Biomedical Engineering Reference
In-Depth Information
will be described. This model is then parameterized for H, O, N, and
H
O from first principle calculations, and the degree of adsorption
and the “pattern” of the adsorbed H on the outer nanotube walls are
explored. This model is then used to investigate the thermodynamic
stability of CNTs exposed to a variety of atmospheric gases, including
air as a function of the relative (ambient) humidity.
2
7.2
Computational Modeling
When claiming a phase transition has occurred, or that the chemical
bonding in a material has altered, it is very important to accurately
characterize the structure of the system. Empirically, an sp
bond is
said to be “broken” when the separation distance between the two C
atoms exceeds the dissociation length, or significantly greater than
the C-C bond length of 1.54 Å characteristic of diamond. Similarly
the breaking of an sp
3
2
bond is assumed when the atomic separation
distance significantly exceeds 1.42 Å characteristic of graphite. Most
molecular visualization programs use an algorithm based on this
concept to decide when (and how) to render the bonds of a given
input structure. However, visualizations of this type can often be
misleading, since the volume dilations of nanomaterials (due to
surface tension) can result in variations in the typical bond lengths,
angles, and dissociation length throughout the structure. The average
C-C bond length in CNTs and fullerenes is 1.44 Å, which is already
longer than the graphitic 1.42 Å. Therefore, a more reliable method of
establishing the formation, dissociation, and character of C-C bonds
is to calculate the electronic charge density (ECD) surrounding two
C atoms and use this to identify and/or characterize any interaction
in between [20, 27].
The calculations in this chapter have been carried out using
density functional theory (DFT) within the generalized gradient
approximation (GGA), with the exchange-correlation functional of
Perdew and Wang (PW91) [45]. This has been implemented via the
Vienna Ab-initio Simulation Package (VASP) [46, 47], which spans
reciprocal space with a plane-wave basis. All calculations were
performed with the valence orbitals expanded in a plane-wave basis
up to a kinetic energy of 290 eV. The linear tetrahedron method (LTM)
with Blöchl corrections was used for the Brillouin zone integrations,
with a Monkhorst-Pack k-point mesh [48].