Modeling Pressure Induced Structural Modification of Armchair Single-Wall Nanotubes

Based on the helical and rotational symmetries and Tersoff-Brenner potential with couple of modified parameters, we investigate the variation of bond length/lengths in equilibrium structure due to tube length as well as due to applied hydrostatic pressure for a series of high symmetry armchair (n,n) single-wall nanotubes having different radii. Assuming that two different bond lengths dictate the tube geometry, these are monitored as a function of radius. It turns out that one of these bond lengths is greater than bond length of graphite whereas other one was less than it. These deviations from graphite value appear to be related to the curvature-induced rehybridization of the carbon orbitals. Lengths are found to have very important effect on the values of both bond lengths. The results under hydrostatic pressure indicate many linear behaviors having different slopes in the values of bond lengths with increasing pressure leading to a pressure induced-phase transition. This behaviour is strongly dependent on the tube radius. We also calculate the bulk moduls for this structure which reflects clearly this behavior of armchair nanotubes and thus predicts mechanical resilience of nanotubes.Comment: 15 pages, 22 references, 6 figures. Submitted to Phys. Rev.

Modeling and characterizing single-walled carbon nanotubes by pressure probe

We compare the behavior of bond lengths, cross sectional shape and bulk modulus in equilibrium structure at ambient conditions and under hydrostatic pressure of all the three kinds of uncapped single walled carbon nanotubes. Results of our numerical calculations show that two bond lengths completely describe the structure of achiral SWNT whereas only one bond length is required to determine structure of chiral SWNT. In armchair tubes, one bond length is found to be larger than that of graphitic value while in zigzag tubes one bond length has a constant value. These bond lengths are very sensitive to tube radius. In chiral tubes, the value of bond length is found to depend on the chirality and slightly on the tube radius. Different responses of these bond lengths are found on application of pressure. At some critical pressure, both bond lengths become equal to each other in achiral tubes. An analysis regarding the cross sectional shape of the nanotubes and its pressure dependence has also been done. The shape transition, from circular to oval shape takes place. At this transition, the behavior of bond lengths is found different and dependent on the chirality of the tubes. Chiral tubes with chiral angle which is mid way between zigzag and armchair tubes are found to have most prominent effects of chirality. Thus we demonstrate that pressure is a useful probe to characterize various kinds of carbon nanotubes.Comment: pages 8, references 19, Figures

Structure of chiral single-walled carbon nanotubes under hydrostatic pressure

We investigate the structural parameters, i.e. bond lengths and bond angles of chiral tubes of various chiralities. The procedure used is based on helical and rotational symmetries and Tersoff potential. The results indicate that at ambient condition, there are equal bond lengths and three unequal bond angles in the structure of chiral tubes. The bond length depends much more on the chirality and very slightly on the tube radius. Length of the tubes does not play very significant role on bond length and bond angles. These C-C bonds were recalculated under hydrostatic pressure. The bond length compresses with pressure while the bond angles remain practically unchanged. We also carry out analysis regarding the cross sectional shape of chiral tubes and its pressure dependence. It is found that at some pressures, transition from circular to oval cross section takes place. The transition pressure is found to strongly depend on the radius and chirality of tube. At this transition, corresponding to given elliptical cross section, the bond length for all chiral tubes is identical. This behavior of bond length is different from achiral tubes.Comment: 16 pages, 9 figures, 32 reference

Bond Lengths of Single-Walled Carbon Nanotubes

Results of the bond lengths for various chiralities of single-wall carbon carbon nanotubes (SWNTs) (armchair, zigzag and chiral) are obtained. We use modified helical and rotational symmetries to describe the structure of SWNTs and Tersoff potential to minimize the energy of these tubes. It emerges that in general, two bond lengths are required for obtaining minimum energy structure, in contrast to one bond length commonly used. The difference in bond lengths depends on chirality and radius of achiral tubes. Significantly, even a small deviation from zigzag or armchair character leads to interesting behavior of bond lengths. A reduction in diameter is responsible for difference in the bond lengths of achiral nanotubes. We also calculate the bond lengths under hydrostatic pressure. The behavior of bond lengths for armchair single-wall nanotubes when calculated under pressure shows that the larger bond length decreases faster with pressure in comparison to the shorter bond length. At some critical pressure (depending upon the radius of the tube), the two bond lengths become equal to each other, reversing their difference above this critical pressure. We suggest that this behavior can be exploited to experimentally determine the chirality and radius of the carbon nanotubes, for example by observing the presence and disappearance of modes typical of two different bond lengths. This change occurs only within a few GPa of pressure.Comment: 11 pages, 7 figures, 16 references, 1 table. Submitted to PR

Pressure effects on bond lengths and shape of zigzag single-walled carbon nanotubes

We investigate structural parameters, i.e., bond lengths and bond angles of isolated uncapped zigzag single-wall nanotubes in detail. The bond lengths and bond angles are determined for several radii tubes by using a theoretical procedure based on the helical and rotational symmetry for atom coordinates generation, coupled with Tersoff potential for interaction energy calculations. Results show that the structure of zigzag tubes is governed by two bond lengths. One bond length is found to have a value equal to that of graphite, while the other one is larger. Furthermore, the tube length is found to have significant effect only on larger bond length in zigzag tubes. With the application of the pressure, only the larger bond length compresses, the other one remaining practically constant. At some critical pressure, this bond length becomes equal to constant bond length. This behavior of bond lengths is different from those of armchair tubes. An analysis regarding the cross sectional shape has also been done. At some higher pressure, transition from circular to oval cross section takes place. This transition pressure is found to be equal 2.06GPa for (20,0) tube. Some comparison with chiral tubes has also been made and important differences on bond length behavior have been observed.Comment: pages 21, figures 7 and references 34. In press in Computational Material Science (2008