Positive temperature coefficient effect of LMWPE–UHMWPE blends filled with short carbon fibers

Carbon 42 (2004) 1699–1706 www.elsevier.com/locate/carbon

Positive temperature coefficient effect of LMWPE–UHMWPE blends filled with short carbon fibers Ying Xi, Hisako Ishikawa, Yuezhen Bin, Masaru Matsuo

*

Department of Textile and Apparel Science, Faculty of Human Life and Environment, Nara Women’s University, Nara 630-8263, Japan Received 2 December 2003; accepted 27 February 2004 Available online 8 April 2004

Abstract Composites of ultra-high molecular weight polyethylene (UHMWPE), low molecular weight polyethylene (LMWPE) and carbon fibers (CF) were prepared by gelation/crystallization from solution. The maximum intensity of PTC (positive temperature coefficient), the magnitude being ca. 9 orders, was found for a LMWPE/UHMWPE composition of 9/1 containing 23.5 vol% CF, i.e. a much higher amount of the filler than in the percolation threshold (12–15 vol%). The elimination of the NTC (negative temperature coefficient) effect and a good reproducibility were achieved by using UHMWPE as one of the composite components because of its very high viscosity.
2004 Elsevier Ltd. All rights reserved. Keywords: A. Carbon fibers, Resins; B. Mixing; D. Electrical properties

1. Introduction Most of polymers are typical insulators. To give conductive properties to polymers, carbon black (CB) [1–9], carbon fibers (CF) [10,11] and some metal powders [12] have been utilized as conductive filler. Among these electrically conducting composites, some composites show a sharp resistivity increase when the temperature close with the polymer melting point. This phenomenon is so-called as positive temperature coefficient (PTC) effect. In order to explain PTC mechanism, several theories have been proposed. Some of them are percolation phenomenon, conduction pathway theory, thermal expansion theory, tunnel effect theory and electric field emission theory [1,2,13–16], etc. Nevertheless, these theories still remain some problems to explain experimental results clearly. The remarkable PTC effect was mainly observed for conductor-filled semicrystalline polymer. Because of a sharp increase in electrical resistivity, the PTC materials have a wide range of industrial applications. They can be used as self-regulating heaters, current limiters, over current protectors and resettable fuses. However, there are some application limits because of the several *

Corresponding author. Tel./fax: +81-742-20-3462. E-mail address: [email protected] (M. Matsuo).

0008-6223/$ - see front matter
2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2004.02.027

drawbacks of thermoplastic conductive composites. They are (1) the lack of reproducibility of electrical conductivity due to irregular structure changes in heating/cooling cycles; (2) the decrease of electrical resistivity at the temperature beyond the melting point, which is so-called as NTC (negative temperature coefficient) effect; and (3) the slow response rate of PTC effect associated with an adverse effect on desired switching properties. In previous papers [7–9], the significant PTC effect was reported for LMWPE–UHMWPE–CB blends prepared by the gelation/crystallization from dilute solution, in which LMWPE/UHMWPE composition was 9/ 1 and CB content within the blend was 6.5 vol%. The PTC effect of the specimen prepared by the gelation/ crystallization was much better than that of the specimen prepared by kneading method in molten state [3–6,17–26]. Even so, the drastic increase in electric resistivity at a critical temperature is not sufficient enough to be used as the switching function. To pursue the further improvement, a lot of efforts have been done by trial and error and then the MGII carbon fibers were found to be better used as the conductive filler than carbon black particles. The materials provide the rapid increase and rapid decrease in electrical resistivity at a critical temperature under heating and cooling processes and they ensure the good reproducibility.

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2. Experimental The sample were prepared by using UHMWPE (Hercules 19000/90189) with an average viscosity molecular weight of 6 · 106 , LMWPE (Sumikathene G201) with an average viscosity molecular weight of 4 · 104 , and carbon fibers (MGII from Toho Tenax Co. Ltd.). The scanning electron microscopy photograph of the carbon fibers used in this experiment and their length distribution are shown at Figs. 1 and 2 respectively. A decalin (mixture of cis-, trans-isomer bought from Wako Pure Chemical Industries Ltd.) solution containing UHMWPE, LMWPE and CF particles was prepared by heating the well-blended polymer/solvent mixture at 150 C for 30 min under nitrogen. According to previous research [7–9], the concentrations of UHMWPE and LMWPE against decalin were fixed at 0.5 g/100 ml and 4.5 g/100 ml respectively. Namely, for the blend film, the weight composition (LHWPE/ UHMWPE) was 9/1. The hot homogenized solution was quenched by pouring it into an aluminum tray at room temperature, thus generating a gel. The decalin was allowed to evaporate from the gel under ambient conditions. The nearly dry gels were vacuum-dried for 24 h to

remove residual traces of decalin. The weight compositions of CF and UHMWPE of the blends were varied by 0.5/1, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1. The corresponding CF volume contents calculated against the matrix are 2.1%, 4.2%, 8.0%, 11.6%, 15.0%, 18.0%, 21.0%, 23.5% and 26.0%. Electrical conductivity was measured by high resistance measuring device (HR-100) produced by Iwamoto Seisakusho Co. Ltd. at the different heating rate, using a digital multimeter (Advantest R6441A Digital Multimeter) when the resistivity was lower than 107 X cm. On the other hand, the measurements were done by using a high resistance meter (HP 4339B High Resistivity Meter) when the resistivity exceeded 107 X cm. Incidentally, the measurement was carried out using the specimen with original dimensions of 14 · 7 · 1.5 mm clamped between copper metal jaws. As a preliminary experiment, golden paste was used to ensure complete contact between the specimen surface and the copper jaws. The values, however, were almost equal to those measured without using golden paste. Hence, the following measurements were made by the two terminal method without golden paste. In order to check the reproducibility of electrical conductivity, the measurements of electric resistivity were done as heating cycles. During heating cycles, the samples were expanded. The sample length, i.e. the distance between copper metal jaws, was fixed to the 10 mm and the thermal expansion of the specimen occurred mainly in width and thickness distance. The thermal property of the sample was measured at a heating rate of 5 C/min by differential scanning calorimetry (DSC 6100, SII Exstar 6000) from 20 to 160 C in N2 atmosphere.

3. Results and discussion

Fig. 1. SEM micrograph of the original MGII carbon fibers.

10

Percentage (%)

8 6 4 2 0

0

20

40

60

80 100 120 140 160 180 Length (µm)

Fig. 2. Length distribution of MGII carbon fibers.

Before discussing PTC effect of LMWPE– UHMWPE–CF system, we must emphasize that the intrinsic thermal properties of UHMWPE and LMWPE are hardly affected by the introduction of carbon fibers. In previous papers [7–9,27], the morphology of UHMWPE and LMWPE was confirmed to be independent of carbon black content as fillers. To check the same phenomenon for carbon fibers, the influence of carbon fibers content on LMWPE and UHMWPE crystallization were examined by DSC measurements. In doing so, first of all, the DSC curves of the 90/10 w/w LMWPE–UHMWPE blends were obtained in the absence of CF under three heating runs as the preliminary experiments, which is shown in Fig. 3. After the first thermal cycling (from room temperature to 160 C at a heating rate of 5 C/min, and cooling at room temperature), the crystallinity of the blends decreased, and the endothermic peak of UHMWPE shifted from

Endotherm Heat Flow Exotherm

Y. Xi et al. / Carbon 42 (2004) 1699–1706

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14 Log resistivity ( Ω ·cm)

3rd run 104.2 126.2 2nd run 126.5 103.8 1st run 130.5

80

100

10 8 6 4 2 0

102.5 60

12 (a)

120

140

0

5

160

10 15 20 25 Fiber Volume Content (vol%)

30

Temperature (˚C) Fig. 3. DSC curves of the 90/10 w/w LMWPE/UHMWPE blends in the absence of the filler at three heating runs.

Log resistivity ( Ω ·cm)

130 to 126 C since crystal size becomes smaller during the fast cooling process. From the second run, the DSC curves show similar profile indicating good reproducibility of thermal behavior of LMWPE–UHMWPE blends. Therefore, all the following DSC data reported in the present paper were represented for the second runs. Based on the preliminary experiment, DSC measurements were carried out as a function of CF content to understand the crystallization properties of UHMWPE and LMWPE. The results are listed in Table 1. The introduction of CF caused no significant effect on the thermal properties of the LMWPE/UHMWPE blends. Namely the crystallinity and the grain size estimated from the DSC curves are independent of CF contents. Fig. 4(a) shows the electrical resistivity as a function of fiber volume content at room-temperature. A zigzag drop in resistivity against carbon fiber content is observed, which is generally attributed to percolation phenomenon. At lower fiber contents (2.1–11.6 vol%), the resistivity is more or less equal to the resistivity of pure polymer. When carbon fiber content increases to 15.0 vol%, the resistivity of the blends falls down sharply from 1012 to 104 X cm, indicating the electrical conver-

3.5 (b) 3.0 2.5 2.0 1.5 -1.6

-1.5

-1.4

-1.3

-1.2

-1.1

-1.0

Fig. 4. (a) Electrical resistivity versus volume fraction of carbon fibers; (b) log–log plot of the resistivity against /
/c with /c ¼ 15:0% according to Eq. (1). Straight line was plotted by least-square method and has a slope t ¼ 3:32.

sion of composites at a critical concentration of carbon fibers. A semiconducting character of the composites in this transition region can be explained by a specific conductance mechanism of these materials. Namely, it may be expected that even if a few conducting paths are present, electrons are activated to hop over the nonconducting polyethylene matrix barrier across the gaps between the conducting fibers. When carbon fiber content exceeds the critical concentration, the conduction is predominantly achieved through the fiber contacts and

Table 1 Thermal properties of 90/10 w/w LMWPE/UHMWPE blends with the different carbon fiber content Volume content (vol%)

LMWPE Dhf (J/g)

Tm (C)

Xc a (%)

Dhf (J/g)

Tm (C)

Xc a (%)

0.0 2.1 4.2 8.0 11.6 15.0 18.0 21.0 23.5 26.0

64.22 62.69 59.69 61.30 59.36 58.55 60.04 57.42 59.32 60.39

103.8 102.1 103.3 102.6 102.4 99.9 100.8 100.1 103.3 102.2

26.18 25.56 24.33 24.99 24.20 23.87 24.48 23.41 24.18 24.62

115.05 113.38 112.31 112.35 111.87 113.71 109.80 112.95 113.88 114.04

126.3 125.5 125.9 126.2 125.9 123.0 122.6 122.0 126.5 125.2

46.90 46.22 45.79 45.80 45.60 46.36 44.76 46.05 46.42 46.49

a

-0.9

Log ( φ − φc)

UHMWPE

Calculated from the ratio of the measured Dhf to Dhf of a 100% crystalline polyethylene (245.3 J/g) [28].

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the material behaves as a conductor. The resistivity of composites tends to level off when CF content is beyond 15.0 vol%. As discussed already, the blends were mixed by putting all the components into the decalin solution at 150 C. This method allows more fillers in the blends to obtain the lower resistivity. At the same time, the percolation threshold value is higher than that of conventional conductive polymer blends produced by melt mixing of polymer and fillers, since carbon fibers can be uniformly dispersed and the interparticle distances are longer without kneading or pressing at high pressure. Percolation theory predicts the relationship between the composite resistivity and volume content of the conductive filler as q ¼ q0 ð/
/c Þ


t

ð1Þ

for / > /c

where q0 is a constant, / is the volume content of the filler, /c is the critical volume content at percolation threshold, which is 15.0 vol% in the present paper, t is the exponent characterizing the relationship between q and /. Theoretical consideration has provided that t should be equal to 1.5–1.6. However t value was given to be about 3 experimentally for the composite filled with randomly oriented fibers [10]. For the present composites, t value was determined to be 3.32 from the slop of line shown in Fig. 4(b). In fact, the filler concentration of the desired composites serving as PTC materials should be a little bit higher than the upper limit value estimated by the percolation region [3–5,29]. Accordingly, the sample, where the concentration is higher than or equal to 15.0 vol%, was chosen to test their PTC effects in the present paper. Fig. 5 shows the temperature dependence of the resistivity measured for the blend with 23.5 vol% CF. To compare the thermal behavior of electrical conductivity, the result of LMWPE–UHMWPE–CB blends in previous papers [8,9] is shown together, where the concentration of 13 wt% CB, namely 6.5 vol% CB, was the critical concentration and the LMWPE/UHMWPE was

Log resistivity ( Ω ·cm)

14 12 10 8

a

6

b

4 2 20

40

60

80

100

120

140

160

180

Temperature (˚C) Fig. 5. Resistivity against temperature of: (a) the 90/10 w/w LMWPE/ UHMWPE blends with 23.5 vol% CF; (b) the 90/10 w/w LMWPE/ UHMWPE blends with 6.5 vol% CB.

9/1. As shown in Fig. 5, the better PTC effect is achieved for carbon fiber blends than for carbon black blends. The PTC intensity, which is RP =RRT defined as the ratio of peak resistivity RP to the room temperature resistivity RRT [3], is about 108 –109 . The electrical resistivity of PTC materials changes abruptly at the outset of the melting point 116 C of the UHMWPE. For the semicrystalline polymer such as polyethylene, it is well known that the transformation of the crystalline phase to the amorphous phase causes a significant volume expansion at the related temperature. If this is the case, the interparticle distances of conductive paths increase. Because the thermal expansion coefficient of polymer is two orders of magnitude higher than that of CF, resulting higher resistivity of the material in the melting temperature. For the 90/10 w/w LMWPE/ UHMWPE blends, the thermal expansion of LMWPE is restricted by the unmelted UHMWPE at the melting temperature of LMWPE and then the conductive carbon fibers are connected each other to keep the good electrical conductivity. When the temperature reaches the melting point of UHMWPE, thermal expansion of the blends reaches their maximum and cutting conductive paths cause an instant increase in resistivity. Comparing with carbon black in the blends, carbon fibers in the blends have higher concentration to achieve the lower resistivity at room temperature. Moreover, the migration of carbon fibers caused by active chain mobility under melting point of polyethylene is more difficult than that of carbon black at the same molten viscosity. Therefore, the NTC effect was thought to be eliminated, and the blends with carbon fibers have the better PTC effect and the higher PTC temperature. It has been pointed out that the thermoplastic composites exhibit poor reproducibility of resistivity–temperature curves for different heating/cooling runs. According to previous reports, poor reproducibility of electrical conductivity could be a little improved by crosslinking either chemically with peroxides or by irradiation [4], and by adding rubber as a ‘‘mechanical stabilizer’’ to carbon black/wax mixtures [30] and by using mixtures of two kinds of carbon black with polyethylene [3]. This is obviously due to the fact that the expansion/contraction processes accompanying heating/cooling cycles cause movements of the fillers and the behaviors is irreversible. However, in the case of the blends with UHMWPE [8,9,18,31], the reproducibility of electrical conductivity provided good satisfaction, since UHMWPE minimizes the migration of the carbon fibers and the deformation because of its high viscosity even in the temperature range beyond the melting point. Only the first run is different from the subsequent ones, while the latter runs have very good reproducibility shown in Fig. 6. As the most favorable phenomenon in the latter run, the resistivity increases abruptly at sharp temperature range about 116 C. It is noticed that the

Y. Xi et al. / Carbon 42 (2004) 1699–1706

12

1st run 2nd run 3rd run 4th run

10 8 6 4 2 20

40

60

80 100 120 140 Temperature (˚C)

160

180

Fig. 6. Resistivity against temperature of the 90/10 w/w LMWPE/ UHMWPE blends with 23.5 vol% CF under four runs.

Log resistivity (Ω ·cm)

14

15.0 vol% 18.0 vol% 21.0 vol% 23.5 vol% 26.0 vol%

12 10 8

14 (a) 12 10

6 4 2

heating cooling

8 6 4 2 20

Endotherm Heat Flow Exotherm

latter curves shifted upward and forward in comparison with the first run because of the decrease crystallinity for both UHMWPE and LMWPE after the first runs. This phenomenon agrees well with the DSC result in Fig. 3. Consequently, all the resistivity–temperature curves reported hereafter in this article adopt the second runs. Fig. 7 shows the resistivity of the blends with the different volume content as a function of temperature. The results indicate that the PTC effect is dependent on the carbon fiber content. At highest content (26 vol%), the PTC effect of the composites becomes worst. At lower contents (15.0–18.0 vol%), the PTC intensity is about 106 and the PTC temperature is about 100 C. When the volume content is 23.5 vol%, the PTC intensity reach a maximum about 109 and the PTC temperature is about 116 C. The reason maybe is due to the fact that the smaller inter-fiber distance in the composites becomes narrower with increasing CF content and the higher temperature is required to break off all contacts of carbon fibers. The results of the other research [3–5,29] indicated that only when a filler concentration is a bit higher than the upper limit of the percolation region, the material with PTC effect can be achieved. Furthermore, if a high

conductivity is required, highly filled composites should be employed for switching purposes. Such highly conductive composites, however, seldom show good switching behavior. Therefore, the composites combining high conductivities and significant switching behavior are a contradictory. Nevertheless, in the 90/10 w/w LMWPE/UHMWPE blends with carbon fibers, the PTC effects can be found in a wide concentration range from 15.0 to 23.5 vol%, which has never been reported in the previous literature [3–5,7–9,29]. Fig. 8(a) shows temperature dependence of resistivity of the blend with 23.5 vol% CF under heating and cooling processes, and Fig. 8(b) shows the corresponding DSC curves. It is seen that DSC melting curves of semicrystalline polymers are not identical to the corresponding crystallization curves. The rapid increase and rapid decrease in electrical conductivity happen at the different temperature indicate different thermal behavior during heating and cooling processes. The rapid increase and decrease are in good agreement with different melting and crystallization behaviors estimated from the DSC curves in Fig. 8(b). Namely, the starting temperature of the rapid increase in resistivity corresponds to the outset of melting temperature (about 116 C) of UHMWPE, while the

Log resistivity ( Ω ·cm)

Log resistivity (Ω ·cm)

14

80

100 120 Temperature (˚C)

140

Fig. 7. Resistivity against temperature of the blends with the different CF volume content.

40

60

(b)

80 100 120 140 Temperature(˚C)

160

180

95

cooling

112

heating 126 104 60

60

1703

70

80

90 100 110 120 Temperature(˚C)

130

140

Fig. 8. (a) Resistivity against temperature and (b) DSC curves of the 90/10 w/w LMWPE/UHMWPE blends with 23.5 vol% CF during heating and cooling process.

Y. Xi et al. / Carbon 42 (2004) 1699–1706

starting temperature of rapid decrease corresponds to the end of crystallization temperature of LMWPE (92 C). It is noticeable that a good switching property was found not only in the heating process but also in the cooling process. The effect of heating rate on the PTC effects is shown in Fig. 9. It is seen that the higher the heating rate, the higher the starting temperature of the PTC effects. This is due to the fact that cutting of conducting paths of carbon fibers occurs at higher temperature with increasing the heating rate. Actually the apparent melting point associated with its volume expansion shifted to high temperature side with increasing the heating rate. Here we must emphasize that the electrical properties of the composites are affected by the microstructure change with the CF content increasing. Fig. 10 displays the SEM micrographs for the cross-section area of the blends with various CF concentrations, which was taken

14

heating rate = 1˚C/min

12

heating rate = 9˚C/min

heating rate = 5˚C/min

Log resistivity (Ω ·cm)

1704

10 8 6 4 2

20

40

60

80 100 120 Temperature (˚C)

140

160

180

Fig. 9. Resistivity against temperature of the 90/10 w/w LMWPE/ UHMWPE blends with 23.5 vol% CF at the different heating rate.

from the edge of each specimen. In doing so, the specimen were immersed into liquid nitrogen and split by

Fig. 10. SEM micrographs of freeze fractured surfaces of the 90/10 w/w LMWPE/UHMWPE blends: (a) 2.1 vol%; (b) 8.0 vol%; (c) 15.0 vol%; (d) 21.0 vol%; (e) 26.0 vol% carbon fibers.

Y. Xi et al. / Carbon 42 (2004) 1699–1706

hands. It is shown that the CF particles are oriented randomly in the polyethylene matrix, and the higher the CF content, the more the conducting paths. Namely in photo (c) for 15 vol% carbon fibers, most of fibers are detached but in photo (e) for 26 vol% carbon fibers most of fibers are connected each other. Fig. 11 shows SEM photographs for the cross-section area of the blends with 23.5 vol% carbon fibers as (a) the original blends, (b) the blends after four heating runs and (c) the enlargement of (b). To observe the crosssection, the specimen was cut directly by knife. The existence of voids indicates incomplete adhesion or

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wetting between the polyethylene and the CF particles. The voids would expand at the first heating run reflecting the quite different thermal expansion coefficient between polyethylene and CF. This phenomenon was also confirmed in relation to an increase in both the volume and electrical resistivity of the sample. Following Marr et al. [32,33], it is reported that the void content in the melt decreases to nearly zero and increases sharply with the onset of polymer crystallization. They pointed out that the small-angle neutron scattering measurements can identify the size and concentration of voids in carbon black/polyethylene composites. 4. Conclusion Good PTC effect was achieved using LMWPE– UHMWPE–CF blends prepared by gelation/crystallization from dilute solution. The PTC effect exists in the wide fiber content range. The maximal PTC effect, the intensity of which being about 9 orders of magnitude, was presented with a LMWPE/UHMWPE composition of 9/1 containing 23.5 vol% CF much higher than the percolation threshold value. The elimination of the NTC effect and the improvement of reproducibility of electrical conductivity were found to be achieved by using a very high viscosity semicrystalline polymer as one of the composites such as UHMWPE. The origin of PTC phenomenon was due to the change of the distribution of the interparticle gap width between carbon fibers in the molten state of the polymers. The DSC results indicated that the carbon fibers have no significant influence on the morphology of polyethylene such as the crystallinity and the grain size. References

Fig. 11. The cross-section SEM micrographs of the 90/10 w/w LMWPE/UHMWPE blends with 23.5 vol% CF: (a) the original blends; (b) the blends after four heating runs; (c) the enlargement of (b).

[1] Meyer J. Glass transition temperature as a guide to selection of polymers suitable for PTC materials. Polym Eng Sci 1973;13:462– 86. [2] Meyer J. Stability of polymer composites as positive-temperaturecoefficient resistors. Polym Eng Sci 1974;14:706–16. [3] Narkis M, Ram A, Flashner F. Electrical properties of carbon black filled polyethylene. Polym Eng Sci 1978;18:649–53. [4] Narkis M, Ram A, Stein Z. Electrical properties of carbon black filled crosslinked polyethylene. Polym Eng Sci 1981;21:1049–54. [5] Narkis M, Vaxman A. Resistivity behavior of filled electrically conductive crosslinked polyethylene. J Appl Polym Sci 1984;29: 1639–52. [6] Tchoudakov R, Breuer O, Narkis M, Siegmann A. Conductive polymer blends with low carbon black loading: polypropylene/ polyamide. Polym Eng Sci 1996;36:1336–46. [7] Xu C, Bin Y, Agari Y, Matsuo M. Morphology and electrical conductivity of cross-linked polyethylene-carbon black blends prepared by gelation/crystallization from solution. Colloid Polym Sci 1998;276:669–79. [8] Bin Y, Xu C, Agari Y, Matsuo M. Morphology and electrical conductivity of ultrahigh-molecular-weight polyethylenelow-molecular-weight polyethylene-carbon black composites

1706

[9]

[10]

[11]

[12]

[13] [14]

[15] [16]

[17]

[18]

[19]

[20]

Y. Xi et al. / Carbon 42 (2004) 1699–1706

prepared by gelation/crystallization from solution. Colloid Polym Sci 1999; 277:452–61. Bin Y, Xu C, Zhu D, Matsuo M. Electrical properties of polyethylene and carbon black particle blends prepared by gelation/crystallization from solution. Carbon 2002;40:195–9. Chekanov Y, Ohnogi R, Asai S, Sumita M. Positive temperature coefficient effect of epoxy resin filled with short carbon fibers. Polym J 1998;30:381–7. Vilcakova J, Saha P, Quadrat O. Electrical conductivity of carbon fibres/polyester resin composites in the percolation threshold region. Eur Polym J 2002;38:2343–7. Tavman IH. Thermal and mechanical properties of aluminum powder-filled high-density polyethylene composites. J Appl Polym Sci 1996;62:2161–7. Ohe K, Naito Y. A new resistor having an anomalously large positive temperature coefficient. Jpn J Appl Phys 1971;10:99–108. Klason C, Kubat J. Anomalous behavior of electrical conductivity and thermal noise in carbon black-containing polymers at Tg and Tm . J Appl Polym Sci 1975;19:831–45. Voet A. Temperature effect of electrical resistivity of carbon black filled polymers. Rubber Chem Technol 1980;54:42–50. Allak HK, Brinkman AW, Woods J. I–V characteristics of carbon black-loaded crystalline polyethylene. J Mater Sci 1993;28:117– 20. Jia SJ, Zhang ZC, Fan YM, Weng HM, Zhang XF, Hang RD. Study of the size and numerical concentration of the free volume of carbon filled HDPE composites by the positron annihilation method. Eur Polym J 2002;38:2433–9. Feng JY, Chan CM. Double positive temperature coefficient effects of carbon black-filled polymer blends containing two semicrystalline polymers. Polymer 2000;41:4559–65. Tang H, Chen XG, Luo YX. Studies on the PTC/NTC effect of carbon black filled low density polyethylene composites. Eur Polym J 1997;33:1383–6. Manuela HB, Franciose ED. Electrical conductivity of carbon black-polyethylene composites Experimental evidence of the change of cluster connectivity in the PTC effect. Carbon 2001; 39:375–82.

[21] Luo YL, Wang GC, Zhang BY, Zhang ZP. The influence of crystalline and aggregate structure on PTC characteristic of conductive polyethylene/carbon black composite. Eur Polym J 1998;34:1221–7. [22] Lee GJ, Suh KD, Im SS. Study of electrical phenomena in carbon black-filled HDPE composite. Polym Eng Sci 1998;38:471–7. [23] Zhang MY, Jia WT, Chen XF. Influence of crystallization histories on PTC/NTC effects of PVDF/CB composites. J Appl Polym Sci 1996;62:743–7. [24] Jia WT, Chen XF. PTC effect of polymer filled with carbon black. J Appl Polym Sci 1994;54:1219–21. [25] Jia WT, Chen XF. Effect of polymer-filler Interaction on PTC Behaviors of LDPE/EPDM Blends Filled with carbon blacks. J Appl Polym Sci 1997;66:1885–90. [26] Zhang MQ, Yu G, Zeng HM, Zhang HB, Hou YH. Two-step percolation in polymer blends filled with carbon black. Macromolecules 1998;31:6724–6. [27] Xu C, Agari Y, Matsuo M. Mechanical and electric properties of ultra-high-molecular-weight polyethylene and carbon black particle blends. Polym J 1998;30:372–80. [28] Brandrup J, Immergut EH, Grulke EA, editors. Polymer handbook. 4th ed. New York: Wiley; 1999. [29] Tang H, Piao JH, Chen XF, Luo YX, Li SH. The positive temperature coefficient phenomenon of vinyl polymer/CB composites. J Appl Polym Sci 1993;48:1795–800. [30] Bueche F. A new class of switching materials. J Appl Phys 1973; 44:532–3. [31] Chan CM, Cheng CL, Yuen MMF. Electrical properties of polymer composites prepared by sintering a mixture of carbon black and ultra-high molecular weight polyethylene powder. Polym Eng Sci 1997;37:1127–36. [32] Marr DWM, Wartenberg M, Schwartz KB, Agamalian MM, Wignall GD. Void morphology in polythylene/carbon black composites. Macromolecules 1997;30:2120–4. [33] Oakey J, Marr DWM, Schwartz KB, Wartenberg M. Influence of polyethylene and carbon black morphology on void formation in conductive composite materials: a SANS study. Macromolecules 1999;32:5399–404.