Chemistry Reference
In-Depth Information
In spite the MD and MC methods depend on the potentials that the
forces acting on atoms by differentiating inter atomic potential functions,
the Ab initio techniques are accurate methods which are based on an accu-
rate solution of the Schrödinger equation. Furthermore, the Ab initio tech-
niques are potential-free methods wherein the atoms forces are determined
by electronic structure calculations progressively.
In generally, MD simulations provide good predictions of the mechani-
cal properties of CNTs under external forces. However, MD simulations
take long times to produce the results and consumes a large amount of
computational resources, especially when dealing with long and multi-
walled CNTs incorporating a large number of atoms.
9.4.1.2
CONTINUUM MODELING
Continuum mechanics-based models are used by many researches to in-
vestigate properties of CNTs. The basic assumption in these theories is
that a CNT can be modeled as a continuum structure which has continuous
distributions of mass, density, stiffness, etc. Therefore, the lattice struc-
ture of CNT is simply neglected in and it is replaced with a continuum
medium. It is important to meticulously investigate the validity of con-
tinuum mechanics approaches for modeling CNTs, which the real discrete
nano-structure of CNT is replaced with a continuum one. The continuum
modeling can be either accomplished analytical (micromechanics) or nu-
merically representing FEM.
Continuum shell models used to study the CNT properties and showed
similarities between MD simulations of macroscopic shell model. Because
of the neglecting the discrete nature of the CNT geometry in this method,
it has shown that mechanical properties of CNTs were strongly dependent
on atomic structure of the tubes and like the curvature and chirality effects,
the mechanical behavior of CNTs cannot be calculated in an isotropic shell
model. Different from common
shell model,
which is constructed as an
isotropic continuum shell with constant elastic properties for SWCNTs,
the MBASM model can predict the chirality induced anisotropic effects
on some mechanical behaviors of CNTs by incorporating molecular and
continuum mechanics solutions. One of the other theory is shallow shell
theories, this theory are not accurate for CNT analysis because of CNT is a
