## 3 Results and Discussion
### Electromagnetic Parameters and Loss Mechanisms of Composites  
Since all materials were nonmagnetic, we only focused on analyzing dielectric properties (complex permittivity and dielectric loss tangent). In detail, the real (\(\epsilon^{\prime}\)) and imaginary (\(\epsilon^{\prime\prime}\)) parts of complex permittivity, respectively, represent the storage and dissipation capacity for electromagnetic energy, while the dielectric loss tangent (\(\tan\delta_{\epsilon}=\epsilon^{\prime\prime}/\epsilon^{\prime}\)) stands for the dielectric loss ability [15; 16]. Figure 6a,b shows the relationship between the real and imaginary parts of complex permittivity and frequency (2-18 GHz) for different CB/PLA composites. Dielectric loss mainly includes conduction loss and polarization relaxation loss (electron polarization, ion polarization, dipole polarization, and interfacial polarization). Among them, electron polarization and ion polarization usually occur in the THz and PHz range, so it is not considered in the GHz range [17; 18]. Figure 4: XRD patterns of CB/PLA composites with different CB contents. Figure 5: TG curves of CB/PLA composites with different CB contents. It can be seen that the \(\varepsilon^{\prime}\) and \(\varepsilon^{\prime\prime}\) of pure PLA (0%CB/PLA) tend to be constant in the whole frequency range of 2-18 GHz with slight fluctuation, about 2.3 and 0.1, respectively, indicating that pure PLA is an almost lossless material. In general, with the increase in CB content, the real and imaginary parts of the complex permittivity decrease with the increase in frequency, and the change trend of the two is similar on the whole. Meanwhile, as the CB content increases from 5% to 25%, the real and imaginary parts of the complex permittivity increase significantly, which may be attributed to the conduction loss. The conduction loss is related to the conductive network formed by the CB in the matrix material, according to free electron theory [19, 20]:  
\[\sigma=2\pi\varepsilon_{0}f\varepsilon^{\prime\prime} \tag{1}\]  
where \(\sigma\) is the conductivity, \(\varepsilon_{0}\) is the permittivity of the vacuum, and \(f\) is the frequency of the electromagnetic wave. The conduction loss is mainly determined by the imaginary part of the complex permittivity, and they are positively correlated. Figure 7 shows the measured conductivity of the CB/PLA composites. When CB content was 15%, the conductivity of the composite reached 0.0015 S/cm. At this time, CB initially formed a conductive network in the matrix material. With a further increase in CB content (to 20%), the conductive network was gradually formed, and the conductivity increased significantly. This means that the conduction loss is significantly enhanced. Figure 6: Electromagnetic parameters of different CB/PLA composites: (a) real part of complex permittivity; (b) imaginary part of complex permittivity; (c) dielectric loss tangent. Figure 6c shows the relationship between the dielectric loss tangent and the frequency for different CB/PLA composites. With the increase in CB content, the dielectric loss tangent value increases continuously; the dielectric loss of pure PLA is the smallest and the curve fluctuates slightly, indicating dipole polarization losses. The changing trend of the dielectric loss tangent of 10% CB/PLA, 15% CB/PLA, 20% CB/PLA, and 25% CB/PLA is nearly the same as the curve of the imaginary part of the complex permittivity. There were multiple resonant peaks at 10-18 GHz, which implied the combined effect of conduction and polarization losses. The 25% CB/PLA had the maximum dielectric loss, and a significant peak was found at 18 GHz, corresponding to interfacial polarization [21; 22]. Interfacial polarization usually occurs at the interface of inhomogeneous media and is mainly caused by the accumulation of electron or ion agglomeration at the interface under the action of an applied electric field [23; 24].