Article pubs.acs.org/JPCC
Quantum Molecular Sieving Effects of H2 and D2 on Bundled and Nonbundled Single-Walled Carbon Nanotubes Hirotoshi Kagita,† Tomonori Ohba,*,† Toshihiko Fujimori,‡ Hideki Tanaka,§ Kenji Hata,⊥ Sei-ichi Taira,† Hirofumi Kanoh,† Daiki Minami,‡ Yoshiyuki Hattori,∥ Tsutomu Itoh,# Hyuma Masu,# Morinobu Endo,‡ and Katsumi Kaneko*,‡ †
Graduate School of Science, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan Research Center for Exotic Nanocarbons, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan § Department of Chemical Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan ∥ Faculty of Textile Science and Technology, Shinshu University, 3-15-1 Tokida, Ueda 386-8567, Japan ⊥ Nanotube Research Center, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi Tsukuba, Ibaraki 305-8565, Japan # Chemical Analysis Center, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan ‡
S Supporting Information *
ABSTRACT: The quantum molecular sieving effects of pore-structure-controlled single-walled carbon nanotubes (SWCNTs) for H2 and D2 were evaluated at 20, 40, and 77 K. The adsorption amounts of D2 were larger than those of H2. The lower the adsorption temperature, the greater the difference between the D2 and H2 adsorption amounts. Bundled SWCNTs with interstitial pores of diameter 0.6 nm gave the greatest adsorption difference between D2 and H2 per unit pore volume. Diffusiondominated behavior was observed in the low-pressure region at 20 and 40 K as a result of lower mobility. Bundled SWCNTs with only interstitial pores provided a significant quantum molecular sieving as a result of strongly interacting potential wells. isotherms on single-walled carbon nanohorns at 20−77 K;6,7 they gave a direct explanation for the adsorption differences between D2 and H2 at 77 K, using Feynman−Hibbs (FH) effective potential calculations.8,9 Quantum molecular sieving effects were observed, stimulating related research.10−13 Noguchi et al.14 and Tanaka et al.15 reported quantum molecular sieving effects in SWCNTs observed using lowtemperature-adsorption experiments and quantum simulations using FH potentials. However, ordinary SWCNTs form bundles,16 so we need to take three adsorption sites into account: internal tube spaces, interstitial pore spaces, and external groove sites. The explicit adsorption behaviors of H2 and D2 in simpler SWCNT systems need to be elucidated. In other words, novel quantum adsorption behaviors should be studied using well-characterized SWCNTs. In this article, we report the quantum molecular sieving effects of H2 and D2 for adsorption-space-controlled SWCNTs prepared using the supergrowth (SG) method, over the temperature range 20− 77 K.
1. INTRODUCTION The mass of an H2 molecule is 3700 times that of a quantum electron; therefore, quantum fluctuations of an H2 molecule in a free space are completely negligible. However, when an H2 molecule is confined in a nanometer-scale space, quantum fluctuations are crucial in filling the space with H2 molecules. The extents of the fluctuations of H2 at 20 and 77 K are estimated to be 0.27 and 0.14 nm, respectively, using the de Broglie wavelength, λT = (h2/2πmkT)1/2. Thus, λT depends on the mass of the molecule and the temperature. The λT of D2 is smaller than that of H2 because the molecular mass of D2 is double that of H2. Thus, H2 and D2 are distinguishable in quantum mechanics, although these molecules are identical in classical mechanics. We can therefore separate H2 and D2, based on their quantum nature, using adsorption techniques in nanoscale pores. Kaneko et al. pointed out that He atoms confined in 1 nm slit carbon pores at 4.2 K should be larger than classical He molecules.1 Beenaker pioneered the development of the theory of quantum molecular sieving in cylindrical pores.2 Johnson et al. showed the strong possibility of quantum molecular sieving effects in single-walled carbon nanotubes (SWCNTs), using theoretical methods such as path integral simulation.3−5 However, there has been no clear experimental study on SWCNTs together with quantum simulation because of the difficulty of adsorption measurements under cryogenic conditions. Tanaka et al. reported H2 and D2 adsorption © 2012 American Chemical Society
Received: July 2, 2012 Revised: September 4, 2012 Published: September 8, 2012 20918
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Figure 1. (a) Interaction potential profiles of classical H2 (black), quantum H2 (red), and quantum D2 (blue) and (b) enlarged view in the r range 0.5−1.5 nm.
2. EXPERIMENTAL AND SIMULATION PROCEDURES We used mutually isolated SWCNTs prepared using the SG chemical vapor deposition method.17 The average tube diameter was 2 nm. The SWCNTs associated with each other to form bundles, as a result of capillary force, when the SWCNTs were dispersed in a solution and dried. The capillary force drives the alignment of SWCNT particles, as observed in transmission electron microscopy (TEM) images, as mentioned later. The SWCNTs were sonicated in methanol at 273 K for 12 h and then separated at 423 K after filtration to form bundles, using the capillary force, upon evaporation of methanol. The treated SWCNT samples are denoted by band-SWCNT. The caps were removed by oxidation with a flow of a N2/O2 mixture gas (N2:O2 = 80:20) at a flow rate of 150 mL min−1 at 693 K for 1 h. The oxidized SWCNTs are designated as ox-SWCNTs. The SWCNT samples were characterized using Raman spectroscopy (YAG laser: 532 nm, Ar laser: 633 nm, NRS-3100, JASCO Co.), scanning electron microscopy (SEM) (JSM-6330F, JEOL Co.), and highresolution TEM (JEM-2100F, JEOL Co.). The nanopore structures of the SWCNT samples were determined using N2 adsorption at 77 K after pre-evacuation at 423 K and 0.1 mPa for 2 h using a volumetric apparatus (Autosorb-1, Quantachrome/Malvan). The adsorption isotherms of H2 and D2 on SWCNT samples were measured over the temperature range 20−77 K using laboratory-designed volumetric adsorption equipment. All adsorption isotherms were measured after pretreatment of the samples at 423 K under 0.1 mPa for 2 h. We assumed that an H2 molecule is spherical and used the Lennard-Jones (LJ) potential for the H2−H2 interaction. The LJ parameters we used for H2 were the collision diameter σH = 0.2958 nm and the potential well εff/kB = 36.7 K.18 The effective FH H2−H2 interaction potential was derived from the LJ potential. We used an infinitely long cylindrical tube model with a smooth wall for the H2−SWCNT interaction potential. Then we adopted a well-known analytical function consisting of hypergeometric functions.19 We integrated the pairwise FH effective potential to calculate the quantum H2− or D2− SWCNT interaction potential. The detailed calculation procedures are given in other papers.20,21
with a SWCNT of 2 nm diameter. The interaction potential profile for classical H2 is obtained using the LJ potential function and is identical to that for classical D2. Classical theory cannot distinguish H2 and D2 adsorption behaviors. The quantum interaction potential profiles for H2 and D2 are calculated from the FH effective potential at 40 K. The inner wall of the negative curvature gives a deeper potential minimum than the external wall by about 200 K. Classical H2 or D2 leads to the deepest minima, and the minimum position is closest to the tube wall at r = 1.0 and −1.0 nm. The potential profile also has a very sharp potential valley along the wall. A quantum D2 provides the difference of potential profiles from the classical H2 (or D2) than that of quantum H2. Figure 1 shows that a lighter quantum molecule, that is, quantum H2, gives shallower potential minima at larger distances from the tube wall. 3.2. Nanopore Structure. The SEM images of oxSWCNTs were similar to those of SWCNTs. However, bandSWCNTs had more continuous features than SWCNTs and ox-SWCNTs (Supporting Information, Figure S1), suggesting that band-SWCNTs have unit structures different from those of the other SWCNT samples. The TEM images show a clear difference between band-SWCNTs and the other two SWCNT samples, as shown in Figure 2. We observe highly oriented regions in the associated SWCNTs, and these come from bundle formation. The tube opening of SWCNTs by oxidation was evaluated by measuring the particle density at high pressure using the He buoyancy measuring method.22 The particle densities of SWCNTs, ox-SWCNTs, and band-SWCNTs were 1.56, 2.13, and 1.60 g cm−3, respectively. The ideal density of a graphene sheet is 2.26 g cm−3, evaluated from the density of graphite. The particle density differences of the SWCNTs and ox-SWCNTs are the result of tube opening of the ox-SWCNTs. The tube opening ratio of the ox-SWCNTs was 0.8 and was defined as the density differences of ox-SWCNTs and SWCNTs compared with those of graphene sheets and SWCNTs, if the SWCNTs and band-SWCNTs are completely closed. Figure 3 shows N2 adsorption isotherms of SWCNT samples at 77 K. The adsorption isotherm of N2 in only the internal tube spaces, denoted by int-SWCNT, is evaluated by subtracting the adsorption isotherm of the SWCNT from that of the ox-SWCNT. SWCNTs have only intertube spaces as adsorption sites, whereas ox-SWCNTs have both internal tube spaces and intertube spaces because SWCNTs are closed internal tube spaces for molecules, as mentioned above. The N2 adsorption isotherm of int-SWCNT is of IUPAC type I,
3. RESULTS AND DISCUSSION 3.1. Potential Profiles. Figure 1 shows the interaction potential profiles of classical H2, quantum H2, and quantum D2 20919
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characterized by pore filling of N2 in nanopores, although the other adsorption isotherms are of IUPAC type II, indicating that adsorption on the external surfaces cannot be neglected. These N2 adsorption isotherms were analyzed using highresolution αs-plots using the subtracting pore effect method23 and Dubinin−Radushkevich plots,24 which provide the surface area and nanopore volume, respectively; the values are shown in Table 1. SWCNTs are relatively isolated from each other, Table 1. Porosities of SWCNT, ox-SWCNT, band-SWCNT, and int-SWCNT specific surface area/m2 g−1 nanopore volume/ mL g−1
SWCNT
ox-SWCNT
band-SWCNT int-SWCNT
1200
1900
850
700
0.45
0.83
0.27
0.38
and therefore the intertube spaces evaluated from the N2 adsorption isotherm are large. After bundle formation, the intertube spaces of band-SWCNTs are smaller than those of SWCNTs but have stronger interaction potential wells. The internal tube spaces of ox-SWCNTs are also available for N2 adsorption. The nanopore volume of int-SWCNT corresponds exactly to the difference between the nanopore volumes of oxSWCNT and SWCNT. 3.3. Diffusion-Controlled Quantum Molecular Sieving Effect. Figure 4 shows adsorption isotherms of H2 and D2 on
Figure 2. TEM images of (a) SWCNT, (b) ox-SWCNT, and (c) band-SWCNT.
Figure 3. N2 adsorption isotherms on SWCNT (blue), ox-SWCNT (red), band-SWCNT (black), and int-SWCNT (green).
Figure 4. Adsorption isotherms of H2 (open symbol) and D2 (solid symbol) on SWCNT samples at (a) 40 and (b) 77 K. Blue, SWCNT; red, ox-SWCNT; and black, band-SWCNT. 20920
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SWCNT samples at 40 and 77 K. ox-SWCNT adsorbs the largest amounts of D2 and H2. SWCNT and band-SWCNT adsorb similar amounts of D2 and H2, despite the large difference between their surface areas. All the adsorption amounts of D2 are larger than those of H2, although the D2 and H2 adsorption difference at 77 K is much smaller than that at 40 K. The differences between the D2 and H2 adsorption amounts are slightly smaller than those predicted using FH-type grand canonical Monte Carlo simulations. 15 The D 2 and H 2 adsorption difference for band-SWCNT at 77 K is almost the same as that of ox-SWCNT, although its surface area and nanopore volume are half those of ox-SWCNT. The interstitial pores are preferred adsorption sites for D2 at 77 K. However, this feature disappears at 40 K; the D2 and H2 adsorption difference of band-SWCNT at 40 K is less than half that of SWCNT. The interstitial pores are therefore not involved in selective D2 adsorption at 40 K. This is a result of restricted diffusion in the interstitial pore spaces, even above the critical temperatures. The effective sizes of D2 and H2 at 40 K are larger than those at 77 K. The classical size of H2 is about 0.30 nm, from the LJ parameter. Ordinary molecules can relatively easily access pores whose width is larger than a bilayer of the molecule. When the pore size is smaller than 2 × 0.30 nm (0.60 nm), therefore, serious blockage of pore entrances by strongly preadsorbed molecules occurs. In the case of quantum H2 and D2, fluctuations of quantum molecules become more significant at lower temperatures. The λT of H2 at 40 K is 0.19 nm, whereas that at 77 K is 0.14 nm. Entrance blocking should have a large effect on H2 and D2 adsorption at 40 K since the effective size of a quantum molecule can be approximated by the sum of the LJ size parameter and the λT value. The average effective size of the interstitial pores of bundles is estimated to be 0.5 nm, assuming hexagonal symmetry and bundles of SWCNTs of average diameter 2.0 nm. Entrance blocking of interstitial pores should therefore be predominant at 40 K. This is because there is not enough room for swift diffusion of molecules because of preadsorbed molecules in the pore entrances. The importance of the diffusion factor increases for adsorption at 20 K. Figure 5 shows the adsorption isotherms of D2 and H2 at 20 K in normal and logarithmic pressure scales. (The logarithmic adsorption isotherms at 40 and 77 K are shown in Figure S2, Supporting Information). The normal adsorption isotherms have very steep uptakes at the beginning, indicating that the interaction between H2 or D2 and the SWCNTs is strong compared with the thermal energy at 20 K. The adsorption difference between D2 and H2 at 20 K is striking compared with those at 40 and 77 K. However, we can see opposite tendencies in D2 and H2 adsorptions in the lowerpressure range; the adsorption isotherms of D2 and H2 on oxSWCNTs cross below P/P0 = 10−4. Although we measured the adsorption isotherms at equilibrium, the equilibration is not sufficient in the case of adsorption in micropores under low pressure at low temperature, in particular at 20 K. We need to take the diffusion factor into account to understand the adsorption isotherms accurately. In the higher-pressure region, the ordinary quantum molecular sieving effect was observed, so the diffusion factor was controlled by the pressure and temperature. Quantum molecular sieving and diffusion effects can play important roles in an efficient separation system. We therefore need to design significant interaction potential well differences for two target molecules.
Figure 5. Adsorption isotherms of H2 (open symbol) and D2 (solid symbol) on SWCNTs at 20 K in the linear (top) and logarithmic scales (bottom). Blue, SWCNT; red, ox-SWCNT; and black, bandSWCNT.
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ASSOCIATED CONTENT
S Supporting Information *
SEM images of SWCNTs and adsorption isotherms of H2 and D2 at 40 and 77 K. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected];
[email protected]. jp. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS K.K. and T.F. were supported by Exotic Nanocarbons, Japan Regional Innovation Strategy Program by Excellence, JST. The work was supported by a Grant-in-Aid for Scientific Research and the Strategic Promotion Program for Basic Nuclear Research, the JGC-S Scholarship Foundation, Promotion of Ion Engineering, Murata Science Foundation, Nippon Sheet Glass Foundation, and Global COE Program, MEXT, Japan.
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