St. Hyde et M. Okeeffe, ELASTIC WARPING OF GRAPHITIC CARBON SHEETS - RELATIVE ENERGIES OF SOME FULLERENES, SCHWARZITES AND BUCKYTUBES, Philosophical transactions-Royal Society of London. Physical sciences and engineering, 354(1715), 1996, pp. 1999-2008
The energies of hypothetical and the already found 'graphitic' (sp(2))
carbon networks with hyperbolic ('schwarzites'), elliptic ('fullerene
s') and parabolic ('buckytubes') curvatures are compared with a simple
elastic model of the warping energy of a spontaneously flat graphite
sheet, analogous to bending energy models for amphiphilic membranes, i
nvoking both bend and twist contributions. Splay and saddle splay modu
li are estimated to be 190kT and -65kT, respectively, an order of magn
itude stiffer than typical amphiphilic bilayer membranes. The model ac
counts adequately for relative self-energies of most curved graphitic
networks. Many proposed allotropes of carbon may thus be treated as tw
o dimensional warped layer-structures.