Biomedical Engineering Reference
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the energy of the adsorbates (
), the energy associated with the
rehybridization of the C-C bonds in the region surrounding the
adsorption site (
E
X
E
), and the strain energy due to the curvature of
sp
the CNT (
E
), such that:
S
0
D H
=
E
+
E
+
E
+
E
.
(7.2)
f
C
X
sp
S
Each of these terms will be treated separately in the proceeding
sections.
7.3.1
CNT Cohesive Energy
Beginning with the cohesive energy term,
0
(
E
=
N
E
(sp
2
) +
N
D H
C
)
(7.3)
C
sp
2
C
f
where
N
is the total number of C atoms,
N
is the total number of
2
C
sp
0
2
2
2
D H
sp
-bonded C atoms,
E
(sp
) is the sp
cohesive energy, and
(
C
)
f
2
is the formation energy of a free (isolated) C atom.
) may be
considered as the elastic “stretch energy” of the C-C bonds in the
nanotube and (since the strain energy is treated separately), is the
same as that of a planar graphene sheet. In the absence of gaseous
adsorbates (when the number of gas atoms
E
(sp
N
= 0), then
N
=
N
X
C
sp
2
and a pristine (ideal) CNT is described.
7.3.2
Energy of Adsorbates
As mentioned above, the energy associated with the chemisorbed
gas atoms or molecules will be a function of the coverage (Θ),
the radius (or chirality) of the tube, and of course on the type of
adsorbate. This is expressed by:
0
E
=
E
(Θ,
R
,
X
) =
N
[
E
(Θ,
R
,
X
) +
D H
(
X
)]
(7.4)
X
X
X
ad
f
where
N
is the number of adsorbed atoms or molecules,
X
E
(Θ,
R
,
X
) is the adsorption energy of the gaseous species and
ad
0
D H
) is the formation energy of a free (isolated) gas atom or
molecule. The adsorption energy
(
X
f
E
(Θ,
R
,
X
) may be calculated for
ad
any value of Θ =
N
/
N
[55, 58], with:
X
C
) = 1
____
N
m
E
(Θ,
R
,
X
[
E
(
N
) +
N
-
E
(
N
,
N
)]
(7.5)
ad
C
X
X
C
X
X
where
E
(
N
) is the total energy of a pristine CNT structure
C
(containing
N
carbon atoms in the simulation supercell),
E
(
N
, N
)
C
C
X
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