## 3 Results
### Electromagnetic Properties
\[\left(\varepsilon^{\prime}-\frac{\varepsilon_{s}+\varepsilon_{\infty}}{2} \right)^{2}+\left(\varepsilon^{\prime\prime}\right)^{2}=\left(\frac{ \varepsilon_{s}-\varepsilon_{\infty}}{2}\right)^{2} \tag{1}\]  
where \(\varepsilon^{\prime}\) and \(\varepsilon^{\infty}\) refer to the static dielectric constant and the relative permittivity at boundless frequency, respectively. If [PERSON] relaxation process is occurred in composites, several single semicircles are exhibited in the curve of \(\varepsilon^{\prime}\) and \(\varepsilon^{\prime\prime}\)[47; 48]. As illustrated in Figure 5a-c, the \(\varepsilon^{\prime}\)-\(\varepsilon\)\" plots of pure PVDF-_co_-HFP is mostly disordered, whereas there is plenty of semicircles in the curve of the samples modified by silane groups, verifying that the dielectric loss of Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\)/PVDF-_co_-HFP composites may result from other multiple interfacial polarizations, including Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\)/PVDF-_co_-HFP and Si-modified rGO/PVDF-_co_-HFP interfaces, rather than Debye relaxation [22; 49]. Figure 4: Frequency dependence of the EM parameters of all the samples: (**a**) real permittivity, (**b**) imaginary permittivity, (**c**) real permeability, (**d**) imaginary permeability, (**e**) dielectric loss, and (**f**) magnetic loss. Besides, the lattice defects and the dipole polarization in Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\) fillers is also helpful for enhancing the EMA performance of samples decorated by silane groups owning to the existence of C-O, Si-O species on the surface of Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\) composites. In most cases, the complex magnetic loss usually results from natural resonance, eddy-current effect, and domain-wall displacement [50]. The domain-wall displacement mainly exists in the 1-100 MHz [25; 51], suggesting that the EMA performance of Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\)/PVDF-_co_-HFP composites over the range of 2-18 GHz is not attributed to the domain-wall displacement. For the eddy current effect, it can be calculated by Equation (2) [1; 52]  
\[C_{0}=\mu^{\prime\prime}(\mu^{\prime})^{-2}f^{-1} \tag{2}\]  
If the \(C_{0}\) values are equal to the constant in the 2-18 GHz frequency, the complex magnetic loss only arises from the eddy-current [53]. As shown in Figure 5d, the \(C_{0}\) values of all the samples vary with frequency, indicating that the complex magnetic loss behavior over the range of 2-18 GHz frequency is mainly attributed to the natural resonance [53; 54]. On the basis of the transmission line theory, the EMA performance of Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\)/PVDF-_co_-HFP composites was illustrated by the \(RL\) values, which were calculated by the following equations [47; 55; 56],  
\[Z_{in}=Z_{0}\sqrt{\frac{\mu_{r}}{\varepsilon_{r}}}\text{tanh}\left[j(\frac{2 \pi fd}{c})\sqrt{\mu_{r}\varepsilon_{r}}\right] \tag{3}\]  
\[RL=20\log\left|\frac{Z_{in}-Z_{0}}{Z_{in}+Z_{0}}\right| \tag{4}\]  
where \(Z_{in}\) refers to the normalized input impedance, \(Z_{0}\) belongs to the impedance in free space (\(Z_{0}\) = 377 \(\Omega\)), \(\varepsilon_{r}\) and \(\mu_{r}\) are the complex permittivity and relative permeability, respectively, \(f\) is the microwave frequency, \(d\) is the thickness of the composite, and \(c\) is the velocity of light. As exhibited in Figure 6a, the pure PVDF-_co_-HFP at the thickness of 2 mm exhibits poor \(RL\) values (RL \(<\) -1 dB). After modification with silane groups, the Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\)/PVDF-_co_-HFP composites exhibit the enhanced EMA ability in the range of 2-18 GHz, particularly, the S2 sample modified by Si(2) groups shows high-performance microwave absorption performance in 2-18 GHz  
Figure 5: Cole-code (**a**–**c**) and \(C_{0}\) (**d**) curves for all the samples. frequency. The maximum reflection loss (\(RL_{max}\)) values for S2 sample over the whole frequency range are \(-\)17.1 dB at 15.4 GHz. In addition, the S1 sample exhibits the electromagnetic absorption performance over the 18 GHz.