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Metal Powder-Filled Polyethylene Composites. V. Thermal Properties N. M. Sofian, M. Rusu, R. Neagu and E. Neagu Journal of Thermoplastic Composite Materials 2001; 14; 20 DOI: 10.1106/9N6K-VKH1-MHYX-FBC4 The online version of this article can be found at: http://jtc.sagepub.com/cgi/content/abstract/14/1/20

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Metal Powder-Filled Polyethylene Composites. V. Thermal Properties N. M. SOFIAN AND M. RUSU1 Gh. Asachi Technical University Faculty of Industrial Chemistry Department of Macromolecules Bd. D. Mangeron, No. 71 6600 Iasi, Romania R. NEAGU AND E. NEAGU Gh. Asachi Technical University Faculty of Materials Science Department of Physics Bd. D. Mangeron, No. 71 6600 Iasi, Romania ABSTRACT: Thermal properties—such as thermal conductivity, thermal diffusivity, and specific heat—of metal (copper, zinc, iron, and bronze) powder-filled high-density polyethylene composites are investigated experimentally in the range of filler content 0–24% by volume. Experimental results show a region of low particle content, 0–16% by volume, where the particles are distributed homogeneously in the polymer matrix and do not interact with each other. In this region most of the thermal conductivity models for two-phase systems are applicable. At higher particle content, the filler tends to form agglomerates and conductive chains resulting in a rapid increase in thermal conductivity. KEY WORDS: high-density polyethylene, metal fillers, metal-filled polymers, thermal conductivity.

INTRODUCTION ONDUCTIVE POLYMERIC COMPOSITES obtained by the addition of metal powders to thermoplastic polymers represent an important group of engineering materials, with a great number of applications, such as discharging static electricity, heat conduction, electromagnetic interference shields, electrical heating, and

C

1Author

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to whom correspondence should be addressed. E-mail: [email protected]

Journal of THERMOPLASTIC COMPOSITE MATERIALS, Vol. 14—January 2001 1530-7980/01/01 0020–14 $10.00/0 DOI: 10.1106/9N6K-VKH1-MHYX-FBC4 © 2001 Technomic Publishing Co., Inc.


Metal Powder-Filled Polyethylene Composites. V. Thermal Properties

21

converting mechanical signals to electrical signals [1–16]. These materials are inexpensive, offer better corrosion resistance than metals, and in most cases require only one-step processing, compared to the great number of steps involved in metal processing. Additionally, the conductivity level can be “fixed” in order to satisfy the various requirements of the end user. There are three principal thermal properties used to describe heat transport through a material: thermal conductivity, specific heat, and thermal diffusivity. Knowledge of the thermal conductivity is essential for the prediction of heat flow rates and temperature distributions for steady state conditions. The thermal diffusivity determined the time-dependent conditions for the unsteady state: the transient heat flow and the temperature distribution in the material. These properties are very important from the standpoint of polymer processing and the use of polymer products. The specific heat is an internal molecular property, which is of fundamental importance for the calculations that refer to heat change. These thermal properties are related by the following expression: α=

K Cρ

(1)

where α is thermal diffusivity, K is thermal conductivity, C is specific heat, and ρ is density of material. The rate of heat flow in a nonmetal solid depends on the coupling intensity of atoms and localized atomic vibrational energy. There are intense coupling movements in covalent materials, with the thermal transmission being quite difficult in the case of crystalline networks, which are highly ordered. In glassy state polymers, there are three separate modes of thermal conduction: through longitudinal vibrations of the solid, through three-dimensional vibrations of the solid, and through one-dimensional vibrations along the polymeric chain [17]. In the case of metals, atomic network vibration movements in the thermal conduction process convert thermal energy from one point of the material to another through mobile electrons, which is generally more effective. This paper presents the results obtained regarding the thermal properties of some polymer composite materials that contain high-density polyethylene (HDPE) and various types of metal powders (zinc, copper, iron, bronze).

EXPERIMENTAL Materials The following materials were used to obtain the polymer composites examined in this work:


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N. M. SOFIAN, M. RUSU, R. NEAGU AND E. NEAGU

! high-density polyethylene type Rigidex A 52 BB/088, with melt flow index 0.88 g/10 min, density 0.96 g/cm3 and thermal conductivity 0.505 W/m·K, manufactured by British Resin Products Ltd., England ! zinc powder with the maximum particle dimensions of 5 µm, density 7.14 g/cm3, and thermal conductivity 116 W/m·K, produced by S.C. Ampelum S.A. Zlatna, Romania ! copper powder with the maximum particle dimension of 60 µm, density 8.92 g/cm3, and thermal conductivity 384 W/m·K, produced by S.C. Neferal S.A. Bucuresti, Romania ! iron powder with the maximum particle dimension of 100 µm, density 7.8 g/cm3, and thermal conductivity 80.2 W/m·K, produced by S.C. Sinterom S.A. Cluj-Napoca, Romania ! bronze powder with the maximum particle dimension of 100 µm, density 8.11 g/cm3, and thermal conductivity 64 W/m·K, produced by S.C. Sinterom S.A. Cluj-Napoca, Romania Sample Preparation The polymer-metal mixture was prepared through mixing on a laboratory roll mill with cylinders heated at 155°C. The mixing time was 10 min after the HDPE sheet formed on the front cylinder of the roll mill and after the addition of metal powder. The composite sheet was then transformed into platelets of 1 mm thickness by compression (pre-heating 10 min, compression 5 min at 160°C and 150 daN/cm2, cooling under pressure). The resultant samples are rectangular in shape (62 mm length and 36 mm width). Composites with metal powder concentrations between 0 and 24% by volume were manufactured. The calculation of volumetric concentrations is based on the solid densities of the constituents. Measurements Out of the methods used for experimental determination of these thermal characteristics, we have chosen the transient method, because it is the most suitable for measuring thermal values α, K and C in thin plates and requires only small amounts of material. The transient method is based on heat transfer in a semi-infinite solid theory. Consider a constant thermal flux, F, flowing into a semi-infinite solid (0 ≤ x ≤ ∞). Let V(x,t) be the temperature above ambient at position x at time t. V(x,t) satisfies the relations [18]: 1/ 2

 x2  KV ( x, t ) = (αtx −2 )1/ 2 i erfc   2Fx  4α t 


(2)


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1/ 2

V ( x,2t ) = V ( x, t )

 x2  2i erfc    8αt 

1/ 2

 x2  i erfc    4αt 

(3)

1/ 2

V (0, t ) =

2 F  αt  x  π 

(4)

Experimentally we determine V(x,2t)/V(x,t), and from relations (2) and (3) we obtain K and α. C is calculated from relation (1). The experimental equipment comprises the measuring cell, a regulated direct current (d.c.) supply (1 A), an ammeter of high precision (of class 0.1), a microvoltmeter (of class 0.1), and an XY recorder (Figure 1). The samples used for the measuring are composite material platelets of 62 mm length, 36 mm width and 1 mm thickness. Two packs of sample platelets of 11 mm total thickness are placed on both sides of the heater. The total thickness of the sample on one side of the heater is 11 mm. The heater must be capable of providing a constant thermal flux during measurement. For this reason, ultra-thin constantan

Figure 1. Experimental arrangement.


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foil is used [18]. The temperature coefficient of resistance for this material is essentially zero. A regulated d.c. supply drives current through the heater. A precision ammeter measures the current. The heater is the same length as the sample, but the width is about 1.5 mm less on each side. The differential thermocouple system is composed of thin (0.1 mm diameter) edge-welded copper-constantan wires. The lengths of the thermocouple wires were chosen to ensure negligible heat loss by conduction. The distance x between the heater and the first junction of the differential thermocouple was about 1 mm. The second junction of the thermocouple, which is at ambient temperature, is placed about 0.9 mm above the first junction. The temperature differential is measured by a microvoltmeter with the amplifier’s gain of 1000/0.3 and the XY recorder, used on 10 mV/cm with 1 cm/s speed. The measurements were made at ambient temperature (25°C). The experimental details of this experiment can be found in the literature [17,18]. RESULTS AND DISCUSSIONS Thermal Conductivity There are a number of models in the literature (empirical models or theoretical models) that predict the effective thermal conductivity of two-phase materials [19–21]. Using the potential theory, Maxwell and Eucken [22] obtained a simple relationship for the conductivity of randomly distributed and non-interacting homogeneous spheres in a homogeneous medium: Kc = K p

K m + 2 K p + 2Φ ( K m − K p ) K m + 2K p − Φ( K m − K p )

(5)

where Kc, Kp and Km are, respectively, the thermal conductivity of the composite (metal particle-filled polymer), continuous phase (polymer), and discrete phase (metal particles), and Φ is the volume fraction of filler (discrete phase). This model can predict the effective thermal conductivity at low filler concentrations. For high filler concentrations, particles begin to touch each other and form conductive chains in the direction of heat flow, so this model underestimated the value of effective thermal conductivity in this region. Starting with Tsao’s probabilistic model [23], Cheng and Vachon [24] assumed a parabolic distribution of the discontinuous phase. The constants of the parabolic distribution were evaluated as a function of the discontinuous phase volume fraction. The equivalent thermal conductivity of a unit cube of the mixture is derived in terms of the distribution function and the thermal conductivity of the constituents. The effective thermal conductivity is given for the case Km > Kp:



1 = Kc × ln

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1 C (K p − K m )(K p + B(K m − K p ))

K p + B(K m − K p ) + B / 2 C (K p − K m ) K p + B(K m − K p ) − B / 2 C (K p − K m )

+

1− B Kp

(6)

where B = 3Φ / 2, C = −4 2 / 3Φ . For two-phase materials for which the thermal conductivity of the continuous phase is much smaller than the thermal conductivity of the discrete phase, Kp 100, as long as Φ < 0.667, the effective thermal conductivity of the composite may be approximated by the second term of Equation (6): Kc ≈

Kp

(7)

1− B

The semitheoretical model proposed by Lewis and Nielsen [25] is derived by a modification of the Halpin-Tsai Equation [26] to include the effect of particle shape and orientation or type of packing for a two-phase system: Kc = K p

1 + AβΦ 1 − βΦψ

(8)

where β=

Km / K p − 1 Km / K p + A

and ψ = 1 +

1 − Φm Φ Φ 2m

The constant A is related to the generalized Einstein coefficient kE [27,28]: A = kE − 1

(9)

The constant A depends upon the shape and orientation of the dispersed particles. Φm is the maximum packing fraction of the dispersed particles, which is defined as the true volume of the particles divided by the volume they appear to occupy when packed to their maximum extent. The values of A and Φm for many geometric shapes and orientations are given in Reference [29]. For randomly packed spherical particles, A = 1.5 and Φm = 0.637, whereas for randomly packed aggregates of spheres or for randomly packed, irregularly shaped particles, A = 3 and Φm = 0.637. In the range of high volume content, the particles touch each other and form agglomerates and chains. Equation (5) is no longer valid in the region where particles


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begin to touch each other. Agari and Uno [30] proposed a new model for filled polymers that takes into account the parallel and series conduction mechanism. According to this model, the expression that governs the thermal conductivity of the composite is log Kc = Φ ⋅ C2 ⋅ log K m + (1 − Φ ) ⋅ log(C1 ⋅ K p )

(10)

where C1 and C2 are experimentally determined constants of order unity. C1 is a measure of the effect of the particles on the secondary structure of the polymer, such as crystallinity and the crystal size of the polymer. C2 measures the ease of the particles to form conductive chains; the more easily particles are gathered to form conductive chains, the more the thermal conductivity of the particles contributes to an increase in thermal conductivity of the composite and C2 becomes closer to 1. The experimental values of thermal conductivity are compared with the values calculated with Equations (5), (7), (8) and (10) (Figures 2, 3, 4 and 5). As metal particles form aggregates only at large concentrations and their shapes are not perfectly spherical, the shape factor A in the Lewis-Nielsen model is taken into calculation once equal to 1.5 (the value for randomly packed spherical

Figure 2. Predicted and experimental (o) values of thermal conductivity of HDPE filled with zinc particles versus volume percent of filler.



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Figure 3. Predicted and experimental (o) values of thermal conductivity of HDPE filled with copper particles versus volume percent of filler.

Figure 4. Predicted and experimental (o) values of thermal conductivity of HDPE filled with iron particles versus volume percent of filler.


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Figure 5. Predicted and experimental (o) values of thermal conductivity of HDPE filled with bronze particles versus volume percent of filler.

particles and another time equal to 3 (the value for randomly packed aggregates of spheres, and randomly packed irregularly shaped particles). A low particle content, Φ < 16%, the increase in thermal conductivity with increasing volume content of filler is slow; for 16% metal content, the thermal conductivity is between 1.36 (for iron) and 1.4 (for copper) times that of pure HDPE. It is remarkable that for all metal powders except iron, the thermal conductivity of the studied composites containing 4% filler is smaller than that of unfilled HDPE. We associate this phenomenon with the existence of a discontinuous structure, with a large net surface contact area between powder and polymer and the increase of polymer crystallinity, both of which affect the heat transfer through the polymer matrix. The variation of thermal conductivity at these metal contents indicates that the conductive system is closer to a dispersion system than to an attached system. This implies that the filler distribution in the system was random, and the possibility of formation of conducting metal chains was insignificant. However, since heat flow can take place through molecular vibrations and free electron movement, heat transfer is possible through the matrix polymer. Metal particles are dispersed in the polymer matrix and do not interact with each other, as can be observed from the optical photomicrographs of these com-



29

posite materials (Figure 6). All the models predict higher thermal conductivity than the experimental values. The most appropriate models for filler concentrations up to 16% are given by Equation (10) (when C2 = 0.3, meaning that it is quite difficult for the particles to form conductive chains at low contents), Equation (8) (when A = 1.5, for irregularly shaped particles), and Equation (5). For particle content greater than 16%, conductive chains are exponentially formed by metal particles, causing a large increase in the effective thermal conductivity of the composite. In the range of high volume content, the particles touch each other and form agglomerates and chain, as shown in the optical photomicrographs (Figure 7). All the models fail to predict the thermal conductivity of HDPE/iron and HDPE/bronze composites in this region. For these composites, the thermal conductivity increases more rapidly with filler content than the models predict. In the case of HDPE/copper and HDPE/zinc composites, the following equations predict quite well the thermal conductivity of the composite for filler content

Figure 6. Microscopic photographs of HDPE filled with 4% by volume: (a) zinc particles, (b) copper particles, (c) iron particles, and (d) bronze particles.


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Figure 7. Microscopic photographs of HDPE filled with (a) 20% by volume zinc particles, (b) 24% by volume copper particles, (c) 24% by volume iron particles, and (d) 24% by volume bronze particles.

greater than 16%: Equation (10) when C2 = 0.3, Equation (8) when A = 1.5, and Equation (5). The different shape and dimension of dispersed particles could also cause a variation in the behavior of composites containing the four metals. Thermal Diffusivity The diagrams presenting the thermal diffusivity variation with the metal powder type and concentration in the studied composite materials are represented in Figure 8. Analyzing these diagrams, one may notice that they could be separated into two zones. An insignificant increase of the thermal diffusivity may be observed for metal powder contents smaller than 16%. For metal powder contents above this value, thermal diffusivity increases significantly. The most important increase of this characteristic is observed in the case of iron powder-filled composites (curve 4).



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Figure 8. Thermal diffusivity of HDPE filled with (1) zinc particles, (2) copper particles, (3) iron particles, and (4) bronze particles versus volume percent of filler.

Figure 9. Specific heat of HDPE filled with (1) zinc particles, (2) copper particles, (3) iron particles, and (4) bronze particles versus volume percent of filler.


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Specific Heat The specific heat of studied composite materials was calculated with Equation (1) and is shown in Figure 9 as a function of metal powder volume concentration. A decrease of specific heat is observed when the metal powder content is increased in mixes. The lowest value of specific heat corresponds to the iron/HDPE composite. CONCLUSIONS The thermal conductivity of composite materials obtained by mixing HDPE with sufficient contents of metal powders (copper, iron, bronze, and zinc) is superior to that of unfilled HDPE. For metal powder concentrations between 0 and 16%, the thermal conductivity of the studied composite materials is close to the calculated thermal conductivity using the theoretical models presented in the literature. For filler concentrations above 16%, the thermal conductivity of the studied composite materials increases with the increase in metal powder content. This increase is greater than the theoretical predictions presented in this work. The thermal diffusivity of HDPE/metal powder composite increases with the increase of filler content in a manner similar to that of the thermal conductivity. The specific heat of studied composite materials decreases when the metal powder concentration increases in the studied samples. REFERENCES 1. Kusy, R. P. 1986. Metal-Filled Polymers. ed. S. K. Bhattacharya. New York, NY: Marcel Dekker Inc., 1–132. 2. Ghosh, K. and Maiti, S. N. 1996. J. Appl. Polym. Sci., 60: 323–331. 3. Kilik, R. and Davies, R. 1989. Int. J. Adhesion and Adhesives, 9(4): 224–228. 4. Rusu, M., Darânga, M., Sofian, N. M. and Rusu, D. L. 1998. Materiale Plastice, 35(1): 15–20. 5. Rusu, M., Sofian, N. M. and Rusu, D. L. Proceedings of the International Conference on Materials Science BRAMAT’99, vol. IV: Non-Metallic Material and Environmental Protection, Brasov, February 1999, pp. 93–96. 6. Rusu, M. and Rusu, D. L. 1995. Bul. Inst. Polit. Iasi, XLI(XLV), s. II, 1-4: 89–93. 7. Rusu, M., Darânga, M. and Rusu, D. L. 1996. Bul. Inst. Polit. Iasi, XLII(XLVI), s.II, 1–2: 113–120. 8. Ghosh, K. and Maiti, S. N. 1996. Polym.-Plast. Technol. Eng., 35(1): 15–20. 9. Genetti, W. B. and Grady, B. P. 1996. Polym. Preprints, 37(1): 819–820. 10. Ghosh, K. and Maiti, S. N. 1997. Polym.-Plast. Technol. Eng., 36(5): 703–722. 11. Yang, L. and Schruben, D. L. 1994. Polym. Eng. Sci., 34(14): 1109–1114. 12. Damyanov, S., Kartalov, P. and Miloshev, S. 1985. Bulg. J. Phis., 12(1): 69–78. 13. Maiti, S. N. and Mahapatro, P. K. 1989. J. Polym. Mater., 6: 107–114. 14. Nicornorova, N. I., Stachanova, S. V., Chmutin, I. A., Trotimchuk, E. S., Chernavskii, P. A.,



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