3.6 Electromagnetic characteristics
Complex permittivity \(\varepsilon\) and complex permeability \(\mu\)are two parameters required for studying the absorption properties of materials. Generally, they are expressed by Eq. 3 and Eq. 4. The real parts \(\varepsilon\)’ and \(\mu^{\prime}\) indicate the degree of polarization or magnetization of the absorbing material under the influence of an electric field or magnetic field. The imaginary parts\(\varepsilon"\text{\ and}\) \(\mu"\) respectively represent the measurement of the loss caused by rearrangement of the electrical moment or magnetic moment of the absorbing material under the influence of an applied electric field or magnetic field. The larger the two imaginary parts, the greater the dielectric loss and magnetic loss capability of the absorbing material[38].
\(\varepsilon=\varepsilon^{\prime}-j\varepsilon"\) (Eq. 3)
\(\mu=\mu^{\prime}-j\mu"\) (Eq. 4)
Groups O, C2 and C2S1 are selected for the electromagnetic parameter test. The results are demonstrated in Figure 14-15.
The real and imaginary parts of the complex permittivity of different groups are shown in Figure 14. The values of \(\varepsilon\)’ and\(\varepsilon"\) of Group O are both small, with the range of 1.6-2.5 and 0-0.5, respectively. As can be seen from the chemical composition of cement (see Table 1), the tested cement itself contains a small content of the metal oxides Al2O3,Fe2O3, and MgO. Under the influence of an applied electromagnetic field, they will undergo dielectric polarization, bringing the foam concrete with a certain dielectric loss capability which is poor and negligible. For group C2 mixed with 0.6wt.% carbon fiber, the values of \(\varepsilon\)’ and\(\varepsilon"\) are between 5.9-8 and 0.5-2.2, respectively, which are significantly improved compared with those of group O. Besides, the average value of the imaginary parts is about 1.75 in 4-5 GHz frequency band, indicating that the foam concrete has a larger dielectric loss factor (Eq. 5) and a better dielectric loss capability in this frequency band. For group C2S1, the values of \(\varepsilon\)’ and\(\varepsilon"\) range between 7.9-10.9 and 0.9-3.3, respectively, which are higher than those of the other two groups. The average value of the imaginary parts in 2.2-3 GHz band is about 2.75, which is about 1.75 higher than group C2.
(Eq. 5)
Figure 15 shows the real and imaginary parts of the complex permeability of foam concrete. The real part values of the complex permeability of three groups have little difference at various frequencies, with the range of 0.25-1.4. The imaginary part values of the complex permeability of three groups are between 0 and 0.7, and the two groups mixed with absorbents have higher values in the 0.5-5 GHz band compared to group O. Furthermore, compared with the complex permittivity in Figure 13, carbon fiber and graphite have a relatively poor effect on increasing the values of \(\mu^{\prime}\) and \(\mu"\) of foam concrete. This also corresponds to the loss mechanism of carbon fiber and graphite on electromagnetic waves, which is resistance loss rather than magnetic loss.
The loss characteristics of the material can be characterised by the attenuation constant α (Eq. 6), where f is the frequency of the electromagnetic wave and c is the speed of light, and the larger the value, the more the electromagnetic waves tend to dissipate[39,40]. The calculation results are presented in Figure 16.
(Eq. 6)
The attenuation constant values of Group O are low at different frequencies with the maximum value of only 19.23. It indicates that foam concrete without absorbents has poor electromagnetic wave loss capability, corresponding to the previous conductivity test results. For group C2 with the addition of 0.6wt.% carbon fiber, the attenuation constant value increases with the increasing frequency and the absorption peak appears between 2.5-3.5 GHz with the value of 47.18. At 3.5-5 GHz, the attenuation constant continues to rise and the maximum value is 70.07, increased by 264.38% over that of group O. Group C2S1 has roughly the same change trend of the attenuation constant as group C2, but the absorption peak is earlier and 11.95 higher than that of group C2. The maximum value is 94.6, which is 391.94% higher and 35.01% higher than those of group O and group C2, respectively. As a result, the electromagnetic wave absorption and loss capacities of specimens are improved by adding carbon fiber alone. For Group C2S1, the absorption peak occurs earlier, which widens the bandwidth with the large attenuation constant.
Reflection loss (RL) is a criterion for the electromagnetic wave absorption characteristics of single-layer planar materials, as in equation 7, and a value of less than -10 dB indicates that more than 90% of the electromagnetic wave is absorbed by the material[41]. The results of RL calculations for three sets of specimens from 0 to 10 mm thickness are shown in Figures 17 to 19.
(Eq. 7)
In this equation: Zin -Input impedance of the material
μ r-Relative permeability
ε r-Relative permittivity
Z0 -Wave impedance of free space
μ0 -Permeability of free space
ε0 -Permittivity of free space
d -Thickness of material
Figure 17(a) shows the 3d mapped surface plot of the reflection loss for Group O at different thicknesses and frequencies, and Figure 17(b) shows the corresponding two-dimensional curve. It can be seen from Figure 17 that the Group O has almost no electromagnetic wave loss capability and the reflection loss value reaches its minimum value of -3.58 dB at a thickness of 10 mm. As can be seen from Figure 18, the electromagnetic wave loss capability of group C2 is significantly higher than that of group O. The reflection loss value decreases with increasing specimen thickness and appears to be less than -10 dB, with effective bandwidths of 0.8 GHz, 1.7 GHz and 1 GHz at thicknesses of 6, 8 and 10 mm, respectively. The reflection loss reaches a minimum value of -38.47 dB at 10 mm thickness, an increase of 34.89 in absolute value compared to group O. This indicates that the addition of carbon fibre has a significant improvement in the electromagnetic wave loss performance of the foam concrete. The reflective loss of the foam concrete with graphite compounding at different thicknesses is shown in Figure 19, where the value also decreases with increasing thickness, with effective bandwidths of 2.5 GHz, 1.4 GHz and 0.9 GHz at thicknesses of 6, 8 and 10 mm respectively.