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 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

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

Orientational Ordering and Binding in Alkali doped C60 solids

The binding energy of A3C60, a conductor, is described well by an ionic solid type calculation. This succeeds because there is little overlap between molecular wave functions on neighbouring sites, so that electrons are practically localized on-shell. This leads one to believe that even in A4C60 and A6C60 systems such calculation may suffice. However, for large charge on the anion, there is a possibility for some electrons to delocalize and go into the s-band. We calculate binding energy, keeping these delocalised electrons x, as a parameter and minimize the energy w.r.t. it. We take the intermolecular interaction to be arising out of a C-C potential of 6-exp form and a screened Coulomb interaction between the anions and cations and among themselves. Model calculations are presented for K1C60, K3C60, K4C60 and K6C60 for which the minimum energy state shows no delocalisation. Cohesive Energy dependence on Lattice constant is used to calculate Bulk Modulus for all systems. We have got a reasonably good resemblance with experimental values. Further, we observe that the cohesive energy shows poor resemblance with experimental values. Further, delocalisation of a fraction of electron at the centre of double bond show considerable increase in cohesive energy.Comment: Presented in National Seminar MSTF-2000, Frb. 24-25,2000 SLIET, Indi

Nitrogen clusters inside C60 cage and new nanoscale energetic materials

We explore the possibility to trap polynitrogen clusters inside C60 fullerene cage, opening a new direction of developing nitrogen-rich high energy materials. We found that a maximum of 13 nitrogen atoms can be encapsulated in a C60 cage. The nitrogen clusters in confinement exhibit unique stable structures in polymeric form which possess a large component of (~ 70-80%) single bond character. The Nn@C60 molecules retain their structure at 300K for n<12. The Mulliken charge analysis shows very small charge transfer in N@C60, consistent with the quartet spin state of N. However, for 2<n<10, charge transfer take place from cage surface to Nn compounds and inverse polarization thereafter. These nitrogen clusters when allowed to relax to N2 molecules which are triply bonded are capable of releasing a large amount of energy.Comment: 25 pages Submitted to Carbo

Behaviour of a Bucky-ball under Internal and External Pressures

We study the behaviour of the C60 molecule under very high internal or external pressure using Tersoff as well as Brenner potentials. As a result, we estimate the critical internal and external pressures that lead to its instability. We also calculate stretching force constant and bulk modulus of this molecule at several pressures under which the molecule remains stable. The values of these estimated here at zero pressure agree closely with those obtained in earlier calculations. We also observe that at high pressures, a finite value of parameter of Tersoff potential gives physically acceptable results in contrast to its value zero, which is usually taken for the carbon systems.Comment: 14 pages and 9 figure

Stability of different phases of (C60)2 Structures

We investigate the possible binding configurations of pairs of C60 molecules when pushed against each other. Tersoff potential, which represents intramolecular interactions well, has been used to calculate potential energies. We begin relaxation of atomic coordinates at various distances of separation and for all possible mutual orientations of the two molecules. As a result, we have been able to show that several minimum energy configurations exist. Some of these configurations have not been reported earlier. Only two types of dimer structures, involving interlinkage through a single bond, or through so called 2+2 cycloaddition, have been commonly referred in the literature. Our calculation shows that apart from these configurations, many interesting composite phases also result, such as fused and peanut structures and (5,5) and (10,0) nanotubes. A link with experiment to find these structures can be established by application of suitable critical applied pressure in the solid phase, accompanied by high temperature corresponding to orientational melting so that suitable mutual orientations are available. High energy molecular beams of C60 incident upon C60 layers could also achieve the same.Comment: 27 pages, 29 references, 3 tables and 5 figure

Behavior of Bucky Ball under extreme Internal and External Pressures

We study the behavior of the C60 molecule under very high internal and external pressure using Tersoff potential. As a result, we calculate the critical internal and external pressures leading to its instability. We also calculate stretching force constant, breathing mode frequency and bulk modulus of this molecule. The data estimated here at zero pressure agrees closely to that obtained in earlier calculations. If subjected to extreme pressures the molecule can withstand upto 58.23% of compression and 174.89% of dilation in terms of its volume. We also observe that above some critical external pressure the coordination number of the carbon atoms of C60 molecule suddenly increases resulting in an abrupt change in the bulk modulus of the molecule.Comment: 12 pages, 12 references, 9 figs, 7 table

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

Bulk and Lattice Properties for Rigid Carbon Nanotubes Materials

We use an atom-atom potential between carbon atoms to obtain an interaction potential between nanotubes (assumed rigid), thereby calculating the cohesive energy of a bunch of nanotubes in hexagonal two dimensional packing. The model proposed is quite similar to our earlier work on fullerenes and organic molecular crystals. The results for inter-nanotube distances, energy per unit length, bulk modulus and phonons for inter-nanotube vibrations are obtained and compared with available data from measurements and other available calculations. We also model formation of multi-wall nanotubes. We find the results for various calculated quantities agreeing very well with measured structural parameters and other calculations. The reversible energy stored on compression of the bunch of nanotubes on application of pressure up to 30 Kbar calculated in this rigid molecule model is overestimated by about 30% when compared with measured results, signifying the appreciable flexibility of tubes at high pressures. The model is considered very suitable for incorporating flexible nanotubes in bunches of single and multi-wall nanotube materials of various types.Comment: 22 pages, 8 Figures and 34 reference