*Carbon* **81**(23), 235403, 2010

### CURVATURE-INDUCED EXCESS SURFACE ENERGY OF FULLERENES: DENSITY
FUNCTIONAL THEORY AND MONTE CARLO SIMULATIONS

M. Todt^{1}, F.G. Rammerstorfer^{1},
F.D. Fischer^{2}, P.H. Mayrhofer^{3},
D. Holec^{3}, M.A. Hartmann^{4}

^{1}Institute of Lightweight Design and Structural
Biomechanics,

TU Wien,
Vienna, Austria

^{2}Institute of Mechanics, Montanuniversität
Leoben, Leoben, Austria

^{3}Department of Physical Metallurgy and Materials
Testing,

Montanuniversität Leoben, Leoben, Austria

^{4}Institute of Physics, Montanuniversität
Leoben, Leoben, Austria

**Abstract** -
A continuum formulation of the van derWaals interactions between carbon onion
layers in form of pressure/radius relations is obtained.
The relations are derived analytically considering the doubly-curved geometry
of carbon onion layers.
For finite layer radii it is shown that the van der Waals induced pressures on
opposing faces of two adjacent onion layers are not equal and depend on both
layer radii.
Equilibrium configurations of different double-layer onion models are
calculated using the theorem of stationarity of the total potential energy.
The results are compared with those of simplified models which do not consider
any curvature effects.
It is shown that curvature effects have no significant influence on the
equilibrium interlayer distances, but they significantly change the results for
the radial displacements and, consequently, for the membrane forces in the
layers.
Comparison with Monte Carlo simulations of C60 in C180 and C60 in C240 shows
that the derived van der Waals model represents the radial displacements and
equilibrium interlayer distances better than the simplified models. Thus,
whenever a good representation of the membrane forces is important, e.g., in
stability analysis, the new approach should be used.

(hjb,110203)