15660
J. Phys. Chem. C 2007, 111, 15660-15663
Nanoscale Curvature Effect on Ordering of N2 Molecules Adsorbed on Single Wall Carbon Nanotube† Tomonori Ohba,‡ Taku Matsumura,‡ Kenji Hata,§ M. Yumura,§ S. Iijima,§,| Hirofumi Kanoh,‡ and Katsumi Kaneko*,‡ Graduate School of Science, Chiba UniVersity, 1-33, Yayoi, Inage, Chiba 263-8522, Japan, Center for AdVanced Carbon Materials, National Institute of AdVanced Industrial Science and Technology (AIST), Tsukuba, 305-8565, Japan, and Department of Physics, Japan Science and Technology Corporation, Meijo UniVersity, 1501 Shiogamaguchi, Tenpaku-ku, Nagoya 468-8502, Japan ReceiVed: June 11, 2007; In Final Form: August 23, 2007
The experimental adsorption isotherm of N2 molecules on mutually isolated single wall carbon nanotubes at 77 K agreed well with the grand canonical Monte Carlo simulated one. The N2 adsorption isotherm had two steps stemming from monolayer formation on the internal surface and filling of the residual space of the internal tube pore. Although all of radial distribution functions of molecules adsorbed on the internal, external, and flat surfaces indicated a hexagonal packing structure, the radial distribution functions were different from each other. In particular, the radial distribution function of the monolayer on the internal surface showed an additional peak because of the markedly curved surface.
Introduction In colloid science, it is well-known that the sign of the curvature of the liquid surface gives a crucial effect on the vapor pressure. The Kelvin equation describes the dependence of the vapor pressure of the liquid on the sign and the average radius of the interface curvature. The vapor pressure in equilibrium with a meniscus having a negative curvature of the liquid surface is smaller than that over the flat liquid surface, inducing socalled capillary condensation of vapors in mesopores below the saturated vapor pressure. On the other hand, a liquid drop of the positive curvature has a larger vapor pressure than the flat liquid surface. The dependence of the vapor pressure of liquid surface on the curvature through the Kelvin equation has been widely applicable to various interfacial phenomena. However, the Kelvin equation cannot be applied to liquid interface in nanoscale.1-3 Also, we do not understand sufficiently the liquid interface in nanoscale itself. We have an intensive demand for understanding of nanomaterials and molecular processes on nanostructures. Single wall carbon nanotube (SWCNT) is a representative of nanomaterials;4-8 SWCNTs can have a great surface area of about 2600 m2 g-1 being the surface area of a single graphene sheet. Also, all carbon atoms of SWCNTs are exposed to both-side surfaces, that is, the external and internal surfaces whose curvatures are positive and negative, respectively. Hence, the effect of the nanoscale curvature of the SWCNT surface on the interfacial properties should give an essential insight to nanoscale interfacial science. As SWCNTs have wide application potentials for energy storage, separation, sensing, electronic device, fabrication, and so on, the fundamental understanding of the effect of the nanoscale curvature on the interfacial processes on a SWCNT
should provide a useful guide for the interfacial application. However, widely used SWCNTs contain abundant metallic impurities and form the bundle structure. Fortunately, Hata et al. succeeded to produce highly pure SWCNTs using a sophisticated chemical vapor deposition (CVD) technique;9 almost all SWCNTs do not form the bundle, being isolated from each other. Accordingly, this almost isolated SWCNT is just fit for the study on the effect of the nanoscale curvature sign on the molecular process. In this study, we examined the adsorbed structure of N2 molecules on the external and internal surfaces of the isolated SWCNT at 77 K using grand canonical Monte Carlo (GCMC) simulation and the experimental highresolution adsorption isotherm. Simulation and Experimental Section N2 adsorption isotherms at 77 K were calculated with GCMC simulation on the internal and external surfaces of a sole SWCNT having a tube diameter of 2.5 nm by using the following potential function. The intermolecular interaction between single-center N2 molecules as a function of intermolecular distance r was obtained from 12-6 Lennard-Jones potential.
φff(r) ) 4ff
[( ) ( ) ] σff r
12
-
σff r
6
(1)
Here, ff ) 104.2 kB K and σff ) 0.3632 nm are the N2-N2 potential well depth and the effective diameter, respectively. The smooth structure function was used for the calculation of the interaction potential of a N2 molecule with a SWCNT having infinite length.10,11
φsf ) 4Fsf[σsf12I6 - σsf6I3]
(2)
†
Part of the “Keith E. Gubbins Festschrift”. * Corresponding author. E-mail:
[email protected]. ‡ Chiba University. § National Institute of Advanced Industrial Science and Technology. | Meijo University.
where sf ) 56.04 kB K and σsf ) 0.3524 nm are fitted parameters of the N2-carbon potential depth and effective diameter, respectively, which were obtained using the Lorentz-
10.1021/jp074504w CCC: $37.00 © 2007 American Chemical Society Published on Web 10/09/2007
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J. Phys. Chem. C, Vol. 111, No. 43, 2007 15661
Berthelot rules. F ) 38.2 nm-2 is the number density of carbon atom for the graphene tube. I3 and I6 are expressed by a hypergeometric function F.
I6 )
63π2 9 9 F - ,- ,1;β2 10 2 10 2 2 128(D/2) (1 - β )
(3)
3π2 3 3 F - ,- ,1;β2 4 2 4 2 2 4(D/2) (1 - β )
(4)
I3 )
(
(
)
)
Here, β is defined as 2r/D and r is the distance from the SWCNT center to a N2 molecule. GCMC simulation was conducted by using the Metropolis sampling scheme with creation, deletion, and movement.12-14 A rectangular cell of 6 × 6 × 6 nm3 was used for simulation. The arrival steps to each equilibrium amount are 107. The average number of the amount was obtained after 9 × 106 steps. Snapshots of monolayer on the internal and external surfaces were obtained after the structure optimization by canonical ensemble MC simulation for 1 × 106 steps posterior to the calculation in GCMC simulation. The radial distributions were calculated from N2 positions for these snapshots. The isolated SWCNT was produced by the CVD method reported earlier.9 The SWCNT was characterized with Raman spectroscopy after preheating (532 nm frequency-doubled Nd; YAG laser, JASCO NRS-3100). The high-resolution transmission electron micrograph (TEM) of the SWCNT was measured with JEOL JEM-4000FXII. The N2 adsorption isotherm was measured volumetrically at 77 K using Quantachrome Autosorb 1 after preheating at 423 K and 10 mPa for 2 h. Results and Discussion
Figure 1. TEM image of SWCNT (a) and the distribution of tube diameters (b).
Structural Characterization. Figure 1a shows a high resolution-transmission electron micrograph (TEM) of SWCNT. The electron microscopic observation confirms that there are many isolated SWCNTs and that few of SWCNTs form fine bundles, compared with SWCNT prepared by other methods.15-19 The TEM images give the distribution of the tube diameter as shown in Figure 1b; the distribution has a broad peak around 2.8 nm. Figure 2 shows the Raman spectrum. This SWCNT is not necessarily well-crystalline, because the peak intensity of the D band is considerably large; the intensity ratio IG/ID of the G band against the D band was 1.8. Accordingly, the RBM bands are broad, compared with other SWCNTs produced by laser ablation and arc methods. However, we can evaluate the tube diameter, d, using the following eq 5.20,21
248 /nm d) ωRBM
Figure 2. Raman spectra of SWCNT.
(5)
Here, ωRBM is the RBM frequency. The d values are widely distributed to be 0.95, 1.08, 1.13, 1.21, 1.39, 1.55, and 1.91 nm. We could not determine the RBM bands of bolder SWCNTs in the smaller frequency region. The high-resolution TEM observation also indicated the considerable distribution in the SWCNT diameter, as already shown in Figure 1. Consequently, we took into account the pore size distribution coming from the tube diameter distribution and partial bundle formation. N2 Adsorption Isotherm. The marked difference of the interaction potential profile suggests the stepwise adsorption isotherm. Figure 3 shows the interaction potential profile of a N2 molecule with a SWCNT of the tube diameter ) 2.5 nm. There are interaction potential minima at the monolayer positions of the internal and external tube surfaces. The potential
minimum of the internal surface is much deeper than that of the external surface. Although the potential minimum of the external surface is about 700 K, the potential minimum difference for a N2 molecule on the internal surface and external one is about 300 K. Figure 4 shows experimental and GCMCsimulated N2 adsorption isotherms at 77 K. Both adsorption isotherms have two steps around P/P0 ) 2 × 10-5 and 2 × 10-3. Both adsorption isotherms almost agree with each other. Here, this GCMC-simulated N2 adsorption isotherm was obtained by averaging the adsorption isotherms for SWCNTs whose tube diameters correspond to the pore size distribution shown in Figure 4b. The pore size distribution has two peaks at 1.5 and 2.2 nm. The average tube diameter was evaluated to be 2.5 nm, which almost agrees with the TEM results. The pore volume corresponding to narrow pores is only less than 25% of that of large pores; the small pores should come from internal
15662 J. Phys. Chem. C, Vol. 111, No. 43, 2007
Ohba et al.
Figure 3. Potential profile for an N2 adsorbed on SWCNT.
Figure 5. Snapshots of adsorbed N2 molecules on the internal and external surfaces of SWCNTs.
Figure 6. Radial distributions of N2 adsorbed on the (a) internal, (b) external, and (c) graphite surfaces.
Figure 4. N2 adsorption isotherms (a) at 77 K in experiment (O) and GCMC simulation in the internal nanospaces (b) from optimal PSD, as shown in (b).
tube spaces of small diameter and interstitial pores of fine bundles. Accordingly, we can assume that the predominant adsorption stems from adsorption on an isolated SWCNT of 2.5 nm in diameter. Then, we tried to understand adsorbed structures of N2 molecules on internal and external surfaces of SWCNT of 2.5 nm in diameter. Figure 5 shows snapshots obtained from the GCMC simulation. These snapshots describe elementary adsorption processes of N2 molecules on a sole SWCNT. Adsorption of N2 molecules on the monolayer positions of the internal surface begins at P/P0 ) 5 × 10-5. Then the monolayer formation almost finishes around P/P0 ) 6 × 10-3. Above P/P0 ) 6 × 10-3, the residual space in the tube is filled with the further adsorption, and the monolayer formation on the external surface occurs. Consequently, we can distinguish adsorption processes on the internal and external surfaces with the increase of P/P0. The agreement of the experimental and simulated isotherms guarantees the importance
of the detailed structural analysis of the adsorbed monolayers on the internal and external surfaces of a sole SWCNT. Curvature Dependent Monolayer Structure. Figure 6 shows the radial distributions of monolayers on the internal, external, and flat surfaces. The radial distribution functions of the monolayers on SWCNT surfaces are three-dimensional functions owing to the remarkably curved structures, being different from the two-dimensional radial distribution function on the flat surface. All radial distributions are similar to each other in the short range within 1.2 nm. However, the peak just above 1 nm for the internal monolayer slightly shifts to a shorter distance. It is evident that the distribution features in the long range from 1.2 to 2 nm are different from each other. Only the internal monolayer shows several peaks above 1.2 nm, where radial distributions for external surface of a SWCNT and graphene surface have less peaks. In particular, the radial distribution of N2 on the external surface of a SWCNT has the broadest peaks above 1.5 nm. The peak position of radial distributions is listed in Table 1. All monolayers have basically a hexagonal packing structure, because all peaks other than the peak at 1.3 nm for the internal monolayer can be assigned to the hexagonal packing structure. The peak at 1.3 nm for the internal monolayer stems
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TABLE 1: Peaks for the Radial Distributionsa
a
internal surface
external surface
flat surface
0.40 0.7 0.8 1.05 1.2 1.3 1.42 1.6 1.7
0.4 0.7 0.8 1.08 1.2
0.4 0.7 0.8 1.08 1.2
1.46
1.46
Units are per nanometer.
from the remarkably curved geometry of the hexagonal packing layer. Furthermore, the peak position at 1.05 nm for the internal surface is shorter than those of the external and flat surfaces by 0.03 nm, which is caused by the more intensive confinement effect for the internal monolayer. The presence of the radial distribution peaks at 1.6 and 1.7 nm for the internal monolayer indicates that the monolayer on the internal surface is more ordered than other monolayers. It is noteworthy that the long range ordering of the monolayer corresponds to the depth of the interaction potential between a N2 molecule and the concave surface. This result clearly shows the effect of the nanoscale curvature on the structure of the monolayer of adsorbed molecules on SWCNT. This kind of curvature effect should be clearly elucidated experimentally using Xe and a better isolated SWCNT of good crystallinity in the future. Acknowledgment. This research was founded with Grantin-Aids for Scientific Research from the Japanese Government. Supporting Information Available: Numerical data for N2 adsorption isotherm at 77 K. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Defay, R.; Prigogine, I.; Bellemans, A.; Everett, D. H. Surface Tension and Adsorption; Longmans, Green: London, 1966.
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