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S. X. Drakopoulos et al.
Fig. 10 AC conductivity as a function of frequency for HDPE composites with a carbon nanofibers
(CNFs) and b Multi-wall carbon nanotubes (MWCNTs) for different filler concentrations [67].
Reproduced with permission from Linares et al. Macromolecules 2008, 41, 7090–7097
(MWCNT) are added to high density polyethylene (HDPE). In Fig. 10, it can also
be appreciated that with the increase of fillers concentration, the AC conductivity
becomes increasingly less dependent on frequency [67]. Since there is a contribution
of DC conductivity to the imaginary part of dielectric permittivity
σ dc
ωε 0
when the
s dc becomes sufficiently high, it shadows the molecular dipolar response originating
from the dielectric material resulting into s ac (f,T) ≈ s dc (T). This effect is considerably
more intense in polyolefins such as polyethylene due to their very weak relaxation
strengths (ε = ε s − ε ∞ ).
As it can be appreciated from Fig. 11, the percolation threshold of CNF and
MWCNT in DC current is found to be at 3 and 1% v/v, respectively, which according
to percolation theory, is the concentration where a continuous network of conductive fillers is formed. It is significant to note that the electrical conductivity of the
nanocomposites at the percolation threshold is around 14 orders of magnitude the
one of plain polyethylene, highlighting the enhancement of the electrical properties.
S. X. Drakopoulos et al.
Fig. 10 AC conductivity as a function of frequency for HDPE composites with a carbon nanofibers
(CNFs) and b Multi-wall carbon nanotubes (MWCNTs) for different filler concentrations [67].
Reproduced with permission from Linares et al. Macromolecules 2008, 41, 7090–7097
(MWCNT) are added to high density polyethylene (HDPE). In Fig. 10, it can also
be appreciated that with the increase of fillers concentration, the AC conductivity
becomes increasingly less dependent on frequency [67]. Since there is a contribution
of DC conductivity to the imaginary part of dielectric permittivity
σ dc
ωε 0
when the
s dc becomes sufficiently high, it shadows the molecular dipolar response originating
from the dielectric material resulting into s ac (f,T) ≈ s dc (T). This effect is considerably
more intense in polyolefins such as polyethylene due to their very weak relaxation
strengths (ε = ε s − ε ∞ ).
As it can be appreciated from Fig. 11, the percolation threshold of CNF and
MWCNT in DC current is found to be at 3 and 1% v/v, respectively, which according
to percolation theory, is the concentration where a continuous network of conductive fillers is formed. It is significant to note that the electrical conductivity of the
nanocomposites at the percolation threshold is around 14 orders of magnitude the
one of plain polyethylene, highlighting the enhancement of the electrical properties.