In this paper, we investigate methane encapsulation in five spherical fullerenes C60,C240,C540,C960, and C1500. We exploit the 6–12 Lennard-Jones potential function and the continuum approximation to model the surface binding energies between methane and spherical fullerenes of varying sizes. Our results show that for a methane molecule interacting inside a spherical fullerene, the binding energies are minimized at locations which become closer to the fullerene wall as the size of the fullerene increases. However, we find that the methane molecule would require an applied external force to overcome the repulsive energy barrier in order to be encapsulated into a C60 fullerene. The present modeling indicates that the optimal minimum energy for methane storage in any spherical fullerene occurs for a fullerene with radius 6.17 Å, with a corresponding potential energy of 0.22eV which occurs for a fullerene bigger than a C60 but slightly smaller than a C240 as the ideal spherical fullerene for methane encapsulation. Overall, our results are in very good agreement with other theoretical studies and molecular dynamics simulations, and show that fullerenes might be good candidates for gas storage. However, the major advantage of the approach adopted here is the derivation of explicit analytical formulae from which numerical results for varying physical scenarios may be readily obtained.

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