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 170Å. We have found three different stability regions based on circular cross section radius. Below 10Å radius only the circular cross section tubules are stable. Between 10 and 30Å both circular and collapsed forms are possible, however, the circular cross section SWNTs are energetically favorable. Beyond 30Å (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 κ (n,n) = 963.44 GPa, κ (n,0) = 911.64 GPa, and κ (2n,n) = 935.48 GPa. We also calculated the interlayer spacing between the opposite sides of the tubes and found d (n,n) = 3.38Å, d (2n,n) = 3.39Å, and d (n,0) = 3.41Å. 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) = 16.78Å, a (17,0) = 16.52Å and a (12,6) = 16.52Å. 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.M This article features multimedia enhancements available from the abstract page in the online journal; see http://www.iop.org.

No abstract

No abstract

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The theoretical predictions are in good agreement with the results from Monte Carlo simulations and from previous investigations using integral-equation theory for the ionic density profiles and the zeta potentials of spherical particles at a variety of solution conditions. Like the integral-equation approaches, the density-functional theory is able to capture the oscillatory density profiles of small ions and the charge inversion (overcharging) phenomena for particles with elevated charge density. In particular, our density-functional theory predicts the formation of a second counterion layer near the surface of highly charged spherical particle. Conversely, the nonlinear Poisson-Boltzmann theory and its variations are unable to represent the oscillatory behavior of small ion distributions and charge inversion. Finally, our density-functional theory predicts charge inversion even in a 1:1 electrolyte solution as long as the salt concentration is sufficiently high.