## 3 Results
### Electromagnetic Properties  
In most cases, the complex permittivity (\(\varepsilon\)' and \(\varepsilon\)'') and relative permeability (\(\mu\)' and \(\mu\)'') are two important EM parameters to judge the quality of the microwave absorption performance. In order to obtain the optimal mass fraction of Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\) in PVDF-_co_-HFP, the EMW properties of all the samples with different mass fractions loading were investigated in Figure S4-6 (Supplementary Materials). As a result, the Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\) powders with 30 wt % contents in PVDF-_co_-HFP are the best choice. As shown in Figure 4a,b, the pure PVDF-_co_-HFP has poor permittivity properties. After addition of fillers, the permittivity values of samples have obvious improved, especially, Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\)/PVDF-_co_-HFP composites possess higher dielectric behavior. The \(\varepsilon\)' values of S1 is around 8, and its \(\varepsilon\)'' values reach around 2. Similarly, the \(\varepsilon\)' values of S2 become around 10 and its \(\varepsilon\)'' values are around 3. Based on the free electron theory, \(\varepsilon\)''\(\infty\sigma\)/2\(\pi\varepsilon\)_of_, where \(\sigma\) stands for the conductivity, it can be found that the S2 sample possesses the higher electrical conductivity, which is attributed to the induced dipoles of the existence of C-O, Si-O species on the surface of S2 composite or vibrations of atoms, ions, or electrons in the S2 composite. Furthermore, the real permeability (\(\mu\)') values of S1 and S2 samples are 1.07-0.95 and 1.13-1.01, respectively, which are higher than that of S0 sample without modified by silane groups (about 1.01-0.96) (Figure 4c). Generally, the imaginary permeability (\(\mu\)'') values of composites must be more than 0 [43]. As illustrated in Figure 4d, S2 sample is an exception, its \(\mu\)'' values show negative in the range of 7-18 GHz frequency. The reason is that the negative \(\mu\)'' is attributed to the radiation of the magnetic energy [43]. According to the Maxwell equations [44], the charges transferred in variable electric field is easy to produce the induced magnetic field, which may result in the formation of the magnetic energy [45]. As illustrated in Figure 4e, compared to the dielectric loss tangent (\(tan\delta_{\varepsilon}=\varepsilon\)\"/\(\varepsilon\)\") of the pure PVDF-_co_-HFP (\(tan\delta_{\varepsilon}=0.1\)) and S0 sample (\(tan\delta_{\varepsilon}=0.3\)), the higher \(tan\delta_{\varepsilon}\) values of the Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\)/PVDF-_co_-HFP composites confirm that the silane groups grafted on the rGO surface are more favourable to increase the complex dielectric loss. In particular, S2 sample has the highest \(tan\delta_{\varepsilon}\) values, corresponding to 0.31-0.38. Furthermore, several resonance peaks in the complex \(tan\delta_{\varepsilon}\) indicate that the polarization effects may exist in the composites [46]. As shown in Figure 4f, the magnetic loss of samples in the range of 2-13 GHz are greater than that in the range of 13-18 GHz. However, the complex magnetic loss covers weaker values contrast to the dielectric loss. These results suggest that the EMA performance of Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\)/PVDF-_co_-HFP composites is mainly attributed to dielectric loss rather than magnetic loss. In a general way, the polarization effects of graphene-based composite mainly result from the lattice defects in graphene structure, dipole polarization, or interfacial polarization between rGO and other magnetic metal oxides and polymer matrix, which has an important influence on the complex EMA performance. According to the Cole-Cole semicircle principle, the complex relaxation process can be obtained via Equation (1) [47].