Interaction of Methane with Single-Walled Carbon Nanotubes: Role of Defects, Curvature and Nanotubes Type

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1 Commun. Theor. Phys. (Beijing, China) 53 (2010) pp c Chinese Physical Society and IOP Publishing Ltd Vol. 53, No. 5, May 15, 2010 Interaction of Methane with Single-Walled Carbon Nanotubes: Role of Defects, Curvature and Nanotubes Type M.D. Ganji, 1, M. Asghary, 2 and A.A. Najafi 1 1 Department of Chemistry, Islamic Azad University, Ghaemshahr Branch, Mazandaran, Iran 2 Department of Chemistry, University of Payam-e-noor, Sary, Mazandaran, Iran (Received July 10, 2009; revised manuscript received November 9, 2009) Abstract We investigate the interaction of single-walled carbon nanotubes (SWCNTs) and methane molecule from the first principles. Adsorption energies are calculated, and methane affinities for the typical semiconducting and metallic nanotubes are compared. We also discuss role of the structural defects and nanotube curvature on the adsorption capability of the SWCNTs. We could observe larger adsorption energies for the metallic CNTs in comparison with the semiconducting CNTs. The obtained results for the zig zag nanotubes with various diameters reveal that the adsorption energy is higher for nanotubes with larger diameters. For defected tubes the adsorption energies are calculated for various configurations such as methane molecule approaching to the defect sites pentagon, hexagon, and heptagon in the tube surface. The results show that the introduce defects have an important contribution to the adsorption mechanism of the methane on SWNTs. PACS numbers: h, Fg, Kt, Uw, Ar Key words: methane, SWCNTs, adsorption, encapsulation, ab initio calculations, energy storage 1 Introduction There has been a steady increase in interest over the past years in the natural gas adsorbed on porous materials which is a promising alternative to compressed natural gas (at 20 to 30 MPa) as a suitable nonpollution vehicular fuel and for bulk transportation. [1 2] Methane is one of the major components of natural gas therefore its adsorption behavior in confined pores is of practical and theoretical interest. [3 13] Discovery of novel materials, such as carbon nanotubes has drawn much attention in recent years, because of their unique properties including uniform porosity, high tensile strength, and relative inertness and provides new adsorption materials for storage and transport of natural gas. There have been several works devoted to the investigation of the adsorption behavior of methane on singlewalled carbon nanotube (SWCNT) and multi-walled carbon nanotube (MWCNT). Bekyarova et al. reported volumetric capacity of about 160 v/v for the methane adsorption in an SWCNT. [14] Kaneko et al. investigated the adsorption of methane on SWCNT using a density functional theory method. They showed that SWCNT with disordered structure could be applied as storage media for methane gas. [10] Single-walled carbon nanotubes proved to have better storage performance over other nanostructures like activated carbon of larger surface area indicating the active role of curvature and porous nature of CNTs apart from chirality. [15] Tanaka et al. studied the methane adsorption on isolated SWNTs and idealized graphitic slit pores at 303 K over a range of pore diameters and pressures by the nonlocal DFT. [10] They found that the total excess adsorption on the internal and external surfaces of an isolated SWNT exceeds that for the idealized slit pore with the same size. Their obtained results reveal also that the adsorption capacity of the interior of SWNT is less than that for the silt pore geometry. Sadat Hashemi and co-workers [16] investigated the adsorptive behavior of methane on isolated armchair single-walled carbon nanotubes as a function of temperature and diameter of the nanotubes by using the molecular dynamics (MD) simulation. They concluded that the amount of adsorption is strongly influenced by the applied temperature (increasing the operating temperatures not only decreases the amount of adsorption but also imposes more nanotube distortions) and that the adsorption energy is higher for nanotubes with smaller diameters. In contrast to the many works performed on CNTs, studies on the effects of the surface defects, nanotubes diameter, and chirality on the methane adsorption on CNTs have not been studied theoretically. The main purpose of the present study is to model the adsorption of methane in SWCNTs with tubes of different diameters and types by means of Density Functional (DFT) calculations to gain an understanding of the adsorption mechanisms and to develop adsorption models. Furthermore, the influence of the structural defects on the methane adsorption on the CNTs has also been investigated. In order to study the role of structural defects on methane adsorption, we have introduced defects like pentagon and heptagon in the hexagonal structure of the carbon nanotubes and calculated binding energy E b for different configurations with respect to these defect rings. Corresponding author, ganji md@yahoo.com

2 988 M.D. Ganji, M. Asghary, and A.A. Najafi Vol Computational Methods We have performed the density functional based tight binding (DFTB) method calculations for the structural optimizations of carbon nanotubes and methane molecule by using the recently developed DFTB + code. [17] The DFTB + uses the DFTB method based on a second-order expansion of the Kohn Sham total energy in density functional theory with respect to charge density fluctuations. The DFTB approach uses a tabulated set of integrals derived from ab initio DFT calculations, [18] leading to a substantial speed-up of the method since explicit integration is not required in the method. It is possible to produce parameterizations capable of accuracy close to LDA/GGA with minimal adjustable parameters and also transferable between different systems. Further details of the method have been fully reviewed for instance in Refs. [17] [20]. In this work the Slater Koster (S-K) type parameter set [21] was implemented. The dispersion corrects for the van der Waals interaction have also been considered via the Slater Kirkwood type model. [22] For the present work we have considered five unit cells of (6, 6) armchair tube with 120 carbon atoms and three unit cells of (10, 0) zig zag tube with 120 atoms. The diameter values of (6, 6) and (10, 0) are 8.14 Å and 7.84 Å respectively. It is known that the chiral angle is 30 for armchair metallic type and 0 for zig zag semiconducting tube. In order to evaluate the influence of nanotube curvature on the methane adsorption we have also investigated the interaction between methane molecule and (13, 0) SWCNT (diameter value of about Å). To study the role of structural defects on methane adsorption on carbon nanotubes, defects like pentagon and heptagon are inserted in the normal hexagonal structure of (10, 0) CNTs. Such an insertion of defects slightly deforms the tube as expected. Periodic boundary conditions and a supercell approximation are used. The nanotube centers are separated by 25 Å, perpendicular to their axes, to avoid the interaction between the replicas. We used a Monkhorst Pack grid for k-point sampling of the Brillouin zone. Geometries of the SWCNTs and methane molecule are optimized separately prior to the optimization of the whole system. Structural optimizations are performed using the conjugate gradient algorithm. The total energy calculations (binding energy E b ) are carried out by SIESTA code. [23 24] The core electrons are represented by improved Troullier Martins pseudopotentials, and numerical atomic orbitals basis with polarization is used for valence electrons. Direct diagonalization of Kohn Sham Hamiltonian is used for the Γ-point electronic structure calculations. We have included the electron exchange and correlation effects through Generalized Gradient Approximation (GGA) with Perdew, Burke and Enzerhof (PBE) approach that are suitable for adsorption energy calculations. [25] All total energy calculations were done with a double-ζ plus polarization (DZP) basis set. A cutoff energy of 125 Ry is utilized for the grid integration. From the well known expression for calculating the molecular binding energies, E b is obtained for various cases of our study. E b = E CNT+Methane E CNT E Methane. (1) Here, E CNT, E CNT+Methane, and E Methane are total energy of free carbon nanotube, CNT with adsorbate and single methane molecule respectively. The binding energy values are estimated for different methane configurations. The results for various cases are analyzed and their significance is discussed in the next section. 3 Results and Discussion In this section we first discuss the binding energy (adsorption energy) values of single methane molecule interacting with SWCNTs for the two cases of nanotubes namely metallic (6, 6) and semiconducting (10, 0) nanotubes. CH 4 SWCNT system is optimized starting from nine different initial geometrical configurations. In all the cases the CH 4 molecule is initially oriented so that one hydrogen atom ( CH group)/two hydrogen atoms ( CH 2 ) or three hydrogen atoms ( CH 3 ) is (are) the closest to the nanotube surface. In the starting configuration A1, the hydrogen atom of CH group situated over a carbon atom of the nanotube. In the configurations A2 and A3, the hydrogen is positioned over the centers of two nonequivalent C C bonds, namely, those perpendicular (A2), and non-perpendicular (A3) to the axis for armchair nanotube, respectively (or parallel and non-parallel to the nanotube axis in the case of zigzag SWNT). Finally, the hydrogen atom is situated over the center of a six-member ring in the initial configuration A4. Similar configuration models are considered for the CH 4 molecule approaching the surface of the tube via its CH 2 and CH 3 groups. It should be noted that for the CH 2 configurations two orientations are selected for the methane molecule approaching the hollow site of the tube: namely parallel and perpendicular approach of the H C H bond axis with respect to the tube axis. The orientation schemes employed in modeling CH 4 adsorption are represented in Figs. 1(a) 1(i). After full structural optimization of the considered systems, we observe that methane molecule prefers to be adsorbed on the hollow site of the hexagon ring of metallic (6, 6) CNT via its CH 3 group (A9 configuration). In Table 1 we present the calculated binding energies for all the considered configurations. The obtained binding energies indicate that the affinities of methane molecule for the metallic SWNTs are about 61% stronger than that of the semiconducting one. The binding energy for the energetically favorable complex and the equilibrium distance between the closest atom (H) of the methane to the C atom of the tube are about 0.29 ev ( 6.70 kcal/mol) and

3 No. 5 Interaction of Methane with Single-Walled Carbon Nanotubes: Role of Defects, Curvature and Nanotubes Type Å, respectively. The relatively far equilibrium CH 4 - carbon substrate separation and small binding energy suggest the involvement of only non-covalent interactions in the adsorption. The present results reveal also that methane molecule is weakly bound to the outer surface of the nanotube, having adsorption energies comparable to that for amino acids, nucleic acid bases and gas molecules on carbon nanotubes (see for instance Refs. [26] [33], which reported adsorption energies in the range of about 0.1 to 0.9 ev). Fig. 1 Different configurations of CH 4 molecule approaching the substrate of the (6, 6) nanotube via its CH group (a) over a carbon atom, upon the centers of two nonequivalent C C bonds (b) perpendicular and (c) nonperpendicular to the nanotube axis and (d) above the center of a hexagon of carbon atoms. Similar selected configurations for the CH 4 molecule approaching the surface of the tube via its CH 2 and CH 3 groups are represented in (e) (i). Atom colors: grey carbon, white hydrogen. Table 1(a) Binding energy E b of adsorbed CH 4 molecule on the outer surface of the (a) (6,6) and (b) (10,0) single-walled CNT. Complex CH 4 /CNT (6, 6) A1 A2 A3 A4 A5 A6 A7 A8 A9 Binding Energy/eV Table 1(b) Complex CH 4 /CNT (10, 0) A1 A2 A3 A4 A5 A6 A7 A8 A9 defect-free Binding Energy/eV

4 990 M.D. Ganji, M. Asghary, and A.A. Najafi Vol. 53 To further investigate the interaction between the methane molecule and SWCNTs the encapsulation of methane inside the considered nanotubes has also been examined. We first incorporated the methane molecule inside the CNTs at the center of the tubes, as depicted in Fig. 2, and then performed the optimization procedure for the considered complexes. The optimized geometric structures of the considered systems show that the methane molecule prefers to reside at the center of the tubes. The calculated binding energies for incorporated methane inside the (6, 6) CNT and (10, 0) CNT are 0.43 and 0.38 ev, respectively. It can be seen from the obtained binding energies that the interaction of the methane molecule with the interior surface of the SWC- NTs is stronger than that of exterior one. Furthermore, the methane molecule prefers to be incorporated into the metallic CNTs in comparison to the semiconducting one. To study the effect of the nanotubes curvature (diameter) on the interaction between the methane molecule and SWCNTs we investigated the adsorption/encapsulation of methane molecule on/inside a larger diameter (lower curvature) (13, 0) SWCNT. Following a similar procedure employed in the previous systems, we started by carrying out the optimization process for the methane molecule approaching to the sidewall of the (13, 0) SWCNT. Our calculation results show that the hollow site of the hexagon of the carbon atoms is the most stable adsorption site for the methane molecule approaching to the sidewall of the tube via its CH 2 group, with a binding energy of 0.21 ev and C H binding distance of 2.89 Å. The calculated binding energies for all the considered systems are summarized in Table 2. Fig. 2 Model for CH 4 molecule incorporated into the (a) (6,6) and (b) (10, 0) nanotubes. Table 2 Binding energy E b for CH 4 SWNT (13,0) systems with various initial configurations. Complex CH 4 /CNT (13, 0) A1 A2 A3 A4 A5 A6 A7 A8 A9 Binding Energy/eV Comparing these results with those obtained for the CH 4 /CNT (10, 0) system, we clearly see that the binding energy of the methane is increased for adsorption on larger diameter CNTs with low curvature. Although the high curvature allows the methane molecule to approach the surface more closely but however, the majority of the carbon atoms in high curvature CNT are actually further removed from the atoms of the methane than in the corresponding case on a low curvature CNT. The obtained results reveal also that the methane molecule bound weakly to the inner surface of the (13, 0) SWCNT (E b = 0.13 ev) in comparison to the adsorption on the outer surface of the tube and also to the encapsulation inside the (6, 6) and (10, 0) SWCNTs. In order to examine the influence of structural defects on methane interaction with SWCNTs, similar calculations are performed for the methane molecule interacting with the defected (10, 0) CNT. For this purpose twelve possible configurations are selected for a methane molecule approaching the center of a heptagon, hexagon and pentagon of carbon atoms via its CH, CH 2, and CH 3 groups. The orientation schemes employed in modeling methane adsorption are shown in Fig. 3. After full structural optimization of the considered systems, we find that the adsorption of methane molecule on the heptagon of defected carbon nanotube via its CH 2 group is the most stable state of adsorption. The calculated binding energies for all the considered systems are summarized in Table 3. It can be found from the comparison of calculated binding energies for methane on the defected and defect-free CNTs that there is a considerable increase in the adsorption binding energy of the order of 156% due to the presence of structural defects in CNTs.

5 No. 5 Interaction of Methane with Single-Walled Carbon Nanotubes: Role of Defects, Curvature and Nanotubes Type 991 Table 3 Binding energy E b of adsorbed CH 4 molecule on the outer surface of defected (10, 0) single-walled CNT. Complex CH 4 /CNT (10, 0) CH group CH 2 group CH 3 group defected Pent Hex Hept Pent Hex Hept Pent Hex Hept Binding Energy/eV Fig. 3 Model for different adsorption states for a CH 4 molecule on the sidewall of the (10, 0) nanotube above (a) pentagon, (b) hexagon, and (c) heptagon active site of the tube via its CH group. The similar adsorption states for the CH 2 and CH 3 groups pointing toward the nanotube surface with respect to the pentagon, hexagon, and heptagon defect site rings is represented in (d) (i). Furthermore, we calculate the binding energy of the incorporated methane molecule into the defected (10, 0) CNT. For the encapsulated methane molecule inside the defected (10, 0) nanotube, our results (E b = 0.64 ev) show also about 68% increase in binding energy compared to the confined molecule into the defect-free (10, 0) nanotube. From the discussions of these present results, it is evident that methane molecule might readily form more stable bindings with the inner surface of defected carbon nanotubes in comparison to the outer sidewall of the defected tube and also to the both inner and outer surface of the defect-free nanotubes. To further understanding of the interaction between the methane molecule and SWCNTs, we also analyze the density of state (DOS) for the combined system of CH 4 /CNTs (the most stable adsorbed CH 4 on the outer surface of the (6, 6) CNT) and compar with the corresponding DOS for the individual parts, i.e., CNT and CH 4 molecule separated. Figure 4 shows the total electronic DOS for the considered systems. It can be seen from the figure that the DOS of the combined system is almost exactly the superposition of the DOS of the indi-

6 992 M.D. Ganji, M. Asghary, and A.A. Najafi Vol. 53 vidual parts. This finding highlights that the CH 4 and CNTs are interacting rather weakly, and that no significant hybridization between the respective orbitals of the two entities takes place, the unveiling the small interaction obtained quantitatively in terms of binding energies. We can also see that the DOS of the CNT where the CH 4 is adsorbed shifts down by about 0.01 ev in comparison with a bare CNT. This small shift can be explained by the reduction in effective Coulomb potential due to the charge transfer. On the other hand, the difference in the Fermi level of the CNT (E F = 3.48 ev) and CH 4 /CNT (E F = 3.54 ev) clearly shows a charge transfer between the CNT and CH 4 in the adsorption process. Hence, we perform Mulliken charge analyses to evaluate the amount of electron transfers between the CNT and CH 4 molecule. Charge analysis shows 0.04ē charge transferred from the CNT to the CH 4 molecule for CH 4 /CNT complex. Fig. 4 Comparison between the density of states for an isolated CH 4 molecule (dotted curves), an isolated (6,6) nanotube (dashed curves), and the adsorbed CH 4 on the CNT at equilibrium geometry (CNT CH 4), (solid curves). Fig. 5 Isosurface of the total electron density for CNT (6,6) CH 4 complex where 0.09 is used as an isovalue of total electron density. For clarifying the binding nature in these systems, we investigate the total electron density maps of the electronic densities. Figure 5 represents calculated isosurface maps for (6, 6) CNT CH 4 complex. As it can be seen from the figure the physically adsorbed methane which is far from the tube has almost no effect on the electronic charge distribution of C atoms of the tube, and thus no charge transfer between the CH 4 and CNT orbitals occurs. The study of Mulliken charge analysis and electronic densities emphasizes that there exists a weak interaction between CNTs and CH 4 molecule. 4 Conclusions In summary, we have investigated the interaction of single-walled carbon nanotubes with methane molecule by using the DFT based treatments. The energy values and H C binding distances obtained from the ab initio calculations are typical for the physisorption. The methane affinity for the metallic nanotube is substantially stronger than for semiconducting one. It is found that structural defects have an important contribution to the adsorption mechanism of single-walled carbon nanotubes. The obtained results reveal also a considerable increase in the adsorption binding energy of the order of 156% due to the presence of structural defects in CNTs, which will definitely affect the methane storage capacity in carbon nanotubes. When comparing the results obtained for physisorption on the small-diameter CNT with those of large-diameter one, we see that the interaction strength of methane molecule is smaller for the smaller tube with the higher curvature. Thus, it appears that introducing surface curvature reduces the binding energy between the methane molecule and the substrate. Finally, our first-principles calculations show that the methane molecule is incorporated into the small-diameter nanotubes with or without structural defects can form more stable complex in comparison with the adsorbed molecule on the outer surface of the tubes, excepting the large-diameter nanotubes (diameter > 10 Å). The present obtained results may prove to be an interesting one that needs more attention on the aspect of physisorption in double-walled carbon nanotube and also other nanostructures. Further investigation is under progress on this issue. Hence we are pursuing further investigations involving more computation-expensive calculations to address the effect of methane adsorption on double-walled CNTs promising a suitable material for energy storage. Acknowledgments The authors gratefully acknowledge the support of this work by the Azad University of Ghaemshahr.

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