ENERGETICS, STRUCTURE, MECHANICAL AND VIBRATIONAL PROPERTIES OF SINGLE-WALLED CARBON NANOTUBES

In this paper, we present extensive molecular mechanics and molecular dynamics studies on the energy, structure, mechanical and vibrational properties of single-wall carbon nanotubes. In our study we employed a n accurate interaction potential derived from quantum mechanics. We ex plored the stability domains of circular and collapsed cross section s tructures of armchair (n, n), zigzag (n, 0), and chiral (2n, n) isolat ed single-walled carbon nanotubes (SWNTs) up to a circular cross secti on radius of 170 Angstrom. We have found three different stability reg ions based on circular cross section radius. Below 10 Angstrom radius only the circular cross section tubules are stable. Between 10 and 30 Angstrom both circular and collapsed forms are possible, however, the circular cross section SWNTs are energetically favorable. Beyond 30 ri (crossover radius) the collapsed form becomes favorable for all three types of SWNTs. We report the behavior of the SWNTs with radii close to the crossover radius ((45, 45), (80, 0), (70, 35)) under uniaxial c ompressive and tensile loads. Using classical thin-plane approximation and variation of strain energy as a function of curvature, we calcula ted the bending modulus of the SWNTs. The calculated bending moduli ar e K-(n,K-n) = 963.44 GPa, K-(n,K-0) = 911.64 GPa, and k((2n,n)) = 935. 48 GPa. We also calculated the interlayer spacing between the opposite sides of the tubes and found d((n,n)) = 3.38 Angstrom, d((2n,n)) = 3. 39 Angstrom, and d((n,0)) = 3.41 Angstrom, Using an enthalpy optimizat ion method, we have determined the crystal structure and Young's modul us of (10,10) armchair, (17, 0) zigzag and (12, 6) chiral forms (which have similar diameter as (10,10)). They all pack in a triangular patt ern in two dimensions. Calculated lattice parameters are a((10,10)) = 16.78 Angstrom, a((17,0)) =16.52 Angstrom and a((12,6)) =16.52 Angstro m. Using the second derivatives of potential we calculated Young's mod ulus along the tube axis and found Y-(10,Y-10) = 640.30 GPa, Y-(17,Y-0 ) = 648.43 GPa, and Y-(12,Y-6) = 673.94 GPa. Using the optimized struc tures of (10, 10), (12. 6) and (17, 0), we determined the vibrational modes and frequencies. Here, we report the highest in-plane mode, comp ression mode, breathing mode, shearing mode and relevant cyclop mode f requencies.