Composites: Part A 47 (2013) 63–71

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Composites: Part A

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Compressive relaxation of the stress and resistance for carbon nanotube filledsilicone rubber composite

Luheng Wang ⇑, Yanyan HanCollege of Information Science and Engineering, Northeastern University, Shenyang 110819, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 29 September 2012Received in revised form 4 November 2012Accepted 25 November 2012Available online 14 December 2012

Keywords:A. Polymer–matrix composites (PMCs)B. Electrical properties

1359-835X/$ - see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.compositesa.2012.11.018

⇑ Corresponding author. Tel./fax: +86 024 8368453E-mail address: wangluheng@ise.neu.edu.cn (L. W

The changes in the stress and the electrical resistance of carbon nanotube filled silicone rubber compositeduring compressive stress relaxation are researched quantitatively. The changing tendency of the electri-cal resistance is similar to that of the stress. The experimental data of the electrical resistance and thestress over time can be fitted by the spring–dashpot model based on the viscoelastic theory. Both the finalrelative resistance and the final relative stress increase with the increase of the loading speed anddecrease with the increase of the carbon nanotube concentration. Both the resistance relaxation timeand the stress relaxation time decrease with the increase of the loading speed. The similarity betweenthe compressive resistance relaxation and the compressive stress relaxation is explained by analyzingthe correlation between the changes in the conductive network and the disorientation of the polymermacromolecules.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Conductive polymer composite, which is a viscoelastic material,can be used as a shock absorber film between the curve surfaces ofmodern industry equipment. This kind of composite possessespiezoresistivity [1–9]. Therefore, it can also be used as the sensitivematerial of piezoresistive sensor [10–19] to monitor the interlam-inar stress. In many engineering applications, the shock absorberfilm is in the status of compressive stress relaxation. Therefore, itis necessary to research the changes in the electrical resistance ofthe composite during the compressive stress relaxation.

In 1970s, Voet et al. [20] researched the changes in the stressand electrical resistivity of carbon-filled vulcanizates during stressrelaxation at minute shear strains. Sircar et al. [21] studied thevariations in the stress and electrical resistivity of carbon-filledvulcanizates at moderate and high extensions. They defined thechange in the resistance during stress relaxation as ‘‘resistancerelaxation’’. In 1990s, Kost et al. studied the electrical resistancerelaxation of carbon black filled silicone rubber composite intension tests [22]. They all found that the changing trend of theresistance is similar to that of the stress under the constant strain.However, the research aforementioned is not for the composite incompression.

After 2000, the researchers in Zhejiang University researchedthe resistance relaxation of high-density polyethylene/short car-bon fiber conductive composite during compressive stress relaxa-

All rights reserved.

5.ang).

tion. They carried over the term ‘‘resistance relaxation’’ todescribe the changes in the resistance over time during compres-sive stress relaxation [23]. The researchers in Tsinghua Universitystudied the attenuation of the resistance of carbon nanotube filledsilicone rubber composite during compressive stress relaxation. Todistinguish the resistance relaxation in tension and that in com-pression, they defined the resistance relaxation during the com-pressive stress relaxation as ‘‘compressive stress relaxation’’[7,24]. They also found the similarity between the compressiveresistance relaxation and the compressive stress relaxation. How-ever, the researches aforementioned are needed to be studied fur-ther. For example, in reference [7,24], only one conductive phasecontent and one loading speed were researched. The conductivephase content and the loading speed are two very important influ-encing factors on the properties and applications of conductivepolymer composite. Therefore, the effects of these two influencingfactors on the compressive stress relaxation and the compressiveresistance relaxation are needed to be researched more deeplyand comprehensively.

Carbon nanotube, which was reported in 1990s [25–27], hasmany excellent properties. Some researchers’ works made greatprogress in studying the important properties and applications ofcarbon nanotube [28–38]. In this paper, we used the carbonnanotube as the conductive phase of the conductive polymercomposite to fabricate the piezoresistive material. The term‘‘compressive resistance relaxation’’ was also used to describe theattenuation of the resistance of carbon nanotube filled silicone rub-ber composite over time during the compressive stress relaxation.The experimental data of the compressive stress relaxation and

64 L. Wang, Y. Han / Composites: Part A 47 (2013) 63–71

the compressive resistance relaxation were fitted based on the vis-coelastic theory. Comparing with the previous works [7,24], thefollowing developments were made. Carbon black was replacedby carbon nanotube which has large aspect ratio to be used asthe conductive phase. Furthermore, the effects of the loading speedand the carbon nanotube concentration on the key parameters ofthe fitted functions for the compressive stress relaxation and thecompressive resistance relaxation were researched quantitatively.The phenomena were explained by analyzing the changes in thecarbon nanotube network and the disorientation of the polymermacromolecules during the compressive stress relaxation.

Fig. 2. Experiment set-up for measuring the compressive resistance relaxation ofthe composite.

2. Experimental details

Multi-walled carbon nanotube (Shenzhen Nanotech Port Co.,Ltd., China) were used as a conductive phase. They were madevia chemical vapor deposition, with a purity of >95%. The diameteris 50 nm. The length is 15 lm. The resistivity is less than 1 X cm.Silicone rubber (Shenyang Silicone Plant, China) was used as aninsulating phase. The dielectric constant is 3.0. The dielectricstrength is 15 kV/mm. The hardness is 35 Shore. This kind of sili-cone rubber can be used over a long period time under the temper-ature ranging from �50 �C to 200 �C. Carbon nanotubes weredispersed into silicone rubber by using solution mixing method.Hexane was used as solvent to mix carbon nanotubes into the sil-icone rubber. Mechanical stirring along with ultrasonic vibrationwas used for better filler dispersion. After 3 h of vigorous mixing,the solvent was evaporated. The viscous mixture was molded intorectangle sheets (10 � 10 � 2 mm) for 60 h. Based on our experi-ments results, the basis for the selection of the conductive phasecontents are stated as follows. On the one hand, the high conduc-tive phase content leads to the deterioration of some mechanicalproperties of the composite, e.g. the decrease of flexibility or in-crease of friability of the composite. This statement can be not onlysupported by our previous experiment results, but also verified bythe conclusions in the previous references [39,40]. On the otherhand, the low conductive phase content, which leads to a largeresistance, brings a difficulty to develop the signal processing cir-cuit of piezoresistive sensor. As for the samples we fabricated inthis paper, when the mass ratio of carbon nanotube to silicone rub-ber ranges 0.04–0.16, the composite not only possesses goodmechanical properties (e.g. the sample is flexible and does notcrush during the compression tests), but also has the appropriatevalue of the resistance which simplified the development of thesignal processing circuit. Therefore, the range of the conductive

Fig. 1. SEM micrograph of the fracture of the composite.

phase content aforementioned was selected in this paper. Fig. 1is the SEM (scanning electron microscope) micrograph of thefracture of the composite (the mass ratio is 0.12), showing a gooddispersion of carbon nanotubes in the matrix. The SEMs for thecomposites with other mass ratios also verified this point. Further-more, after the compression tests, there are no cracking and break-ing in the samples we fabricated. The works aforementionedindicate that the composite we fabricated is good for furthertesting.

The schematic of the experiment set-up for measuring thecompressive stress relaxation and the compressive resistancerelaxation of the sample is shown in Fig. 2. The tests were doneat room temperature. The sample was placed between the fixeddisc and the movable head of the material testing machine. Themovable head can be moved by the signal controlled by the com-puter. The sample is compressed to a stress and then the strain iskept constant. The loading speeds are 0.1 mm/min, 0.5 mm/min,1.0 mm/min and 5.0 mm/min. The compression is realized by themovement of the movable head. The changes in the stress andthe electrical resistance of the composite during the compressivestress relaxation were collected by the data collecting part of thematerial testing machine and a digital multimeter (Agilent34410A), respectively. The data for the electrical resistance andthe stress were recorded in the computer. As the background ofthis research is to develop a stress sensor, the data for the stressis far more important than the data for the strain. Therefore, theinitial stress, instead of the initial strain, is used to indicate eachstage of the compressive stress relaxation. The maximum valueof the initial stress in this experiment is 0.9 MPa. For the conve-nience of discussion, ‘‘v’’ was used to represent the loading speed,and ‘‘C’’ was used to represent the mass ratio of carbon nanotube tosilicone rubber.

3. Results and discussion

The electrical resistances under the zero stress for the compos-ites with different carbon nanotube contents are shown in Fig. 3.The results indicate that there is an occurrence of percolation inthe composite. The conclusions on the compressive stress relaxa-tion and compressive resistance relaxation under other initialstresses are the same as those under 0.3 MPa. Therefore, to makethe paper more succinct, we only listed the analyzing results ofthe experimental data under 0.3 MPa in this paper. The changesin the electrical resistance during the compressive stress relaxation

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160

2

4

6

8

10

12

14

16

Mass ratio of carbon nanotube to silicone rubber

Elec

trica

l res

ista

nce

unde

r the

zer

o st

ress

0) Ω

)(lg

(R

Fig. 3. Relation between the carbon nanotube content and the resistance under thezero stress.

L. Wang, Y. Han / Composites: Part A 47 (2013) 63–71 65

of the composites with different carbon nanotube contents areshown in Fig. 4. We can see that the electrical resistance of thecomposite and the attenuation extent of the resistance decreasewith the time during the compressive stress relaxation. To developa further comparison, the relative stress was defined as the ratio ofthe stress at the moment t to the initial stress during the compres-sive stress relaxation, and the relative resistance was defined as theratio of the resistance at the moment t to the initial resistance dur-ing the compressive resistance relaxation. As shown in Fig. 5, thestress and the extent of the stress attenuation decrease with thetime during the compressive stress relaxation. As shown in Fig. 6,

0 500 1000 15000

10

20

30

40

50

Time (s)

Res

ista

nce

(MΩ

)

(1) C=0.04

Res

ista

nce

(k)

0 500 1000 15000

5

10

15

20

25

30

Time (s)

Res

ista

nce

(kΩ

)

(3) C=0.12

v=0.1mm/min

v=0.5mm/min

v=1.0mm/min

v=5.0mm/min

v=0.1mm/min

v=0.5mm/min

v=1.0mm/min

v=5.0mm/min

Fig. 4. Changes in the resistance during the compressive stress relaxation of the composireferred to the web version of this article.)

the changing tendency of the resistance is similar to that of thestress during the compressive stress relaxation. We also researchedpreliminarily the compressive stress relaxation of the compositewith other kinds of carbon nanotube (The diameter and the lengthof the carbon nanotubes are 30 nm and 15 lm), the change instress during the compressive stress relaxation is similar.

The similarity between the compressive resistance relaxationand compressive stress relaxation aforementioned is the macro-scopic behavior of changes in the inner-structure of the compositeduring the compressive stress relaxation. Carbon nanotubes andsilicone rubber macromolecules constitute a three dimensionalconductive network in the matrix. The changes in the carbon nano-tubes and the changes in the silicone rubber macromolecules con-cur during the compressive stress relaxation. There are interactionsbetween silicone rubber macromolecules and carbon nanotubesduring compressive stress relaxation as well as compressive resis-tance relaxation. Along with the disorientation of the silicone rub-ber macromolecules, the carbon nanotubes also change during thecompressive stress relaxation. The attenuation in the stress duringthe compressive stress relaxation (Fig. 5) is related to the changesin the three dimensional network composed of silicone rubbermacromolecules and carbon nanotubes. The attenuation in theelectrical resistance (Fig. 6) is related to the changes in the conduc-tive network during the compressive stress relaxation.

As shown in Fig. 7, the polymer segments curl gradually duringthe compressive stress relaxation, leading to the decrease of theaverage end-to-end distance and the increases of the conforma-tional entropy with the time. Combined with the disorientationof the polymer segments aforementioned, the change in the con-ductive network occurs during the compressive stress relaxation.Based on the previous research [41–43], the carbon nanotubesinside may bend, have a large curvature, and debonding from therubber matrix when the stress exceeds the interfacial bond

0 500 1000 15000

50

100

150

200

Time (s)

Ω

(2) C=0.08

0 500 1000 15000

1

2

3

4

5

6

Time (s)

Res

ista

nce

(kΩ

)

(4) C=0.16

v=0.1mm/min

v=0.5mm/min

v=1.0mm/min

v=5.0mm/min

v=0.1mm/min

v=0.5mm/min

v=1.0mm/min

v=5.0mm/min

tes. (For interpretation of the references to colour in this figure legend, the reader is

0 500 1000 15000.2

0.4

0.6

0.8

1

Time (s)

Rel

ativ

e st

ress

(1) C=0.04

0 500 1000 1500 20000.2

0.4

0.6

0.8

1

Time (s)

Rel

ativ

e st

ress

(2) C=0.08

DataFitted curve

0 500 1000 1500 2000

2000

0.4

0.6

0.8

1

Time (s)

Rel

ativ

e st

ress

(3) C=0.12

0 500 1000 1500 20000.4

0.6

0.8

1

Time (s)

Rel

ativ

e st

ress

(4) C=0.16

v=0.1mm/min

v=0.5mm/min v=1.0mm/min

v=5.0mm/min

v=0.1mm/min

v=0.5mm/min v=1.0mm/min

v=5.0mm/min

v=0.1mm/min

v=0.5mm/min v=1.0mm/min

v=5.0mm/min

v=0.1mm/min v=0.5mm/min

v=1.0mm/min

v=5.0mm/min

Fig. 5. Relative stress over time and the fitting curves. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of thisarticle.)

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

Time (s)

Rel

ativ

e re

sist

ance

(1) C=0.04

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

Time (s)

Rel

ativ

e re

sist

ance

(2) C=0.08

DataFitted curve

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

Time (s)

Rel

ativ

e re

sist

ance

(3) C=0.12

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

Time (s)

Rel

ativ

e re

sist

ance

(4) C=0.16

v=0.1mm/min

v=0.5mm/min

v=1.0mm/min

v=5.0mm/min

v=0.1mm/min

v=0.5mm/min

v=1.0mm/min

v=5.0mm/min

v=0.1mm/min

v=0.5mm/min

v=1.0mm/min

v=5.0mm/min

v=0.1mm/min

v=0.5mm/min

v=1.0mm/min

v=5.0mm/min

Fig. 6. Relative resistance over time and the fitting curves. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of thisarticle.)

66 L. Wang, Y. Han / Composites: Part A 47 (2013) 63–71

(1) At the moment zero

(2) At the moment t during the compressive stress relaxation

d(0)

d(t)

Silicone rubber macromolecule

Carbon nanotube

Conductive phase Tunneling film

Conductive phase Tunneling film

Fig. 7. Schematic view of the network composed of the carbon nanotubes and polymer segments.

L. Wang, Y. Han / Composites: Part A 47 (2013) 63–71 67

strength during the compression. Moreover, the carbon nanotube,as a whole unit, moves under the compression. If the gap betweenthe adjacent carbon nanotubes is small enough, the tunneling ef-fect occurs. The insulating film where the tunneling effect occursis defined as a ‘‘tunneling film’’, which contributes to the total con-ductivity of the composite. The movements of carbon nanotubesunder the compression aforementioned can be equivalent to thechanges in the tunneling films. Tunneling films and carbon nano-tubes constitute the conductive paths in the matrix. As the resistiv-ity of carbon nanotube is far less than that of the composite, theresistivity of the composite is mainly decided by the resistivity ofthe tunneling film between the adjacent carbon nanotubes. Theconductive path, which connects the two electrodes, is defined asa contributive conductive path. A tunneling film, which is locatedin the contributive conductive path, is defined as a contributivetunneling film. The changes in the electrical resistances of all thecontributive tunneling films contribute to the total changes inthe resistance of the composite under the compression. Accordingto the theory of tunneling effect [44–47], the total electrical resis-tance of the composite R can be calculated by:

R ¼XN

j¼1

XM

i¼1

2h2Dði; jÞ exp 4pDði;jÞffiffiffiffiffiffiffiffi2mup

h

� �

3e2Sði; jÞffiffiffiffiffiffiffiffiffiffiffi2mu

p0BB@

1CCA

2664

3775�18>>><

>>>:

9>>>=>>>;

�1

ð1Þ

where S(i, j) and D(i, j) represent the effective cross sectional areaand the thickness of the ith contributive tunneling film in the jthcontributive conductive path, respectively, u the height of potentialbarrier, e electron charge, m electron mass, h Plank’s constant.

According to the Eq. (1), the decrease (increase) of the effectivecross-section area of the tunneling film contributes to the increases(decreases) of the resistance. The decrease (increase) of the thick-ness of contributive tunneling film leads to the decrease (increase)of the resistance. The increase (decrease) of the number of contrib-utive tunneling films in each column contributes to the increase(decrease) of the resistance. The decrease (increase) of the numberof the conductive paths in the composite contributes to the in-crease (decrease) of the resistance. The destruction (formation) ofthe contributive conductive paths leads to the decrease (increase)of the number of them, which leads to the increase (decrease) ofthe total resistance of the composite. As discussed aforementioned,the changes in the conductive network lead to the two oppositechanging trends in the electrical resistance of the composite. Theinfluence factors which lead to the increasing trend are definedas ‘‘positive factors’’, whereas the influence factors which lead tothe decreasing trend are defined as ‘‘negative factors’’. The resultsin Fig. 4 indicate that the effect of the ‘‘negative factors’’ isdominant, and the advantages of the ‘‘negative factors’’ over the‘‘positive factors’’ decrease with the time during the compressivestress relaxation.

Fig. 8. Spring and dashpot model of conductive polymer composite.

68 L. Wang, Y. Han / Composites: Part A 47 (2013) 63–71

The changes in the electrical resistance and the stress duringthe compressive stress relaxation can be analyzed quantitativelyas follows. According to the viscoelastic theory, the stressrelaxation of the viscoelastic material can be described by themodel composed of the springs and dashpots (Fig. 8 (1)).Kri(i = 1, 2, . . ., m) represents the ith spring and gri represents theith dashpot. The stress does not decline to zero because the sampleis a crosslink composite. Therefore, we add a paralleled springKrM in the model. The fitted function for the compressive stressrelaxation can be given by:

rðtÞ ¼ rð1Þ þXm

j¼1

½rj � expð�t=srjÞ� ð2Þ

where r(t) and r(1) represent the relative stress at the moment tand 1, srj is the jth exponential, rj is the jth correspondingcoefficient.

As the changing tendency of the resistance is similar to that ofthe stress, the compressive resistance relaxation of the compositecan be described by a model (Fig. 8 (2)), which is similar to the mod-el (Fig. 8 (1)) for the compressive stress relaxation. Kri(i = 1, 2, ..., m)represents the ith spring and gri represents the ith dashpot. The

mathematical models of the compressive resistance relaxationand the compressive stress relaxation should also be similar. There-fore, we use a function, the mode of which is similar to the Eq. (1), tofit the data of the electrical resistance as follows:

rðtÞ ¼ rð1Þ þXm

i¼1

½Ri � expð�t=sriÞ� ð3Þ

where r(t) and r(1) represent the relative resistance at the momentt and 1, sri is the ith exponential, Ri is the ith correspondingcoefficient.

The fitted curves of the compressive resistance relaxation andthe compressive stress relaxation (m = 3) are shown in Figs. 5and 6 (the solid curves). The exponentials in the Eq. (2), which rep-resent the stress relaxation times, reflect the attenuation speeds ofthe stress. They are related to the sizes of the polymer segments.The exponentials in the Eq. (3), which represent the resistancerelaxation times, reflect the attenuation speeds of the resistance.The change in the conductive network is related to the movementof the polymer segments. Each resistance relaxation time corre-sponds to a movement speed of the equivalent movement elementcomposed of the polymer segments.

1

2

3

0

0.5

1

1.5

2

2.5

v (mm/min)i

lg( τ σ

i) (s

)

1

2

3

0

1

2

3

v (mm/min)i

lg( τ

ri) (s

)

0.10.5

1.05.0

0.10.5

1.05.0

(1) Stress relaxation time

(2) Resistance relaxation time

Fig. 9. Effects of the loading speeds on the stress relaxation times and theresistance relaxation times.

0

0.2

0.4

0.6

0.8

1

σ( ∞

)

(1) Final relative stress

0.04 0.08

0.12 0.16

0.1 0.5

1.0 5.0

Carbon nanotube content

v (mm/min)

0

0.1

0.2

0.3

0.4

r (∞

)

(2) Final relative resistance

0.04 0.08

0.12 0.16

0.1 0.5

1.0 5.0

Carbon nanotube content v (mm/min)

Fig. 10. Effects of the loading speeds and the conductive phase contents on the finalrelative stresses and final relative resistances.

L. Wang, Y. Han / Composites: Part A 47 (2013) 63–71 69

The effects of the loading speed on the stress relaxation timesand resistance relaxation times of the composites with differentmass ratios are the same as that of the composite with the massratio of 0.04. Therefore, to make the paper more succinct, we onlylisted the results for the composite with the mass ratio of 0.04 inFig. 9. As shown in Fig. 9 (1), the stress relaxation times are in threeorders of magnitudes. All of them decrease with the increase of theloading speed. The results indicate that the polymer segments canbe equivalent to three kinds of the movement elements. The disori-entation of the polymer segments under the higher loading speedis faster than that under the lower loading speed. As shown inFig. 9 (2), the resistance relaxation times are also in three ordersof magnitudes and decrease with the increase of the loading speed.The results indicate that they correspond to the three kinds of theequivalent movement elements. The changes in the resistance andthe stress are related with each other. The higher the loadingspeed, the faster the attenuation speeds of the stress and theresistance.

Each coefficient in the Eq. (2) represents the total attenuationvalue of the stress for each movement element. They contributeto the final relative stress (the stress at the infinite moment). Asshown in Fig. 10 (1), the final relative stresses decrease with the in-crease of the loading speed and increase with the increase of thecarbon nanotube content. Each coefficient in the Eq. (3) representsthe total attenuation value of the resistance for each movement

element. They contribute to the final relative resistance (the resis-tance at the infinite moment). As shown in Fig. 10 (2), the final rel-ative resistances decrease with the increase of the loading speedand increase with the increase of the carbon nanotube content.These results regarding the final relative stress and the final rela-tive resistance aforementioned indicate that the total disorienta-tion extent of the macromolecule increases with the increase ofthe loading speed and decreases with the increase of the conduc-tive phase content. Through comparison between the final relativestress and the final relative resistance, we can see that the totalattenuation of relative stress is less than that of the relative resis-tance during the compressive stress relaxation.

As discussed aforementioned, the effects of the conductivephase content and the loading speed on the resistance relaxationtimes and the final relative resistance of the compressive resis-tance relaxation are similar to those on the stress relaxation timesand the final relative stress of the compressive stress relaxation.These results verify further the fact that the disorientation of themacromolecule is directly related with the changes in the conduc-tive network during the compressive stress relaxation.

4. Conclusions

The compressive resistance relaxation of carbon nanotube filledsilicone rubber composite can be fitted by a function, the mode ofwhich is similar to the spring–dashpot model for the compressivestress relaxation. The effects of the loading speed and the carbonnanotube content on the key parameters of the fitted function forthe compressive resistance relaxation are the same as those forthe compressive stress relaxation. The final relative resistance and

70 L. Wang, Y. Han / Composites: Part A 47 (2013) 63–71

the final relative stress decreases with the increase of the loadingspeed and increases with the increase of the carbon nanotube con-centration. The resistance relaxation times and the stress relaxationtimes decrease with the increase of the loading speed. The similar-ity between the compressive stress relaxation and the compressiveresistance relaxation is directly related to the correlation betweenthe disorientation of the macromolecules and the changes in theconductive network during the compressive stress relaxation.

The diameter and the length of the carbon nanotubes, whichwere used as the conductive phase of the composite in this paper,are 50 nm and 15 lm, respectively. We also investigated thecarbon nanotube filled silicone rubber composite with differentconductive phase contents under different loading speeds (Thediameter and the length of the carbon nanotubes are 30 nm and15 lm). The results indicate that the conclusions are the same asthose in this paper. Furthermore, we also studied the carbon blackfilled silicone rubber composite with different conductive phasecontents under different loading speeds (The specific surface areais 320 m2/g). The results indicate preliminarily that the conclusionsof carbon-black-filled-system are the same as those of carbon-nanotube-filled-system drawn in this paper. In the future, we willcontinue to use other kinds of carbon nanotubes (with differentdiameters and lengths) or carbon blacks (with different specificsurface areas) as the conductive phase of the composites. The com-pressive resistance relaxation of them will be further studied toverify that the conclusions in this paper can be applied to moreconventional conductive polymer composite.

Acknowledgments

This work was supported by ‘‘the Specialized Research Fund forthe Doctoral Program of Higher Education’’ (20100042120037),‘‘the Fundamental Research Funds for the Central Universities’’(N110404028, N090404002), ‘‘the Shenyang’s Science and Tech-nology Plan Project’’ (F12-277-1-16, F10-205-1-63).

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