Structural relationship between degree of unsaturation with polarizability of (5,5) armchair single-wall carbon nanotubes

Study about properties of nanotubes with medicinal and electronic applications have been made the highly useful and effective results for applications in different areas of science. One of the main recognized structures of nanotubes is ( 5,5) single wall tube ( SWCN). Graph theory is an area of mathematics that is closely related to both topology and combinatory concepts. Topological indices are the digital value combined with chemical constitution purporting for correlation of chemical structures with various chemical and physical properties that have constructed the effective and useful mathematical methods for finding good relationship between several data of the properties in these materials. One of the useful numerical and structural items in unsaturated compounds is degree of unsaturation ( D-U). In this study, the relationship between this index ( D-U), the length of these nanotubes ( r) and the polarizability ( P. 10 239 CV 21 m 2) is represented as an important electronic property of nanotube ( 5,5) armchair SWCN. By the simple model presented here, in good approximation can calculate the polarizability and can be used the approximated values in electronic structures and electrical properties studies of this type of nanotubes. The interesting results of relationship among D-U and the polarizability of these nanotubes are presented.