Quantitative Relationship Study of Mechanical Structure Properties of Empty Fullerenes

Abstract

Since the discovery of fullerenes (C n ), one of the main classes of carbon compounds, the unusual structures and properties of these molecules and by the many potential applications and physicochemical properties have been discovered and were introduced. Up to now, various empty carbon fullerenes with a different magic number “n,” such as C20, C60, C70, C80, C180, C240 and so on, have been obtained. The mechanical property of these classes of carbon allotropes is one of the main properties which is attractive for investigation and application in the fullerenes. Topological indices are the digital value combined with chemical constitution purporting for correlation of chemical structures with various chemical and physical properties. Topological indices have been successfully used to construct effective and useful mathematical methods for finding good relationships between structural data and the various chemical and physical properties. To establish a good structural relationship between the structures of fullerenes (n) with the structural mechanical properties here was utilized the number of carbon atoms of the fullerenes “n.” In this study, the relationship between this index with diameter (h o , Å´), volume (V o , Å´3) molecular energy (E o ×l0−16 J), endurance load (Fmax) and compressive stiffness of empty fullerenes 1–4 (n=20, 60, 80, and 180) are presented. The results were extended for other empty fullerenes 5–25.