Properties of Aluminum Filled Polypropylene Composites

Properties of Aluminum Filled Polypropylene Composites

Properties of Aluminum Filled Polypropylene Composites A.F. Osman and M. Mariatti School of Materials & Mineral Resources Engineering, Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Penang, Malaysia Received: 12 August 2005 Accepted: 22 December 2005

SUMMARY Polymers and metals have a long history of use in diverse applications. Metal filled polymer composites are nothing new, as the first attempt to combine these two classes of materials was made in the earlier years of the 20th century. The composites made by incorporation of powdery metal fillers into thermoplastic polymers combine the advantageous properties of metals and plastics. They offer light weight, resistance to corrosion, rapid fabrication rates and a wide range of moduli etc. In the present study, aluminum filled polypropylene (PP) composites with different filler particle shapes and filler loadings varying from 0% to 55% by volume were prepared. The effect of filler loadings and filler particle shapes on the properties of the composites was identified. The percolation concentrations were between 15% and 30% by volume for flaky aluminium filled PP composites, whereas with spherical aluminium particles the percolation concentrations were between 30% and 45% by volume. A steep decrease in electrical resistivity and a pronounced decrease in tensile strength and elongation at break on addition of the metal filler occurred for all investigated systems. Thermal characterization studies showed that the addition of aluminium reduced the crystallinity of the polypropylene and slightly retarded its thermal degradation. High void levels must be taken into account in evaluating the results.

1. INTRODUCTION The insulating nature of plastic materials offers many significant advantages in electrical applications. Their inherently high resistivity makes them ideal candidates for applications in which insulation of high electrical currents and voltages are essential. However, these advantages may become serious disadvantages in applications for which static buildup and electromagnetic shielding are critical factors, controlling the function of either the individual component or the entire piece of equipment. So, making polymers sufficiently conductive is essential to some electrical applications1. The composites made by incorporating powdery metal fillers into polymers combine the advantages of metals and plastics. Their properties are relevant to situations where the discharge of static electricity,

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Rapra Technology, 2006

Polymers & Polymer Composites, Vol. 14, No. 6, 2006

heat conduction, electromagnetic interference shields, galvanothermy and switching are the focus of attention. These materials are cost-effective. They offer better corrosion resistance than metals, and in most cases require only one-step processing. Additionally, the conductivity level can be ‘fixed’ to satisfy the requirements of the end user2,3. It is important to understand the difference between conductive plastics and conducting or conductive polymers, terms that are sometimes used interchangeably. In this discussion, conductive plastics are inherently nonconductive materials that are made conductive by incorporating conductive additives (filler or reinforcement). The conductive fillers provide the electrical properties and the polymeric matrix provides the mechanical properties. Conductive fillers typically used in the plastics industry include metal powders such as gold, silver, nickel, indium and copper, and carbon black or graphite powder4.

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In contrast, inherently conductive polymers with conducting backbone molecules, such as polyacetylenes, are the latest alternative to metalfilled polymers. Currently, however, conductive polymers are not highly commercialized in the plastics industry because of their instability at elevated temperatures2,3. Recognition of the importance of metal-filled polymers has led to literally hundreds of commercial carbon-filled and metal-filled thermoplastic and thermosetting products. By adding conductive fillers to polymers, materials can be designed with specific properties tailored to each application. For composite materials to be used in conductive applications, they should have an electrical conductivity in the range of 10-12 to 10-8 Siemens/cm (S/cm) for electrostatic discharge (ESD) applications, 10-8 to 10-2 S/cm for moderately conductive applications and 10-2 S/cm and higher for shielding applications5. The performance of conductive polymer composites made by incorporating powdery metal filler in the polymer depends on many factors such as the type, concentration, aspect ratio, and conductivity of the filler, as well as the plastic material selected. The influence of those factors on the mechanical properties and electrical characteristics of the composites has been studied by many researchers6-8. In most cases, these factors are all interrelated and therefore must be addressed collectively to yield the most cost-effective material selection and meet the application requirements9. The behaviour of composites made with an insulating matrix and conductive filler is extremely important to understand. The reason is that the composite changes from an insulator to a conductor over a very narrow range of filler concentration. This transition is called the percolation phenomenon, and the critical metal volume fraction is called the percolation threshold. The critical volume fraction needed to induce electrical conductivity in a composite is strongly dependent on the shape of the filler particles8. Until recently, most of the metal fillers used in composite materials were either spherical or irregularly shaped isotropic particles. These small isotropic particles are needed in high concentrations to produce an electrically conductive composite. The mechanical property and density advantages are usually lost because of the high filler loadings required. In the past few years, anisotropic metal particles such as fibers, flakes, and ribbons have become available. In these forms, metals are

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more attractive because lower concentration levels are possible2. The influence of the type of polymer and filler on the electrical characteristics has been studied by many workers6-9. Very little work, however, has been done on the question of how filler particle shape affects the properties of a composite. One study did investigate the effect of shape and filler volume fraction on the properties of nickel and copper powder filled poly(vinyl chloride) and epoxy resins, but this work was focused on the effect of the shape of two different metals10. To our knowledge, no studies have been carried out to determine the effect of spherical and flaky aluminium on the properties of PP composites. Two shapes of aluminium particle were used in this study, spherical and flaky. The effect of shape and concentration on the properties of the composite materials was measured.

2. EXPERIMENTAL PROCEDURE 2.1 Materials The PP homopolymer used in this study was TITANPRO PM-255, produced by Titan PP Polymers (M). The fine aluminum flake was supplied by BDH Laboratory Supplies. The average particle size of the flaky aluminum powder was 20.3 μm. The spherical aluminum powder (325 mesh; 99.5% metal) was supplied by Alfa AESAR, a Johnson Matthey Company. The average particle size of the spherical aluminium particles was 2.75 μm.

2.2 Sample Preparation Metal filled polymer composites were obtained by mixing the polymer and metal filler in specific combinations. The aluminum fillers were mixed with the PP matrix using a Thermo Haake Polydrive, with a rotor speed of 40 rpm at 180 °C for 15 minutes. This internal mixer machine was an enclosed mixer with a mixing chamber having two counter-rotating rotors. The weight of PP and aluminium powder was measured according to the required volume fraction, which was varied 0 to 55%. The samples were compression moulded at 180 °C, with a preheating time of 10 minutes and a pressure of 147 MPa for about 2 minutes, to produce composite sheets. In this study, the mixing and compression moulding were not carried out under vacuum because of the limitations of the system. The composite sheets were cut to the dimension required for sample testing.



2.3 Testing The density of the composites was measured by an AccuPyc 1330 Gas Pycnometer type Micromeritics. The weight fraction (Wf) was measured by physical ashing (or resin ‘burn-off’) according to ASTM D2584-94. The volume percentage of void was determined according to ASTM 2734-70. The tensile test was carried out using an Instron Universal Testing Machine Model 3366. The dimensions of the sample were in accordance with ASTM D638 Standard Type IV. The gauge length was fixed at 50 mm. The test was carried out at room temperature (23 + 2 °C) and with a crosshead speed of 50 mm/min. The determination of surface electrical resistivity was then carried out using an Advantest Digital Ultra High Resistivity Meter, Model R8340/8340 A. The thermal properties of the composite materials were measured using a Differential Scanning Calorimetry (DSC) type TA Instruments Model Q10 V8.2. The heating rate was 5 °C/min and the temperature range was from room temperature to 250 °C. The percentage crystallinity of the polymer was calculated by comparing the enthalpy of melting with that for 100% crystalline material (the enthalpy of 100% crystalline PP = 209 J/g)11. Thermogravimetric analysis (TGA) was carried out using a Perkin Elmer TGA 7 analyser. The temperature range for thermal analysis was from 50 °C to 700 °C, and the heating rate was set at 20 °C/min in a nitrogen atmosphere. A scanning electron microscope (SEM) (Leica Cambridge Ltd S360) was used to observe the morphology of the composite materials.

3. RESULTS AND DISCUSSION

filled PP composites showed higher Wf, resulting in higher density values than spherical Al filled PP composites at the same volume fraction. In this study, the void content was measured according to ASTM 2734-70. According to the measurement, the void contents of the composites filled with 30% of flaky and spherical Al were 22% and 30%, respectively, and the composites filled with 55% of flaky and spherical Al exhibit 25% and 37% of voids, respectively. Large amounts of voids were present in the composites since the processing equipment used in this study had no vacuum facility. The voids could also affect the electrical and mechanical properties of the composite. For example, large amount of voids would prevent the formation of a continuous metal-to-metal network, decreasing the conductivity. Furthermore, PP does not adhere well to metal, and this also helps the formation of voids around filler particles. The flaky Al filled PP composites had a higher density, since they had fewer voids than the spherical aluminium filled PP. Besides, the flat flaky particles could be packed more densely together in the polymer matrix than the spherical ones. The flaky particles easily overlapped with each other. This may have reduced the number of voids in the system. As shown in Figure 1, the values of the theoretical density based on the Rule of Mixtures were higher than the experimental density for the same filler loading. The low experimental values might be due to the formation of voids caused by particles stacking, or by poor bonding between the filler and the resin, and further voids might be induced during hot press moulding caused by entrapped air or bubbles in the composites.

3.1 Density and Filler Weight Fraction (Wf) The effect of aluminum filler loading on the experimental and theoretical density and the filler weight fractions (Wf) of the Al filled PP composites is shown in Figure 1. The theoretical density of the composite materials was obtained by using the Rule of Mixture equation: ρtheory= ρfVf + ρmVm where ρ= density, Vm= matrix volume fraction and Vf = filler volume fraction. The volume fractions in the equation are referred to the volume of polymer and filler used during the preparation of the composites, for example Vf varies from 0 to 0.55. As expected, the density and Wf of both flaky and spherical Al filled PP composites increased with increasing filler loading. However, the flaky


3.2 Tensile Properties The tensile strength of aluminium filled PP composites decreased with increasing filler loading, as shown in Figure 2. The trend was in accordance with previous studies on zinc in high density polyethylene (HDPE)2,7, PP-stainless steel12, etc. Even though flaky and spherical aluminium filled PP composites showed low tensile strength at higher filler loadings, the composites are still usable in electrical applications where load bearing is not required. The sharp, flat, thin and angular shape of flaky particles result in higher contact stresses than the spherical ones. The lower tensile strength of the composite system is due to the inability of the filler particles to transfer the applied stress13. The flaky composites fail more easily than those containing spherical particles.

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Figure 1. The theoretical density, experimental density and fiber weight fraction (Wf) of flaky and spherical Al filled PP composites

Figure 2. Tensile strength versus filler loading (vol%) of flaky and spherical Al filled PP composites

Apart from the shape factor, poor filler distribution at high loadings might also contribute to the lower tensile strength of the composites. In general, at low filler contents, the metal particles are dispersed individually in the polymeric matrix. Increasing the filler content caused agglomeration of the particles.

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The presence of particle agglomerations resulted in metal-to-metal contacts instead of polymer-tometal ones, which indicates the lack of interfacial interaction/adhesion among the particles. This subsequently resulted in a reduction in tensile strength at high filler contents.



Another possible explanation of the decreasing trend in the strength of aluminium filled PP composites is the degree of crystallinity of PP. Theoretically, the mechanical strength of a crystalline polymer is governed by its crystalline structure. The degree of crystallinity of PP can be defined as the fraction of the total polymer that is in the crystalline state, and this was determined using DSC. A higher degree of crystallinity correlates with better tensile properties, especially tensile strength4,7. Table 1 summarizes the melting temperature (Tm), the heats of melting (ΔHm) and percent crystallinity of the composites. The result shows that the degree of crystallization and the heat of melting (ΔHm) of the flaky and spherical particle filled PP composites decreased with increasing filler loading. 30% by volume of flaky filler produced composites in which the resin had a lower degree of crystallinity than was found with spherical aluminium particles, whereas at 55% volume, the degree of crystallinity of both systems was broadly similar. Incorporation of any foreign inclusions especially of filling materials, modifies the degree of crystallinity and by implication, the mechanical characteristics. The drop in crystallinity with the addition of aluminium filler suggests that the filler hindered the crystal growth and hence reduced the crystallinity. However, no significant changes were observed in the melting point of the resin on the addition of filler. This is in accordance with previous work by Rusu et al.7 where the melting points of unfilled HDPE and of the resin with 20% by volume of zinc are similar. Accordingly, the degree of crystallinity explains why the overall tensile strength of flaky aluminium filled PP composites was lower than that of spherical Al filled PP composites at the same filler loading. Comparisons between the stress-strain behaviour of unfilled PP, 30% aluminium (flaky and spherical)

filled PP and 55% aluminium (flaky and spherical) filled PP are shown in Figure 3. In general, the use of spherical particles resulted in a higher maximum stress than flaky ones, compare the samples with 30% and 55% filler by volume. As expected in both types of composite, the strain at break decreased drastically with increasing filler content. Earlier work by Rusu7 on zinc filled high density polyethylene (HDPE) polymer composites also showed a similar trend with the elongation/ strain at break reducing with increasing filler loading. The more elastic the polymer matrix, the higher the elongation at break will be. The elastic component is contributed mainly by the polymer4. The addition of filler increases the brittleness. Thus, when subjected to tensile mode deformation, composites with 30% filler failed in a brittle manner with a low tensile strength. It is of interest to study the effect of morphology on the fracture behaviour of the composites. Our observations of the fracture surfaces were consistent with the slight decrease in the strain at break. The morphology indicated a gradual change of tensile fracture behaviour from ductile to brittle, as the filler loading increased. Figure 4 shows the fracture surface of unfilled polypropylene, and of composites with 30% and 55% of flaky aluminium. From the micrographs, it was obvious that the fracture behaviour of unfilled PP was ductile. (Ductile fracture is characterized by gross plastic deformation, indicated by a fibrillar structure). The 30% volume samples showed a mixed failure mode. On the other hand, the 55% volume samples showed brittle failure. Brittle fracture surfaces display little or no macroscopically visible plastic deformation and they requires less energy to form. The brittleness

Table 1. Melting temperature (Tm), heat of melting (ΔHm) and percent crystallinity of the resin in the filled composites Composite 100% PP PP/Al (Flaky) PP/Al (Spherical)

Filler loading (vol %)

Tm (oC)

ΔHm (J/g)

Crystallinity (%)

-

163.29

83.88

40.50

30%

164.50

57.62

27.82

55%

162.88

42.02

20.29

30%

164.79

61.97

29.92

55%

164.43

39.54

19.09


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Figure 3. Comparisons of the tensile stress-strain curve between unfilled PP, 30% and 55% flaky Al filled PP and 30% and 55% spherical Al filled PP composites

35

Stress (MPa)

30

100% PP

25 70% PP30% Al (flaky)

20

45% PP55% Al (flaky)

15 10

70% PP-30% Al (spherical)

5 0 0

1

2

3

4

5

6

45% PP-55% Al (spherical)

Strain (%)

can be associated with the disappearance of plastic deformation of the polymer matrix. The lack of plastic deformation on the fracture plane explains the sharp drop in the strain at break. Figure 5 shows the effect of filler shape and filler loading on the Young’s modulus of flaky and spherical particle filled composites. As expected, the results indicate that the modulus increased with increasing filler loading. Generally, fillers with higher stiffness than that of the matrix improve the modulus of polymer composites2. The modulus of aluminium is 69GPa, which is much higher than that of the PP matrix (1.441 GPa). So the modulus of the composites increased with filler loading. The tensile modulus of the flaky PP composites was markedly higher than that of the spherical Al filled PP composites. The larger size of the flaky particles compared to the spherical ones may have increased the rigidity of the polymer matrix. Another factor is the shape of the flaky particles10. Flaky particles with greater width and smaller thickness than that of the spherical ones can be packed more closely and with fewer voids. Furthermore, flaky shape fillers with a high aspect ratio show better stiffening than particles with high particle symmetry10,14.

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3.3 Surface Electrical Resistivity Figure 6 shows the effect of metal loading on the surface resistivity of the composites. As expected, the surface resistivity of both flaky and spherical particle filled composites decreased with increasing filler loading. A recent study by Zue8 on tin-polypropylene composites also showed a similar trend whereby the electrical resistivity decreased with increasing filler loading. Investigations have shown that metal-filled plastics exhibit insulating properties until the percolation a threshold concentration of conductive filler is achieved. Theoretically, below the critical volume fraction or concentration, Φ, conductive aluminium particles are electrically isolated, and no significant decrease in resistivity is observed. At the critical concentration, Φ, however, a continuous conductive network is established throughout the PP phase, predominantly due to metal-to-metal contacts. As a result, the resistivity decreases dramatically by some orders of magnitude. For flaky Al filled PP composites, a sudden and large reduction occurred in the range 15% < Φ < 30% by volume. On the other hand, the percolation threshold is observed to occur in the range 30% < Φ < 45% by volume for spherical particles. However, theory suggests that percolation thresholds occur over a very narrow concentration range whereas there was a wide range in the present study. Flaky particle filled PP composites were found to have a lower percolation threshold than those of spherical



Figure 4. Fractured surface of (a) Unfilled PP, (b) 30% Al (flaky) filled PP, and (c) 55% Al (flaky) filled PP. Notes: The plastic deformation shown by fibrillar structure is obviously seen in (a), and it disappeared in (c) with higher filler content (55% volume)

(a)

Plastic deformation shown by fibrillar structure indicates ductile fracture behaviour

(b) Ductile behaviour

(c) No fibrillar structure which indicates brittle fracture behaviour


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Figure 5. Young’s modulus versus filler loading (vol%) of Al (flaky) and Al (spherical) filled PP composites

Figure 6. Log volume resistivity versus filler loading (vol%) of flaky and spherical filled PP composites

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Al filled PP composites. Increasing the filler content above the critical loading did not appreciably reduce the resistivity. Flaky and spherical particle filled composites did not show much decrease in resistivity on changing from 30% to 55% or from 45% to 55% of filler loading, respectively. As mentioned earlier, the electrical conductivity of a composite is generally characterized by its dependence on filler volume fraction. The thought is that, as the filler level is increased, the metal particles begin to contact each other, and a continuous path is formed through the volume of the sample for electrons to travel. The formation of a conductive network is based on the principle of percolation theory10,15. Here, aluminum is the conductive filler and it acts as a channel for the electrons to flow through. The electrons are free to flow through aluminum particles. However, when they reach the last of a sequence of aluminum particles, they encounter the polymer matrix, which blocks the flow of the electrons. Once enough filler has been added, the particles begin to come in contact with each other, forming a complete path for the electrons to travel throughout the full volume of the composite. Accordingly, this explains why the electrical resistivity decreases with increased filler loading. The number of particle-to-particle contact of the filler is the most important factor, and electrical continuity relies on chance contacts between them. Attention should be paid to the fact that the filler particle shape, dimensions and size have a major effect on the effectiveness of metal-to-metal contacts

and could alter the conductivity of the composite2,8. Flaky particle filled composites showed a lower percolation threshold than spherical particle types. The high specific surface area of flaky particles increased the probability of metal-to-metal contacts and accounted for the low percolation threshold. The flat surfaces of the flaky particles tended to overlap. If the overlap is such that the flakes actually touch, metal flakes can provide electrical pathways through the composite10. Bhattacharya2 has also suggested that the flat surfaces of flaky particles develops a large contact area. He added that the more structured or elaborately shaped the particle, the more likely it is to contact a nearest neighbour and form a continuous network. Perfectly spherical fillers, which arguably have the least elaborate shape, reach the percolation threshold at higher filler loadings than flaky ones. Figures 7 and 8 show the metal filler distribution for flaky spherical systems, respectively, according to filler loading (15%, 30% and 55% by volume). The increase in filler loading resulted in better metal-tometal contact. However, flaky fillers showed better filler metal-to-metal contact than spherical ones at the same filler loadings. The critical volume fraction required to achieve the percolation threshold also depends strongly on the aspect ratio. The percolation threshold for metal-polymer composites decreased rapidly with increasing aspect ratio8,15. The aspect ratio of flaky aluminium was much greater than that of the spherical grade, which had an aspect ratio of unity. This helps to explain the difference in percolation threshold.

Figure 7. (a) SEM micrograph of 85% PP-15% Al (flaky) composite (500X, (b) SEM micrograph of 70% PP-30% Al (flaky) composite (500X), and (c) SEM micrograph of 45% PP-55% Al (flaky) composite (500X)

(a)

(b)


(c)

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Figure 8. (a) SEM micrograph of 85% PP-15% Al (spherical) composite (500X), (b) SEM micrograph of 70% PP-30% Al (spherical) composite (500X), and (c) SEM micrograph of 45% PP-55% Al (spherical) composite (500X)

(a)

(b)

(c)

The above results indicate that the shape and the aspect ratio of the metal particles are the two principal factors that should be carefully examined when making conductive plastic-based composites containing metal particles. Using metal particles with larger aspect ratios helps to reduce the minimum metal content required to reach a certain conductivity value16.

At similar filler loadings it was found that the total weight loss of the spherical particle filled PP composites was higher than that of the flaky equivalents. The weight of filler was measured by subtracting the total weight loss from the total weight. The amount of filler in the flaky particle samples was higher than the amount in spherical particle analogues.

3.4 Thermogravimetric Analysis

The weight of filler measured by TGA was in accordance with the measurements by physical ashing (as discussed in Section 3.1). Overall, filler particle shape did slightly influence the thermal stability of the matrix and there was a slight change in IDT, FDT, T50% and weight loss values which depended on the filler shape.

The TGA results for unfilled PP, 30% and 55% volume of filled PP are summarized in Table 2. As the filler concentration increased, the thermograms shifted towards the right and the initial decomposition temperature (IDT), decomposition at 50% weight loss (T50%) and final decomposition temperature (FDT) increased. The initial decomposition temperatures were around 5.7 °C and 14.7 °C higher for 30% and 55% flaky aluminium filled PP than for neat PP, respectively. The fillers improved the polymer’s thermal stability. Higher thermal stability was observed with 55% filled PP than with 30% filled samples. The addition of filler slows down the decomposition reaction, raising the temperature of onset of degradation and improving thermal stability. Rusu et al.7 reported that the addition of zinc particles to high-density polyethylene (HDPE) matrix increased the thermal stability of the resin.

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4. CONCLUSIONS Aluminium (flaky and spherical) filled PP composites with different filler loadings have been investigated. The tensile strength and strain at break decreased with increasing filler loading. However, as expected, the density, voids and modulus increased with increasing filler loading. The surface electrical resistivity of the flaky particle filled PP composites showed a lower critical volume fraction or percolation threshold than the spherical equivalents. The higher specific surface area of the flaky particles resulted in a higher number of metalto-metal contacts, hence reducing the percolation threshold. The filled composites showed higher thermal stability than unfilled PP.



Table 2. IDT, T50%, FDT and weight loss on heating of the composites by TGA Samples PP (100%) PP/Al (Flaky) PP/Al (Spherical)

Filler Loading (vol %)

IDT (oC)

T50% (oC)

FDT (oC)

Total weight loss (%)

Weight of filler (%)

-

403.76

462.02

490.03

98.18

0

30%

409.42

471.88

522.42

67.65

32.35

55%

418.51

485.89

535.22

47.73

52.27

30%

405.36

475.11

520.95

70.98

29.02

55%

415.49

476.06

501.81

55.02

44.98

IDT: Initial decomposition temperature T50%: Decomposition temperature at 50% weight loss FDT: Final decomposition temperature

ACKNOWLEDGEMENTS

8.

The authors would like to thank Universiti Sains Malaysia (Grant No: 6035077).

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9.

Weidenfeller, B. Hofer, M. and Schiling, F., Composites Part A: Applied Science and Manufacturing, 33(8), (2002), 1041-1053.

10.

Mamunya, Y.P., Davydenko, V.V., Pissis, P. and Lebedev, E.V., European Polymer Journal, 38, (2002), 1887-1897.

11.

Margolina, A. and Wu, S., Polymer, 29, (1985), 2170.

12.

Song, T.T., Ming, Q.Z., Min, Z.R., Han, M.Z. and Fang, M.Z., Polymer and Polymer Composites, 9(4), (2001), 257-264.

13.

Bigg, D.M., in Proceedings of ANTEC, Society of Plastics Engineers, 25, (1979) 583-588.

14.

Wypych, G., in “Handbook of Fillers, 2nd Edition”, ChemTec Publishing, Toronto, (2000), 225-228.

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Parker, D.B.V., in “Fillers for Plastics”, edited by W.C. Wake, Iliffe, London, (1971), 129.

2.

Bhattacharya, S.K., in “Metal Filled Polymers, (Properties and Applications)” Markel Dekker, Inc., New York, (1996), 165-199.

3.

Mark, H.F., in “Encyclopedia of Polymer Science and Technology, Third Edition” John Wiley and Sons, Inc., New York, (2003), 652691.

4.

Osswald, T.A. and Menges, G., in “Materials Science of Polymers for Engineers” Hanser Publishers, Munich Vienna New York, (1996), 394-396.

5.

Strong, A.B., in “PLASTICS Materials and Processing, Second Edition”, Prentice Hall, Brigham Young University, (1996), 210-211.

15.

Stauffer, D., in “Introduction of Percolation Theory”, Taylor and Francis, London, (1985).

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16.

Xie, P., Gu, P. and Beaudoin, J., J. Materials Science, 31, (1996) 4093-4097.

7.

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