ABSTRACT

The reason why carbon has many different structural forms is that carbon atoms can constitute multiple distinct types of valence bonds referred to as the hybridization of atomic orbitals. Carbon is the sixth element of the periodic table and has the lowest atomic number of any elements in column IV of the periodic table. Each carbon atom has four valence electrons in 2s, 2px, 2py, and 2pz atomic orbitals, which are important in constituting covalent bonds in carbon materials. In comparison with the binding energy of the valence bonds, the energy difference between the 2p energy levels and the 2s energy level in carbon atom is small. Therefore, the wave functions for these four valence electrons can easily mix with each other, leading to the redistribution of these four electrons in the 2s and three 2p atomic orbitals so as to raise the binding energy of the carbon atom with its nearest neighbors. The mixture of 2s and 2p atomic orbitals is called the hybridization of orbitals, and the mixture of a single 2s electron with one, two, or three 2p electrons is called spn hybridization with n = 1, 2, 3 [1, 2]. Thus the 2s and 2p atomic orbitals can hybridize to form three possible hybridizations: sp, sp2, and sp3. The different bonding states induce certain structural arrangements, so that sp bonding gives rise to one-dimensional chain structures, sp2 bonding to planar structures and sp3 bonding to regular tetrahedral structures. Each carbon atom has (n + 1) s bonds in spn hybridization. These s bonds form a certain n-dimensional structural arrangements. For example, two s bonds form a one-dimensional (1D) chain structure in sp hybridization. In sp2 hybridization, three s bonds form a planar structure in graphite. Because graphite has strong in-plane trigonal bonding, it is the stable ground state of carbon under ambient conditions [3, 4]. The sp3 hybridization gives a regular three-dimensional (3D) tetrahedron called diamond structure. In addition to the bulk phase of carbon, small carbon clusters have attracted much attention in the past 20 years [5]. Fullerenes and CNTs were discovered in 1985 [6] and 1991 [7], respectively. In fullerenes and CNTs, there exist planar local structures due to the sp2hybridization. Therefore, a CNT can be described as a graphene layer (a single layer of graphite) rolled into a cylindrical shape with axial symmetry.