An Analytical Model for Lithium Storage in Spherical Fullerenes

In this paper, the encapsulation of lithium atoms in spherical fullerenes of varying sizes is investigated. The 6–12 Lennard–Jones potential function and the continuum approximation, in which it is assumed that the atoms can be replaced with a uniform distribution across the surface of the molecules, are exploited to model the interaction energies between lithium atoms and spherical fullerenes. Thus, the total interaction energies can be approximated by applying surface integrations. The results show that for a lithium atom interacting inside a spherical fullerene, the interaction energies are minimized at a position that approaches the fullerene wall as the size of the fullerene increases. However, the results show that an external force would need to be applied to a lithium atom in order to overcome the repulsive energy barrier so that it can be encapsulated in C N fullerenes with a radius of less than 2 Å. The present study indicates that the optimal radius that gives the minimum energy for the storage of Li inside C N fullerenes occurs for a fullerene with a radius of ≈ 2.4 Å. Overall, this study provides an analytical formulation that may facilitate rapid computational results, and an application of this work is in the design of future high-energy-density batteries that utilize C N fullerenes.