Technical NoteA novel correlation for predicting the thermal conductivity of heterogeneous nanofiller polymer composites under effects of thermal contact resistance
Introduction
Advanced polymer composite materials used in potential applications that require higher thermal conductivity (TC, hereafter), such as flexible polymers in electronic packaging and encapsulations, satellite devices, and areas where good heat dissipation, low thermal expansion, and light weight are needed [1], [2], [3]. The thermally conductive fillers such as graphite, carbon black, carbon fibers, and ceramic or metal particles are embedded into the matrix so that the TC of pure polymers can be enhanced effectively. The planar graphite has very high TC, up to 3000 W/(m-K) [4]. The polymer composites filled with thermally conductive particles have advantages due to their easy processability, low cost, and durability against corrosion. In addition, Tavman [5] reported more reasons in the use of filler.
Various theoretical and empirical models have been suggested for many years in order to predict the TC of composite materials. Maxwell model [6], Lewis and Nielsen model [7], [8], Agari and Uno model [9], or Bruggeman model [10] are pronounced models which have been employed in many previous studies. Tavman [11] indicated that the Agari and Uno model effectively estimates the TC of aluminum-powder-filled high-density polyethylene composites at high filler content. He et al. [12] indicated that both the effective medium theory (EMT) and Nielsen models can give good predictions of the TC at a low filler VF. More details of the TC prediction models was discussed in [13]. However, the above-mentioned TC models are case-sensitive, and do not provide a reliable and universal prediction on the TC, since they do not incorporate various geometric parameters such as the filler volume fraction (VF, hereafter), the TC ratio between particle filler and the matrix. In addition, these models considered for predicting the TC of composite materials with single kind of, or homogenous filler material.
Another kind of filler which has recently received an interest in the TC enhancement of pure polymers, is core–shell nanoparticle. Zhou et al. [14] indicated that the TC was remarkably improved by adding core–shell Ag/SiO2 nanoparticles into polyimide matrix. Kim et al. [15] reported the significant enhancement of the TC using FeCr metal core–aluminum oxide shell particles with a highly mesoporous shell layer compared to the use of uni-modal particles. Recently, Ngo and Byon have performed an extensive study and a numerical analysis on the TC of core–shell nanoparticle polymer composites, and provided optimal conditions for enhancing and achieving the maximum TC [16], [17].
Heterogeneous fillers or hybrid fillers have been regarded as an effective method for enhancing TC of composites, as reported in previous studies. Lee et al. [18] found that the TC of composites filled with spherical particles and fibrous fillers are effectively higher than the base material at low and intermediate filler content. Xu et al. [19] also indicated that using a hybrid filler at a volume ratio of 1:6 gives enhanced TC than the use of each single filler. Furthermore, the TC of polymer composites can be improved by the addition of nanofillers into the polymer-matrix containing the micro fillers, as reported by Sanada et al. [20]. Adding modified aluminum fiber and aluminum nanoparticle into polyimide (PI) matrix gained very high TC (from around 0.11 W/(m-K) for pure thermoplastic PI [21] up to 15 W/(m-K)) and low relative permittivity [22]. More recently, Ngo and Byon [23] have studied numerically synergic effects of hybrid filler and found an existence of maximum effective thermal conductivity (ETC) under appropriate conditions. While these studies have performed the effectiveness of heterogeneous fillers to the TC of composite, no research considers a generalized correlation for predicting effectively the TC of composites with heterogeneous nanofillers under the effects of thermal contact resistance (TCR).
The objective of this study is to examine extensively the effects of TCR on the ETC of composites with heterogeneous-filler-nanoparticles. The effects of other important parameters are also taken into account, such as the TC ratios between the filler particles and the matrix material, and the VFs of each nanofiller particle. Consequently, a novel correlation is proposed for predicting the ETC, which is as a function of five non-dimensional parameters: two TC ratios, two VFs, and the TCR. In addition, the interesting behaviors of ETC with heterogeneous fillers are also considered and discussed.
Section snippets
Numerical methodology
Composite material consisting of homogeneous filler material and matrix material was considered in our previous study [24]. In the present study, composite materials with heterogeneous filler nanoparticles are studied. Figure shows the unit cell and boundary conditions used for the numerical study. It is assumed that each particle is isolated and homogenously distributed inside the matrix material. In addition, the TCs are constant for all spherical heterogeneous-particles (kp1, kp2) and matrix
Results
Increasing the TC of polymer composites with the increase of filler content for both homogeneous and heterogeneous fillers was reported in previous studies [20], [26], [27]. This was verified in the present study, as clearly shown in Fig. 2. This figure also indicates that ETC of nanoparticle-filled polymer composite materials depends on the VF of one filler (ϕ1) only if the VF of remaining filler (ϕ2) is very small (ϕ2 = 10−4, solid line in Fig. 2). Therefore, the ETC increases as the ϕ1
Conclusions
An investigation on the thermal behaviors in composites containing heterogeneous filler nanoparticles has been performed by a numerical approach. Based on the numerical results, a novel correlation for predicting the TC of composite materials has been proposed. Consequently, the major results obtained in the present study are drawn as:
- (1)
The ETC decreases as the TCR of both nanoparticles increases, and its variation depends on the relationship between the TCRs of hybrid filler (Rc1∗ and Rc2∗).
Acknowledgments
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2014R1A2A2A01007081).
Ich-Long Ngo received the B.S. in Aeronautical engineering department, Hanoi University of Science and Technology (2009), and M.S. in mechanical engineering department, Changwon National University (2013). He received Ph.D. in School of mechanical engineering, Yeungnam University (YU) (2015). He is currently working as research professor in YU.
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Ich-Long Ngo received the B.S. in Aeronautical engineering department, Hanoi University of Science and Technology (2009), and M.S. in mechanical engineering department, Changwon National University (2013). He received Ph.D. in School of mechanical engineering, Yeungnam University (YU) (2015). He is currently working as research professor in YU.
Chan Byon received the B.S., M.S. and Ph.D. in mechanical engineering department from KAIST. He has been a visiting scholar in UCLA (2009) and Imperial College London (2012). He is currently working as a professor in Yeungnam University.