Equilibrium Configuration Simulation Of Single And Double Walled Carbon Nanotubes By Molecular Mechanics

In 1991 scientists synthesized the one dimensional carbon material, carbon nanotubes,for the first time, using the electric arc deposition method. Because of their prominentmechanical, electrical and thermal properties, they have been the focal points of research inmany different fields. In order to investigate the excellent mechanical, electrical and thermalproperties of carbon nanotubes, scientists use experimentation and computer simulationmethods. However the diameter of carbon nanotubes is in the nanometer range and theirlength can be in the micrometer range. It is difficult for modern experimental technique todirectly measure the mechanical properties of carbon nanotubes, so the physics of carbonnanotubes is intimately bound up with the fields of computational nano-science,computational nano-technology and computational materials science.In order to correctly simulate the carbon nanotubes, the first thing is to establish an exactmechanical model. Usually the model is given by the foregone atomic structure or crystallattice, however it can not make sure that every atom in the model is in equilibrium state. Inthis paper the relation between the total potential energy and the coordinate of atoms areestablished by using the molecular mechanics method, modified Morse potential andLennard-Jones potential. The equilibrium configuration of carbon nanotubes can be obtainedby minimizing the total energy associated with each atom.Based on the molecular mechanics theory, this paper uses the modified Morse potentialto describe the bond and angle potential and the Lennard-Jones potential to describe the vonder waals interaction. The initial structure of graphite is obtained through lattice constants andthe initial structure of carbon nanotube is established by rolling the planar sheet to a cylinderwithout stretching. This paper uses the Newton-Raphson iteration to release thenon-equilibrium forces. The equilibrium structure is obtained when certain convergencecondition is satisfied. The equilibrium structure and elastic properties such as Young'smodulus and Poisson's ratio of different diameter of armchair and zigzag tubes are discussed.Then the elastic properties and structure of ((5,5),(10,10)) double walled carbon nanotube arediscussed.Results of this paper show that in equilibrium state diameter of single walled carbonnanotube increases and length decreases. The changes are sensitive to the tube diameter andhelicity. Young's modulus of carbon nanotubes are also size dependent. Young's modulus of both armchair and zigzag tubes increase monotonically and approach Young's modulus ofgraphite when the tube diameter is increased. Poisson's ratio decrease when tube diameter isincreased and is close to that of graphite.