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structure must expand relative to an isolated two-dimensional solid. Thus, there is
competition between the length scales set by the Kr±Kr and Kr±graphite interac-
tions. An important question was thus whether or not this competition could lead
to an in commensurate phase at low temperatures. This is a situation in which
boundary conditions again become an important consideration. If periodic bound-
ary conditions are imposed, they will naturally tend to produce a structure, which
is periodic with respect to the size of the simulation cell. In this case a more
profitable strategy is to use free edges to provide the system with more freedom.
The negative aspect of this choice is that finite size effects become even more
pronounced. This question has been studied using a Hamiltonian and some men-
tioned equations.
1.3.2.1.8
COMPARISON OF SOME SIMULATION METHODS
As noted from the above works, the large numbers of numerical studies on CNT
dynamics were based on MD simulations. In the classical MD simulations, all de-
grees of freedom due to the electrons are ignored, as well as quantum effects. So
a more accurate description is needed, i.e., potentials between electron-electron,
electron-ion as well as ion-ion interactions should be considered. In this respect,
the ab initio density functional theory (DFT) and Car-Parrinello molecular dy-
namics (CPMD) were used in the study. DFT calculation, which is known as time
consuming and considering more details about the electrons and the ions, can
give more interactions and corrections about electron-electron, electron- ion and
ion-ion, which are disregarded in classical MD. Considered these corrections, the
simulated Young's moduli of CNTs would be more credible. But it can only simu-
late the static state. CPMD, which combines the MD simulation with quantum
mechanics, treats the electronic degrees of freedom in the framework of DFT. It
makes a balance between efficiency and precision, while considering the dynamic
effect. However, the dynamic processes, performing in the CPMD still restricted
to small system, which is a main disadvantage of CPMD. Here compendiously
compared the threedifferent methods in
Table 1.6
[129]. It is apparent from non-
hexagonal SWNT with a (n,m) chirality, cannot be achieved using REBO-based
MD simulations. The effect of the increase of the conjugated electronic structure
with increased stabilization is beyond the capability of simple many-body po-
tentials. Further, the second chief objective of the metal cluster, namely keeping
the carbon structure open for continued sidewall growth by incoming new car-
bon feedstock cannot be achieved without “cheating”: that is, a supply of carbon
from the outside of the metal cluster always results in complete encapsulation and
“death of the catalyst”.
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