Dielectric properties of paper-based composites at microwave frequency

Abstract

A kind of paper-based composite was prepared with short carbon fibers (CFs) and para-aramid fibrids through the process of papermaking. The dielectric properties of the paper-based composites at microwave frequency were investigated. Based on the Lichtenecker Rule, the dielectric constants of CFs in composites at different CF concentrations were calculated. The absorbing performances of paper-based composites were calculated from the test results of electromagnetic parameters. It was shown that for the composites loaded with 1 mm CFs, the real part of complex permittivity rises at first then tends to be stable with the increase of the CF content, and the imaginary part rises at first then falls slightly, while for composites loaded with 3 or 6 mm CFs, both the real and imaginary part of complex permittivity grows at first and then falls rapidly with the CF content increasing. When the CF content is below 10 wt%, the composites containing longer CFs have larger permittivity at the same concentration. The Lichtenecker Rule is found to be not suitable for the system studied in this paper, especially when the content of CFs is high. The variations of reflectance and absorbance with the content of CFs generally have analogous trends . It is also found that to achieve better absorbing performance, the length and content of CFs together with the thickness of composites should be considered. In this study, the lowest reflection loss at 10 GHz reaches –27.59 dB when the paper-based composite is loaded with 1 mm CFs at the concentration of 10 wt% and the optimum thickness of 1.84 mm.

Keywords

dielectric absorbing properties paper carbon fiber para-aramid fibrids

The paper-based composites are a type of fiber materials made through the wet forming process. Compared with other forming methods of fibrous composites, such as weaving, knitting, needle punching and non-woven technology, papermaking has the following characteristics:
various fibrous raw materials can be combined together flexibly, which means it has outstanding designability;

fibers can get well distributed in non-wovens using papermaking technology;¹

the orientation of most fibers is random on the X,Y plane, with only a few fibers arranging along the Z-axis or in some other directions.

Since the 1970s, the technologies to prepare paper-based materials of high performance that use synthetic fiber as raw materials have become a very active research field.² Among these paper-based materials, aramid paper-based composites may be the most typical kind. Aramid, the full name of which is aromatic polyamide fiber, is defined as follows: more than 85% amido bonds (-CONH-) are linked to two benzene rings directly.³ Owing to its unique molecular structure, aramid paper-based composites have many excellent characteristics and are widely used in various fields, especially aviation. They are generally made into honeycombs and used in antenna windows and radomes,⁴ playing the role in load-carrying and wave-transmitting. Moreover, in recent years, there have also been some researches on the application of aramid paper in radar absorbing materials (RAMs) of structural type that have dual functions of absorption and load bearing. In the existing related literature, aramid paper are made into honeycombs as well, followed by being impregnated with resins loaded with absorbing agents, such as carbon black.^5,6 However, to the best of our knowledge, there are no reported results on the design of microwave-absorbing paper, which can be made into absorbing honeycombs without extra addition of absorbing agents.

Some researchers have studied the influences on the absorbing properties of other absorbing materials, such as resin/conductive filler composites,^7–9 conductive fiber fabrics^10,11 and so on. However, because of their unique structure and random fiber orientation, the situation for paper-based composites may be different. As is well known, it is necessary to know quantitative knowledge of dielectric properties to avoid costly cut-and-try experiments during the design of absorbing materials.¹² Extensive literature exists for the problem of calculating the effective macroscopic permittivity for a given material sample as a function of its structure and the characteristic of its constituent components.¹³ The related classical mixing rules include the Maxwell–Garnett rule, the Bruggeman rule, coherent potential rule and so on. However, all these formulas are derived with many limits, such as the content, distribution, geometry of inclusions and the permittivity contrasts between the inclusion and the matrix.¹⁴

There are two species of aramid: para-aramid and meta-aramid. In this study, paper-based composites composed of short CFs (the absorbing agents) and para-aramid fibrids (the matrix) were prepared through the process of papermaking by choosing different lengths and contents of CFs. The selection of the materials is based on following considerations. Firstly, short carbon fibers (CFs) possess elevated electric conductivity; meanwhile, they are less likely to form continuous current to become strong reflectors of electromagnetic waves than CF yarn, which makes them good absorbing agents.⁹ Secondly, aramid fibrid is a kind of fiber prepared by special technics; unlike most fibers, it presents a microscopic structure of membrane and has a large specific surface,¹⁵ thus it can cover or wrap short CFs and has a good contact with CFs, which helps in dissipating electromagnetic waves. It is also a material of low dielectric constant, which contributes to making the intrinsic impedance of the composites close to that of the free space when it acts as a matrix. In addition, the paper-based composites composed of them have a three-dimensional porous structure with a number of irregular pores, which together with the wrinkles on the para-aramid fibrids makes the multi-reflection of electromagnetic waves and contributes to attenuation.⁴ In this study, the dielectric constant and dielectric loss of paper-based composites at microwave frequency were studied systematically. Microwave-absorbing properties were calculated from the results of electromagnetic parameters measured.

Experimental details

Materials

The CFs M-125T, C-103T and C-106T were provided by Kureha Chemical (Shanghai) Co., Ltd. The parameters of CFs are as follows. The lengths of M-125T, C-103T and C-106T CFs are 1, 3 and 6 mm, respectively. They all have diameter of 18.0 µm, density of 1.63 gċcm^–3, tensile strength of 670 MPa and elongation of 2.2%. The para-aramid fibrids were provided by Teijin Aramid Asia Co., Ltd and their appearance is shown in Figure 1.They are light yellow and irregularly shaped, seemingly. Their properties are presented in Table 1.
Figure 1.
The appearance of para-aramid fibrids.

Table 1.
Properties of para-aramid fibrids

Fiber type Beating degree (SR) Average length (mm) Average width (µm) Density (gcm^–3)

Para-aramid fibrids 79 0.42 21.2 1.40

Preparation of paper-based composites

In this research, paper-based composites with the same grammage of 65 g/m² were prepared by the following steps.
Carbon fibers were dispersed in deionized water by defibering for 3 min in a pulp disintegrator (L&W 991509, Sweden). Para-aramid fibrids were dispersed in deionized water by defibering for 2 min in a stirrer (Philips HR2024, Holland).

The two kinds of dispersion mentioned above were blended and diluted to form a slurry.

Most of the water was drained from the slurry to form a wet hand sheet through a rapid-Köthen sheet former (PTI RK3-KWTjul, Austria) whose forming section was a circle 20 cm in diameter. Figures 2(a) and (b) are pictures of the sheet former and the sheet obtained.

The sheet was pressed for further removal of water with a sheet press (KRK 2569, Japan).

The sheet was then dried at 90℃ for 15 min.

The sheet was calendered to improve the smoothness of the sheet and the thickness was adjusted to 90-100 µm.

Figure 2.
The pictures of the sheet former and the hand sheet obtained.

The accurate thicknesses of the sheets were measured with a thickness gauge (L&W251, Sweden) at the pressure of 50 KPa. The porosity of the sheets were calculated according to the equation $P = (\frac{1 - (w_{1} / ρ_{1} + w_{2} / ρ_{2}) \times G}{t \times 100}) \times 100 %$ , where w₁ and w₂ are the mass fractions of CFs and para-aramid fibrids, respectively, in % units, $ρ_{1}$ and $ρ_{2}$ are the densities of CFs and para-aramid fibrids, respectively, in g/cm³ units, G is the grammage in g/m² units and t is the thickness in µm units. Similarly, the volume fractions of CFs and para-aramid fibrids were calculated according to the equations $v_{1} = \frac{w_{1} \times G}{ρ_{1} \times t \times 100} \times 100 %$ and $v_{2} = \frac{w_{2} \times G}{ρ_{2} \times t \times 100} \times 100 %$ , respectively, where v₁ and v₂ are the volume fractions of CFs and para-aramid fibrids, respectively, in % unit. Table 2 shows the parameters of each sheet.
Table 2.
Characteristics of paper-based composites

Serial number Length of CFs (mm) Content of CFs (wt%) Thickness (µm) Porosity (%) Volume fraction of CFs (%) Volume fraction of PAFs (%)

1-1 1 0.1 92 49.23 0.04 50.73

1-2 1 1 90 49.52 0.43 50.05

1-3 1 3 92 48.71 1.33 49.96

1-4 1 5 94 49.75 2.17 48.08

1-5 1 10 95 51.00 4.27 44.73

1-6 1 20 84 45.52 9.63 44.85

1-7 1 30 91 49.79 13.51 36.70

1-8 1 40 88 48.95 18.59 32.46

1-9 1 50 96 54.43 21.06 24.52

2-1 3 0.1 83 46.48 0.05 53.47

2-2 3 1 87 48.27 0.44 51.29

2-3 3 3 88 45.94 1.40 52.66

2-4 3 5 94 50.43 2.14 47.43

2-5 3 10 95 51.60 4.22 44.19

2-6 3 20 89 48.52 9.10 42.38

2-7 3 30 91 50.48 13.32 36.19

2-8 3 40 97 55.23 16.30 28.47

2-9 3 50 98 55.15 20.72 24.13

3-1 6 0.1 86 47.43 0.05 52.52

3-2 6 1 92 51.00 0.42 48.58

3-3 6 3 93 49.92 1.30 48.78

3-4 6 5 97 52.47 2.06 45.47

3-5 6 10 95 51.52 4.22 44.26

3-6 6 20 88 48.32 9.13 42.54

3-7 6 30 85 47.43 14.14 38.42

3-8 6 40 89 51.20 17.77 31.03

3-9 6 50 91 53.31 21.57 25.12

CFs: carbon fibers; PAFs: para-aramid fibrids.

The characterization of micromorphology

The micromorphology of paper-based composites was observed by a scanning electron microscope (SEM; Zeiss EVO, Germany).

The measurement of complex permittivity and permeability

The complex permittivity and permeability of the paper-based composites were measured by the waveguide method according to the standard GJB 1651A-201 ×-5012 and the test system is shown in Figure 3. The samples were rectangular with a size of 22.86 mm × 10.16 mm and set upright in the waveguide. Figure 4 shows the cross-sectional view of the waveguide with a sample. A vector network analyzer (WILTRON 37269 A, USA) was used to measure the amplitude and phase of the complex reflection coefficient at the frequency of 10 GHz. The complex reflection coefficient of the single system was measured, as was that of the system with a sample, so that the complex reflection coefficient of a single sample was obtained. As the measuring system could be regarded as an equivalent two-terminal network, there was a clear relationship between the complex reflection coefficient and the complex electromagnetic parameters. Thus, the complex permittivity and permeability of each sample were acquired.
Figure 3.
The schematic diagram of the test system.

Figure 4.
The cross-sectional view of the waveguide with a sample.

The evaluation of microwave-absorbing properties

Based on the measured complex permittivity and permeability, the microwave-absorbing properties were evaluated by Equations (1) and (2):¹⁶
$R = 20 log | \frac{Z_{1} - Z_{0}}{Z_{1} + Z_{0}} |$
(1)

$Z_{1} = \sqrt{\frac{μ}{ɛ}} \cdot \tanh (\frac{i \cdot 2 π fd}{c} \sqrt{μ ɛ})$
(2)
where R is the reflection loss in dB units, Z₀ is the characteristic impedance of free space, Z₁ is the input impedance of the absorbing material, c is the velocity of light, f is the frequency of electromagnetic waves and d is the thickness of an absorbing material in mm units. ɛ and μ are the measured complex permittivity and permeability, respectively.

Results and discussion

Micromorphology of paper-based composites

Figures 5(a)-(d) are SEM photos of the paper-based composites, from which it is seen that the CFs randomly orient on the X,Y plane and disperse in the para-aramid fibrids. CFs are covered or wrapped by the thin membranes of para-aramid fibrids.
Figure 5.
The scanning electron microscope images of paper-based composites (1 mm carbon fibers, 10 wt%): (a) the surface: ×100; (b) the surface: ×1000; (c) the cross-section: ×100; (d) the cross-section: ×1000.

Dielectric properties of paper-based composites

As the paper-based composites prepared above are non-magnetic, that is, the real part of the complex permeability is close to 1 and the imaginary part of the complex permeability tends to be zero, only the dielectric properties are discussed below. Figures 6(a) and (b) show that, for composites loaded with 1 mm CFs, both the real and imaginary part of the complex permittivity rises with the increase of the content of CFs from 0.1 to 30 wt%, and when the content of CFs is above 30 wt%, the real part tends to be stable and the imaginary part declines slightly. However, for composites loaded with 3 or 6 mm CFs, when the content is below 10 wt%, both the real and imaginary parts of the complex permittivity increase with the content increasing, while they begin to decrease when CF content is higher than 10 wt%.
Figure 6.
(a) The real part of complex permittivity versus the content of carbon fibers (CFs) for paper-based composites. (b) The imaginary part of complex permittivity versus the content of CFs for paper-based composites. (c) The dielectric loss versus the content of CFs for paper-based composites.

It is well known that there is a link between the macroscopically measured permittivity and three molecular parameters: the number N of contributing elementary particles per unit volume; the polarizability $α$ ; and the locally acting electric field $E'$ that acts on the particle.¹⁷ Unlike a polymer-matrix composite, air is an important part of the heterogeneous system investigated here, even occupying approximately half of the whole volume, which can be seen from Table 2. In the present study, the value of polarizability largely depends on electronic polarization caused by the displacement of electrons and interfacial polarization, a phenomenon that appears in heterogeneous media consisting of different phases, attributed to the accumulation of charges at the interfaces.⁷ It is well known that in CFs carbon atoms are combined by covalent bonds forming atomic layers with the structure of hexagonal mesh, and delocalized $π$ bonds are formed above and below the atomic layers.¹⁸ On the other hand, these atomic layers are basically parallel to the fiber axis.¹⁹

When the CFs are short, they are well dispersed. Consequently, they are easily separated from each other by the matrix. As the content becomes larger in the range of this work, both the interfacial areas between phases and the number of contributing particles per unit volume are larger. Therefore, electronic polarization and interfacial polarization become more obvious, followed by the increase of the permittivity. For the longer CFs, the delocalized $π$ bonds occupy in wider range, which means the electrons have more space to be displaced and the electronic polarization becomes more obvious. So composites loaded with longer CFs have larger permittivity as the content is below 10 wt%. However, the permittivity of composites loaded with 3 and 6 mm CFs begins to go down rapidly when the content is above 10 wt%. This may be attributed to the following reason: as the content of longer CFs becomes larger, CFs become more difficult to disperse uniformly; in addition, they tend to get entangled with each other and form the structure of lap joint in the process of sheet forming.

The calculated dielectric constant of CFs in paper-based composites

Many people have researched the relationship between dielectric constant of mixtures and that of each component^20,21 and many empirical formulas have been achieved, one of which is the Lichtenecker Rule, expressed as $\log ɛ = \sum V_{i} \log ɛ_{i}$ ,²² where ɛ is the dielectric constant of composites, $ɛ_{i}$ is the dielectric constant of component i and V_i* is the volume fraction of component i. In this study, the dielectric constant of paper-based composites was measured as above. According to the previous literatures,²³ the dielectric constant of para-aramid is assumed to be 4. Based on the Lichtenecker Rule, the dielectric constant of CFs in paper-based composites at different concentrations was calculated and the results are shown in Table 3, where ɛ represents the measured dielectric constant of paper-based composites and $ɛ_{2}'$ represents the calculated dielectric constant of CFs. As CFs can be regarded as conductive materials, their dielectric constant approaches infinite. From Table 3 it can be seen that the Lichtenecker Rule may not be suitable for the system studied in this paper, especially when the content of CFs is high. That may be attributed to the following reasons.
Short CFs have a large L/D ratio compared to granular incidents, which influences the polarization situation of inclusion.

There is a very large difference between the dielectric constant of CFs and that of para-aramid fibrids. The polarization of CFs and para-aramid fibrids may influence each other significantly.

The system is a heterogeneous one composed of at least three different phases. The distribution of components and interaction between each component of this system may be quite different from that of a homogeneous system composed of two phases. In addition, the interaction between CFs increases as the content of CFs goes up.

Table 3.
Dielectric constant of carbon fibers (CFs) in paper-based composites calculated by the Lichtenecker Rule

Serial number Length of CFs (mm) Content of CFs (wt%) Measured dielectric constant of composites ɛ Calculated dielectric constant of CFs $ɛ_{2}'$

1-1 1 0.1 2.71 10²⁹³

1-2 1 1 5.39 10⁹⁹

1-3 1 3 7.30 10⁴²

1-4 1 5 12.1 10³⁶

1-5 1 10 16.9 10²³

1-6 1 20 23.6 10¹¹

1-7 1 30 28.2 10⁹

1-8 1 40 26.2 10⁷

1-9 1 50 28.0 10⁶

2-1 3 0.1 3.00 10³³⁷

2-2 3 1 6.02 10¹⁰⁶

2-3 3 3 15.9 10⁶³

2-4 3 5 28.2 10⁵⁴

2-5 3 10 49.3 10³⁴

2-6 3 20 43.5 10¹⁵

2-7 3 30 43.8 10¹¹

2-8 3 40 39.8 10⁹

2-9 3 50 35.1 10⁷

3-1 6 0.1 4.76 10⁸⁰⁰

3-2 6 1 10.4 10¹⁷²

3-3 6 3 24.8 10⁸⁵

3-4 6 5 33.2 10⁶¹

3-5 6 10 47.9 10³⁴

3-6 6 20 47.2 10¹⁶

3-7 6 30 34.1 10⁹

3-8 6 40 38.5 10⁸

3-9 6 50 29.4 10⁶

Reflectance, absorbance and transmittance of paper-based composites

Generally, reflection loss is used to characterize the absorbing performance of a material in actual applications, which represents the reflection when the medium on one side of the sample is air and the medium on the other side is metal. As total reflection will occur when electromagnetic waves reach a metal plate, all the waves that penetrate the sample will be reflected again. As a result, the incident waves are turned into reflection waves and absorbed waves. However, if we want to know how many waves are respectively reflected, absorbed and penetrate the sample when electromagnetic waves reach the surface of the sample, reflectance, absorbance and transmittance should be calculated under the condition that the medium on both sides of the sample is air. Figure 7 shows the variations of reflectance, absorbance and transmittance, respectively, with the content of CFs under the latter condition. Figure 6(c) presents the variations of dielectric loss with the content of CFs. The dielectric loss is well known to be defined to divide the real part of the complex permittivity by the imaginary part of the complex permittivity. It can be seen from Figure 7 that no matter which of these three kinds of the CFs are loaded, the variations of reflectance and absorbance with the content of CFs generally have analogous trends. Moreover, the curves of reflectance versus the content of CFs match well with the corresponding curves of the real part of complex permittivity versus the content of CFs, while the curves of absorbance versus the content of CFs match well with the corresponding curves of the dielectric loss versus the content of CFs. That may be because the greater the difference of the real part of the complex permittivity between the sample and the air is, the more easily reflection happens on the interface between the sample and the air when the electromagnetic wave is incident on the sample surface. The greater the imaginary part of the complex permittivity is, the more electromagnetic wave is dissipated in the sample as heat, which also means that more electromagnetic wave is absorbed by the sample. What is more, in this study, the real and imaginary part of the complex permittivity roughly have the same variation trend with the CF content changing.
Figure 7.
The reflectance, absorbance and transmittance respectively versus the content of carbon fibers for paper-based composites. R: reflectance; A: absorbance; T: transmittance.

Microwave-absorbing performances of paper-based composites

Table 4 presents absorbing performances of each paper-based material, including the minimum reflection loss (Min RL) and the optimum thickness, which are defined as follows. For a material with a certain composition, structure and distribution of inclusions, its complex permittivity remains the same while the minimum reflection loss changes with the thickness of the material changing. If the reflection loss at a certain thickness is lower than that at other thicknesses, this thickness is called the optimum thickness, and the corresponding reflection loss is called the minimum reflection loss.
Table 4.
Absorbing performances of each paper-based material.

Serial number Length of CFs (mm) Content of CFs (wt%) Min RL (dB) Optimum thickness (mm)

1-1 1 0.1 –0.95 ± 0.003 5.28 ± 0.20

1-2 1 1 –7.52 ± 0.8 3.47 ± 0.008

1-3 1 3 –12.48 ± 0.9 2.93 ± 0.3

1-4 1 5 –16.55 ± 0.8 2.22 ± 0.008

1-5 1 10 –27.59 ± 0.5 1.84 ± 0.07

1-6 1 20 –9.41 ± 0.9 1.52 ± 0.04

1-7 1 30 –8.05 ± 0.28 1.38 ± 0.04

1-8 1 40 –12.55 ± 0.4 1.46 ± 0.12

1-9 1 50 –14.96 ± 2.0 1.42 ± 0.029

2-1 3 0.1 –3.97 ± 2.3 4.98 ± 0.11

2-2 3 1 –22.14 ± 1.0 3.20 ± 0.17

2-3 3 3 –8.02 ± 1.4 1.81 ± 0.16

2-4 3 5 –5.11 ± 0.7 1.33 ± 0.15

2-5 3 10 –3.93 ± 0.5 0.99 ± 0.02

2-6 3 20 –4.29 ± 0.4 1.06 ± 0.06

2-7 3 30 –4.84 ± 0.6 1.08 ± 0.07

2-8 3 40 –6.19 ± 1.1 1.15 ± 0.05

2-9 3 50 –10.99 ± 0.2 1.26 ± 0.024

3-1 6 0.1 –21.67 ± 0.7 3.51 ± 0.04

3-2 6 1 –6.12 ± 0.7 2.09 ± 0.14

3-3 6 3 –3.89 ± 0.4 1.33 ± 0.14

3-4 6 5 –3.24 ± 0.28 1.12 ± 0.08

3-5 6 10 –2.85 ± 0.27 0.96 ± 0.09

3-6 6 20 –3.93 ± 0.21 1.01 ± 0.05

3-7 6 30 –5.36 ± 0.5 1.22 ± 0.08

3-8 6 40 –6.43 ± 0.7 1.17 ± 0.05

3-9 6 50 –4.80 ± 1.3 4.08 ± 0.15

CFs: carbon fibers.

Table 4 shows that besides the thickness of composites, the length and content of CFs should be considered simultaneously to achieve better absorbing performance. In general, if shorter CFs are used, a higher content should be chosen to match, while a lower content is enough if longer CFs are used. Specifically, in this work, in order to obtain reflection loss below -20 dB, composites loaded with 1 mm CFs should have a content of about 10 wt%, composites loaded with 3 mm CFs should have a content of around 1 wt%, and a content of about 0.1 wt% is enough for composites loaded with 6 mm CFs. This may be because longer CFs form the structure of the lap joint more easily and a network can be formed with fewer fibers. Thus, the length of CFs affects the interaction between the incident electromagnetic wave and the composites, shown by the apparent value of reflection loss. In addition, it can be inferred from Table 4 that although paper-based composites composed of para-aramid fibrids and CFs have pore structure with high porosity of about 50%, they also have good microwave-absorbing performance; for some of the samples the own reflection loss was below -10 dB, and for some even below -20 dB at the optimum thickness. This can be attributed to the fact that paper-based composites have a three-dimensional network structure and there are massive irregular pores inside paper-based composites. The structure is like that of a microwave anechoic chamber, where there are many small pyramids. When incident waves reach the paper-based composites, they are multi-reflected and gradually attenuated.²⁴

Conclusions

In this paper, paper-based composites were prepared through the process of papermaking with short CFs and para-aramid fibrids. The dielectric and microwave-absorbing properties at 10 GHz were investigated. The results are summarized as follows.
The length of CFs has a significant effect on the complex permittivity of paper-based composites. When composites are loaded with 1 mm CFs, the real part of the complex permittivity rises at first then tends to be stable with the increase of the CF content, and the imaginary part of the complex permittivity rises at first then falls slightly. However, for composites loaded with 3 or 6 mm CFs, both the real and imaginary parts of the complex permittivity rise at first and then fall rapidly with the CF content increasing. The composites loaded with longer CFs have larger values of permittivity at the same concentration below 10 wt%.

Based on the Lichtenecker Rule, the dielectric constants of CFs in composites at different CF concentrations were calculated. It was found that the Lichtenecker Rule may not be suitable for the system studied in this paper, especially when the content of CFs is high.

Besides the thickness of composites, the length and content of CFs should be considered simultaneously in the preparation of paper-based composites to achieve better absorbing performance. In this study the lowest reflection loss at 10 GHz reaches -27.59 dB when the paper-based composite is loaded with 1 mm CFs at the concentration of 10 wt% at the optimum thickness of 1.84 mm.

Fiber type	Beating degree (SR)	Average length (mm)	Average width (µm)	Density (g*cm^–3)
Para-aramid fibrids	79	0.42	21.2	1.40

Serial number	Length of CFs (mm)	Content of CFs (wt%)	Thickness (µm)	Porosity (%)	Volume fraction of CFs (%)	Volume fraction of PAFs (%)
1-1	1	0.1	92	49.23	0.04	50.73
1-2	1	1	90	49.52	0.43	50.05
1-3	1	3	92	48.71	1.33	49.96
1-4	1	5	94	49.75	2.17	48.08
1-5	1	10	95	51.00	4.27	44.73
1-6	1	20	84	45.52	9.63	44.85
1-7	1	30	91	49.79	13.51	36.70
1-8	1	40	88	48.95	18.59	32.46
1-9	1	50	96	54.43	21.06	24.52
2-1	3	0.1	83	46.48	0.05	53.47
2-2	3	1	87	48.27	0.44	51.29
2-3	3	3	88	45.94	1.40	52.66
2-4	3	5	94	50.43	2.14	47.43
2-5	3	10	95	51.60	4.22	44.19
2-6	3	20	89	48.52	9.10	42.38
2-7	3	30	91	50.48	13.32	36.19
2-8	3	40	97	55.23	16.30	28.47
2-9	3	50	98	55.15	20.72	24.13
3-1	6	0.1	86	47.43	0.05	52.52
3-2	6	1	92	51.00	0.42	48.58
3-3	6	3	93	49.92	1.30	48.78
3-4	6	5	97	52.47	2.06	45.47
3-5	6	10	95	51.52	4.22	44.26
3-6	6	20	88	48.32	9.13	42.54
3-7	6	30	85	47.43	14.14	38.42
3-8	6	40	89	51.20	17.77	31.03
3-9	6	50	91	53.31	21.57	25.12

Serial number	Length of CFs (mm)	Content of CFs (wt%)	Measured dielectric constant of composites ɛ	Calculated dielectric constant of CFs $ɛ_{2}'$
1-1	1	0.1	2.71	10²⁹³
1-2	1	1	5.39	10⁹⁹
1-3	1	3	7.30	10⁴²
1-4	1	5	12.1	10³⁶
1-5	1	10	16.9	10²³
1-6	1	20	23.6	10¹¹
1-7	1	30	28.2	10⁹
1-8	1	40	26.2	10⁷
1-9	1	50	28.0	10⁶
2-1	3	0.1	3.00	10³³⁷
2-2	3	1	6.02	10¹⁰⁶
2-3	3	3	15.9	10⁶³
2-4	3	5	28.2	10⁵⁴
2-5	3	10	49.3	10³⁴
2-6	3	20	43.5	10¹⁵
2-7	3	30	43.8	10¹¹
2-8	3	40	39.8	10⁹
2-9	3	50	35.1	10⁷
3-1	6	0.1	4.76	10⁸⁰⁰
3-2	6	1	10.4	10¹⁷²
3-3	6	3	24.8	10⁸⁵
3-4	6	5	33.2	10⁶¹
3-5	6	10	47.9	10³⁴
3-6	6	20	47.2	10¹⁶
3-7	6	30	34.1	10⁹
3-8	6	40	38.5	10⁸
3-9	6	50	29.4	10⁶

Serial number	Length of CFs (mm)	Content of CFs (wt%)	Min RL (dB)	Optimum thickness (mm)
1-1	1	0.1	–0.95 ± 0.003	5.28 ± 0.20
1-2	1	1	–7.52 ± 0.8	3.47 ± 0.008
1-3	1	3	–12.48 ± 0.9	2.93 ± 0.3
1-4	1	5	–16.55 ± 0.8	2.22 ± 0.008
1-5	1	10	–27.59 ± 0.5	1.84 ± 0.07
1-6	1	20	–9.41 ± 0.9	1.52 ± 0.04
1-7	1	30	–8.05 ± 0.28	1.38 ± 0.04
1-8	1	40	–12.55 ± 0.4	1.46 ± 0.12
1-9	1	50	–14.96 ± 2.0	1.42 ± 0.029
2-1	3	0.1	–3.97 ± 2.3	4.98 ± 0.11
2-2	3	1	–22.14 ± 1.0	3.20 ± 0.17
2-3	3	3	–8.02 ± 1.4	1.81 ± 0.16
2-4	3	5	–5.11 ± 0.7	1.33 ± 0.15
2-5	3	10	–3.93 ± 0.5	0.99 ± 0.02
2-6	3	20	–4.29 ± 0.4	1.06 ± 0.06
2-7	3	30	–4.84 ± 0.6	1.08 ± 0.07
2-8	3	40	–6.19 ± 1.1	1.15 ± 0.05
2-9	3	50	–10.99 ± 0.2	1.26 ± 0.024
3-1	6	0.1	–21.67 ± 0.7	3.51 ± 0.04
3-2	6	1	–6.12 ± 0.7	2.09 ± 0.14
3-3	6	3	–3.89 ± 0.4	1.33 ± 0.14
3-4	6	5	–3.24 ± 0.28	1.12 ± 0.08
3-5	6	10	–2.85 ± 0.27	0.96 ± 0.09
3-6	6	20	–3.93 ± 0.21	1.01 ± 0.05
3-7	6	30	–5.36 ± 0.5	1.22 ± 0.08
3-8	6	40	–6.43 ± 0.7	1.17 ± 0.05
3-9	6	50	–4.80 ± 1.3	4.08 ± 0.15

Footnotes

Acknowledgements

The authors would like to thank Professor Tang Jiaming and Dr Zhao Gang from Xidian University for their assistance with measurements.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by National High-Tech Research and Development Projects (grant number 2012AA03A208) and Guangdong Province Strategic Emerging Industry Core Technology Research (grant number: 2011A091102006).

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