ИСТИНА

This is a course of 10 lectures, annotation: This course gives a compact and relatively simple introduction to physics and chemistry of novel carbon nanomaterials including fullerenes, graphene and nanotubes. The emphasis will be on the electron structure of these materials and the relation between the electron structure and their physical properties. For the understanding of the material the basic knowledge of quantum mechanics and condensed matter physics is required. The lecture is partitioned in three main sections: in the first part the physics and chemistry of fullerenes is reviewed, in the second we consider graphene and in the third – carbon nanotubes. Each part starts with a brief historical introduction, followed by a discussion of the electron model (the tight-binding method for periodic structures of graphene and carbon nanotubes), applied to the description of the material. In the end of each part possible applications are reviewed. We start by considering various forms of carbon, first – two well-known allotropes, which are graphite and diamond, and then moving on to nanostructure materials: fullerenes, carbon nanotubes and graphene. Attention will be given to a detailed analysis of the electron shells of carbon atom and molecular orbital theory applied to carbon. Based on the sp2 and sp3 hybridization mechanisms we will describe various types of C-C bonds, and substantiate the Hückel method for pi-orbitals of molecular structures and pi-delocalized states. Finally, we will solve the derived equations and discuss their implications for carbon materials. The first part of the lecture is devoted to fullerenes and their derivatives, beginning with the discovery of the cage-like C60 molecule known as buckminsterfullerene, or simply, as fullerene. The structure of the C60 fullerene is very symmetric: it has the shape of a truncated icosahedron exhibiting two edge lengths – so-called single and double C-C bonds. The molecule has a very high icosahedral symmetry (Ih) with 120 group elements. The macroscopic production of solids containing fullerenes resulted in a substantial progress in the field of carbon nanostructures leading to the appearance of fullerites and fullerides, peapods and endofullerenes. We then consider phase transitions, polymerization and superconductivity in fullerene-based solids (fullerides), and discuss the experimental methods of fullerene production and their applications. The second part of the lecture deals with graphene which can be considered as a single layer of graphite – fundamental carbon structure having two dimensional (2D) translational symmetry. We discuss the direct and reciprocal lattices of graphene, the primitive unit cell and the first Brillouin zone. From that following the tight-binding model, we obtain the dispersion law for graphene resulting in a linear dependence at the Fermi energy. This implies unusual properties of electrons and holes in the neighborhood of the Fermi level – for example, the Klein paradox. We then proceed to so called double layer graphene discussing its physics and compare it with the single layer graphene, after which we consider graphene nanoribbons with the zigzag and armchair edge profiles. Depending on the edge profile, graphene nanoribbons can be metallic or semiconducting. In the end, some magnetic effects of graphene and examples of its applications are given. In the third part of the lecture we discuss the properties of carbon nanotubes. A single walled carbon nanotube (SWCNT) can be obtained from a single layer graphene – by rolling the graphene sheet into a tube and joining back up on itself. One can define a vector in terms of the graphene lattice sites to completely describe the structure of any SWCNT and predict key properties, which is called the chiral vector. The chiral vector, therefore, is fully defined by two integer multiples (n, m). Knowing these integers one can obtain the diameter of the tube and its chiral angle. Using the zone-folding method, we obtain the dispersion law for any SWCNT, characterized by the pair of indices (n, m), from the dispersion law of the parent graphene structure. On the basis of the dispersion law we discuss which carbon nanotubes are metallic and which are semiconducting. We finish by describing prospective applications of carbon nanotubes. In the end a summary of the reviewed carbon nanostructures is given.