in this study. Simulated adsorption isotherms of N2 in the interstitial pores of hexagonally bundled tubes were calculated over the relative pressure P/P0 range of 10-6 to 1 for various interparticle spacings of 0.4, 0.6, 0.7, 0.8, and 1.2 nm, which was the tube wall-to-wall distance D from the central SWNH particle to the nearest-neighbor SWNH particles. Here, P0 is the saturated vapor pressure. XRD measurement was carried out using Mo KR radiation (60 kV, 300 mA). Perfectly close porosity of the SWNH particles was evidenced by the particle density from the high pressure helium buoyancy measurement,15 and thereby the measured isotherm of the SWNH colloids was compared with the simulated one. The N2 adsorption isotherms on the SWNH were measured in the range of P/P0 from 10-6 to 1 using a gravimetric method after preheating to 473 K and at less than 1 mPa. 3. Results and Discussion Figure 1a shows the XRD pattern of the SWNH assemblies and the radial distribution function. Peaks originating from the graphite-like structure are observed. The diffraction peaks at s ) 18, 30, 35, and 54 nm-1 were assigned to reflections from the graphite lattice planes of (002), (10), (004), and (11), respectively. Since there were graphite cores after oxidation at
Figure 2. Adsorption isotherms of N2 on SWNH with logarithmic relative pressure (a) and rate of tube volume to total volume versus D (b).
high temperature, these diffraction peaks stemmed from the graphite cores. The peaks at s ) 12 and 16 nm-1 cannot be assigned to the graphite lattice. This was ascribed to partially oriented structures producing narrow interstitial nanopores. We transformed the diffraction pattern into a radial distribution to elucidate the peaks at 12 and 16 nm-1. Figure 1b shows the radial distribution function. The first and second peaks at 0.12 and 0.22 nm indicate the nearest carbon-carbon distance and second-neighbor distance of a graphene sheet, respectively. The peak at 0.34 nm is the distance between the stacked layers of the graphite core. The short peaks at 0.45 and 0.6 nm cannot be assigned to the graphite structure. Accordingly, the broad peaks at 0.45 and 0.6 nm must stem from the interparticle periodicity of the SWNH assemblies. Thus, the SWNH colloids must have two kinds of mutually associated structures. If this explanation is correct, interstitial porosity characterization with N2 adsorption should give a consistent result. An experimental adsorption isotherm of N2 on SWNH at 77 K is shown in Figure 2a. N2 adsorption starts even below P/P0 ) 10-6. The shape of the adsorption isotherm has two plateaus, one below P/P0 ) 10-4 and one near 0.1, and a gradual increase between them is observed. The steep slope above P/P0 ) 0.1 is caused by adsorption on the external surfaces of the SWNH colloids. Accordingly, the adsorption below P/P0 ) 0.1 is ascribed to adsorption in the interstitial pores of the SWNH assemblies. These different adsorption processes may be associated with different adsorption sites in the interstitial nanopores. Since the XRD study clearly showed the presence of partially oriented structures, there must be two kinds of adsorption sites in the interstitial spaces between the tube parts and wider void spaces near the corn parts. The former sites have a much stronger molecule-carbon wall interaction potential than the latter. Therefore, we presume that N2 molecules are adsorbed
Structure of Nanopores in SWNH Colloids
J. Phys. Chem. B, Vol. 109, No. 18, 2005 8661
Figure 3. DR plot of N2 adsorption on SWNH.
Figure 5. Snapshots of N2 molecules in interstitial pores of D ) 0.7 nm. Interstitial pore is surrounded by three SWNH particles, as shown in the top figure. SWNH particle is removed to show the top of filling structures of N2 molecules in the middle and bottom figures.
Figure 4. Simulated adsorption isotherms in bundled SWNH particles with D ) 0.4 (O), 0.7 (4), and 1.2 (0) nm. ], single SWNH particle; ---, experiment.
in the interstitial spaces between tubes below P/P0 ) 10-4 and in the void spaces near the corn parts in the P/P0 range from 10-4 to 0.1. The adsorbed amounts corresponding to the two plateau areas in the N2 adsorption isotherm were 50 and 125 mg g-1, respectively. The above assumption indicates that interstitial pore volumes from the tube and corn sites were 0.056 and 0.099 mL g-1, respectively. Here, liquid N2 density (0.808 g cm-3) was used to evaluate the volume of each pore. The interstitial nanopores between the tube and corn parts were termed intertube interstitial nanopores and corn-part interstitial nanopores, respectively. The rate of the intertube interstitial pore volume to the total interstitial pore volume was calculated to be 0.36. We can calculate the pore volumes of intertube and corn-part interstitial pores as a function of the nearest-neighbor tube wall-to-wall distance D in the hexagonal symmetry, as shown in Figure 2b. Here we corrected the volume excluded by adsorbed N2. The experimental rate corresponds to that of D ) 0.67 nm, which roughly corresponds to the peak of the radial distribution at 0.6 nm in the XRD study. The effective space in the interstitial channel can be regarded as a quasi onedimensional pore of cylindrical shape for N2 adsorption. The quasi one-dimensional pore width was evaluated using a simple geometric calculation assuming a hexagonal bundle structure when D ) 0.7 nm. Thus, the evaluated pore width was 0.6 nm. RS analysis is considered one of the most reliable methods for determining average nanopore structures.16,17 The adsorption mechanism in the interstitial channel differs from that in the slit-shaped pore.14,18 In the previous study, we recommended that the adsorption isotherm of N2 in internal tube spaces of SWNT of 8.0 nm diameter should be used as the standard isotherm in RS analysis of cylindrical pores.14 The specific
surface area, external surface area, nanopore volume (W0), and average pore size (w), from RS analysis were 374 m2 g-1, 40 m2 g-1, 0.15 mL g-1, and 1.8 nm, respectively. Here the w value from the RS plot is the average value of the tube and corn parts. Thus, we must distinguish adsorption in the intertube pores from that in the corn parts. Dubinin-Radushkevich (DR) analysis is applied to determine the effective pore geometry of quasi one-dimensional pores.19-23 The DR equation is given by eq 3.19
[ ( ) { ( )} ]
W ) W0 exp -
RT βE0
2
ln
P0 P
2
(3)
Here, W is the amount of adsorption at P/P0. β is an affinity coefficient and E0 is the characteristic adsorption energy. Two linear regions of the DR plot were observed in {ln(P0/P)}2 values from 10 to 70 and from 70 to 160, as shown in Figure 3. The upward bend near the ordinate comes from adsorption on wider nanopores. The two linear regions of 10-70 and 70160 on the abscissa in Figure 3 give nanopore volumes of 0.18 and 0.11 mL g-1, respectively. These volumes (0.18 and 0.11 mL g-1) stem from the total interstitial pores and intertube interstitial pores between the tube parts, respectively. We also used GSA to study the interparticle distance because of the need to confirm D from a different point of view and to investigate the molecular arrangement. Figure 4 shows simulated isotherms of N2 in the interstitial pores of SWNH assemblies with different D values of 0.4, 0.7, and 1.2 nm and of N2 on the external surface of a single SWNH particle for comparison. Here, the GCMC simulation gives adsorption isotherms in interstitial pores composed of seven particles with a hexagonal bundle structure. The simulated adsorption amounts were adjusted to compare them with the experimental ones using the factor determined in the previous work.2 These simulated isotherms for the bundled model express the experimental
8662 J. Phys. Chem. B, Vol. 109, No. 18, 2005
Ohba et al. the intertube interstitial pores of SWNH at 77 K form the solid β-phase structure observed at low temperature. Thus, adsorption of N2 on SWNH colloids at 77 K is not necessarily simple and comparison of a GCMC-simulated adsorption isotherm with an experimental one is required to elucidate the nanopore structure of SWNH colloids. This study showed that a GCMC simulation aided adsorption technique is quite effective for this purpose. Acknowledgment. This work was supported by a Research Fellowship from the Japan Society for the Promotion of Science for Young Scientists and by the Nanocarbon Technology Project (NEDO).
Figure 6. Simulated radial distribution of N2 in intertube and cornpart interstitial pores, R-phase of bulk N2, and β-phase of bulk N2 in order from the top.
isotherm better than that for the single SWNH particle model. Hence, the simulation also supports the presence of bundled structures, as did the XRD study. The simulated isotherm in the interstitial pores of D ) 0.7 nm is the best fit for the experimental one, agreeing with the above results. The present study shows that intertube interstitial nanopores can be regarded as quasi one-dimensional pores. The N2 molecular state in a quasi one-dimensional pore was examined using snapshots from the GCMC simulation. Figure 5 shows that N2 adsorption in the intertube interstitial pores began predominantly at P/P0 ) 5 × 10-5, forming a one-dimensional molecular column. Adsorption in the corn-part interstitial pores started at P/P0 ) 0.1. Figure 6 shows the radial distributions of N2 molecules confined in the intertube and corn-part interstitial pores at P/P0 ) 0.1. The distribution in the intertube interstitial pores has sharper peaks than those in the corn-part interstitial pores. Both radial distributions have sharp peaks at 0.40 nm, stemming from the nearest-neighbor distance. The radial distribution of N2 confined in the intertube interstitial pores has additional peaks at 0.70, 0.80, 1.05, 1.15, and 1.40 nm, indicating the presence of a considerable long-range order. Consequently, a solidlike structure must be formed in the pores. Solid N2 has R-, β-, and γ-phases.24-27 The R- and β-phases have a cubic structure below 36 K and a hexagonal one above 36 K, respectively. A γ-phase was observed above 350 MPa. Therefore, we compared the radial distributions of bulk solid N2 in the R- and β-phases with that of N2 adsorbed in the intertube interstitial pores. The observed peaks of the adsorbed N2 were approximately similar to those of bulk solid N2 in the β-phase. Hence, it is probable that N2 molecules adsorbed in
References and Notes (1) Murata, K.; Kaneko, K.; Kokai, F.; Takahashi, K.; Kasuya, D.; Yudasaka, M.; Iijima, S. Chem. Phys. Lett. 2000, 14, 331. (2) Ohba, T.; Murata, K.; Kaneko, K.; Steele, W. A.; Kokai, F.; Takahashi, K.; Kasuya, D.; Yudasaka, M.; Iijima, S. Nano Lett. 2001, 1, 371. (3) Murata, K.; Kaneko, K.; Steele, W. A.; Kokai, F.; Takahashi, K.; Kasuya, D.; Hirahara, K.; Nisha, J. A.; Yudasaka, M.; Iijima, S. J. Phys. Chem. B 2001, 105, 10210. (4) Iijima, S.; Yudasaka, M.; Yamada, R.; Bandow, S.; Suenaga, K.; Kokai, F.; Takahashi, K. Chem. Phys. Lett. 1999, 309, 165. (5) Bandow, S.; Kokai, F.; Takahashi, K.; Yudasaka, M.; Qin, L. C.; Iijima, S. Chem. Phys. Lett. 2000, 321, 514. (6) Steele, W. A.; Bojan, M. J. AdV. Colloid Interface Sci. 1998, 7677, 153. (7) Stan, G.; Cole, M. W. Surf. Sci. 1998, 395, 280. (8) Ohba, T.; Kanoh, H.; Kaneko, K.; Murata, K.; Yudasaka, M.; Iijima, S. Stud. Surf. Sci. Catal. 2002, 144, 521. (9) Jorge, M.; Seaton, N. A. Mol. Phys. 2002, 100, 2017. (10) Ohba, T.; Nicholson, D.; Kaneko, K. Langmuir 2003, 19 (14), 5700. (11) Cracknell, R. F.; Nicholson, D.; Quirke, N. Mol. Phys. 1993, 80 (4), 885. (12) Maddox, M.; Ulberg, D.; Gubbins, K. E. Fluid Phase Equilib. 1995, 104, 145. (13) Bojan, M. J.; Steele, W. A. Carbon 1998, 36, 1417. (14) Ohba, T.; Kaneko, K. J. Phys. Chem. B 2002, 106 (29), 7171. (15) Murata, K.; Kaneko, K.; Kanoh, H.; Kasuya, D.; Takahashi, K.; Kokai, F.; Yudasaka, M.; Iijima, S. J. Phys. Chem. B 2002, 106 (43), 11132. (16) Setoyama, N.; Suzuki, T.; Kaneko, K. Carbon 1998, 36, 1459. (17) Sing, K. S. W. Carbon 1989, 27, 25. (18) Ohba, T.; Suzuki, T.; Kaneko, K. Chem. Phys. Lett. 2000, 326, 158. (19) Dubinin, M. M. Chem. ReV. 1960, 60, 235. (20) Ohba, T.; Suzuki, T.; Kaneko, K. Carbon 2000, 38, 1892. (21) Chen, S. G.; Yang, R. T. Langmuir 1994, 10 (1), 4244. (22) Cleary, D. H.; Stoeckli, F. Carbon 2000, 38, 1309. (23) Ohba, T.; Kaneko, K. Langmuir 2001, 17, 3666. (24) Vegard, L. Nature 1929, 124, 672. (25) Streib, W. E.; Jordan, T. H.; Lipscomb, W. N. J. Chem. Phys. 1962, 37, 2962. (26) Schuch, A. F.; Mills, R. L. J. Chem. Phys. 1970, 52 (12), 6000. (27) Powell, B. M.; Dolling, G.; Nieman, H. F. J. Chem. Phys. 1983, 79 (2), 982.
