Structure and Properties Of Fullerenes
STRUCTURE AND PROPERTIES OF FULLERENES Abstract The fullerenes are allotropes of carbon. The structural formulae for the fullerenes differ from the other allotropes due to the unusual arrangement of the carbon atoms. The layers and the arrangement of the fullerene allotrope can be represented in the algebraic expressions. The algebra involved in the fullerene definitions gives the mathematical representation of the atom arrangement and the dimension of different molecular layers. The graph theory gives some theorems of the fullerene regarding the established hypothesis and facts. The fullerene graphs use algebraic concepts to support the expressions. The structural configurations of the fullerenes can be given in the form of matrices or diagrams which follow a given format. The graph theory simplifies the representation and definitions by establishing given rules and definitions. This paper gives the general background of the fullerenes and the general mathematics involved in the modeling of the fullerene structures. The graph theory explains the arithmetic in fullerene theory by use of the algebra concepts. Chapter 1: IntroductionHistory of Fullerenes The discovery of fullerenes and its structural elucidation paved the way for defining fullerene graphs. The discovery of fullerenes is attributed to the contribution of the Nobel laureates Harold Kroto, Robert Curl, and Richard Smalley [4; Section 1]. These scientists discovered a novel allotrope of carbon in which the carbon atoms formed close shells. The first fullerene…
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