percolation threshold increases with the mean value of the aspect ratio a ¼ kLi/d.
Therefore, the concentration of particles necessary for the onset of percolation for
fibers is up to many orders of magnitude less as compared to spherical particles. To
obtain optically transparent electric conductive composites, one must apply
extremely thin, long fibers, which are usually achieved with nanotubes or nanowires.
In any real length distribution, kLi
3 /kL
3 i 1 is valid. Assuming fibers of equal length
L, then Eq. (10.15) boils down to:
p c ¼ 0:7
d
L
ð10:16Þ
In simple terms, Eq. (10.16) states that using long fibers reduces the percolation
threshold, as they have a huge aspect ratio. Furthermore, as the nanomaterial used
as electric conductive filler is significantly more expensive than the polymer matrix,
the application of nanotubes or nanowires with large aspect ratio is the most
economic.
Some typical experimental results for the electrical conductivity of a carbon
nanotube/PMPV (poly(p-phenylenevinylene-co-2,5-dioctoxy-m-phenlyenevinylene))
nanocomposite are shown in Figure 10.27. Here, there is a clear and sudden
increase in electrical conductivity at the percolation threshold between 7 and 8 vol%
carbon nanotubes. Additionally, a second characteristic feature of this type of
nanocomposite is apparent, namely that the electrical conductivity shows saturation.
This means that, for each combination of electrical conductive filler and insulator, a
characteristic maximal conductivity is observed. (Even in this example, where an
unusually high concentration of nanotubes was necessary to obtain percolation, it
shows clearly the characteristic parameter of electric conductivity in a percolation
system.)
0
5
10
15
20
25
30
35
40
mass fraction nanotubes [%]
10
-10
10
-09
10
-08
10
-07
10
-06
10
-05
10
-04
10
-03
10
-02
10
-01
10
00
electric
conductivity
[Sm
-1 ]
Figure 10.27 Experimental results on the electric conductivity of a carbon nanotube/PMPV
nanocomposite [16]. Note the sudden increase in conductivity at the percolation threshold.
10.4 Electrical Conductivity of Nanocomposites j289
Therefore, the concentration of particles necessary for the onset of percolation for
fibers is up to many orders of magnitude less as compared to spherical particles. To
obtain optically transparent electric conductive composites, one must apply
extremely thin, long fibers, which are usually achieved with nanotubes or nanowires.
In any real length distribution, kLi
3 /kL
3 i 1 is valid. Assuming fibers of equal length
L, then Eq. (10.15) boils down to:
p c ¼ 0:7
d
L
ð10:16Þ
In simple terms, Eq. (10.16) states that using long fibers reduces the percolation
threshold, as they have a huge aspect ratio. Furthermore, as the nanomaterial used
as electric conductive filler is significantly more expensive than the polymer matrix,
the application of nanotubes or nanowires with large aspect ratio is the most
economic.
Some typical experimental results for the electrical conductivity of a carbon
nanotube/PMPV (poly(p-phenylenevinylene-co-2,5-dioctoxy-m-phenlyenevinylene))
nanocomposite are shown in Figure 10.27. Here, there is a clear and sudden
increase in electrical conductivity at the percolation threshold between 7 and 8 vol%
carbon nanotubes. Additionally, a second characteristic feature of this type of
nanocomposite is apparent, namely that the electrical conductivity shows saturation.
This means that, for each combination of electrical conductive filler and insulator, a
characteristic maximal conductivity is observed. (Even in this example, where an
unusually high concentration of nanotubes was necessary to obtain percolation, it
shows clearly the characteristic parameter of electric conductivity in a percolation
system.)
0
5
10
15
20
25
30
35
40
mass fraction nanotubes [%]
10
-10
10
-09
10
-08
10
-07
10
-06
10
-05
10
-04
10
-03
10
-02
10
-01
10
00
electric
conductivity
[Sm
-1 ]
Figure 10.27 Experimental results on the electric conductivity of a carbon nanotube/PMPV
nanocomposite [16]. Note the sudden increase in conductivity at the percolation threshold.
10.4 Electrical Conductivity of Nanocomposites j289