*Phys.Rev. B* **81**(23), 235403, 2010

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

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

^{1}Department of Physical Metallurgy and Materials
Testing,

Montanuniversität Leoben, Leoben, Austria

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

^{3}Institute of Mechanics, Montanuniversität
Leoben, Leoben, Austria

^{4}Institute of Lightweight Design and Structural
Biomechanics,

TU Wien,
Vienna, Austria

**Abstract** -
Carbon nanostructures are investigated using a multiscale approach based on
density functional theory (DFT) and Monte Carlo (MC) simulations.
The structure of small fullerenes is calculated using DFT, and simple models
are employed to determine classical potential functions which are then used in
MC simulations to investigate larger structures.
The structural parameters as obtained by DFT and by MC simulations are cross
validated for small fullerenes, allowing to understand the effect of the
approximations made in MC simulations.
It is found that MC overestimates the numerical value of the excess surface
energy of carbon nanostructures but the functional dependence, i.e., the decay
exponent as a function of the fullerene size, is accurately described.
The MC results reveal that bond torsion is the dominant term of the total
curvature energy. The combination of DFT and MC allows to get reliable
estimates for the excess surface energy of fullerenes as a function of radius
for a wide range of fullerene sizes, which may serve as an important input for
large-scale finite-element modeling of more complex systems.

(hjb,100607)