## 3 Results and Discussion
### Microwave Absorption Performance of Composites  
Generally, the microwave absorption performance of composites can be evaluated by the reflection loss (RL) and effective absorption bandwidth (EAB, the frequency range corresponding to RL \(<-10\) dB) [34, 35, 36]. The smaller the RL, the better the performance. RL below \(-10\) dB indicates that \(>90\%\) of the electromagnetic wave can be absorbed [9]. According to the transmit-line theory, RL is usually obtained by Equations (3) and (4) [37, 38, 39, 40]:  
\[RL=20\lg\left|\frac{Z_{in}-Z_{0}}{Z_{in}+Z_{0}}\right| \tag{3}\]  
\[Z_{in}=Z_{0}\sqrt{\frac{\mu_{r}}{\varepsilon_{r}}}\tanh\left[j\left(\frac{2\pi fd }{c}\right)\sqrt{\mu_{r}\varepsilon_{r}}\right] \tag{4}\]  
where \(Z_{0}=\sqrt{\frac{\mu_{r}}{\varepsilon_{r}}}\approx 377\)\(\Omega\) is the impedance of free space, \(Z_{in}\) is the input impedance of the absorber, \(\varepsilon_{r}\) and \(\mu_{r}\) are the relative complex permittivity and permeability, respectively, \(j\) is the imaginary unit, \(f\) is the frequency of the incident microwave, \(d\) is the thickness of the absorbing material, and \(c\) is the velocity of light in free space. Figure 9 is a three-dimensional plot of RL for CB/PLA composites with different thicknesses in the frequency range of 2-18 GHz. Figure 9a shows that pure PLA has no microwave absorption performance and is a wave-transmitting matrix. On the contrary, with the addition of CB, the absorbing properties of the composites gradually increased, but neither 5% nor 10% CB/PLA could achieve an effective absorbing effect. However, with the further increase in CB content, the absorbing properties of the composites were significantly improved and showed strong absorbing properties at smaller thicknesses, especially 25% CB/PLA. When the thickness was 2.1 mm, the minimum RL was \(-45.47\) dB (13.68 GHz), and the EAB was 5.36 GHz (10.72-16.08 GHz; Figure 9f). In order to meet the thin and light requirements of the MAMs, the density of the composite was further tested, and the density of the 25% CB/PLA composite was only 1.19 g/cm\({}^{3}\). The density was lower than that of pure PLA (1.25 g/cm\({}^{3}\)), which meets the requirements of lightweight material with broad application prospects. Figure 8: Cole-Cole curves of CB/PLA composites with different CB contents: (**a**) 0% CB; (**b**) 5% CB; (**c**) 10% CB; (**d**) 15% CB; (**e**) 20% CB; and (**f**) 25% CB. The impedance matching \(Z\) and attenuation constant \(\alpha\) are the two critical factors that affect the material's excellent absorbing properties, which can be calculated by using Equations (5) and (6) [41, 42]. \[Z=\left|\frac{Z_{in}}{Z_{0}}\right|\propto 1 \tag{5}\]  
\[\alpha=\frac{\sqrt{2}\pi f}{c}\sqrt{\left(\mu^{\pi}\varepsilon^{\prime\prime} -\mu^{\prime}\varepsilon^{\prime}\right)+\sqrt{\left(\mu^{\prime\prime} \varepsilon^{\prime\prime}-\mu^{\prime}\varepsilon^{\prime}\right)^{2}+\left( \mu^{\prime\prime}\varepsilon^{\prime}+\mu^{\prime}\varepsilon^{\prime\prime }\right)^{2}}} \tag{6}\]  
Figure 10 shows the impedance matching and attenuation constants of the CB/PLA composites. Generally, the impedance matching of the absorbing material should exceed 0.3, and the closer to 1, the better the impedance matching of the material [43, 44, 45]. Figure 10a,b shows opposite trends: with the increase in CB content, the impedance matching gradually decreased, while the attenuation constant increased continuously. As shown in Figure 10b, the special peak's position in the figure is the same as in Figure 6c. Ideal MAMs require balance between suitable impedance-matching characteristics and strong attenuation capabilities [46]. A comprehensive comparison shows that, with the highest attenuation constant, the impedance matching of 25% CB/PLA was higher than 0.3 in the frequency range of 2-18 GHz, so the microwave absorption performance of 25% CB/PLA was best. Figure 10: (**a**) Impedance matching; (**b**) attenuation constant of CB/PLA composite.