Chemistry Reference
In-Depth Information
equilibrate by two- and three-body collisions towards the most stable species, which
appears to be unique cluster containing 60 atoms.”
These early suggestions, however, were based on larger graphene sheets in the
case of nanotubes or they supposed degradation or fusion of various ring fragments.
In our recent molecular dynamics simulations we have shown the existence of various
patterns cut out from the graphene which transformed to C
60
and C
70
fullerenes or
nanotubes depending on the initial pattern structures (László and Zsoldos
2012a
,
b
,
2014
). The greater application of fullerenes and nanotubes faces the lack of selective
growth and assembly processes. Our results can initiate new experimental researches
for improving the existing carbon nanostructure productions and to develop a new,
structure selective nanolithography of fullerenes, nanotubes and other carbon struc-
tures. We are aware of the fact that nowadays patterning of graphene is not yet at
atomic precision, but there are promising experimental achievements (Avouris et al.
2007
; Chen et al.
2007
; Tapasztó et al.
2008
; Feng et al.
2012
).
First we review the molecular dynamics method which was used in our previous
calculations (László and Zsoldos
2012a
,
b
,
2014
), after the methods of experimental
patterning will be shown. Then we present various geometrical patterning of graphene
which are not applicable for self organizing production of fullerenes. Than we present
the method of coding the final structure in the initial one. As new results we suggest
new patterns for formation of C
n
fullerenes with (72
≤
≤
100). In the conclusion
we analyse our results and regarding new experimental results we extend the meaning
of patterning to hydrocarbon patterns as well.
n
2.2
Tight Binding Molecular Dynamics Calculation
Although our system contained only about 100 carbon atoms we were using a tight
binding method in our molecular dynamics simulations as we had to make a great
number of runs. The inter atomic forces were calculated with the help of a density
functional tight binding (DFTB) model (Porezag et al.
1995
). In such a model the
total energy is written in the form of
N
P
k
E
=
2M
k
+
E
bond
+
E
rep
(2.1)
k
=
1
where
E
bond
=
n
i
ε
i
(2.2)
i
is the tight binding electronic energy where the summation goes over all of the
eigenstates of the tight binding Hamiltonian matrix H. The value
n
i
of the occupation
number is 2, 1 or 0 depending of the occupation of the eigenfunctions
m
ψ
i
(
r
)
=
C
ν
i
φ
ν
(
r
−
R
ν
)
(2.3)
ν
