Continuum modelling of spherical and spheroidal carbon onions
Nanomechanics Group, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia
Corresponding author: a firstname.lastname@example.org
Revised: 12 April 2007
Published online: 16 May 2007
Carbon nanostructures are of considerable interest owing to their unique mechanical and electronic properties. Experimentally, a wide variety of different shapes are obtained, including both spherical and spheroidal carbon onions. A spheroid is an ellipsoid with two major axes equal and the term onion refers to a multi-layered composite structure. Assuming structures of either concentric spherical or ellipsoidal fullerenes comprising n layers, this paper examines the interaction energy between adjacent shells for both spherical and spheroidal carbon onions. The Lennard-Jones potential together with the continuum approximation is employed to determine the equilibrium spacing between two adjacent shells. We also determine analytical formulae for the potential energy which may be expressed either in terms of hypergeometric or Legendre functions. We find that the equilibrium spacing between shells decreases for shells further out from the inner core owing to the decreasing curvature of the outer shells of a concentric structure.
PACS: 02.30.Rz – Integral equations / 34.20.-b – Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions / 62.25.+g – Mechanical properties of nanoscale materials
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007