Electrical Properties of Percolative Polystyrene/Carbon Nanofiber ...

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G. D. Liang and S. C. Tjong: Electrical Properties of Percolative Polystyrene/Carbon Nanofiber Composites

Electrical Properties of Percolative Polystyrene/Carbon Nanofiber Composites G. D. Liang and S. C. Tjong Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

ABSTRACT Polystyrene/carbon nanofiber nanocomposites (PS/CNF) were prepared by melt compounding. The dielectric and electrical conducting properties of the PS/CNF nanocomposites were investigated. The conductivity and dielectric constant of the polymer composites were significantly enhanced by adding CNF at a very low loading level of 1.7 vol%. The dielectric constant also increased in the same way as a result of percolation. Furthermore, the resistivity of the PS/1.7 vol% CNF nanocomposite was greatly dependent on temperature. A sharp increase in resistivity of PS/1.7 vol% CNF nanocomposite was observed at 60-150 ºC, being related to the mobility of PS macromolecular chains near the glass transition temperature. Index Terms – Carbon nanofiber, polystyrene, nanocomposite, conductivity, dielectric constant, resistivity, percolation, excluded volume, electron microscopy.

1 INTRODUCTION CONDUCTING polymer composites filled with metal particles [1-3] and carbon blacks [4-7] have found widespread applications as materials for electromagnetic interference shields of electronic devices. Such conventional microcomposites generally require large particle concentration to achieve desired electrical characteristics. This leads to poor processability and inferior mechanical performances of the microcomposites. Development of lightweight conducting polymer composite materials with enhanced electrical properties remains one of the main challenges for materials scientists. Recently, carbon nanofibers (CNFs) and carbon nanotubes have attracted growing interest as reinforcement materials for polymers due to their unusual structural, chemical and physical characteristics. These nanofillers have been found to improve the electrical, mechanical and thermal properties of polymers at very low filler content compared to conventional microcomposites [8 – 13]. However, the relatively high cost of single-wall carbon nanotubes (SWNTs) and multi-wall carbon nanotubes (MWNTs) have precluded their widespread applications as fillers for polymer nanocomposites. In contrast, vapor grown CNFs having diameters of ~ 50 – 200 nm are more cost effective because they can be massproduced catalytically using gaseous hydrocarbons in the presence of small amounts of metal catalysts [14]. It is well recognized that the electrical properties of the polymer composites are critically governed by the type, size and concentration of reinforcements, dispersion of fillers within polymeric matrix as well as the processing techniques Manuscript received on 29 June 2007, in final form 25 September 2007

[15].The electrical properties of the conducting filler/insulating polymer composites are often analyzed in term of the percolation theory. At low filler concentration, fillers are individually dispersed within polymeric matrix. This results in the composites having poor electrical conducting properties. Beyond a critical concentration, known as percolation threshold, the fillers are linked together to form a continuous network within polymeric matrices. This is companied by several orders of magnitude increases in the conductivity and dielectric properties [16]. The percolation threshold ( φc ) of composites depends on the structural factors (e.g. size and shape) of the fillers used. The φc of composites tends to decrease with increasing aspect ratio of the fillers. For asymmetric fillers with high aspect ratio, the φc value predicted theoretically is much smaller than 1% [17, 18]. For polymers filled with CNTs or CNFs with large aspect ratios, the conducting paths can be formed more readily. This facilitates electron transport, thereby yielding low percolation threshold. A very low percolation threshold of ~ 0.2 wt% has been determined experimentally in nanocomposites based on SWNTs and poly(butylene terephtahalate) prepared by in-situ polycondensation [19]. In some cases, the experimental φc values of CNT or CNF filled polymers deviate from those predicted from theoretical models. From the search of literature, the experimental percolation threshold of meltcompounded MWNT filled polypropylene (PP) composites is 1 vol% [20]. A larger value of percolation concentration of 5 vol% was recorded for the PP/CNF composites [21]. This difference is caused by the agglomeration of nanofillers in polymer matrices. Nanofillers with large surface areas tend to

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agglomerate into clusters during composite fabrication [2224]. This paper aims to study the electrical behavior of meltcompounded polystyrene (PS) nanocomposites filled with CNFs.

2 EXPERIMENTAL 2.1 SAMPLE PREPARATION The PS/CNF nanocomposites were prepared by meltblending commercial PS pellets (Dow Chemical Company; Styron 667) with CNF powders (Nanostructured and Amorphous Materials Inc) in a Brabender mixer. The outer diameter of CNFs ranged from 80 - 200 nm and the length of CNFs varied between 0.5 - 20 μm. To disperse CNFs into the polymer matrix uniformly and to avoid thermal degradation of the polymer matrix, the mixing time was set to 15 min at 200 °C. The blended mixtures were then hot pressed at 250 °C under 10 MPa into plates of 1 mm thickness. Disk samples of 12 mm diameter were punched from these plates. 2.2 MORPHOLOGICAL OBSERVATION The morphology of composites was observed in an optical microscope (Olympus BH2-UMA) equipped with a camera (Olympus DP 11). The specimens were placed between two microscopic glass slides and then mounted on a hot stage. They were held at 230 ºC for 5 min and quickly cooled to room temperature for optical microscopic observation. Ultrathin specimens for TEM observation were cut from the middle section of compression-molded plaque using a Reichert Ultracut microtome under cryogenic conditions. The films were retrieved onto the Cu grids and dried in a vacuum system at 50 ºC. They were then examined with Philips CM20 transmission electron microscope. The morphology of fracture surface of samples was examined with scanning electron microscopy (SEM, JEOL JSM model 820). The samples were fractured in liquid nitrogen. They were coated with a thin layer of gold prior to SEM observation. 2.3 DIFFERENTIAL SCANNING CALORIMETRY (DSC) The glass transition temperatures of neat polystyrene and its nanocomposites were determined with a TA Instruments DSC (model 2910) under a nitrogen atmosphere. The specimens of about 5 mg were sealed in aluminum pans. They were heated to 230 °C at a rate of 10 °C/min, followed by cooling to 20 °C at a rate of -10 °C/min. The change of heat flow versus time was recorded. 2.4 ELECTRICAL PROPERTY MEASUREMENTS Samples for the dielectric and resistivity measurements were coated with silver paint prior to the tests. Two metallic electrodes were then connected to the samples via silver wires. The dielectric constant and conductivity of samples were measured by employing an impedance analyzer (Agilent model 4294) in the frequency range of 40-107 Hz.

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3 RESULTS AND DISCUSSION Figure 1a is an optical micrograph showing typical microstructure of the PS/1.7 vol% CNF nanocomposite. Most CNFs are uniformly dispersed within PS matrix and some CNF agglomerates are still found. A similar dispersion of CNFs in PS matrix is observed in the TEM micrograph as shown in Figure 1b.

10 μm

(a)

(b) Figure 1. (a) Optical and (b) TEM nanocomposite.

micrographs of PS/1.7 vol% CNF

Figure 2 shows the effect of CNF volume fraction on the electrical conductivity of PS/CNF nanocomposites. The conductivity of the nanocomposites first rises slowly with increasing CNF content, but enhances abruptly when the CNF content reaches 1.7 vol%. This is a typical behavior of percolative composites. The conductivity of PS/1.7 vol% CNF nanocomposite reaches as high as 3.9 ×10-5 S m-1, being five orders of magnitude larger than that of PS matrix. The relationship between the CNF content and conductivity can be described by the following power law equation:


σ = σ where

σ0

0

φ 1− φc

CNF content reaches 1.7 vol%, an apparent network of CNFs throughout the fracture surface is established (Figure 4c).

− s

(1)

is the conductivity of PS matrix,

φc

is the

percolation threshold and s is a critical exponent. As can been seen from Figure 2, the experimental values agree reasonably with Eq. 1 when φc = 1.71 % and s = 1.3. The dielectric constant of the PS/CNF nanocomposites vs CNF volume fraction is shown in Figure 3. Similarly, the percolation phenomenon is observed. The dielectric constant of PS/1.7 vol% CNF nanocomposite is 221, being two orders of magnitude larger than that of neat PS. The dependence of dielectric constant of PS/CNF nanocomposites on the CNF volume content can be expressed by the following power law relation:

ε = ε where

ε 0 is

0

φ 1− φc

-3

10

-5

10

-7

10

-9

200 150 100 50 0

(2)

0.0

the dielectric constant of PS matrix,

φc

0.4

0.8

1.2

1.6

CNF content (vol%)

is the

f=50 Hz

Figure 3. Variation of dielectric constant of PS/CNF nanocomposites with CNF content at room temperature.

The percolation concentration of polymer composites containing conductive fillers of large aspect ratios can be satisfactorily predicted by using the excluded volume concept proposed by Balberg [17,25,26]. For three dimensions system, the critical volume fraction φ c of fillers can be related to the total exclude volume of filler Vex by the following equation [17]:

⎛

φc = 1 − exp⎜⎜ −

-1

σ (s m )

f=1k Hz

− s′

percolation threshold, and s ′ is the critical exponent. From Figure 3, the experimental datum points are in good agreement with Eq. (2) with φc = 1.71 % and s ′ = 0.9.

10

250

Dielectric constant

216

⎝

where

Vex

is

VexV ⎞ ⎟ = 1 − exp(− N cV ) Ve ⎟⎠

the product of

(3)

the critical number

density N c and the excluded volume Ve of fillers, V is the

0.0

0.4 0.8 1.2 CNF content (vol%)

1.6

Figure 2. Variation of conductivity of PS/CNF nanocomposites with CNF content at room temperature.

Figure 4 shows the SEM micrographs of cryogenic fractured surfaces of representative PS/CNF nanocomposites. The CNF is recognized as bright dots or rods. It can be seen that CNFs are uniformly dispersed throughout entire fracture surfaces of the PS/CNF nanocomposites investigated. In the PS/CNF nanocomposites with low CNF loading, CNFs are independently distributed within polymeric matrix (Figure 4a). However, CNFs begin to link to each other with increasing CNF loading to 0.5 vol% (Figure 4b). When the

real volume of one filler particle. On the basis of Balberg model, Celzard et al linked the excluded volume with the critical volume fraction φ c of a capped cylinder of length L and diameter W by the following equation [18]:

[

]

⎛ Vex (π / 4)W 2 L + (π / 6)W 3 ⎜ φc = 1 − exp⎜ − 3 2 2 ⎝ (4π / 3)W + 2πW L + (π / 2)WL

[

]

⎞ ⎟ ⎟ ⎠

(4)

Balberg demonstrated that the excluded volume of the objects is confined within two limits [26]. The value of Vex is 1.4 for infinitely thin cylindrical particles and 2.8 for spherical fillers [17]. The critical concentration of cylindrical



particles system can be determined using Vex of 1.4 as the lower limit and 2.8 as an upper limit [18], i.e.

⎛ 1.4V 1 − exp⎜⎜ − ⎝ Ve

⎞ ⎛ ⎟ ≤ φc ≤ 1 − exp⎜ − 2.8V ⎟ ⎜ V e ⎠ ⎝

⎞ ⎟ ⎟ ⎠

(5).

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Based on this double inequality, the critical concentrations are determined to be 0.276% ≤ φc ≤ 5.8% . As both the length (0.5 - 20 μm) and diameter (80 - 200 nm) of the CNFs vary considerably, a broad percolation concentration range is determined. Comparing to the predicted value, experimentally-determined percolation threshold is in the concentration range predicted, being close to the lower limit. Figure 5 shows the variation of conductivity with frequency for the PS/CNF nanocomposites. It is found that the conductivity of pure PS and PS/CNF nanocomposites with low CNF loading increases linearly with increasing frequency under a slope of unity. This is a typical characteristic for non-conductive materials. However, the conductivity of the PS/1.7 vol% CNF nanocomposite shows a plateau at low frequency and deflects at 3.5 kHz. This obeys the power law dependence σ ∝ f for f >3.5 kHz. The critical exponent, x, is determined to be 0.5. x

-1

σ (s m )

a

10

-1

10

-3

10

-5

10

-7

10

-9

PS+0.8 vol% CNF PS+1.1 vol% CNF PS+1.7 vol% CNF

PS PS+0.3 vol% CNF PS+0.5 vol% CNF

10

2

10

3

4

5

10 10 Frequency (H z)

10

6

10

7

Figure 5. Plots of conductivity of PS/CNF nanocomposites vs. frequency at room temperature.

b

Figure 6 shows the dielectric constant as a function of frequency for pure PS and PS/CNF nanocomposites. From Figure 6, it can be seen that the dielectric constants of neat PS and its nanocomposites are nearly independent of frequency. For the PS/1.7 vol% CNF nanocomposite, the dielectric constant decreases slowly at low frequency regime, but falls markedly with increasing frequency at f > 3.5 kHz. The dependence of the dielectric constant of the PS/1.7 vol% CNF nanocomposite can be described by ε ∝ f for f > 3.5 kHz. The critical exponent, y, is determined to be 0.4. As a result, x + y = 1 is fulfilled for the PS/1.7 vol% CNF nanocomposite. The frequency dependences of conductivity and dielectric constant of the polymer composites can be interpreted in terms of the polarization between conductive clusters and anomalous diffusion of charge carries within each cluster [27]. When the CNF content exceeds the percolation concentration significantly, the conductivity is mainly controlled by the inter-connected paths of percolating clusters at low frequency regime. However, the capacitor effect between the clusters predominates at high frequency regime. Therefore, the conductivity of the composites −y

c Figure 4. SEM micrographs showing cryogenic fractured surfaces of (a) PS/0.1 vol% CNF, (b) PS/0.5 vol% CNF and (c) PS/1.7 vol% CNF nanocomposites. The arrows denote CNFs.

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Dielectric constant

remains unchanged up to a critical frequency, above which the conductivity increases with increasing frequency.

10

3

10

2

10

1

PS PS+0.3 PS+0.5 PS+0.8 PS+1.1 PS+1.7

10

2

10

3

4

5

vol% vol% vol% vol% vol%

10 10 10 Frequency (Hz)

6

CNF CNF CNF CNF CNF

10

7

temperature in heating process, the movement of the PS macromolecular chains destroys the CNF conductive network, resulting in an increase of resistivity of the PS/1.7 vol% CNF nanocomposite at temperatures > 60 ºC. On the other hand, when temperature drops below the transition temperature during cooling, the mobility of PS macromolecules decreases and CNF paths are re-built in the composites, leading to a decrease of resistivity. Similar results have been observed in the semicrystalline polymer composites filled with carbonic materials near melting temperatures of polymers [28-32]. Such positive temperature coefficient effect was also reported for amorphous polymer composites filled with conductive fillers. However, positive temperature coefficient effect observed in amorphous polymer composites near glass transition temperature is weaker than that of the semicrystalline polymer composites near the melting temperature due to insignificant change in the mobility of polymer chains near glass transition [33, 34].

Figure 6. Plots of dielectric constant of PS/CNF nanocomposites vs. frequency at room temperature.

-3 o

10

-4

10

-5

10

-6

10

-7

-1

σ (S m )

-140 C

o

10

2

o

-140 C o -20 C o 40 C o 90 C o 120 C

o

120 C

3

4

-100 C o 20 C o 60 C o 100 C

10 10 10 Frequency (Hz)

5

10

6

Figure 7. Variation of conductivity of PS/CNF nanocomposites with frequency at various temperatures.

CNF PS/1.7 vol% CNF, heating PS/1.7 vol% CNF, cooling

10 σ ( 25oC) /σ

In order to investigate the conducting mechanism, the conductivity of PS/CNF nanocomposites at percolation threshold at various temperatures is also measured. Figure 7 shows the conductivity of the PS/1.7 vol% CNF nanocomposite as a function of frequency at various temperatures. It is found that conductivity of the nanocomposite keeps unchanged at low frequency regime for the investigated temperature range. This value can be referred as ‘dc conductivity’. The variation of resistivity, being reciprocal of the dc conductivity of pristine CNF and PS/1.7 vol% CNF nanocomposite, normalized to their corresponding value at 25 ºC, with temperature is presented in Figure 8. The resistivity values were measured in heating at a rate of 10 °C min-1. It can be seen that resistivity of pristine CNF and its nanocomposite is almost independent of temperature at low temperature regime, but rises as temperatures are above 60 ºC. However, a significant increase in resistivity, known as positive temperature coefficient effect, is observed for the PS/1.7 vol% CNF nanocomposite at temperature > 60 ºC. It is apparent that this increase of resistivity is not caused by the CNF filler, but rather associated with the polymer matrix. To investigate the reversibility of the temperature dependence on resistivity of PS/1.7 vol% CNF nanocomposite, the resistivity of the nanocomposite was also determined in cooling process at a rate of -10 °C min-1 and presented in Figure 8. The resistivity of PS/1.7 vol% composite drops sharply as temperature decreases from 90 °C to 60 °C. Therefore, the temperature dependence of resistivity for the PS/1.7 vol% CNF composite is reversible. This is due to reversible transition of PS matrix between plastic and rubbery phases as temperature changes. At low temperatures, the PS macromolecular chains act as stiff rods and the mobility of macromolecules is strictly prohibited. At high temperatures, PS macromolecular chains relax as random coils and are able to move easily. As temperature rises above the transition

10

1

-150 -100 -50

0

50

100 150

Temperature ( oC) Figure 8. σ (25ºC)/σ for pristine CNF and PS/1.7 vol% CNF nanocomposite as a function of temperature.


heating scans cooling scans


219

ACKNOWLEDGEMENT PS+1.7vol% CNF PS+0.3vol% CNF

The work described in this paper was fully supported by a strategic research grant (No. 7001988), City University of Hong Kong.

PS

REFERENCES endo

[1]

PS+1.7vol% CNF

[2]

PS+0.3vol% CNF [3]

PS

40

60

80 100 120 140 160 180 200

[4]

o

Temperature ( C) [5] Figure 9. DSC heating and cooing traces of PS and its nanocomposites. [6]

Figure 9 shows the DSC heating and cooling traces of neat PS and its nanocomposites during heating and cooling processes. The glass transition occurs at 90-100 ºC for neat PS and its nanocomposites during heating. The glass transition temperature determined in cooling process for pristine PS and its composites (80 – 90 ºC) is lower than that in heating process. This is because the glass transition temperature of amorphous polymers is greatly dependent on the measurement methodology. As temperature is increased, PS enters a rubbery phase from the rigid plastic phase. The movement of the PS macromolecular chains near its glass transition temperature damages the CNF conducting pathways embedded within polymeric matrix. On the other hand, when temperature is decreased below the glass transition temperature, mobility of PS macromolecules decreases and CNF network are re-established in the composites. This is in sharp contrast with the reported work in which a much higher temperature (near the melting point of matrix polymer) can disrupt the conducting filler network [28 -32].

[7]

[8]

[9]

[10]

[11]

[12] [13]

4 CONCLUSION The electrical properties of PS/CNF nanocomposites are strongly dependent on CNF content. Conductivity and dielectric constant of PS/CNF nanocomposites first increase gradually with the increase of CNF content, and rise abruptly as the CNF content reaches 1.7 %. This dependence of conductivity and dielectric constant on CNF content can be satisfactorily described by the percolation theory. The resistivity of the PS/1.7 vol% CNF nanocomposite is found to be temperature dependent. A sharp increase in resistivity of PS/1.7 vol% CNF nanocomposite is observed in temperature range of 60-150 ºC, being associated with the glass transition of PS matrix.

[14] [15] [16] [17] [18] [19]

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[31] X. J. He, J. H. Du, Z. Ying, and H. M. Cheng, "Positive Temperature Coefficient Effect in Multiwalled Carbon Nanotube/High-Density Polyethylene Composites", Appl. Phys. Lett., Vol. 86, pp. 062112-1 062112-3, 2005. [32] Y. H. Song, Q. Zheng, "Influence of Annealing on Conduction of HighDensity Polyethylene/Carbon Black Composites", J. Appl. Polym. Sci., Vol. 105, pp. 710-717, 2007. [33] J. Chang, A. Ho, W. K. Chin, "Behaviors of the Positive Temperature Coefficient of Resistance of Poly(styrene-co-n-butylacrylate) Filled with Ni-Plated Core-Shell Polymeric Particles", J. Polym. Sci. Part B: Polym. Phys., Vol. 45, pp. 322-329, 2007. [34] Y. Wan, D. J. Wen, “Stability of Thermo-sensitive Properties of Carbon-black/Styrene-butadiene-rubber Composite membranes”, Smart Mater. Struct., Vol. 14, pp.941-948,2005. G. D. Liang was born in 1976 in China. He received the B.S. and M.S. degrees in polymer science from Hefei University of Technology. He recently graduated from City University of Hong Kong with a Ph.D. degree in materials science. He has published more than 30 journal articles during the past 5 years.

S.C. Tjong received the B.S. degree in physics from National Taiwan University in 1973. He then received the M.S. and Ph.D degrees in materials science from University of Manchester, U.K in 1974, and 1976, respectively. He was a visiting scientist at the University of Texas at Austin (1979-1980) and Case Western Reserve University (1980-82). He is currently Professor in Physics and Materials Science, City University of Hong Kong. He is a fellow member of the Institute of Materials, Mining and Minerals (U.K.) and a member of the American Chemical Society. His present research interests include electrical, mechanical and structural behavior of polymers/composites and structure-property relationships of metal matrix composites. He has published more than 310 journal articles, 12 book chapters and edited one book.