Plane polarized-longitudinal Phonons in realistic low dimensional systems

A realistic one-dimensional system has not only longitudinal phonons, but also possible transverse modes, which derive their restoring force from longitudinal interaction. We show that transverse motion results in a quartic displacement term in transverse direction as the first non-vanishing term in the potential energy. This results in solution of a composite longitudinal motion superimposed by a transverse motion propagating along the length direction identified as a plane polarized phonons. Interestingly, solutions of the quartic nonlinear equation have been expressed accurately, though approximately in terms of sinusoidal solutions by modifying the periodicity of sin function. The phonons along the transverse direction, now with a weakened frequency compared to the longitudinal has interesting impact- it gives rise to negative Gruneisen parameter with a value of -1 and is responsible for negative thermal expansion in the low temperature regime. Similar results of graphene sheet based on consideration of transverse (surface ripple like) modes to the planar direction, provides explanation to the observed negative thermal expansion in low temperature regime. The concept of plane polarized phonons seems new and interesting. All dynamics of atomic motion, despite involving quartc nonlinear equation is expressible in terms of simple harmonic motion. The most important feature of the transverse modes of an open surface or chain is their dependence on lateral or longitudinal modes, and as soon as more chains or more surfaces are added, bulk interactions are initiated and longitudinal dependence of transverse motion is lost and so also very distinguishing thermodynamic properties.Comment: 4 pages, 3 figures and 8 reference

Thermal expansion in 2D honeycomb structures: Role of transverse phonon modes

Graphene and its derivatives including hexagonal BN are notorious for their large negative thermal expansion over a wide range of temperature which is quite unusual. We attempt to analyze this unusual behavior on the basis of character of the phonon modes. The linear thermal expansion coefficients (LTEC) of two-dimensional honeycomb structured pure graphene, h-BN and B/N doped graphene are studied using density functional perturbation theory (DFPT) under quasi harmonic approximation. The dynamical matrix and the phonon frequencies were calculated using VASP code in interface with phonopy code. The approach is first applied to pure graphene to calculate thermal expansion. The results agree with earlier calculations using similar approach. Thereafter we have studied the effect of B/N doping on LTEC and also compared it with LTEC of h-BN sheet. The LTEC of graphene is negative in the whole temperature range under study (0-1000K) with a room temperature (RT) value of -3.51X10-6K-1. The value of LTEC at room temperature becomes more negative with B/N doping in graphene as well as for h-BN sheet. In order to get an insight into the cause of negative thermal expansion, we have computed the contribution of individual phonon modes of vibration. We notice that it is principally the ZA (transverse acoustic) mode which is responsible for negative thermal expansion. It has been concluded that transverse mode in 2D hexagonal lattices have an important role to play in many of the thermo dynamical properties of 2D structures.Comment: 18 pages, 37 references and 11 figures. arXiv admin note: text overlap with arXiv:1107.2469, arXiv:cond-mat/0412643 by other authors. Some change in the language an 3 new references adde

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

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.

Modification of Thermal Conductivity of PMMA and PC by making their Nanocomposites with Carbon Nanotubes

PMMA and Poly carbonate (PC) are wonderful low cost materials which can be easily tailored and shaped. However they have poor mechanical, thermal and electrical properties which are required to be enhanced in several applications where along with high strength, a quick heat transfer becomes a necessity. Carbon nanotubes (CNT) are excellent new materials having extraordinary mechanical and transport properties. In this paper we report results of fabricating composites of varying concentrations of CNTs with PMMA and PC and measurements of thermal conductivity data by a simple transient heat flow. The samples in disk shapes of around 2 cm diameters and 0.2 cm thickness with CNT concentrations varying up to 10 wt percent were fabricated. By keeping one end of the discs at steam temperature, the temperature of the other end was noted for each sample after 10 s. The rise in temperature was correlated with thermal conductivity which was appropriately calibrated. We found that both PMMA and PC measured high thermal conductivity with increase in the concentration of CNTs. The thermal conductivity of PMMA rose from about 0.2 W/mK to 0.4 W/mK at 10 wtpercent of CNT whereas for PC, it rose from about 0.2 W/mK to 0.9 W/mK at 10 wt percent of CNT. It is thus observed that modification in thermal properties is easily achieved by making CNT based composites using only up to 10 wt percent of CNTs in PMMA and PC and enabling quicker heat dissipation in these materials.Comment: 8 pages, 4 figures, 9 references,FiNSTA '14-International Conference on Frontiers in Nano Science, Technology and Application

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

Model for High Temperature Phase of C70 Solid

Depending on the temperature, the C70 solid crystallizes in several structures. At high temperature (T > 340K), the ellipsoidal C70 molecule rotates freely in all directions and may be treated as a uniform thick spherical shell with inner and outer radii as the minimum and the maximum distance of C-atom from the center of the molecule. At lower temperatures the free rotations of molecules freeze out. We have calculated the lattice parameters, energies and bulk modulus at the minimum energy configuration of fcc and hcp phase of pure C70 solid at high temperature using a simple model based on atom-atom potential.Comment: 13 pages, 6 figures and 12 references, reported in part in DAE Symposiu

Implicit Phonon Shifts and Thermodynamical Properties of Rigid Carbon Nanotube Ropes

We calculate phonon shifts of external modes of a bunch of carbon nanotubes. A simple model based on atom-atom potential has been used to calculate the implicit anharmonicity in the phonons of carbon nanotube bundles having rigid tubes, with the assumption that under hydrostatic pressure only the intertube distance in the bunch varies. Such a model is important as long carbon nanotube ropes will be an extension of a fixed length ropes as is done here. Various bulk and thermodynamic properties like thermal expansion, bulk modulus and the Gruneisen constants and external phonon shifts which naturally enter into the calculation are also described and compared with the available data. The specific heat capacity has also been calculated.Comment: 31 pages, 6 figures, 4 tables and 26 reference

Model for Pressure Induced Deformations in Carbon Nanotube Materials

We report the results of a model calculation for studying the effects of hydrostatic pressure on a bunch of carbon nanotubes. At pressures that we work with, the deformation in axial direction comes out to be negligibly small. We find that hydrostatic pressure is an ideal probe to study the radial deformations of the nanotubes. The nanotubes are considered to be flexible, identified by a flattening of cylinders under pressure through a parameter f. We use the 6-exponential and Brenner potentials to account for inter and intra-tube interactions respectively. We calculate the total energy of the deformed tubes in bunches. The free energy thus calculated enables us to calculate phase changes at various pressures. From our calculations, we find the phase transformation to occur at about 5GPa.Comment: 11 pages, 8 figures and 15 reference

DFT study of optical properties of pure and doped Graphene

Ab-initio calculations based on density functional theory (DFT) have been performed to study the optical properties of pure graphene and have been compared to that of individual boron (B), nitrogen (N) and BN co-doped graphene sheet. The effect of doping has been investigated by varying the concentrations of dopants from 3.125 % (one atom of the dopant in 32 host atoms) to 6.25 % (six dopant atoms in 50 host atoms) for individual B and N doping and from 37.5 % (one B/N pair in 32 host atoms) to 18.75 % for BN co-doping. Positions of the dopants have also been varied for the same concentration of substitution doping. The dielectric matrix has been calculated within the random phase approximation (RPA) using VASP (Vienna ab-initio Simulation Package) code. The dielectric function, absorption spectrum and energy loss-function of single layer graphene sheet have been calculated for light polarization parallel and perpendicular to the plane of graphene sheet and compared with doping graphene. The calculated dielectric functions and energy-loss spectra are in reasonable agreement with the available theoretical and experimental results for pure graphene. It has been found that individual B and N doping does not significantly affect the imaginary dielectric function and hence the absorption spectra. However, significant red shift in absorption towards visible range of the radiation at high doping is found to occur for the B/N co-doping. The results can be used to tailor the optical properties of graphene in visible region.Comment: 21 pages, 11 figures and 21 reference