Constitutive Models for Analysis and Design of Multifunctional Technological Materials

Abstract

Single-walled carbon nanotubes (CNT) can be viewed as one (or more) graphene sheet(s) rolled into a seamless tube with a diameter of the order of nanometres. The way in which the graphene sheet is wrapped is represented by a pair of indices (n,m) of the vector C that is called the chiral vector, C = n a ₁ + m a ₂. The integers n and m denote the number of unit vectors a ₁ and a ₂ along two directions in the honeycomb crystal lattice of graphene, as shown in Fig. 6.1a. If m = 0, they are called “zigzag” nanotubes and if n = m, they are called “armchair” nanotubes. For any other values of n and m the nanotubes are called “chiral”, because the chains of atoms spiral around the tube axis instead of closing around the circumference. The magnitude of the chiral vector