Anisotropic Dielectric Properties of Short Carbon Fiber Composites. FU Jin-Gang, ZHU Dong-Mei, ZHOU Wan-Cheng, LUO Fa

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1 第 27 卷第 11 期无机材料学报 Vol. 27 No 年 11 月 Journal of Inorganic Materials Nov., 2012 Article ID: X(2012) DOI: /SP.J Anisotropic Dielectric Properties of Short Carbon Fiber Composites FU Jin-Gang, ZHU Dong-Mei, ZHOU Wan-Cheng, LUO Fa (State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi an , China) Abstract: Dielectric materials based on short carbon fiber (C sf ) dispersed inside epoxy resin (EP) matrix composites were prepared. The complex permittivity of two types of distributions over the frequency range from 2.6 GHz to 8.2 GHz was reported. The effects of orientation with different content and length of carbon fibers on dielectric properties were investigated. It is found that axial permittivity of carbon fibers is several times larger than their radial permittivity. The real and imaginary parts of complex permittivity increase gradually with increasing the C sf contents in the composites, and the fiber length also affects the anisotropic property greatly. The two layered transmission line model is used to explain the phenomena. Key words: anisotropic; dielectric properties; composite materials; short carbon fiber Microwave-absorbing materials have attracted much attention because of their ability to eliminate electromagnetic wave pollution, which is mainly caused by gigahertz electronic systems and telecommunications [1]. The fiberfilled absorbing composites can obtain high values of dielectric constant at a low concentration of filling agent, as well as pronounced microwave dielectric dispersion, which are features of doubtless practical interest [2]. Another advantage of using fibers lies in that fiber absorbents have significant anisotropic electromagnetic parameters, which can be used to achieve better microwave absorbing properties by tailoring orientation of short fibers [3-4]. Among the fiber absorbents studied, such as carbon fibers, SiC fibers and polycrystalline iron fibers, polymer-derived SiC fibers are the most promising one due to their considerably low density, adjustable electrical resistivity [4-6]. Uncoated carbon fibers and metal-coated carbon fibers are added to polymer matrices as conducting elements to produce composites characterized by enhanced electrical conductivity to increase permittivity of neat resin [7-9]. However, in most cases, to obtain higher permittivity at microwave frequencies, composites with fiber at higher weight concentrations are adopted. Carbon fibers are used as reinforcement with randomly distribution [5, 10], even no reports focused on these properties of oriented short carbon fibers composites. In order to reveal their anisotropic dielectric properties, dielectric materials based on short carbon fiber (C sf ) dispersed inside epoxy resin (EP) matrix composites were prepared, and their anisotropic electromagnetic parameters were studied. 1 Experimental The thermoplastic matrix used in this study is epoxy resin (E-44), and solid PAN carbon fiber (T300-1k, shown in Fig. 1) supplied by Nantong Sengyou Carbon Fiber Company, Jiangsu, China, with an electrical resistivity of Ω cm and the average diameter of 7.8 μm. The content of C sf in the epoxy resin matrix varied from 0.25wt% 1wt%, and the carbon fibers were cut into three different lengths: 2 mm, 3 mm and 4 mm, respectively. The C sf was proportionally weighed and dispersed by an ultrasonic bath at room temperature for 30 min in acetone medium. Filled epoxy resin materials were obtained by Fig. 1 SEM image of carbon fiber Received date: ; Modified date: ; Published online: Foundation item: National Natural Science Foundation of China( ) Biography: FU Jin-Gang(1987 ), male, candidate of master degree. fjg @163.com Corresponding author: ZHU Dong-Mei, professor. dzhunwpu@nwpu.edu.cn

2 1224 无机材料学报第 27 卷 mixing liquid epoxy resin with a certain amount of C sf by means of a Haake mixer. After adding hardener( polyamide resin with low molecular weight 650), the mixtures were stirred and then coated by hand. The hybrid mixtures were postcured at 100 for 30 min. The thickness of oriented samples was about 2 mm in this study. The cross-section morphologies of the composites were observed by scanning electron microscope (SEM, Model SUPRA55, Zeiss, Germany). The dielectric permittivity of the specimens was measured by the rectangle wave-guide method, which was based on the measurements of the reflection and transmission modules, in the fundamental rectangle wave-guide mode TE10 by Agilent E8326B PNA series network analyzer (Palo Alto, CA). Both the real and the imaginary parts of the permittivity calculated with the reflection and transmission coefficients. For a dielectric material (μ = 1, μ = 0) the relative error varies between 1% (pure dielectric) and 10% (highly conductive materials). When the oriented fibers are parallel to the direction of the electric field, axial permittivity can be obtained shown in Fig. 2(a). Otherwise, radial permittivity can be obtained when the oriented fibers are against to the direction of the electric field shown in Fig. 2(b). 2 Results and discussion The optical microscope and SEM images of the oriented composites are shown in Fig.3, indicating the short fibers are well oriented along the shear direction (Fig. 3(a)). As can be seen, the short carbon fibers are physically integrated after postcured at 100 which is very important for the C sf to maintain the dielectric properties in the composites. And there are no agglomerations found (Fig. 3(b)). We suggest that the C sf used in our research are relatively short, and the mass of C sf used is relatively low. The material properties of the greatest importance to microwave interaction of a dielectric material are the complex permittivity, ε= ε + jε. The dielectric constant ε of a material is a function of its capacitance [7]. On the other hand, the ε represents the capacity of dielectric loss in the Fig. 2 Sketch of the dielectric test Fig. 3 The images of optical microscope( 50) (a) and SEM (b) of the oriented composites microwave frequency under an applied electric field [11]. The complex permittivities of two types of distribution of carbon fibers over the frequency range from 2.6 GHz to 8.2 GHz were characterized. The real and imaginary components of the complex permittivity for both the two materials as functions of concentration and length as well as distributions are presented in Fig. 4 to Fig.6, respectively. The effective complex permittivity is significantly anisotropic. The axial permittivity is shown in Fig. 4 and Fig.5. From Fig. 4, when filled with 3 mm carbon fiber, the real part (ε ) of the permittivity of composites varies from to and the imaginary part (ε ) varies from 2 6 to 33 62, with the content of C sf in the range from 0.25wt% to 1wt%. When the content of C sf is 0.5wt%, the real part get maximum values 42 with 2 mm C sf and 112 with 4 mm C sf at 2.6 GHz, while the imaginary part increase from 6 to 30 with increasing fiber length from 2 mm to 4 mm at 2.6 GHz (Fig. 5). It is obviously that the complex permittivity increase with increasing C sf content and length. And at each length, the real parts of the complex permittivity decrease smoothly while the imaginary part increase slightly with increasing frequency. The radial permittivity data illustrated in Fig. 6 indicates a much weaker interaction with microwaves over this frequency range than the previous specimens. As with the former specimens tested, ε decreases smoothly with increasing frequency. Maximum ε values occur at the low

3 第 11 期 FU Jin-Gang, et al: Anisotropic Dielectric Properties of Short Carbon Fiber Composites 1225 Fig. 4 The axial permittivity of the composites with different concentration of 3 mm C sf frequency limit (2.6 GHz). These increase with content from 7 at 0.25wt% to 18 at 1wt% in Fig. 6(a). And the imaginary part increase from 1 to 11, respectively. The magnitude of content dependence generally diminishes with increasing frequency. It is well known that the capacitance of a material is a function of its dielectric constant ε, and ε is proportional to the quantity of charge stored on either surface of the sample under an applied electric field, and the ε represents the capacity of dielectric loss. When subjected to an alternating electrical field, the free electrons shift with the alternating electrical field. In order to overcome the electrical resistance, the microwave energy is dissipated and converted to thermal energy, which is the combined effect of relaxation polarization loss and electric conductance loss. Therefore, the loss can be expressed as follows: ε '' = εc'' + εi'' (1) Where ε C is the loss factor due to conductivity, ε I is another one due to electronic relaxation polarization. Although polarization plays a role in the imaginary part, free electrons have more effects on it, due to the good electrical conductivity of carbon fibers [12]. According to the free electric theory, ε could therefore be obtained to be [11] σ ε'' εc '' = (2) 2πε0 f Eq. (2) shows that σ plays the dominating role in ε. Fig. 5 The axial permittivity of the composites with different fiber lengths (The fiber content is 0.5wt%) Fig. 6 The radial permittivity of the composites with different fiber content (The fiber length is 3 mm)

4 1226 无机材料学报第 27 卷 To explain the effects of fiber concentration, length, and distribution on the dielectric properties, the following simple model has been proposed. The anisotropic distribution of C sf (Fig. 7(a)) is approximated by a network of fibers separated by the insulating EP polymer matrix. Each fiber is assumed to be conductive with an equivalent resistor, and coupled to its neighbor by a capacitor (Fig. 7(b)). Under an applied electric field, only coupling capacitors and resistors in the electric field direction are considered. And we assume that the electric field distribution between the coupled conductors of the microstrip is uniform and parallel or perpendicular to the fiber. In this way, the model comes to be a two layer microstrip transmission line (Fig. 7(d)) formed by the series connection of a resistor (R tot ) and a capacitor (C tot ) (Fig. 7(c)). The capacitor is modeled in the two-layer structure of Fig. 7(d) by a corresponding capacity for the up layer. For the both situations, the complex permittivity increase with the increasing carbon fiber content. The value of C tot is inversely to the distance between fibers. The distance between inclusions decreases with increasing concentration. For the low concentration, the interaction between coupled fibers is much weaker than high concentration, meaning lager thickness H, otherwise, leading to a higher capacitance and, hence, a larger value of C tot, characterized by ε. The ε also increase with increasing fiber length. It is observed that ε =80 is obtained when the sample is added with 0.75wt%, 4 mm fiber, and 79 is obtained when the sample is added with 1wt%, 3 mm fiber. In order to get higher value of ε, we can use longer fiber instate of increasing fiber concentration, meaning a smaller distance between conductive inclusions and hence, a higher coupling. The two layered model for the fiber is able to predict the conductivity of the composites. By increasing concentration or fiber length, the thickness of conductive layer H i is enhanced, corresponding, the higher conductivity σ in Eq. (2). It means higher energy loss, characterized by ε. By comparing Fig. 4 and Fig. 6, it is observed that the effective complex permittivity is significantly anisotropic. For example, the real part of the axial permittivity is about five times (filled with 1wt% 3 mm fiber) as high as that of the radial permittivity. In the two layered transmission line model, there are more capacitors in the series connection system, because each resistor is shorted in the direction of each transmission line when the electric field is perpendicular to fibers. As we know, C tot is calculated by the following law: 1 1 = Ctot C (3) n When the capacitors series are connected, the more coupled conductors, the lower C tot value. On the other hand, the conductivity parallel to the direction of carbon fibers is higher than that perpendicular to the carbon fiber direction, because that the current could not cross the space among fibers and could only flow between the cross sections [13]. Those may be the reasons why we can get high axial permittivity. 3 Conclusion From the experimental studies, it was found that the distribution of embedded fibers affected the dielectric permittivity of composites at microwave frequencies. Composites with axial distributed (parallel to electric field) show higher permittivity compared to that with radial distributed (perpendicular to electric field) fibers. The results also showed that both the fiber content and length can be used to adjust the dielectric properties of the composites. The two layered transmission line model formed by the series connection of a resistor and a capacitor can explain the phenomena well. Both capacitivity and conducticity were considered in this model. References: [1] Hayt W, Buck J. Engineering Electromagnetics. New York: McGraw-Hill, [2] Saib Aimad, Bednarz Lukasz, Daussin Rapael. Carbon nanotube composites for broadband microwave absorbing materials. IEEE T Microw Theory, 2006, 54(6): [3] Neo C P, Vijay K. Optimization of carbon fiber composite for microwave absorber. IEEE Trans Electromagn Compatibility, 2004, 46(1): [4] Chu Zengyong, Cheng Haifeng, Zhou Yongjiang. Anisotropic microwave absorbing properties of oriented SiC short fiber sheets. Materials and Design, 2010, 31(6): [5] Ling Qincai, Sun Jianzhong, Zhao Qian, et al. Microwave absorbing properties of linear low density polyethylene/ethylene-octene Fig. 7 The two layered microstrip transmission line model on fiber-filled composites copolymer composites filled with short carbon fiber. Materials Science and Engineering: B, 2009, 162(3):

5 第 11 期 FU Jin-Gang, et al: Anisotropic Dielectric Properties of Short Carbon Fiber Composites 1227 [6] Wu Mingzhong, He Huahui, Zhao Zhensheng, et al. Electromagnetic anisotropy of magnetic iron fibres at microwave frequencies. J. Phys. D: Appl. Phys., 2001, 34(7): [7] Dang Zhimin, Shen Yang, Fan Lizhen, et al. Dielectric properties of carbon fiber filled low-density polyethylene. J. Appl. Phys., 2003, 93(9): [8] Hussain F A, Zihlif A M. Electrical properties of nickel-coated carbon fiber/nylon 66 composite. Composite Materials Journal of Thermoplastic, 1993, 6(2): [9] Yang Y, Zhang B S, Xu W D, et al. Preparation and electromagnetic characteristics of a novel iron-coated carbon fiber. Journal of Alloys and Compounds, 2004, 365(1/2): [10] Igor Maria De Rosa, Adrian Dinescu, Fabrizio Sarasini, et al. Effect of short carbon fibers and MWCNTs on microwave absorbing properties of polyester composites containing nickel-coated carbon fibers composites. Composites Science and Technology, 2010, 70(1): [11] Cao MaoSheng, Song Weili, Hou Zhiling, et al. The effects of temperature and frequency on the dielectric properties, electromagnetic interference shielding and microwave-absorption of short carbon fiber/silica composites. Carbon, 2010, 48(3): [12] Chung D D L. Electromagnetic interference shielding effectiveness of carbon materials. Carbon, 2001, 39(2): [13] Wang Xiaoyan, Luo Fa, Yu Xinmin, et al. Influence of short carbon fiber content on mechanical and dielectric properties of C fiber /Si 3 N 4 composites. Scripta Materialia, 2007, 57(4): 定向分布碳纤维复合材料介电性能研究 伏金刚, 朱冬梅, 周万城, 罗发 ( 西北工业大学凝固技术国家重点实验室, 西安 ) 摘要 : 以碳纤维为填充物, 环氧树脂为基体, 制备了碳纤维 / 环氧树脂介电复合材料. 介绍了两种分布方式对复合材料介电性能的影响, 分别研究了两种分布方式的介电常数随碳纤维含量和长度的变化规律. 在 2.6~8.2 GHz 频率范围内, 轴向介电常数是径向介电常数的数倍 ; 实部和虚部都随着碳纤维含量的增加而增大 ; 碳纤维长度也对介电性能的各向异性影响显著. 双层微波传输带模型可以合理地解释这些规律. 关键词 : 各向异性 ; 介电性能 ; 复合材料 ; 短切碳纤维中图分类号 : TB34 文献标识码 : A