ISSN 1995-4212, Polymer Science, Series D, 2016, Vol. 9, No. 4, pp. 377–381. © Pleiades Publishing, Ltd., 2016. Original Russian Text © I.A. Aleksandrov, P.V. Prosuntsov, 2016, published in Klei, Germetiki, Tekhnologii, 2016, No. 5, pp. 17–21.
Determination of the Effect of Carbon Nanosized Particles on Thermophysical Characteristics of Polymer Composite Materials I. A. Aleksandrova and P. V. Prosuntsovb, * aInstitute
of Engineering and Technological Informatics, Russian Academy of Sciences, per. Vadkovskii 18–1A, Moscow, 127055 Russia b Bauman State Technical University, ul. Vtoraya Baumanskaya 5, Moscow, 105005 Russia *e-mail:
[email protected] Received January 26, 2016
Abstract—Models are developed for calculation of the thermal conductivity of a polymer binder modified with different contents of carbon nanotubes (CNTs). Comparison of the computation data with the experimental results shows that the introduction of CNTs cannot significantly increase the thermal conductivity of the binder due to the presence of air cavities around CNTs. Keywords: polymer composite materials, carbon nanotubes, thermal conductivity, size stability DOI: 10.1134/S199542121604002X
INTRODUCTION Owing to a complex of high stress-strain [1], thermophysical [2] and other properties, polymer composite materials find increasing application. Traditionally the key problems for constructions made of polymer composite materials are believed to be their strength and stability. Nevertheless, in recent years, growing attention has been drawn to constructions with size stability [3]. “Size stability” in this case means the ability of a material to retain its size and shape to the greatest extent under the effect of variable power and thermal loads. An efficient technique for creation of thermally stable constructions seems to be the use of polymer composite materials with low values of linear thermal expansion coefficient and high thermal conductivity. An increase in the material thermal conductivity yields a reduction in the temperature drops and, thereby, a decrease in the temperature deformations [4]. The thermophysical characteristics of a reinforcing filler usually significantly exceed the properties of a binder. The appearance of nanosized fillers enabled improvement of the mechanical and thermophysical properties of matrix materials to values comparable with the properties of reinforcing fillers. Today, growing attention is being drawn to the development of polymer composite materials (PCMs) based on fillers made of carbon nanomaterials—carbon nanotubes (CNTs) and carbon nanofibers. Therefore, increasing the thermal conductivity of a binder via development and approbation of the methods for introduction of nanomodifiers into matrix materials is an urgent task.
The goals of the present work are to calculate the thermal conductivity of a matrix material based on modeling of heat transfer in the binder with variable content of CNTs and compare the data obtained with the results of experimental studies. EXPERIMENTAL To determine thermal conductivity, the principle of selecting an elementary cell of nanomodified binder and calculation of the coefficient of its generalized conductivity was used [5]. To study the effect of a modifier made of carbon nanotubes on the thermophysical characteristics of the epoxy binder, threedimensional geometrical models of elementary cells were developed that reflect the main geometrical properties of a CNT–binder system and take into account the key factors for the transfer process (Fig. 1). Upon modeling of CNT distribution in the binder medium in the form of cylindrical bodies, a series of assumptions are made. The first is that CNTs are represented as a hexagonal network of carbon atoms rolled into a jointless cylinder, which is sealed from the butt end with a half of a fullerene molecule. At the present time, the process of CNT preparation does not allow their production in the form of fullerenes from hexahedral networks: defective penta- and tetrahedral cells of carbon atoms are present, and it is difficult to determine the content of defective tubes due to the labor-intensiveness and cost of such an assessment. Therefore, it is assumed that the tubes considered in modeling do not ref lect possible ornateness.
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ALEKSANDROV, PROSUNTSOV B: 05 Temperature Type: Temperature Unit: °C Time: 1 26.05.2014 10:25 25.003 Max 24.47 23.891 23.334 22.778 22.222 21.666 21.110 20.554 19.998 Min
Y 0.000
Z
0.800 m 0.200
X
0.600
Fig. 2. Temperature field of the elementary cell.
Fig. 1. Geometrical model of the elementary cell.
During distribution of CNTs over the binder volume, some of the dispersed CNTs join into agglomerates. This is caused by the fact that each particular concentration of nanotubes requires a choice of modes for introduction depending on the rheological properties of a medium into which they are introduced. The choice of introduction mode must include the step of binder curing, since the formation of agglomerates is possible up to completion of the gel formation stage. Determination of the volume content of agglomerates in the binder and their effect on nanocomposite characteristics does not seem to be possible. Therefore, it was assumed that the distribution of nanotubes over the whole volume of the binder is uniform. To calculate the thermal conductivity of the binder with the nanomodifier, the model of heat transfer was used, which entails that, on two opposite walls of the elementary cell, there are given magnitudes of temperature that are constant over the surface but different (the drop is no more than 5°C). The other facets of the elementary cells are considered to be thermally isolated. Modeling of heat transfer was carried out using Ansys Workbench finite-element analysis [6]. The temperature field of the elementary cell was obtained (Fig. 2), and the heat flow through a side wall of the cell was determined. To determine the thermal conductivity, the Fourier law was used:
q , l ΔT where λ is the thermal conductivity coefficient of the binder with the nanomodifier, W/(m K); q is the heat flow through the side cell wall, W/m2; l is the length of λ=
the elementary cell edge, m; and ΔT is the difference between the initial temperatures of opposite cell walls, K. To carry out experimental studies, a series of samples of the nanomodified binder were prepared based on Araldite CY 179 epoxy resin, HY 917 curing agent, and DY 070 catalyst. The modifier used was Baytubes C150 P CNTs. Introduction of carbon nanotubes into the binder was performed via ultrasonic treatment with an LUZD-1,5/21-3,0 ultrasonic dispersion system. Samples were prepared with a weight fraction of nanotubes of from 0 to 0.5% with a 0.1% step. After curing of the half-finished samples, they were mechanically treated, proceeding from the requirements for carrying out measurements. The experimental investigation of the temperature conductivity was carried out by the laser flash method using a NETZSCH LFA 427 unit [5]. The thermal capacity was determined with a DSC 204 F1 Phoenix LFA 427 highly sensitive differential scanning calorimeter manufactured by NETZSCH [7]. Densities of the samples were determined by gyroscopic weighing. The thermal conductivity of the material was determined from the following expression:
λ = aC pρ, where a is temperature conductivity, m2/s; Cp is thermal conductivity, J/(kg K); and ρ is density, kg/m3. RESULTS AND DISCUSSION To analyze the effect of CNT concentration on the thermal conductivity of the nanomodified binder, elementary cells with randomly oriented inclusions (with a weight fraction from 0.1 to 0.5%, with a 0.1% step) were constructed. The initial data used for modeling are presented in Table 1.
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(a)
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(b)
Y 0.000
0.700
Z
0.350
Y X
0.000
0.700 0.350
Z
X
Fig. 3. Three-dimensional model of the elementary cell at CNT wt content (a) 0.1 and (b) 0.5%.
Thermal conductivity, λ, W/(m K)
0.8 0.7
1
0.6 0.5 0.4 0.3 2
0.2 0.1 0
0.1 0.2 0.3 0.4 Weight fraction of CNT, %
0.5
Fig. 4. Dependence of the thermal conductivity of the nanomodified epoxy binder on CNT weight fraction: (1) calculation data (finite-element analysis); (2) experimental data.
Figure 3 presents the models of elementary cells that contain 0.1 and 0.5 wt % of cylindrical inclusions of CNTs. Figure 4 shows the results of calculation and experimental definition of the thermal conductivity of the nanomodified binder randomly reinforced with CNTs in amounts of from 0 to 0.5 wt %. As can be seen from Fig. 4, the deviation of the calculated values of thermal conductivity from the experimental data lies in the range of from 104 to 257%. Structural analysis of Baytubes C 150 P CNTs performed earlier using scanning electron microscopy [8] showed that the actual diameter of nanotubes exceeds the nominal data in by two or three times. An increase in the diameter of nanotubes can be caused by the presence of an ornate structure at the atomic level formed on the tube surface during preparation. It is POLYMER SCIENCE, SERIES D
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Fig. 5. Model of the elementary cells with an air shell around cylindrical CNTs.
natural to think that the presence of such a structure does not allow the binder to come into contact with the nanotube surface. To determine the effect of possible air inclusions on the thermal conductivity of nanomodified binder, models of elementary cells with an air shell around Table 1. Properties of the components used for modeling of the elementary cell Cell component Parameter CNT binder Length, nm Diameter, nm Density, kg/m3 Thermal conductivity, W/(m K)
1000 13 130 100
1200 0.23
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ALEKSANDROV, PROSUNTSOV
(a)
(b)
Fig. 6. Models of the elementary cells with an air shell at CNT weight fraction of (a) 0.1 and (b) 0.5%.
(a)
(b)
Fig. 7. Models of the elementary cells with an air shell around CNTs. The value of the shell relative to the CNT diameter is (a) 10 and (b) 50%.
Thermal conductivity, W/(m K)
0.8 0.7
cylindrical CNTs were constructed (Fig. 5). The air shells were constructed for all the previously considered models of elementary cells of the binder randomly reinforced with CNTs in the amount of from 0.1 to 0.5 wt % with a 0.1% step (Fig. 6). The value of air shells around CNTs varied from 10 to 50% of the nanotube diameter (Fig. 7).
1
0.6 0.5
2
0.4
3
The results of calculation of the thermal conductivity of the nanomodified epoxy binder depending on the value of air inclusions around CNTs are presented in Table 2.
0.3 4
7
0.2 5 0.1 0
6 0.1
0.2 0.3 0.4 Filler weight fraction, %
Fig. 8. Dependence of thermal conductivity of the nanomodified binder on the CNT weight fraction at different values of air inclusions around CNTs, % relative to the CNT diameter: (1) 0, (2) 10, (3) 20, (4) 30, (5) 40, (6) 50, and (7) experimental data.
0.5
The dependence of thermal conductivity of the nanomodified epoxy binder on CNT concentration at different values of air inclusions is presented graphically in Fig. 8. As can be seen from Fig. 8, the model of an elementary cell of the binder with the content of air inclusions equal to 30% of the nanotube diameter corresponds to the experimental data best of all.
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Table 2. Calculated thermal conductivity of the nanomodified epoxy binder depending on the weight fraction and value of air shells around CNTs CNT concentration, wt % 0.0 0.1 0.2 0.3 0.4 0.5
Thickness of air inclusions, % relative to the CNT diameter 0
10
20
30
40
50
0.23 0.15 0.12 0.12 0.10 0.06
0.23 0.11 0.06 0.04 0.01 0.02
thermal conductivity, W/(m K) 0.23 0.45 0.61 0.65 0.65 0.75
0.23 0.32 0.40 0.46 0.47 0.53
0.23 0.31 0.35 0.37 0.34 0.32
0.23 0.25 0.24 0.22 0.20 0.14
CONCLUSIONS Comparison of the results of modeling and experimental investigations on thermal conductivity of the nanomodified binder samples showed that the application of existing technologies for introduction of the modifier into the binder volume does not allow one to realize the potential of CNTs: the presence of air inclusions in nanotube cavities not only does not improve the thermal conductivity of the nanomodified binder, but can even reduce it.
2.
3. 4.
ACKNOWLEDGMENTS This work was supported in part by the Ministry of Education and Science of the Russian Federation, subsidy agreement no. 14.577.21.0095 of August 25, 2014, unique identifier of applied research investigations no. RFMEFI57714X0095.
5. 6. 7. 8.
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polysulfone modified epoxy binders,” Glass Physics and Chemistry 40 (5), 543–548 (2014). A. N. Muranov, G. V. Malysheva, V. A. Nelyub, I. A. Buanov, I. V. Chudnov, and A. S. Borodulin, “Investigation of properties of polymeric composition materials about a heterogeneous matrix,” Polym. Sci., Ser. D 6 (3), 256–259 (2013). D. I. Chung, Composite Materials. Science and Applications, Springer-Verlag London Limited, 2010. K. V. Mikhailovskii, P. V. Prosuntsov, and S. V. Reznik, “Development of highly polymeric composite materials for space structures,” Vestn. Mosk. Gos. Tech. Univ. im. N. E. Baumana, Ser. “Mashinostr.,” No. 3, 98–106 (2012). G. N. Dul’nev and Yu. P. Zarichnyak, Thermal Conductivity of Mixtures and Composites: Handbook (Energiya, Leningrad, 1974) [in Russian]. Ansys Inc. http://www.ansys.com. NETZSCH Group. http://www.netzsch-thermalanalysis.com. I. A. Aleksandrov, I. A. Buyanov, I. V. Chudnov, et al., “Study of microstructure of nano-modified polymer composites,” Nauka Obraz., No. 7
Translated by K. Aleksanyan
