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hollow glass bead composites
Composites: Part B 56 (2014) 431–434
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Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Estimation of thermal conductivity for polypropylene/hollow glass bead composites Ji-Zhao Liang ⇑ Research Division of Green Function Materials and Equipment, College of Industrial Equipment and Control Engineering, South China University of Technology, Guangzhou 510640, PR China
a r t i c l e
i n f o
Article history: Received 10 March 2013 Received in revised form 7 July 2013 Accepted 19 August 2013 Available online 29 August 2013 Keywords: A. Polymer–matrix composites B. Thermal properties C. Analytical modeling D. Thermal analysis
a b s t r a c t The thermal conductivity of hollow glass bead (HGB)-filled polypropylene (PP) composites was estimated using the thermal conductivity equation of inorganic hollow microsphere-filled polymer composites published in the previous paper. The estimations were compared with the measured data of the PP composites filled with two kinds of HGB with different size (the mean diameter was respectively 35 lm and 70 lm). The results showed that the predictions of the thermal conductivity were in good agreement with the measured data except to individual data points. Furthermore, both the estimated and measured thermal conductivity decreased roughly linearly with increasing the HGB volume fraction when the HGB volume fraction was less than 20%; the influence of the particle diameter on the thermal conductivity was insignificant. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Thermal conductive polymeric composites have been paid more and more attention in the past two decades [1–4]. Rigid hollow microspheres (e.g. hollow glass beads, hollow ceramic beads, rigid hollow plastic beads, etc.) contain inert gas, and have some advantages, such as low thermal conductivity coefficient and density. In addition, these micro-particles do not generate important stress concentration in the interface between the fillers and the matrix owing to their smooth spherical surface [5]. They are, therefore, usually used to fill and modify resins in polymeric industry and coating industry. Generally, polymer/hollow micro-sphere composites have good thermal and sound insulation, low density and good mechanical and rheological properties [6–13]. This type of composite is applied in building materials, space-flight and the aviation industry. The heat transfer process in porous materials is very complicated, especially for polymer composites. It is quite important, therefore, to understand the heat transfer mechanisms of heat transfer in polymer composites. Thermal conductivity is an important characteristic of heat transfer properties of materials [14]. For porous materials, several researchers [15,16] derived some thermal conductivity equations based on the Maxwell expression, or established a more accurate formula for calculating the effective thermal conductivity of porous materials [17]. Relatively, the models proposed respectively by Nielsen [18] and Cheng–Vachon [19] ⇑ Tel.: +86 02087114739. E-mail address: [email protected] 1359-8368/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2013.08.072
may better estimate the thermal conductivity of filled composite materials, while the Agari–Nagai equation can predict the thermal conductivity of the composites with high-loading [20]. Liang [21] analyzed the thermal conductivity of a porous material with closed spherical and cylindrical holes. Suvorov et al. [22] studied the thermal conductivity of hollow emery filled composites. Recently, Hill and Supancic [23] proposed an indirect method to determine this interfacial boundary resistance by preparing large-scale ‘‘macromodel’’ simulations of the polymer–ceramic interface. They also investigated the effects of similar size and shape of platelet-shaped particles on the thermal conductivity of polymer/ceramic composite materials [24]. Yu et al. [25] measured the thermal conductivity of polystyrene–aluminum nitride composite, and found that the thermal conductivity of composites was higher for a polystyrene particle size of 2 mm than that for a particle size of 0.15 mm. The thermal conductivity of the composite was five times that of pure polystyrene at about 20% volume fraction of aluminum nitride (AIN) for the composite containing 2 mm polystyrene particles. Hollow glass bead (HGB) contains inertia gas, and have some advantages, such as low thermal conductivity coefficient and light. In addition, these hollow micro-particles do not generate important stress concentration in the interface between the inclusions and the matrix owing to their smooth spherical surface. In the previous work, Liang and Li [6] measured the thermal conductivity (keff) of HGB-filled polypropylene (PP) composites by means of a thermal conductivity instrument, and simulated the heat-transfer process in PP/HGB composites by using finite element method (FEM) with ANSYS software [26]. More recently, Liang and Li [27] analyzed the heat transfer mechanisms in polymer/hollow
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microspheres composites, and established a mathematical model for predicting the thermal conductivity. The objectives in this paper are to predict the thermal conductivity of the PP/HGB composites applying this mathematical model and to compare the predictions with the experimental data. 2. Modeling 2.1. Heat transfer mechanisms in polymer/hollow micro-sphere composites In general, the thermal conductivity in thermal insulation materials is the combined effect of heat conduction, convection and radiation. According to the second law of thermodynamics, heat always transfer spontaneously from high temperature body to low temperature one. Namely, heat transfer will conduct in where there is difference in temperature. Generally, insulation materials only reduce the strength of heat exchange, and have a property of blocking heat transfer. Polymer/hollow micro-spheres composite is a kind of ternary composites, it includes three phases, namely resin, gas and spherical shell. During heat transfer in polymer/hollow micro-spheres composites, when heat quantity is close to a hollow microsphere, only a small part of heat quantity will conduct by it, while greater part of heat quantity will move around it due to its low conductivity, as shown in Fig. 1. Because of low thermal conductive coefficient of the hollow micro-spheres and longer heat transfer route and complication in the filled systems, the thermal conductivity of these composites will be reduced. It can be seen from Fig. 1 that the heat transport in inorganic hollow microsphere filled polymer composites has three kinds of ways: (1) thermal conduction by solid; (2) heat radiation on the surface between neighboring hollow particles; (3) the natural thermal convection of gas in the hollow particles. After finishing the experiments, Skochdopole [28] pointed out that the natural thermal convection of the gas in a micro-bubble would not occur when the bubble diameter was less than 4 mm. Because the diameter of the hollow micro-spheres as fillers is usually less than 0.1 mm, the natural thermal convection of the gas in it may be neglected. Furthermore, polymer composite works usually under lower temperature conditions where the proportion of the thermal radiation in the total heat transfer is very small, hence the thermal radiation may also be neglected. Generally, the heat transfer process in inorganic hollow microspheres filled polymer composites is more complicated, because they are a type of material with three phases, namely resin, gas and spherical shell. 2.2. Effective thermal conductivity equation of polymer/hollow microsphere composites On the basis of the law of minimal thermal resistance [29] and the equal law of the specific equivalent thermal conductivity, a
Fig. 1. Heat transfer model of polymer/hollow sphere composites.
mathematical model for describing the relationship between the effective thermal conductivity and other materials parameters of polymer/hollow micro-sphere composites is derived [27]:
keff
8 2 !13 ! 1 1 <1 6/f 3 2/f 3 4p qs qa ¼ 1 þ 24kp þp kg :kp p 3/f 9p qg qa 9 1 ! !#1 = qg qs þ ka ð1Þ kp ; qg qa
where qg, qa and qs are the effective densities of the spherical shell, gas and micro-sphere respectively, /f is the volume fraction of the hollow micro-spheres, kp, kg and ka are the thermal conductivities of polymer matrix phase, micro-spherical shell phase and gas phase, respectively. 3. Experimental 3.1. Raw materials An injection grade of polypropylene (PP) with trade mark of CJS-700, supplied by Guangzhou petrochemical Co., Ltd. in China, was used as the matrix resin, the density and melt flow index (230 °C, 2.16 kg) of the resin were 0.91 g/cm3 and 12 g/10 min, respectively. Two kinds of hollow glass beads (HGB) supplied by Molüs Co., Ltd. in German, TK35 and TK70, with different size were used as the fillers in this work. The mean diameters of the fillers were 35 lm and 70 lm, and the density was 680 kg/m3 and 210 kg/ m3, respectively. The surface of the particles was pretreated with silane coupling agent by the supplier. The particle size distribution of the fillers was measured by means of a laser size instrument (Model LS-C(I)) supplied by Omik Co., Ltd. in Zhuhai, China. 3.2. Sample preparation After mixing simply, the PP resin and the HGB with different proportions were compounded in a twin-screw extruder [6]. The blending was conducted in a temperature range of 160–230 °C and screw speed of 25 r/min, and then the extrudate was granulated to produce the composites. The volume fractions of the HGB were 0%, 5%, 10%, 15% and 20%. The specimens for thermal conductivity measurement were molded by using an injection molding machine in temperature range of 160–240 °C after drying the composites. The specimens were the square plates; the length and thickness of the specimen were 50 mm and 6 mm, respectively. 3.3. Apparatus and methodology The thermal conductivity of the composites was measured by means of a protecting heat plate method in this test, and the main apparatus was a protecting heat flow type of thermal conductivity instrument (model NF-7) supplied by South China University of Technology. Two thermocouples were set on the two cold faces of the test pieces, and two thermocouples were set on the two heated face of the test pieces. The temperatures and heating power were measured as soon as the heat transfer reached the steady state. All measured data were collected and recorded by a computer. The environmental temperature for test was 27 °C. The specimens was plates with length of 50 mm, width of 50 mm and thickness of 6 mm. 4 measuring points were set up equally on a plate, and the average was reported for each specimen [6]. The physical property parameters including density and thermal
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0.30
4. Results and discussion
4.2. Estimation of effective thermal conductivity
0.10
0.30 PP/TK35 PP/TK70
0.25
0.20
0.15
5
10
15
20
25
φf (%) Fig. 2. Measured values of effective thermal conductivity of PP/HGB composites.
0
10
20
30
40
φf (%) Fig. 3. Comparison between predictions and measurements of effective thermal conductivity for PP/TK35 system.
0.30 Theory Experiment
0.25 0.20 0.15 0.10 0.05 0.00
The density of the spherical shell was 2210 kg/m3, and the thermal conductivity was 0.17934 W/m K. The gas in the beads was an inert gas, and the density and thermal conductivity were 0.0899 kg/m3 and 0.0228 W/m K, respectively. The thermal conductivity and density of the PP resin were 0.2 W/m K and 915 kg/ m3, respectively. Substituting the physical data including density, thermal conductivity and volume fraction of the HGB and resin for the PP/ TK35 and PP/TK70 composite systems into Eq. (1), one may estimate the effective thermal conductivity keff of the composites corresponding to different volume fraction of hollow glass beads, and the results are as shown in Figs. 3 and 4. With an increase of the HGB volume fraction, the theoretical estimations of keff of PP/ HGB composites decreases linearly, and the values of keff for PP/
K eff (W.m-1.K-1)
0.15
0.00
K eff (W.m-1.K-1)
Fig. 2 shows the dependence of the effective thermal conductivity (keff) of PP/TK35 and PP/TK70 composite systems on the volume fraction (/f). It can be seen that the keff of the composites decreases with an addition of /f. When /f is less than 15%, the values of keff of PP/35 filled system are greater than those of PP/70 filled system. This indicates that the heat insulation properties for the composite systems with filled bigger diameter of hollow micro-spheres are better at lower inclusion concentration. This because that when the thick to diameter ratio of hollow micro-spheres is fixed, the bigger the particle size, there is more gas in it (density reduction) under constant range of particle diameter, resulting in reduction of the effective thermal conductivity. When /f is more than 15%, the values of keff of PP/35 filled system are lower than those of PP/70 filled system. It might be that the number of TK35 with small particle diameter increases obviously at higher filler concentration, leading to improvement of the heat insulation properties of materials.
0
0.20
0.05
4.1. Experimental results
0.10
Theory Experiment
0.25
K eff (W.m-1 .K -1)
conductivity of the filler and matrix resin in Eq. (1) were got from the suppliers. To understand the dispersion and distribution situation of the filler particles in the PP matrix, the impact fracture surface of the composites was observed using the scanning electron microscope (SEM, model S440) supplied by Leica Cambridge Co., Ltd. in UK. The samples were gold coated before SEM examination.
0
5
10
15
20
25
30
35
40
φf (%) Fig. 4. Comparison between predictions and measurements of effective thermal conductivity for PP/TK70 system.
TK35 system are slightly higher than those for PP/TK70 system under the same conditions. 4.3. Comparison and analysis Plotting respectively the measured data of the effective thermal conductivity from the experimental of these two filled PP composite systems (as shown in Fig. 3) into Figs. 3 and 4, one can verify preliminarily Eq. (1). It may be observed that the theoretical estimations of the effective thermal conductivity are good consistent with the measured data, and keff decreases linearly with an increase of /f, expect to individual data point. The maximum relative error is 4.15% for PP/TK70 composite system, and the maximum relative error is 9.51% for PP/TK35 composite system. In the previous work, Liang and Li [26] simulated the two dimension heat transfer process in these filled systems stated above by using ANSYS software, and the results showed that the trend of the simulations are similar to the theoretical predictions. This indicates that mathematical model (1) may describe better the relationship between the effective thermal conductivity of inorganic hollow micro-spheres filled polymer composites and material parameters when the concentration of the particles is low and the dispersion of these inclusions in the resin matrix is uniform. Fig. 5 is the SEM photograph of the fracture surface of the PP/ TK35 composite with volume fraction of 20%. Fig. 6 is the SEM photograph of the fracture surface of the PP/TK70 composite with volume fraction of 20%. It can be observed from Figs. 5 and 6 that the
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the experimental measured data within the filler volume fraction range from 0% to 20%. This indicated that Eq. (1) might predict better the thermal conductivity of the polymer/hollow microsphere composites, especially at low the filler concentration. Acknowledgement The authors would like to thank Mr. F.H. Li who is from the South China University of Technology for his helping in this study. References
Fig. 5. SEM photograph of fracture surface of PP/TK35 composite (/f = 20%).
Fig. 6. SEM photograph of fracture surface of PP/TK70 composite (/f = 20%).
dispersion and distribution of the HGBs in the PP matrix are roughly uniform. The one of the assumptions based by Eq. (1) was that the dispersion and distribution of the HGBs in the PP matrix were roughly uniform [27]. According to the preliminary verification results, Eq. (1) should be practicable for the polymer composites filled with inorganic hollow particles when the filler concentration is not high (such as volume fraction from 0% to 20%). 5. Conclusions The experimental measured thermal conductivity of the PP/ HGB composites showed that the effect of the content of the hollow glass beads on the thermal properties of the filled PP composites was significant. The values of the thermal conductivity decreased roughly linearly with increasing of the particle volume fraction. While the influence of the particle diameter on the thermal conductivity for the PP/HGB composite was insignificant. The values of the thermal conductivity for the PP/HGB composites estimated using Eq. (1), and the estimations were compared with the experimental measured data. The results were shown that the estimations of the thermal conductivity were roughly close to
[1] Im H, Kim J. Enhancement of the thermal conductivity of aluminum oxideepoxy terminated poly(dimethyl siloxane) with a metal oxide containing polysiloxane. J Mater Sci 2011;46:6571–80. [2] Li B, Zhong WH. Review on polymer/graphite nanoplatelet nanocomposites. J Mater Sci 2011;46:5595–614. [3] Liang JZ. Thermal conductivity of PP/Al(OH)3/Mg(OH)2 composites. Composites Part B 2013;44(1):248–52. [4] Liang JZ. Estimation of thermal conductivity of PP/Al(OH)3/Mg(OH)2 composites. J Polym Eng 2012;32(6–7):401–6. [5] Tsui CP, Chen DZ, Tang CY, Uskokovic PS. Prediction for debonding damage process of glass beads-reinforced modified polyphenylene oxide under simple shear. J Mater Process Technol 2005;167:429–37. [6] Liang JZ, Li FH. Measurement of thermal conductivity of hollow glass bead filled polypropylene composites. Polym Test 2006;25(4):527–31. [7] Liang JZ. Tensile and impact properties of hollow glass bead-filled PVC composites. Macrom Mater Eng 2002;287:588–91. [8] Liang JZ. Mechanical properties of hollow glass bead-filled ABS composites. J Therm Comp Mater 2005;18(5):407–16. [9] Liang JZ. Tensile and flexural properties of hollow spheres-filled ABS composites. J Elast Plast 2005;37(4):361–70. [10] Liang JZ. Impact fracture behavior and morphology of hollow glass bear-filled ABS composites. J ASTM Inter 2006;3(4):1–7. [11] Liang JZ. Impact fracture behavior and morphology of hollow glass bead-filled polypropylene composites. J Mater Sci 2007;42(3):841–6. [12] Ryu CH, Bae YC, Lee SH, Yi S, Park YH. Rheological properties of hollow sphere loaded polymer melts. Polymer 1998;39(25):6293–9. [13] Liang JZ, Zhong MQ. Melt extrudate swell behavior of polypropylene composites filled with hollow glass beads. J Polym Eng 2012(4/5):259–63. [14] Liang JZ, Liu GS. A new heat transfer model of inorganic particulate-filled polymer composites. J Mater Sci 2009;44(17):4715–20. [15] Russell HW. Principles of heat flow in porous insulation. J Am Ceram Soc 1935;18:1–5. [16] Kingery WD. Conductivity of multicomponent systems. J Am Ceram Soc 1959;42:617–22. [17] Loeb AL. A theory of thermal conductivity of porous materials. J Am Cream Soc 1954;37:96–100. [18] Nielsen LE. Thermal conductivity of particulate-filled polymers. J Appl Polym Sci 1973;29:3819–25. [19] Cheng S, Vachon R. A technique for predicting the thermal conductivity of suspensions: emulsions and porous materials. Int J Heat Mass Trans 1970;13:537–42. [20] Agari Y, Ueda A, Nagai S. Thermal conductivity of a polymer composite. J Appl Polym Sci 1993;49:1625–30. [21] Liang XG, Qu W. Effective thermal conductivity of gas–solid composite materials and the temperature difference effect at high temperature. Int J Heat and Mass Trans 1999;42:1885–90. [22] Suvorov SA, Fishchev VN, Kapustina SN, Kopylova SV, Nekhlopochina MG. Thermal conductivity of composites with a filler of hollow spherical corundum granules. Refractories 1989;29:689–93. [23] Hill RF, Supancic PH. Determination of the thermal resistance of the polymer– ceramic interface of alumina-filled polymer composites. J Am Ceram Soc 2004;87(10):1831–5. [24] Hill RF, Supancic PH. Thermal conductivity of platelet-filled polymer composites. J Am Ceram Soc 2002;85(4):851–7. [25] Yu SZ, Hing P, Hu X. Thermal conductivity of polystyrene–aluminum nitride composite. Compos Part A – Appl Sci Manufact 2002;33(2):289–92. [26] Liang JZ, Li FH. Simulation of heat transfer in hollow-glass-bead-filled polypropylene composites by finite element method. Polym Test 2007;26(3):419–24. [27] Liang JZ, Li FH. Heat transfer in polymer composites filled with inorganic hollow micro-spheres: I. A theoretical model. Polym Test 2007;26(8):1025–30. [28] Skochdopole RE. The thermal conductivity of foam plastics. Eng Prog 1961;57:55–8. [29] Chen ZS, Qian J, Ye YH. Theoretical derivation of effective thermal conductivity of composites. J China Univ Sci Technol 1992;22(4):416–23.
Contents lists available at ScienceDirect
Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Estimation of thermal conductivity for polypropylene/hollow glass bead composites Ji-Zhao Liang ⇑ Research Division of Green Function Materials and Equipment, College of Industrial Equipment and Control Engineering, South China University of Technology, Guangzhou 510640, PR China
a r t i c l e
i n f o
Article history: Received 10 March 2013 Received in revised form 7 July 2013 Accepted 19 August 2013 Available online 29 August 2013 Keywords: A. Polymer–matrix composites B. Thermal properties C. Analytical modeling D. Thermal analysis
a b s t r a c t The thermal conductivity of hollow glass bead (HGB)-filled polypropylene (PP) composites was estimated using the thermal conductivity equation of inorganic hollow microsphere-filled polymer composites published in the previous paper. The estimations were compared with the measured data of the PP composites filled with two kinds of HGB with different size (the mean diameter was respectively 35 lm and 70 lm). The results showed that the predictions of the thermal conductivity were in good agreement with the measured data except to individual data points. Furthermore, both the estimated and measured thermal conductivity decreased roughly linearly with increasing the HGB volume fraction when the HGB volume fraction was less than 20%; the influence of the particle diameter on the thermal conductivity was insignificant. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Thermal conductive polymeric composites have been paid more and more attention in the past two decades [1–4]. Rigid hollow microspheres (e.g. hollow glass beads, hollow ceramic beads, rigid hollow plastic beads, etc.) contain inert gas, and have some advantages, such as low thermal conductivity coefficient and density. In addition, these micro-particles do not generate important stress concentration in the interface between the fillers and the matrix owing to their smooth spherical surface [5]. They are, therefore, usually used to fill and modify resins in polymeric industry and coating industry. Generally, polymer/hollow micro-sphere composites have good thermal and sound insulation, low density and good mechanical and rheological properties [6–13]. This type of composite is applied in building materials, space-flight and the aviation industry. The heat transfer process in porous materials is very complicated, especially for polymer composites. It is quite important, therefore, to understand the heat transfer mechanisms of heat transfer in polymer composites. Thermal conductivity is an important characteristic of heat transfer properties of materials [14]. For porous materials, several researchers [15,16] derived some thermal conductivity equations based on the Maxwell expression, or established a more accurate formula for calculating the effective thermal conductivity of porous materials [17]. Relatively, the models proposed respectively by Nielsen [18] and Cheng–Vachon [19] ⇑ Tel.: +86 02087114739. E-mail address: [email protected] 1359-8368/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2013.08.072
may better estimate the thermal conductivity of filled composite materials, while the Agari–Nagai equation can predict the thermal conductivity of the composites with high-loading [20]. Liang [21] analyzed the thermal conductivity of a porous material with closed spherical and cylindrical holes. Suvorov et al. [22] studied the thermal conductivity of hollow emery filled composites. Recently, Hill and Supancic [23] proposed an indirect method to determine this interfacial boundary resistance by preparing large-scale ‘‘macromodel’’ simulations of the polymer–ceramic interface. They also investigated the effects of similar size and shape of platelet-shaped particles on the thermal conductivity of polymer/ceramic composite materials [24]. Yu et al. [25] measured the thermal conductivity of polystyrene–aluminum nitride composite, and found that the thermal conductivity of composites was higher for a polystyrene particle size of 2 mm than that for a particle size of 0.15 mm. The thermal conductivity of the composite was five times that of pure polystyrene at about 20% volume fraction of aluminum nitride (AIN) for the composite containing 2 mm polystyrene particles. Hollow glass bead (HGB) contains inertia gas, and have some advantages, such as low thermal conductivity coefficient and light. In addition, these hollow micro-particles do not generate important stress concentration in the interface between the inclusions and the matrix owing to their smooth spherical surface. In the previous work, Liang and Li [6] measured the thermal conductivity (keff) of HGB-filled polypropylene (PP) composites by means of a thermal conductivity instrument, and simulated the heat-transfer process in PP/HGB composites by using finite element method (FEM) with ANSYS software [26]. More recently, Liang and Li [27] analyzed the heat transfer mechanisms in polymer/hollow
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microspheres composites, and established a mathematical model for predicting the thermal conductivity. The objectives in this paper are to predict the thermal conductivity of the PP/HGB composites applying this mathematical model and to compare the predictions with the experimental data. 2. Modeling 2.1. Heat transfer mechanisms in polymer/hollow micro-sphere composites In general, the thermal conductivity in thermal insulation materials is the combined effect of heat conduction, convection and radiation. According to the second law of thermodynamics, heat always transfer spontaneously from high temperature body to low temperature one. Namely, heat transfer will conduct in where there is difference in temperature. Generally, insulation materials only reduce the strength of heat exchange, and have a property of blocking heat transfer. Polymer/hollow micro-spheres composite is a kind of ternary composites, it includes three phases, namely resin, gas and spherical shell. During heat transfer in polymer/hollow micro-spheres composites, when heat quantity is close to a hollow microsphere, only a small part of heat quantity will conduct by it, while greater part of heat quantity will move around it due to its low conductivity, as shown in Fig. 1. Because of low thermal conductive coefficient of the hollow micro-spheres and longer heat transfer route and complication in the filled systems, the thermal conductivity of these composites will be reduced. It can be seen from Fig. 1 that the heat transport in inorganic hollow microsphere filled polymer composites has three kinds of ways: (1) thermal conduction by solid; (2) heat radiation on the surface between neighboring hollow particles; (3) the natural thermal convection of gas in the hollow particles. After finishing the experiments, Skochdopole [28] pointed out that the natural thermal convection of the gas in a micro-bubble would not occur when the bubble diameter was less than 4 mm. Because the diameter of the hollow micro-spheres as fillers is usually less than 0.1 mm, the natural thermal convection of the gas in it may be neglected. Furthermore, polymer composite works usually under lower temperature conditions where the proportion of the thermal radiation in the total heat transfer is very small, hence the thermal radiation may also be neglected. Generally, the heat transfer process in inorganic hollow microspheres filled polymer composites is more complicated, because they are a type of material with three phases, namely resin, gas and spherical shell. 2.2. Effective thermal conductivity equation of polymer/hollow microsphere composites On the basis of the law of minimal thermal resistance [29] and the equal law of the specific equivalent thermal conductivity, a
Fig. 1. Heat transfer model of polymer/hollow sphere composites.
mathematical model for describing the relationship between the effective thermal conductivity and other materials parameters of polymer/hollow micro-sphere composites is derived [27]:
keff
8 2 !13 ! 1 1 <1 6/f 3 2/f 3 4p qs qa ¼ 1 þ 24kp þp kg :kp p 3/f 9p qg qa 9 1 ! !#1 = qg qs þ ka ð1Þ kp ; qg qa
where qg, qa and qs are the effective densities of the spherical shell, gas and micro-sphere respectively, /f is the volume fraction of the hollow micro-spheres, kp, kg and ka are the thermal conductivities of polymer matrix phase, micro-spherical shell phase and gas phase, respectively. 3. Experimental 3.1. Raw materials An injection grade of polypropylene (PP) with trade mark of CJS-700, supplied by Guangzhou petrochemical Co., Ltd. in China, was used as the matrix resin, the density and melt flow index (230 °C, 2.16 kg) of the resin were 0.91 g/cm3 and 12 g/10 min, respectively. Two kinds of hollow glass beads (HGB) supplied by Molüs Co., Ltd. in German, TK35 and TK70, with different size were used as the fillers in this work. The mean diameters of the fillers were 35 lm and 70 lm, and the density was 680 kg/m3 and 210 kg/ m3, respectively. The surface of the particles was pretreated with silane coupling agent by the supplier. The particle size distribution of the fillers was measured by means of a laser size instrument (Model LS-C(I)) supplied by Omik Co., Ltd. in Zhuhai, China. 3.2. Sample preparation After mixing simply, the PP resin and the HGB with different proportions were compounded in a twin-screw extruder [6]. The blending was conducted in a temperature range of 160–230 °C and screw speed of 25 r/min, and then the extrudate was granulated to produce the composites. The volume fractions of the HGB were 0%, 5%, 10%, 15% and 20%. The specimens for thermal conductivity measurement were molded by using an injection molding machine in temperature range of 160–240 °C after drying the composites. The specimens were the square plates; the length and thickness of the specimen were 50 mm and 6 mm, respectively. 3.3. Apparatus and methodology The thermal conductivity of the composites was measured by means of a protecting heat plate method in this test, and the main apparatus was a protecting heat flow type of thermal conductivity instrument (model NF-7) supplied by South China University of Technology. Two thermocouples were set on the two cold faces of the test pieces, and two thermocouples were set on the two heated face of the test pieces. The temperatures and heating power were measured as soon as the heat transfer reached the steady state. All measured data were collected and recorded by a computer. The environmental temperature for test was 27 °C. The specimens was plates with length of 50 mm, width of 50 mm and thickness of 6 mm. 4 measuring points were set up equally on a plate, and the average was reported for each specimen [6]. The physical property parameters including density and thermal
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0.30
4. Results and discussion
4.2. Estimation of effective thermal conductivity
0.10
0.30 PP/TK35 PP/TK70
0.25
0.20
0.15
5
10
15
20
25
φf (%) Fig. 2. Measured values of effective thermal conductivity of PP/HGB composites.
0
10
20
30
40
φf (%) Fig. 3. Comparison between predictions and measurements of effective thermal conductivity for PP/TK35 system.
0.30 Theory Experiment
0.25 0.20 0.15 0.10 0.05 0.00
The density of the spherical shell was 2210 kg/m3, and the thermal conductivity was 0.17934 W/m K. The gas in the beads was an inert gas, and the density and thermal conductivity were 0.0899 kg/m3 and 0.0228 W/m K, respectively. The thermal conductivity and density of the PP resin were 0.2 W/m K and 915 kg/ m3, respectively. Substituting the physical data including density, thermal conductivity and volume fraction of the HGB and resin for the PP/ TK35 and PP/TK70 composite systems into Eq. (1), one may estimate the effective thermal conductivity keff of the composites corresponding to different volume fraction of hollow glass beads, and the results are as shown in Figs. 3 and 4. With an increase of the HGB volume fraction, the theoretical estimations of keff of PP/ HGB composites decreases linearly, and the values of keff for PP/
K eff (W.m-1.K-1)
0.15
0.00
K eff (W.m-1.K-1)
Fig. 2 shows the dependence of the effective thermal conductivity (keff) of PP/TK35 and PP/TK70 composite systems on the volume fraction (/f). It can be seen that the keff of the composites decreases with an addition of /f. When /f is less than 15%, the values of keff of PP/35 filled system are greater than those of PP/70 filled system. This indicates that the heat insulation properties for the composite systems with filled bigger diameter of hollow micro-spheres are better at lower inclusion concentration. This because that when the thick to diameter ratio of hollow micro-spheres is fixed, the bigger the particle size, there is more gas in it (density reduction) under constant range of particle diameter, resulting in reduction of the effective thermal conductivity. When /f is more than 15%, the values of keff of PP/35 filled system are lower than those of PP/70 filled system. It might be that the number of TK35 with small particle diameter increases obviously at higher filler concentration, leading to improvement of the heat insulation properties of materials.
0
0.20
0.05
4.1. Experimental results
0.10
Theory Experiment
0.25
K eff (W.m-1 .K -1)
conductivity of the filler and matrix resin in Eq. (1) were got from the suppliers. To understand the dispersion and distribution situation of the filler particles in the PP matrix, the impact fracture surface of the composites was observed using the scanning electron microscope (SEM, model S440) supplied by Leica Cambridge Co., Ltd. in UK. The samples were gold coated before SEM examination.
0
5
10
15
20
25
30
35
40
φf (%) Fig. 4. Comparison between predictions and measurements of effective thermal conductivity for PP/TK70 system.
TK35 system are slightly higher than those for PP/TK70 system under the same conditions. 4.3. Comparison and analysis Plotting respectively the measured data of the effective thermal conductivity from the experimental of these two filled PP composite systems (as shown in Fig. 3) into Figs. 3 and 4, one can verify preliminarily Eq. (1). It may be observed that the theoretical estimations of the effective thermal conductivity are good consistent with the measured data, and keff decreases linearly with an increase of /f, expect to individual data point. The maximum relative error is 4.15% for PP/TK70 composite system, and the maximum relative error is 9.51% for PP/TK35 composite system. In the previous work, Liang and Li [26] simulated the two dimension heat transfer process in these filled systems stated above by using ANSYS software, and the results showed that the trend of the simulations are similar to the theoretical predictions. This indicates that mathematical model (1) may describe better the relationship between the effective thermal conductivity of inorganic hollow micro-spheres filled polymer composites and material parameters when the concentration of the particles is low and the dispersion of these inclusions in the resin matrix is uniform. Fig. 5 is the SEM photograph of the fracture surface of the PP/ TK35 composite with volume fraction of 20%. Fig. 6 is the SEM photograph of the fracture surface of the PP/TK70 composite with volume fraction of 20%. It can be observed from Figs. 5 and 6 that the
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the experimental measured data within the filler volume fraction range from 0% to 20%. This indicated that Eq. (1) might predict better the thermal conductivity of the polymer/hollow microsphere composites, especially at low the filler concentration. Acknowledgement The authors would like to thank Mr. F.H. Li who is from the South China University of Technology for his helping in this study. References
Fig. 5. SEM photograph of fracture surface of PP/TK35 composite (/f = 20%).
Fig. 6. SEM photograph of fracture surface of PP/TK70 composite (/f = 20%).
dispersion and distribution of the HGBs in the PP matrix are roughly uniform. The one of the assumptions based by Eq. (1) was that the dispersion and distribution of the HGBs in the PP matrix were roughly uniform [27]. According to the preliminary verification results, Eq. (1) should be practicable for the polymer composites filled with inorganic hollow particles when the filler concentration is not high (such as volume fraction from 0% to 20%). 5. Conclusions The experimental measured thermal conductivity of the PP/ HGB composites showed that the effect of the content of the hollow glass beads on the thermal properties of the filled PP composites was significant. The values of the thermal conductivity decreased roughly linearly with increasing of the particle volume fraction. While the influence of the particle diameter on the thermal conductivity for the PP/HGB composite was insignificant. The values of the thermal conductivity for the PP/HGB composites estimated using Eq. (1), and the estimations were compared with the experimental measured data. The results were shown that the estimations of the thermal conductivity were roughly close to
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