Eng8450 + MWNT
Sample annealed 15 minutes in the press (140 C)
Around 30 minutes between put the sample in the
equipment and to start the experiment
DC decrease with
Eng
Eng + 0,05 MWNT
Eng + 0,1 MWNT
Eng + 0,5 MWNT
Eng + 1,0 MWNT
Eng + 3,0 MWNT
Eng + 6,0 MWNT
Eng + 12,0 MWNT
low amount of CNT!!!!!
-3
10
-5
S (S/cm)
10
-7
10
DC region
-9
10
Dielectric region
-11
10
-13
10
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Freq. [Hz]
How we can understand this “rare” behavior?
Symmetric Hopping Model
Based on the study of the displacement of a charge carrier
from one position to another close by
The nearest-neighbor jump rate (frequency) is:
   0  exp(    E )

1
kB T
It is possible to show that the transition from DC to AC is determined
by the smallest jump rate (c) , and the transition will be given by:
DC  AC  c  t  1
n  q2
 D ( )
From this model is showed that:  ( ) 
kB T

D ( )   v(0)  v(t )  e  t dt
0
So, it is possible to think that the presence of nanotubes increase the
activation energy for the jump-rate of charge carriers or decrease its diffusion
processes. At higher amount the last is compensated by the percolation
process.
Another approach based on the same arguments define the probability
for a electron (“hole”) transition from state “a” to “b”, as:
pab   ab exp( qab )   ab exp( 2   ab  R)  exp( 
Wab
)
kB T
Wab  (a  b )  ( Ea  Eb ) /4  (a  b )
2
’s are the reorganization energy
It is showed that the response of the system to an alternating field is:
 ( ) 
  e 2  N s2
12  k B  T
   [ R 2 P( R, qab , qba )]
 2  ab 
qab  qba  ln 




The major contribution to the conductivity comes from polymer
pair elements satisfying the last assumption!!!
The response at very low frequencies involve pair states with very low
transition rates. As a consequence the rare transitions from pair
states into new states become more significant.
Again, the presence of nanotubes could change the dynamic
of charge carriers, decreasing the conductivity
Another theory is based on the equivalent circuit concept:
Any solid with spatially varying free
charge conductivity and uniform
charge dielectric constant
At high frequencies the conductive regions are important
and at low frequencies the isolated areas limit the charge carrier motion.
Under AC conditions, it is defined:
 ( )   ' ( )  i   ' ' ( )
Resistor
contribution
Conductance
contribution
Eng8450 + MWNT
-1
10
-3
10
Eng
Eng + 0,05 MWNT
Eng + 0,1 MWNT
Eng + 0,5 MWNT
Eng + 1,0 MWNT
Eng + 3,0 MWNT
Eng + 6,0 MWNT
Eng + 12,0 MWNT
S' (S/cm)
-5
10
-7
10
’ is related with the current
through the resistors
Below the percolation point, the high frequency
area is influenced by the CNT (conductive)
At low frequency, the isolated-region (bulk
polymer) make the greater contributions
-9
10
-11
10
-2
10
Eng
Eng 0,05 MWNT
Eng 0,1 MWNT
Eng 0,5 MWNT
Eng 1,0 MWNT
Eng 3 MWNT
Eng 6 MWNT
Eng 12MWNT
-4
’’ is related with the current
through the capacitors
S'' (S/cm)
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10 10
Freq. [Hz]
-6
10
-8
10
-10
10
-12
The presence of CNT does not affect
the conductance of the sample below
the percolation point
10
-14
10
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Freq. [Hz]
Eng8450 + SWNT
-5
10
Same behavior!!!
Eng
Eng + 0,05 SWNT
Eng + 0,1 SWNT
Eng + 1,0 SWWT
-6
10
-7
10
CNTs affect the resistor contribution
of the composite, and
at low frequencies changes in the
dynamic of the polymers due to CNT
decrease their conductivity
S (S/cm)
-8
10
-9
10
-10
10
-11
10
-12
10
-13
10
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Freq. [Hz]
-7
-5
10
10
10
-9
-7
10
-8
S'' (S/cm)
S' (S/cm)
10
-10
10
-11
10
10
-9
10
-10
10
-11
10
-12
10
-12
10
-13
10
Eng
Eng + 0,05 SWNT
Eng + 0,1 SWNT
Eng + 1,0 SWNT
-6
10
Eng
Eng + 0,05 SWNT
Eng + 0,1 SWNT
Eng + 1,0 SWWT
-8
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Freq. [Hz]
-13
10
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Freq. [Hz]
The effect of the dynamic of the polymer on the conductivity
is confirmed by the relaxation process observed in some composites
1E-5
1E-7
Eng + 1.0 SWNT
Eng + 1,0 SWNT original
Eng + 1,0 SWNT ann 3 hrs
3 hrs annealing
140 C
1E-8
1E-9
1E-11
1E-10
1E-11
1E-12
-2
-1
0
1
2
3
4
5
6
10 10 10 10 10 10 10 10 10
Freq. [Hz]
1E-5
1E-6
1E-8
1E-9
1E-13
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Freq. [Hz]
1E-4
Eng + 0.05 SWNT
1E-7
S (S/cm)
1E-9
3 hrs annealing
140 C
Eng + 1,0 SWNT original
Eng + 1,0 SWNT ann 3 hrs
1E-6
S'' (S/cm)
S (S/cm)
1E-7
S' (S/cm)
1E-6
1E-8
1E-10
1E-12
1E-10
1E-11
1E-12
-2
-1
0
1
2
3
4
5
6
10 10 10 10 10 10 10 10 10
Freq. [Hz]
1E-14
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Freq. [Hz]
Eng8450
Effect of the temperature
1E-6
S (S/cm)
1E-7
120 C
140 C
190 C
1E-8
1E-9
1E-10
1E-11
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Frequency (Hz)
Annealing Studies for some Eng/MWNT samples
Effect of the amount of filler
-4
1,0x10
-10
|Sig| [S/cm]
|Sig| [S/cm]
1,0x10
Pure Eng
-11
12% MWNT
-5
1,0x10
1,0x10
1Hz
1% MWNT
-12
1,0x10
0
5000
10000
15000
-6
1,0x10
0
Time [s]
1E-3
-5
10
|Sig| [S/cm] 1% MWNT before annealing
|Sig| [S/cm] 1% MWNT after annealing
-6
10
5000
10000
Time [s]
15000
|Sig| [S/cm] before annealing 12WNT
|Sig| [S/cm] after annealing 12WNT
-7
Sigma (S/cm)
Sigma (S/cm)
10
-8
10
-9
10
-10
10
-11
10
1E-4
1E-5
-12
10
-13
10
-2
-1
0
1
2
3
4
5
6
10 10 10 10 10 10 10 10 10
Frequency (Hz)
1E-6
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Frequency (Hz)
Annealing Studies for some Eng samples
Effect of the kind of filler
-10
-9
1,0x10
1% MWNT
|Sig| [S/cm]
|Sig| [S/cm]
1,0x10
-11
1,0x10
1% SWNT
-10
1,0x10
-11
1,0x10
-12
1,0x10
0
5000
10000
15000
0
Time [s]
-4
-5
10
|Sig| [S/cm] 1% MWNT before annealing
|Sig| [S/cm] 1% MWNT after annealing
-6
10
-7
Sigma (S/cm)
Sigma (S/cm)
10
-8
10
-9
10
-10
10
-11
10
-12
10
-13
10
-2
-1
0
1
2
3
4
5
6
10 10 10 10 10 10 10 10 10
Frequency (Hz)
5000
10000
Time [s]
15000
10
|Sig| [S/cm] before annealing 1% SWNT
-5
|Sig| [S/cm] after annealing 1% SWNT
10
-6
10
-7
10
-8
10
-9
10
-10
10
-11
10
-12
10
-13
10
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Frequency (Hz)
Annealing Studies for some Eng samples
Effect of the kind of matrix
-11
-11
1,0x10
|Sig| [S/cm]
|Sig| [S/cm]
1,0x10
Eng
1% MWNT
-12
1,0x10
PE3732C
1% MWNT
-12
1,0x10
-13
1,0x10
-13
0
5000
10000
15000
1,0x10
0
5000
Time [s]
10000
15000
Time [s]
-5
10
|Sig| [S/cm] 1% MWNT before annealing
|Sig| [S/cm] 1% MWNT after annealing
-6
10
-5
10
-7
-8
10
-7
10
Sigma (S/cm)
Sigma (S/cm)
10
-9
10
-10
10
-11
10
-12
10
-8
10
-9
10
-10
10
-11
10
-12
10
-13
10
|Sig| [S/cm] before annealing 1WNT
|Sig| [S/cm] after annealing 1WNT
-6
10
-2
-1
0
1
2
3
4
5
6
10 10 10 10 10 10 10 10 10
Frequency (Hz)
-13
10
-2
-1
0
1
2
3
4
5
6
10 10 10 10 10 10 10 10 10
Frequency (Hz)
Annealing Studies for some Eng samples
Effect of the kind of matrix
Eng
12% MWNT
|Sig| [S/cm]
1,0x10
-7
1,0x10
-4
1,0x10
1Hz
|Sig| [S/cm]
-3
-5
PE3732C
12% MWNT
-8
1,0x10
-9
1,0x10
1,0x10
-10
1,0x10
0
-6
1,0x10
Sigma (S/cm)
1E-3
5000
10000
Time [s]
15000
1E-5
|Sig| [S/cm] before annealing 12WNT
|Sig| [S/cm] after annealing 12WNT
1E-4
1E-5
5000
10000
Time [s]
15000
|Sig| [S/cm] before annealing PE 12% MWNT
|Sig| [S/cm] after annealing PE 12% MWNT
1E-6
Sigma (S/cm)
0
1E-7
1E-8
1E-9
1E-10
1E-6
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Frequency (Hz)
1E-11
-2
-1
0
1
2
3
4
5
6
10 10 10 10 10 10 10 10 10
Frequency (Hz)
Annealing Studies for some Eng samples
Effect of the kind of matrix
|Sig| [S/cm]
-9
1,0x10
PE3732C
1% SWNT
-12
1,0x10
-10
1,0x10
-11
1,0x10
-13
1,0x10
0
5000
10000
Time [s]
0
15000
-5
10
-5
10
-6
10
-7
10
-8
10
-9
10
-10
10
-11
10
-12
10
-13
10
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Frequency (Hz)
Sigma (S/cm)
-4
Sigma (S/cm)
|Sig| [S/cm]
-11
1,0x10
Eng
1% SWNT
5000
10000
Time [s]
15000
10
-6
10
-7
10
-8
10
-9
10
-10
10
-11
10
-12
10
-13
10
-14
10
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Frequency (Hz)
Eng8450 + MWNT
Effect of the strain on the composite dynamic
2E-12
Shear strain 100%
S (S/cm)
1,9E-12
Stop Shear strain
1,8E-12
0.5 % MWNT
1,7E-12
1,6E-12
1 Hz
1,5E-12
0
500
1000
Time [s]
1500
The system is not able to
relax during the shear-strain of 300%
Small relaxation during
shear-strain of 100% 1% MWNT
1,6E-12
1,6E-12
Shear strain 10%
stop strain
Shear strain 100%
S (S/cm)
S (S/cm)
1,2E-12
1E-12
300% strain
1,4E-12
1,4E-12
1,2E-12
1 Hz
1E-12
1 Hz
Stop strain
8E-13
8E-13
0
1000
2000
Time [s]
3000
0
1000
2000
Time [s]
3000
Eng8450 + MWNT
Effect of the strain on the composite dynamic
3% MWNT
1E-6
1E-6
Shear strain 300%
1E-7
Stop shear strain
1E-8
1E-9
100 Hz
0
1500
3000
4500
6000
Time [s]
1E-4
S (S/cm)
1E-5
Original
2 hrs and strain 100%
2 hrs and strain 300
1E-6
1E-7
S (S/cm)
S (S/cm)
Shear strain 100%
1E-7
Stop shear strain
1E-8
1E-9
0
1500 3000 4500 6000 7500
Time [s]
The shear-strain disrupt the conductivity
but only in the beginning, after that the
system relax independent of the strain!!!!
At this condition the kinetic of the relaxation
is modified by the external forces
1E-8
1E-9
-2
-1
0
1
2
3
4
5
6
10 10 10 10 10 10 10 10 10
Freq. [Hz]
The location of this peak is
shear-strain dependent!!!
Eng8450 + MWNT
Effect of the strain on the composite dynamic
6% MWNT
-5
10
-5
10
300% shear strain
Shear strain 100%
-6
Stop Shear strain
-7
10
S (S/cm)
S (S/cm)
-6
10
10
Stop shear strain
-7
10
100 Hz
100 Hz
-8
10
-8
0
1500
3000 4500
Time [s]
6000
10
0
1500
3000
4500
Time [s]
1E-3
S (S/cm)
1E-4
original
strain 100, 3 hrs
strain 300, 3 hrs
1E-5
1E-6
1E-7
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Freq. [Hz]
It is clear that the drop in conductivity
depends of the shear-strain, and again the
system is able to relax independent of the
shear-strain!!!!
Eng8450 + MWNT
Effect of the strain on the composite dynamic
12% MWNT
Shear-strain 5%
1E-4
1E-4
S (S/cm)
S (S/cm)
Shear-strain 10%
Stop Shear-strain
0
1E-4
1000
2000 3000
Time [s]
4000
5000
S (S/cm)
Shear-strain 50%
0
1000
2000 3000
Time [s]
0
1000
2000 3000
Time [s]
4000
5000
4000
5000
Shear-strain 100%
1E-4
Stop Shear-strain
1E-5
1E-5
S (S/cm)
1E-5
Stop Shear-strain
Stop Shear-strain
1E-5
0
1000
2000 3000
Time [s]
4000
5000
Eng8450 + MWNT
Effect of the strain on the composite dynamic
12% MWNT
-2
10
Shear-strain 300%
1E-4
original
6 hrs annealing and shear strain
-3
S (S/cm)
S (S/cm)
10
10 Hz
-4
10
-5
10
Stop Shear-strain
-6
10
0
1000
2000 3000
Time [s]
4000
-1
10
5 strain
10 strain
50 strain
100 strain
300 strain
0
1000 2000 3000 4000 5000
Time [s]
0
10
1E-4
1
0,1
-2
10
5000
1
2
3
10 10 10
Freq. [Hz]
5%
50%
4
10
5
10
6
10
100% 300%
10%
S (S/cm)
Normalized conductivity
1E-5
1E-5
0
5000 10000 15000 20000 25000
Time [s]
Eng8450 + SWNT
Effect of the strain on the composite dynamic
0.05% SWNT
1,28E-011
1E-5
Shear strain 100%
S (S/cm)
1,24E-011
1E-6
1E-7
S (S/cm)
1,20E-011
Stop shear strain
1,16E-011
10 Hz
0
200 400 600 800 1000 1200
Time [s]
1E-8
1E-9
1E-10
1E-11
1,12E-011
1E-12
-2
-1
0
1
2
3
4
5
6
10 10 10 10 10 10 10 10 10
Freq. [Hz]
1.0% SWNT 1E-5
1E-9
1E-6
1E-11
1E-12
1 Hz
0
2000
original
annealing 3 hrs and strain
1E-7
1E-10 Shear strain 100%
S (S/cm)
S (S/cm)
original
Annealing 3 hrs and strain
1E-8
1E-9
1E-10
Stop shear strain
1E-11
4000
1E-12
-2
-1
0
1
2
3
4
5
6
10 10 10 10 10 10 10 10 10
Frequency (Hz)
6000
Time [s]
8000
PE3732C + MWNT
Sample annealed 15 minutes in the press (140 C)
Around 30 minutes between put the sample in the
equipment and to start the experiment
-5
10
-6
10
-7
10
Same behavior than Eng
sample, the changes are related
with the resistor contribution
S (S/cm)
-8
10
-9
10
PE
PE + 0,05% MWNT
PE + 0,1% MWNT
PE + 0,5% MWNT
PE + 1,0% MWNT
PE + 3,0% MWNT
PE + 6,0% MWNT
PE + 12,0% MWNT
-10
10
-11
10
-12
10
-13
10
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
-5
Frequency (Hz)
10
-5
-6
10
-7
10
S' (S/cm)
10
-9
10
-10
10
S'' (S/cm)
PE
PE + 0,05WNT
PE + 0,1% MWNT
PE + 0,5% MWNT
PE + 1,0% MWNT
PE + 3,0% MWNT
PE + 6,0% MWNT
PE + 12,0% MWNT
-8
-11
10
-12
10
-13
10
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Frequency (Hz)
10
-6
10
-7
10
-8
10
-9
10
-10
PE
10
PE + 0,05% MWNT
PE + 0,1% MWNT
-11
10
PE + 0,5% MWNT
PE + 1,0% MWNT
-12
10
PE + 3,0% MWNT
PE + 6,0% MWNT
-13
PE + 12,0% MWNT
10
-14
10
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Frequency (Hz)
PE3732C + SWNT
Sample annealed 15 minutes in the press (140 C)
Around 30 minutes between put the sample in the
-5 equipment and to start the experiment
10
PE
PE + 0,05% SWNT
PE + 0,1% SWNT
PE + 0,5% SWNT
PE + 1,0% SWNT
-6
10
-7
10
S (S/cm)
-8
10
-9
10
-10
10
-11
10
-12
10
-13
10
-9
10
PE
PE + 0,05% SWNT
PE + 0,1% SWNT
PE + 0,5% SWNT
PE + 1,0% SWNT
-10
-1
0
1
3
4
-11
-12
10
-13
-2
-1
0
1
5
-6
10
10
2
S'' (S/cm)
S' (S/cm)
10
-2
6
7
10 10 10 10 10 10 10 10 10 10
Frequency (Hz) 10-5
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Frequency (Hz)
PE
10
PE + 0,05% SWNT
-7
PE + 0,1% SWNT
10
PE + 0,5% SWNT
-8
PE + 1,0% SWNT
10
-9
10
-10
10
-11
10
-12
10
-13
10
-14
10
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Frequency (Hz)
PE3732C + MWNT
Effect of the processing on the composite dynamic
6% MWNT
-5
10
PE original
PE + 6,0% MWNT original
PE + 6,0% MWNT no-aligned
-6
10
-7
10
S (S/cm)
-8
10
-9
10
-10
10
-11
10
-12
10
-13
10
-2
-1
0
1
2
3
4
5
6
7
10 10 10 10 10 10 10 10 10 10
Frequency (Hz)
This plot shows that the decrease in the conductivity is associated with the
morphology of CNTs in the polymeric matrix
PE3732C + MWNT
Effect of the strain on the composite dynamic
0.05% SWNT
1% MWNT
1,2E-12
Shear strain 50%
6,99E-12
|Sig| [S/cm] strain 10 and 100%
|Sig| [S/cm] strain 200
6,96E-12
6,93E-12
Stop Shear strain
S (S/cm)
S (S/cm)
1,1E-12
1E-12
9E-13
10 Hz
6,9E-12
0
1000
2000
Time [s]
1% SWNT
1,2E-12
1,1E-12
1E-12
1000
2000
Time [s]
3000
10% strain
100% strain
200% strain
|Sig| [S/cm] 1WNT 10 and 100% strain
|Sig| [S/cm] strain 200% 1WNT
6% MWNT
-11
4,0x10
8E-13
S(S/cm)
S (S/cm)
0
-11
6,0x10
9E-13
7E-13
6E-13
5E-13
8E-13
3000
-11
2,0x10
0
1000
2000
Time [s]
3000
0
1000
2000
Time [s]
3000
4000
PE3732C + MWNT
6% MWNT
-5
-11
10
6,0x10
|Sig| [S/cm] PE 6WNT ann 1
|Sig| [S/cm] PE 6% MWNT antes ann
|Sig| [S/cm] PE 6WNT after strain
-6
10
-11
4,0x10
Sigma (S/cm)
-7
-11
S(S/cm)
2,0x10
10
-8
10
-9
10
-10
10
-11
10
-12
0
1000 2000 3000 4000 5000 6000
Time [s]
10
-2
-1
0
1
2
3
4
5
6
10 10 10 10 10 10 10 10 10
Frequency (Hz)
PE3732C + MWNT
Effect of the strain on the composite dynamic
12% MWNT
5E-7
Stop shear strain
4E-7
shear strain 50%
S (S/cm)
3E-7
2E-7 shear strain 10%
Stop shear strain
1000 Hz
1E-7
0
1000
2000
Time [s]
3000
4000
PE3732C + MWNT
Effect of the strain on the composite dynamic
12% MWNT
-5
10
-7
1,0x10
|Sig| [S/cm] after ann 12WNT
|Sig| [S/cm] after strain 10% 12WNT
|Sig| [S/cm] after strain 100% 12WNT
10% strain
-6
10
-8
Sigma (S/cm)
S(S/cm)
1,0x10
100% strain
-9
1,0x10
-10
1,0x10
|Sig| [S/cm] strain 10% 12WNT
|Sig| [S/cm] strain 100% 12WNT
-7
10
-8
10
-9
10
-11
1,0x10
0
1000
2000
3000
Time [s]
-7
1,0x10
100% strain, 1 min
-2
-1
0
1
2
3
-8
S(S/cm)
-9
Effect of time
100% strain, 20 min
-10
1,0x10
-11
1,0x10
0
1000 2000 3000 4000 5000 6000
Time [s]
5
6
Strain-induced insulation!!!
1,0x10
1,0x10
4
10 10 10 10 10 10 10 10 10
Frequency (Hz)
PE3732C + SWNT
Effect of the strain on the composite dynamic
0.05% SWNT
Shear strain 50%
6,96E-12
6,93E-12
Stop Shear strain
10 Hz
6,9E-12
0
1000
2000
Time [s]
3000
1E-6
1E-7
original
annealing 1 hr and strain
1E-8
S (S/cm)
S (S/cm)
6,99E-12
1E-9
1E-10
1E-11
1E-12
1E-13
-2
-1
0
1
2
3
4
5
6
10 10 10 10 10 10 10 10 10
Frequency (Hz)