Hydrogen Storage in Single-Walled and Multi-Walled Carbon Nanotubes
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Mat. Res. Soc. Symp. Proc. Vol. 593 © 2000 Materials Research Society
hydrogens (i) at the exterior of the tube wall, (ii) at the interior of the tube wall, and (iii) in empty space inside SWNTs are identified by the DF calculations, whereas only exteriors of concentric shells are favored in multi-wall nanotubes (MWNTs) for large storage of hydrogens. In case of SWNTs, maximum hydrogen storage capacity increases with tube diameters, whereas in case of MWNTs, this value is independent of tube diameters. The maximum storage capacity is mainly determined by the repulsive forces between H2 molecules and those between H2 molecules and the tube wall. THEORETICAL APPROACHES We adopt in this work self-consistent charge density-functional-based tight-binding (SCC-DFTB) approach. The SCC-DFTB method uses a basis of numerically obtained s and p atomic orbitals. Hamiltonian overlap matrix elements are evaluated by two-center approach. Charge transfer is taken into account through the incorporation of a self-consistency scheme for Mulliken charges based on the second-order expansion of the Kohn-Sham energy in terms of charge density fluctuations. The diagonal elements of the Hamiltonian matrix employed are then modified by the charge-dependent contributions in order to describe the change in the atomic potentials due to the charge transfer. The off-diagonal elements have additional chargedependent terms due to the Coulomb potential of ions. They decay as 1/r and thus account for the Madelung energy of the system. Further details of the SCC-DFTB method have been published elsewhere [12]. Although the SCC-DFTB approaches are very efficient to describe the systems quantum mechanically, the accuracy test is demanded in some cases. In order to check the validity of SCC-DFTB approach, we also perform state of art technique, the DF total energy calculations based on the local density approximation (LDA) and generalized gradient approximation (GGA) [13]. The exchange-correlation energy in LDA is parameterized by Perdew and Wang's scheme [14] and Becke's corrected exchange functional [15] is adopted in GGA calculations. Allelectron Kohn-Sham wavefunctions are expanded in a local atomic orbital basis. All orbitals including core electrons, are taken into account throughout the calculations. In the doublenumerical basis set, C-2s and C-2p orbitals are represented by two basis functions each, and a 3d-type wave function on carbon atom is used to describe polarization. The convergency criterion for the structure optimization is that all forces be < 0.001 a.u.. Structure optimization is done by the SCC-DFTB and LDA schemes. The GGA calculations are done with structures optimized by LDA whenever necessary. RESULTS AND DISCUSSION We choose armchair nanotubes with different diameters in our calculations. Supercells of eight layers (four layers) of(5,5) and (10,10) nanotubes for SWNTs are used in our SCC-DFTB (LDA and GGA) calculations. The convergence on the supercell size was tested with six layers of tubes. No appreciable changes were obser
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