[C₇₆] – Fullerenes: Enumeration of Isomer Substitutions in Terms of Apical, Edge and Face Differentiation

Abstract

The discovery of fullerenes in quasicrystals having a symmetry of icosahedral point groups stimulated the interest to the usage of symmetry point groups having axes of the 5th order incompatible with the symmetry of infinite crystal lattice. Of interest are the crystals obtained from the [C₆₀]–[C₁₀₀] molecules. These molecules may form crystals (fullerides) together with other chemical elements and radicals. The structures having carbon layers forming lengthy hollow cylinders (carbon nanotubes ending with half-spherical cap) are distorted halves of fullerene molecule. Some nanotubes have open ends. Nanotubes combine the properties of a molecule with one-dimensional solid body. They are characterized by a large variety of properties perspective for applications. A method is proposed of the property prediction for the series of isomer substitutions of basic structure making use of the polygonal number splitting of the Pascal triangle (Smolyakov et al., Abstract of the XVIII Mendeleev conference on general applied chemistry, vol 2, Moscow, 23–28 Sept 2007, p 524; Nilov et al., Fullerenes C₆₀ – C₈₀: enumeration of exohedral substitution isomers and methods of thermodynamical properties estimation, In: Abstracts of VIII international conference solid state chemistry and contemporary micro- and nanotechnologies, Kislovodsk, 14–19 Sept 2008, pp 366–368 (in Russian); Smolyakov, About construction of additive schemes calculation of alkanes properties in the third approximation, Calculation methods in physical chemistry, KSU, Kalinin, pp 39–68, 1988; Smolyakov et al. C₆₀ and C₇₈ fullerenes: identification of exohedral substitution isomers. In: Abstracts of IX national conference on crystal growth, Moscow, 16–20 Oct 2000, pp 650 (in Russian); Yu et al., Vestnik Tver State Univ Ser Chem 2(30):87–94, 2007 (in Russian); Smolyakov et al. Rare Mater Technol 28:626–636, 2009). With the aid of the analysis of molecule structural elements On the basis of the analysis of fullerene molecule structural elements a formula is obtained for the calculation of fullerene thermodynamical properties. Calculations are made for ${\hbox{C}}_{\rm{p298K}}^{\rm{o}}$, ΔH_subl, of gaseous clusters [C₆₀]–[C₁₀₀], not studied experimentally.