International Journal of Polymer Science

Volume 2018, Article ID 8190190, 10 pages

https://doi.org/10.1155/2018/8190190

## Thermal and Electrical Conductivity of Unsaturated Polyester Resin Filled with Copper Filler Composites

The Scientific and Technological Research Council of Turkey, Defense Industries Research and Development Institute (TÜBİTAK SAGE), 06261 Ankara, Turkey

Correspondence should be addressed to Kemal Yaman; rt.vog.katibut@namay.lamek

Received 28 December 2017; Revised 19 February 2018; Accepted 11 March 2018; Published 29 April 2018

Academic Editor: Zhiyuan Xiong

Copyright © 2018 Kemal Yaman and Özer Taga. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Thermal and electrical conductivity of unsaturated polyester resin with copper filler composite material are investigated both theoretically and experimentally. In the experiments, polyester matrix is combined with dendrite-shape copper to determine the effects of both filler size and content on thermal and electrical conductivity, respectively. It is observed that the increase in the concentration causes the thermal and electrical conductivity of composite mixture to grow up. It has also been observed that the both thermal and electrical conductivity increase with increasing filler particle size.

#### 1. Introduction

Nowadays in many applications, thermal and electrically conductive polymer-based composites can replace metals. This technology is widely used because it introduces a new material that includes the thermal, insulation, and electrical properties of polymer materials. The advantages of polymers over metals are low density, corrosion and oxidation resistance, lightness, electromagnetic interference (EMI) protection, higher chemical resistance, and higher producibility. These superior features can be easily adjusted to different and widely applications [1, 2].

Too many studies in the literature are investigating the addition of nonpolymeric fillers to improve the physical properties of polymer. The addition of fillers with high thermal and electrical properties increases the thermal and electrical conductivity beyond the neat resin of the composite but cannot reach the level of pure filler material. The main motivation in this study is the theoretical and experimental investigation of the effects of particle size and concentration of dendritically shaped copper particles used as filler materials on thermal and electrical conductivity. Some of the existing studies examined in this subject are summarized as follows.

In a similar study, Choi et al. [1] investigate the thermal conductivity of polyacrylate matrix aluminum and multiwalled carbon nanotube filled composites. For the fixed filler concentration, the composite loaded with 13 *μ*m aluminum dust had a higher thermal conductivity than the 3 *μ*m powder, and the composite filled with the two powder mixtures showed a synergistic effect on the thermal conductivity. The thermal conductivity of the composites strongly depended on the size and content of fillers. Moreira et al. [3] used unsaturated polyester resin (UPR) as binder and alumina and tenorite (copper oxide) as conductive particles in nanosize. The results showed that the thermal conductivity increases with particle concentration, as expected.

Agrawal and Satapathy [4] have proposed a new theoretical method to calculate the one-dimensional heat conduction, and thermal conductivity of typical particulate filled polymer composite systems. In their experimental work, epoxy binder was applied with aluminum nitrite filler material. The thermal conductivity of the composite increases with the addition of filler particle and the rate of increase of thermal conductivity is rapid for high volume fraction, that is, above 35% as compared with low volume fraction. In another study in which both thermal and electrical conductivities were examined together, Zhou et al. [5] reported that the thermal and electrical conductivity are related to the particulate shape and size as well as the added particle concentration. At higher filler loads, the thermal conductivity has increased dramatically. Heat-conductive aluminum particles encapsulated by a polymer matrix could not contact each other at a low filler loading, resulting in the low thermal conductivity. This result is due to the high interfacial thermal contact resistance between the filler powder and the polymer matrix. The thermal and electrical conductivities of PVDF with flaky Al mixture composite is higher than spherical shape filler one. The thermal conductivity of the composite was found to be four times higher than the neat matrix for nickel-HDPE matrix composite [6].

The measurement of some parameters of the materials, such as thermal diffusivity, thermal conductivity, and thermal expansion coefficient, is very important for applications used especially in the manufacturing of devices. The thermal diffusivity given in Section 3.1, (m^{2}s^{−1}), is an important thermophysical parameter that measures how effectively the phonons carry heat from the sample. However, the measurement of heat exchange or thermal impedance for a given material's heat exchange is essentially determined by the thermal effusivity, (Ws^{1/2 }m^{−2} K^{−1}). The* e* is another important thermophysical parameter for quenching operations as much as for surface heating or cooling processes. These quantities are defined by and , where is the thermal conductivity, is the specific heat capacity, and is the bulk density. The known thermal conductivity of and can be obtained from [7]. The variation of these parameters with respect to filler content will be given in Section 3.1 in more detail.

Considering the theoretical background of thermal conductivity, some predictive models of thermal conductivity emerge. The Maxwell Theoretical Model is the main focal point for most of these models. This model uses potential theory to obtain a precise solution for the conductivity of a system with spherical, noninteracting particles in a continuous matrix state [3–5, 8–10].where , , and are the thermal conductivities of the composite, matrix, and filler respectively, and is the volume fraction of filler. The Hashin-Shtrikman model is described as one of the best ways to estimate the lower limit when no information is available about the particle distribution in the matrix [6]. This lower limit can be expressed by the following equation:where , , and are the thermal conductivities of the composite, matrix, and filler, respectively, and is the volume fraction of filler.

Budiansky has provided a consistent way called “self-consistent” to calculate for composites. This model can be related to the calculation of a similar electrostatic problem. The model allows us to determine the thermal conductivities of the N-component system, which knows only the thermal conductivities of pure materials () and volume parts () with respect to (4) [11]:For a seconder system consisting of matrix and filler, (2) can be rewritten to the form given by (3)–(6):The Lewis–Nielsen model is defined by (8) and (9) for various shapes of fillers, as shown as follows [3, 4, 8, 11–13]:where is a variable which depends on the shape of the particles and is the maximum insertion fraction. Various values and have been reported in the literature in different forms and different packing geometries (e.g., hexagonal, face and body centered cubic, simple cubic, and random). It is difficult to select correct values for and in order to calculate the thermal conductivities with respect to the filler content.

In the study of Krupa, the Lewis–Nielsen theoretical model reveals experimental data significantly. The above parameters obtained by adaptation of experimental data have the following values: = 5.5 ± 0.7 and = 0.6 ( = 0.982) [6]. According to the Tavman [14], and are taken as 3 and 0.64, respectively. The Budiansky and the Maxwell model give the closest tendency with our experimental data for the lower concentrations. The comparison results will be given in Section 3.

#### 2. Experimental Study

Dendrite-shape copper powder with 75 *μ*m average particle size is used as conductive filler material. The copper powder is sieved into 15–25 *μ*m, 25–32 *μ*m, 32–45 *μ*m, 45–53 *μ*m, 53–63 *μ*m, 63–75 *μ*m, 75–90 *μ*m, 90–106 *μ*m, 106–120 *μ*m, 120–150 *μ*m, and 150–180 *μ*m fractional size groups (See in Figure 2) in order to test the effect of particle size on thermal and electrical conductivity. The SEM image of dendritic-shaped copper particle is shown in Figure 1. As can be seen in SEM image, the dendritic-shaped particle structure has much more contact surface area than the spherical and flake structures.