## 3 Results and Discussion
### EM Wave Absorption Properties  
The EM properties of all the samples were measured within the frequency range of 8.2-18 GHz. The EM parameters include relative complex permeability (\(\mu_{\rm r}=\mu^{\prime}-\rm j\mu^{\prime\prime}\)) and permittivity (\(\epsilon_{\rm r}=\epsilon^{\prime}-\rm j\epsilon^{\prime\prime}\)). The real parts of these EM parameters (\(\epsilon^{\prime}\) and \(\mu^{\prime}\)) indicates the electric and magnetic storage ability, while the imaginary parts (\(\epsilon^{\prime\prime}\) and \(\mu^{\prime\prime}\)) are related to the dielectric and magnetic energy dissipation, respectively [20]. An ideal absorptive material is required to possess good impedance matching characteristics, which demands that the material possess optimized EM parameters. As shown in Figure 7a,b, the synthesized C-Fe\({}_{3}\)O\({}_{4}\) has the least \(\epsilon^{\prime}\) and \(\epsilon^{\prime\prime}\) among the samples which indicate poor dielectric loss properties. Therefore, the C-Fe\({}_{3}\)O\({}_{4}\) was loaded in PVDF matrix at different percentage loading. The \(\epsilon^{\prime}\) and \(\epsilon^{\prime\prime}\) of the composite progressively improved with an increase in the amount of C-Fe\({}_{3}\)O\({}_{4}\) loaded in the PVDF matrix. This enhancement could be associated with improved conductivities, and this alternatively shows consistency with the effective medium theory [21]. Figure 7a  
Figure 5: FTIR spectrum of C-Fe\({}_{3}\)O\({}_{4}\) nanoparticles. Figure 6: Hysteresis loop of the C-Fe\({}_{3}\)O\({}_{4}\) nanoparticles, inset is the magnified low field hysteresis curve. shows that the \(\varepsilon^{\prime}\) decreased slowly with an increase in frequency (X-band) showing a distinctive frequency dispersion seen in many Fe\({}_{3}\)O\({}_{4}\)-based composites [12; 22; 23]. Such phenomenon occurs when dipoles could not respond quickly to the high-frequency alternating E-Field, resulting in a decrease in the magnitude \(\varepsilon^{\prime}\) and \(\varepsilon^{\prime\prime}\)[24]. In compliance with the free electron theory,  
\[\varepsilon^{\prime\prime}=\sigma/2\pi\varepsilon_{\text{o}}\text{f} \tag{11}\]  
where f, \(\sigma\), \(\varepsilon_{\text{o}}\) are the frequency, conductivity, and the dielectric constant of vacuum, respectively. It can be deduced that increase in conductivity (\(\sigma\)) will increase the \(\varepsilon^{\prime\prime}\), and thus favors the absorption of the EM wave [25]. It can be observed that the samples show several resonance peaks, particularly at Ku-band frequency. This behavior can be seen in previous reported Fe\({}_{3}\)O\({}_{4}\)-based composites [9; 26]. Furthermore, the resonance was observed to rise with an increase in the amount of C-Fe\({}_{3}\)O\({}_{4}\) loaded in the PVDF matrix. This finding suggested that multiple polarization mechanisms occur in the samples with alteration of the EM field frequency [27]. Firstly, electron mobility between Fe\({}^{2+}\) and Fe\({}^{3+}\) ions as the wave travel within the material can generate dipole polarization. Also, the presence of heterogeneous component with different permittivity and conductivity can generate Maxwell-Wagner polarization often referred to as interfacial polarization [13]. In addition, the porous network and void spaces that exist in the C-Fe\({}_{3}\)O\({}_{4}\) nanoparticles as observed in the FESEM images, can also provide multiple path ways for EM propagation and attenuation. The conjugation of C-Fe\({}_{3}\)O\({}_{4}\) and PVDF increased the degree of polarization which further contributes to higher values of \(\varepsilon^{\prime\prime}\). Hence, since the \(\varepsilon^{\prime}\) and \(\varepsilon^{\prime\prime}\) accounts for EM storage and dissipation, it is clear that the C-Fe\({}_{3}\)O\({}_{4}\)/PVDF possesses high dielectric loss ability which would greatly enhance its MAP. Figure 7c,d presents the \(\upmu^{\prime}\) and \(\upmu^{\prime\prime}\) values of the samples, which reveals that all samples exhibit moderate magnetic loss ability.