Biomedical Engineering Reference
In-Depth Information
p RL
p RLρ
a cylindrical approximation (so that
A =
2
, and
N
= 2
), we
C
may divide through by
N
and make the necessary cancellations to
C
obtain:
3
3
E
( , , )
R X
A h
h
S
(7.9)
N
N
24
R
2
24
R
2
C
C
where
is the atomic number density of the CNT. Thus, the strain
energy per atom is inversely proportional to the square of the radius
of curvature (providing the size dependence), with a coefficient that
will depend on the gas species and will be a function of the degree of
coverage Θ (since
ρ
κ
will be a function of Θ):
 
3
h
1
E
,
X
(7.10)
.
S
 
 
24
2
2
R
R
Like the adsorption energy, the dependence on coverage and
radius are obtained by undertaking a series of simulations and fitting
to a simple function, as described in a later section.
7.3.5
Thermodynamic Expansion
Recombining these terms Eq. (7.2) becomes:
0
2
0
0
 
 

H
N
E
(sp )
N
H
( )
C
N
E
( , , )
R X
H
( )
X
f
2
C
f
X
ad
f
sp
3
3
(7.11)
N
E
(sp )
N
N
E
 
E
( , , )
R X
3
3
X DB S
sp
sp
4
or, per C atom, the formation enthalpy can be calculated for any size
and chirality using:
N
-
N
N
0
D
H
3
C
3
3
sp
sp
f
2
3
E
(sp )+
E
(sp )+
E
DB
N
N
N
4
C
C
C
0
+
 
E
( , , )- + ( )
( , ) .
R X
E
D
H
X
b
DB
f
E
X
(7.12)
0
f
S
+ ( )+
D
H
C
2
R
This has the associated criteria that
N
+
N
=
N
, 0 ≤
N
2
2
3
sp
sp
C
sp
N
, and for a given degree of coverage Θ =
N
/
N
, where 0 ≤
N
C
X
C
X
Θ
will depend upon the
adsorption pattern, which will be discussed in more detail in the
next section. As Θ increases, the probability of clustering increases,
so this parameter is important in determining the fraction of isolated
versus clustered adsorption sites.
N
. Note that the numerical value of Θ
max
C
max
 
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