## 3 Results
### Electromagnetic Properties
Moreover, as shown in Figure 6b-e, the calculated \(RL\) values of samples decorated by silane groups in the range of 2-18 GHz are higher than that of pure PVDF-\(co\)-HFP and S0 samples without modified by silane groups. The \(RL_{max}\) values for S1 and S2 samples are \(-\)27.7 dB at 3.3 GHz with d = 9 mm and \(-\)32.1 dB at 3.68 GHz with d = 7 mm, respectively. Meanwhile, S2 sample exhibits a wide absorption frequency bandwidth of 4.8 GHz (RL \(<\)\(-\)10 dB) at d = 2 mm, demonstrating that Si(2) silane coupling agent is beneficial to improving the EMW absorption broadband of the absorber. To judge the high-efficiency EMW absorption properties of Si-modified rGO@Fe\({}_{3}\)O\({}_{4}\)/PVDF-\(co\)-HFP composite in the range of 2-18 GHz, the attenuation constant \(\alpha\), as one of influence factors, can be described by [23; 57]  
\[\alpha=\frac{\sqrt{2}\pi f}{c}\times\sqrt{\left(\mu^{\prime\prime}\varepsilon^{ \prime\prime}-\mu^{\prime}\varepsilon^{\prime}\right)+\sqrt{\left(\mu^{\prime }\varepsilon^{\prime\prime}+\mu^{\prime\prime}\varepsilon^{\prime}\right)^{2 }+\left(\mu^{\prime\prime}\varepsilon^{\prime\prime}-\mu^{\prime}\varepsilon ^{\prime}\right)^{2}}} \tag{5}\]  
where \(f\) refers to the microwave frequency and \(c\) refers to the velocity of light. As illustrated in Figure S7 (Supplementary Materials), the S2 sample has the largest attenuation constant values in all the samples in the range of 2-18 GHz, suggesting that the microwave absorption performance of S2 samples is superior to that of S0 and S1 samples over the range of 2-18 GHz. That result is in good agreement with the Figure 6a. Except for the high \(\alpha\) values, the impedance matching also plays a significant role in the enhanced microwave attenuation. Here, the modulus of the relative impedances \(Z=|Z_{in}\)/\(Z_{0}|\) have been calculated by the following Equations (3). When the \(Z\) value is almost equal to 1, meaning that the incident EMW can be completely inside the absorber, and then converted into other forms of energy, such as thermal energy [21; 58]. As described in Figure S8 (Supplementary Materials), after decoration with silane coupling agent, the \(Z\) values of S1 and S2 samples are less than that of S0 sample. Particularly, the \(Z\) values in the S2 sample are closer to 1 in the range of 2.6-4 GHz, confirming that the S2 sample exhibits the high-efficiency absorption performance at the thickness of 7-9 mm. Figure 6: Frequency dependence of the calculated \(RL\) values of all the samples in the range of 2–18 GHz: (**a**) the thickness of 2 mm, (**b–e**) at different thickness. In addition, a quarter-wavelength theory also has been further supplied to explain the EMW absorption principle, the relationship between the thickness (\(t_{m}\)) and the relative frequency (\(f_{m}\)) can be characterized by equation [47; 59; 60],  
\[t_{m}=nc/\left(4f_{m}\left(|\varepsilon_{r}|\left|\mu_{r}\right|\right)^{1/2} \right)n=1,3,5,\ldots\ldots. \tag{6}\]  
where \(|\varepsilon_{r}|\) and \(|\mu_{r}|\) refers to the modulus of the complex permittivity and relative permeability, respectively. As illustrated in Figure S8 (Supplementary Materials), the black line is the calculated matching thickness (\(t_{m}\)_fit_) and the red spots denote the experimental matching thickness (\(t_{m}\)_exp_). For S2 sample, the values of \(t_{m}\)_exp_ almost coincide with that of the \(t_{m}\)_fit_ (n = 1), explaining that the excellent EMW performance of S2 sample is mainly attributed to the interference absorption. Based on the above-mentioned analysis, we have proposed EMA mechanism to explain the reason why S2 sample possesses the high-efficiency absorption ability (Scheme 2). First, after modification with Si(2) silane coupling reagent, there are several dipole polarization in Si(2)-rGO@Fe\({}_{3}\)O\({}_{4}\) fillers owning to the existence of C-O, Si-O group, which is helpful for enhancing the dielectric loss performance (Figure 5c) [14].