In this thesis we present the realistic pair potential which can be used for different carbon fullerenes C60, C70, C76, C84, and C96 . The pair potential can be generated from the well-known Girifalco potential. In order to calculate the structure factor, S(q), and the radial distribution function, g(r), for C60, the Girifalco potential modeled to sticky hard sphere potential to find several important range parameters. Also we present analytical expressions for the structure factor, S(q), and the radial distribution function, g(r), for nanopartical fluid of carbon fullerene . The radial distribution function, g(r), is obtained via the inverse Laplace transform of the structure factor, S(q). The obtained expression of S(q) is based on the Laplace transform of the radial distribution function, g(r), for sticky hard sphere potential. The comparison of S(q) with computer simulation results indicates that the best choice of the sticky hard sphere range parameter _ equals to minimum potential position rm.