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 an accurate interaction potential derived from quantum mechanics. We explored the stability domains of circular and collapsed cross section structures of armchair (n, n), zigzag (n, 0), and chiral (2n, n) isolated single-walled carbon nanotubes (SWNTs) up to a circular cross section radius of 170 Å. We have found three different stability regions based on circular cross section radius. Below 10 Å radius only the circular cross section tubules are stable. Between 10 and 30 Å both circular and collapsed forms are possible, however, the circular cross section SWNTs are energetically favorable. Beyond 30 Å (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 compressive and tensile loads. Using classical thin-plane approximation and variation of strain energy as a function of curvature, we calculated the bending modulus of the SWNTs. The calculated bending moduli are K_(n,n) = 963.44 GPa, K_(n,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 Å, d_(2n,n) = 3.39 Å, and d_(n,0) = 3.41 Å. Using an enthalpy optimization method, we have determined the crystal structure and Young's modulus 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 pattern in two dimensions. Calculated lattice parameters are a_{(10, 10)} = 16.78 Å, a_{(17, 0)} = 16.52 Å and a_(12,6) = 16.52 Å. Using the second derivatives of potential we calculated Young's modulus along the tube axis and found Y_(10,10) = 640.30 GPa, y_(17,0) = 648.43 GPa, and Y_(12,6) = 673.94 GPa. Using the optimized structures of (10, 10), (12, 6) and (17, 0), we determined the vibrational modes and frequencies. Here, we report the highest in-plane mode, compression mode, breathing mode, shearing mode and relevant cyclop mode frequencies.