Continuum modelling of spherical and spheroidal carbon onions |
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Authors: | D Baowan N Thamwattana J M Hill |
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Institution: | (1) Nanomechanics Group, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia |
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Abstract: | 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. |
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Keywords: | 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 |
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