Eng8450 + MWNT Eng8450 + MWNT Sample annealed Sample annealed 15 minutes 15 minutes in the press (140 C) in the press (140 C) Around Around 30 minutes 30 minutes between put the sample in the between put the sample in the equipment and to start the experiment equipment and to start the experiment 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 -13 10 -11 10 -9 10 -7 10 -5 10 -3 Eng E ng + 0,05 M W NT E ng + 0,1 M W NT E ng + 0,5 M W NT E ng + 1,0 M W NT E ng + 3,0 M W NT E ng + 6,0 M W NT E ng + 12,0 M W NT S (S/cm ) F req.[H z] Dielectric region Dielectric region DC region DC region DC DC decrease with decrease with low amount of CNT!!!!! low amount of CNT!!!!!
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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 Dielectric.
Another approach based on the same arguments define the probability for a electron (“hole”) transition from state “a” to “b”, as: ’s are the reorganization energy It is showed that the response of the system to an alternating field is: 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
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Eng8450 + MWNTEng8450 + MWNTSample annealed Sample annealed 15 minutes15 minutes in the press (140 C) in the press (140 C)
Around Around 30 minutes30 minutes between put the sample in the between put the sample in the equipment and to start the experimentequipment and to start the experiment
10-2 10-1 100 101 102 103 104 105 106 10710-13
10-11
10-9
10-7
10-5
10-3
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
)
Freq. [Hz]
Dielectric regionDielectric regionDC regionDC region
DCDC decrease with decrease with low amount of CNT!!!!!low amount of CNT!!!!!
How we can understand this “rare” behavior?How we can understand this “rare” behavior?
)exp(0 E
Symmetric Hopping ModelSymmetric Hopping Model
1 tACDC c
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:
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:
So, it is possible to think that the presence of nanotubes increase theactivation energy for the jump-rate of charge carriers or decrease its diffusion
processes. At higher amount the last is compensated by the percolation process.
dtetvvD
DTkqn
t
B
0
2
)()0()(
)()(
TkB
1
From this model is showed that:
Another approach based on the same arguments define the probabilityAnother approach based on the same arguments define the probabilityfor a electron (“hole”) transition from state “a” to “b”, as:for a electron (“hole”) transition from state “a” to “b”, as:
)exp()2exp()exp(Tk
WRqpB
abababababab
)(4/)()( 2bababaab EEW
’s are the reorganization energy
It is showed that the response of the system to an alternating field is:
)],,([12
)( 222
baabB
s qqRPRTkNe
ab
baab qq 2ln
The major contribution to the conductivity comes from polymerThe major contribution to the conductivity comes from polymerpair elements satisfying the last assumptionpair elements satisfying the last assumption!!! !!!
The response at The response at very low frequenciesvery low frequencies involve pair states with very low involve pair states with very low transition rates. As a consequence the rare transition rates. As a consequence the rare transitions from pair transitions from pair
states into new states become more significantstates into new states become more significant..
Again, the presence of nanotubes could Again, the presence of nanotubes could change the dynamic change the dynamic of charge carriersof charge carriers, decreasing the conductivity, decreasing the conductivity
Another theory is based on the equivalent circuit concept:Another theory is based on the equivalent circuit concept:
At high frequencies the conductive regions are important and at low frequencies the isolated areas limit the charge carrier motion.
Any solid with spatially varying free Any solid with spatially varying free charge conductivity and uniformcharge conductivity and uniform charge dielectric constantcharge dielectric constant
)('')(')( iUnder AC conditions, it is defined:Under AC conditions, it is defined:
Resistor contribution
Conductancecontribution
10-2 10-1 100 101 102 103 104 105 106 107
10-11
10-9
10-7
10-5
10-3
10-1
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/c
m)
Freq. [Hz]
Eng8450 + MWNTEng8450 + MWNT
10-2 10-1 100 101 102 103 104 105 106 10710-14
10-12
10-10
10-8
10-6
10-4
10-2 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
S''
(S/c
m)
Freq. [Hz]
’ is related with the current through the resistors
’’ is related with the current through the capacitors
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
The presence of CNT does not affectthe conductance of the sample below
the percolation point
Eng8450 + SWNTEng8450 + SWNT
10-2 10-1 100 101 102 103 104 105 106 10710-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
Eng Eng + 0,05 SWNT Eng + 0,1 SWNT Eng + 1,0 SWNT
S''
(S/c
m)
Freq. [Hz]
10-2 10-1 100 101 102 103 104 105 106 10710-13
10-12
10-11
10-10
10-9
10-8
10-7
Eng Eng + 0,05 SWNT Eng + 0,1 SWNT Eng + 1,0 SWWT
S' (
S/c
m)
Freq. [Hz]
10-2 10-1 100 101 102 103 104 105 106 10710-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5 Eng Eng + 0,05 SWNT Eng + 0,1 SWNT Eng + 1,0 SWWT
S (S
/cm
)
Freq. [Hz]
Same behavior!!!Same behavior!!!
CNTs affect the resistor contribution of the composite, andat low frequencies changes in the dynamic of the polymers due to CNT decrease their conductivity
The effect of the dynamic of the polymer on the conductivity The effect of the dynamic of the polymer on the conductivity is confirmed by the is confirmed by the relaxation processrelaxation process observed in some composites observed in some composites
10-2 10-1 100 101 102 103 104 105 1061E-12
1E-11
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5
S (S
/cm
)
Freq. [Hz]
10-2 10-1 100 101 102 103 104 105 1061E-12
1E-11
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5
S (S
/cm
)
Freq. [Hz]
Eng + 1.0 SWNTEng + 1.0 SWNT
Eng + 0.05 SWNTEng + 0.05 SWNT
3 hrs annealing3 hrs annealing 140 C140 C
3 hrs annealing3 hrs annealing 140 C140 C
10-2 10-1 100 101 102 103 104 105 106 1071E-14
1E-12
1E-10
1E-8
1E-6
1E-4 Eng + 1,0 SWNT original Eng + 1,0 SWNT ann 3 hrs
S''
(S/c
m)
Freq. [Hz]
10-2 10-1 100 101 102 103 104 105 106 1071E-13
1E-11
1E-9
1E-7 Eng + 1,0 SWNT original Eng + 1,0 SWNT ann 3 hrs
S' (
S/c
m)
Freq. [Hz]
10-2 10-1 100 101 102 103 104 105 106 1071E-11
1E-10
1E-9
1E-8
1E-7
1E-6 120 C 140 C 190 C
S (S
/cm
)
Frequency (Hz)
Eng8450Eng8450Effect of the temperatureEffect of the temperature
Annealing Studies for some Eng/MWNT samplesAnnealing Studies for some Eng/MWNT samples
10-2 10-1 100 101 102 103 104 105 10610-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5 |Sig| [S/cm] 1% MWNT before annealing |Sig| [S/cm] 1% MWNT after annealing
Sig
ma
(S/c
m)
Frequency (Hz)
1% MWNT1% MWNT
12% MWNT12% MWNT
10-2 10-1 100 101 102 103 104 105 106 1071E-6
1E-5
1E-4
1E-3 |Sig| [S/cm] before annealing 12WNT |Sig| [S/cm] after annealing 12WNT
Sig
ma
(S/c
m)
Frequency (Hz)
1Hz
0 5000 10000 150001,0x10-6
1,0x10-5
1,0x10-4
|Sig
| [S
/cm
]
Time [s]
Effect of the amount of fillerEffect of the amount of filler
0 5000 10000 150001,0x10-12
1,0x10-11
1,0x10-10
|Sig
| [S
/cm
]
Time [s]
Pure EngPure Eng
Annealing Studies for some Eng samplesAnnealing Studies for some Eng samplesEffect of the kind of fillerEffect of the kind of filler
Eng8450 + SWNTEng8450 + SWNTEffect of the strain on the composite dynamicEffect of the strain on the composite dynamic
0.05% SWNT0.05% SWNT
0 200 400 600 800 1000 1200
1,12E-011
1,16E-011
1,20E-011
1,24E-011
1,28E-011
S (S
/cm
)
Time [s]
Shear strain 100%
Stop shear strain
10 Hz
10-2 10-1 100 101 102 103 104 105 1061E-12
1E-11
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5 original Annealing 3 hrs and strain
S (S
/cm
)
Freq. [Hz]
1.0% SWNT1.0% SWNT
0 2000 4000 6000 80001E-12
1E-11
1E-10
1E-9
S (S
/cm
)
Time [s]
Shear strain 100%
Stop shear strain
1 Hz
10-2 10-1 100 101 102 103 104 105 1061E-12
1E-11
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5
original annealing 3 hrs and strain
S (S
/cm
)
Frequency (Hz)
PE3732C + MWNTPE3732C + MWNTSample annealed Sample annealed 15 minutes15 minutes in the press (140 C) in the press (140 C)
Around Around 30 minutes30 minutes between put the sample in the between put the sample in the equipment and to start the experimentequipment and to start the experiment
10-2 10-1 100 101 102 103 104 105 106 10710-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
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
S (S
/cm
)
Frequency (Hz)
10-2 10-1 100 101 102 103 104 105 106 10710-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
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
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
S''
(S/c
m)
Frequency (Hz)
Same behavior than Eng Same behavior than Eng sample, the changes are related sample, the changes are related
with the with the resistor contributionresistor contribution
PE3732C + SWNTPE3732C + SWNTSample annealed Sample annealed 15 minutes15 minutes in the press (140 C) in the press (140 C)
Around Around 30 minutes30 minutes between put the sample in the between put the sample in the equipment and to start the experimentequipment and to start the experiment
10-2 10-1 100 101 102 103 104 105 106 10710-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
PE PE + 0,05% SWNT PE + 0,1% SWNT PE + 0,5% SWNT PE + 1,0% SWNT
S (S
/cm
)
Frequency (Hz)
10-2 10-1 100 101 102 103 104 105 106 10710-13
10-12
10-11
10-10
10-9 PE PE + 0,05% SWNT PE + 0,1% SWNT PE + 0,5% SWNT PE + 1,0% SWNT
PE PE + 0,05% SWNT PE + 0,1% SWNT PE + 0,5% SWNT PE + 1,0% SWNT
S''
(S/c
m)
Frequency (Hz)
PE3732C + MWNTPE3732C + MWNTEffect of the processing on the composite dynamicEffect of the processing on the composite dynamic
6% MWNT6% MWNT
10-2 10-1 100 101 102 103 104 105 106 10710-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
PE original PE + 6,0% MWNT original PE + 6,0% MWNT no-aligned
S (S
/cm
)
Frequency (Hz)
This plot shows that the decrease in the conductivity is associated with the This plot shows that the decrease in the conductivity is associated with the morphology of CNTsmorphology of CNTs in the polymeric matrix in the polymeric matrix
PE3732C + MWNTPE3732C + MWNTEffect of the strain on the composite dynamicEffect of the strain on the composite dynamic