# Study on the Absorbing Properties of V-Doped MoS2
## 3 Result and Discussion
### The Absorbing Properties of VMS and VMSA  
As depicted in Figure 3, the complex dielectric constant (\(\varepsilon_{r}=\varepsilon^{\prime}-je^{\prime\prime}\)) of three distinct mixing ratios of the sample VMS and paraffin wax, as well as the complex dielectric constant image of a mixture comprising VMSA (with a filling amount of 40 wt%) and paraffin wax, were illustrated. During the process of sample re-preparation and detection, the mixture of the sample and paraffin was processed into a ring-shaped specimen using relevant abrasive tools. The VMS samples were mixed with paraffin at mass ratios of 30 wt%, 40 wt%, and 50 wt%, and were correspondingly labeled as VMS-30, VMS-40, and VMS-50. And the VMSA sample with a 40 wt% filler loading was designated as VMSA-40. As illustrated in Figure 3a, the dielectric constant (\(\varepsilon\)) exhibits a weakening trend with increasing frequency, which can be elucidated by the [PERSON] relaxation theory. Specifically, as the frequency of the EM field increases, the dipole motion within the material cannot keep pace with the rapidly changing EM field, leading to a relaxation phenomenon. Consequently, the dielectric constant begins to vary with frequency, and its value gradually diminishes. The \(\varepsilon^{\prime}\) value of the VMS-30 sample is the lowest, while the \(\varepsilon^{\prime}\) values of the VMSA-40 and VMS-50 samples are essentially coincident and higher than those of the other samples. With increasing sample filling ratio, the \(\varepsilon^{\prime}\) of VMS gradually rises. When the sample filling ratio reaches 50 wt%, the \(\varepsilon^{\prime}\) range is between 33 and 31. The change trend of the \(\varepsilon^{\prime\prime}\) for the four samples is analogous to that of \(\varepsilon^{\prime}\). However, the \(\varepsilon^{\prime\prime}\) value of the VMSA-40 sample is  
Figure 2: VMS and VMSA characterization. (**a**) XRD pattern (**b**) Microstrain analysis (**c**–**e**) XPS spectra of the Mo 3d, V 2p, and S 2p orbitals, respectively, (**f**–**i**) SEM images  
higher than that of VMS-40, with a value range of 27-29. Based on the obtained XRD and XPS results, the doping of V as a donor center injects electrons into the conduction band of MoS2, forming a high concentration of charge carriers, which leads to the enhancement of electromagnetic parameters [23]. In summary, as the filling amount of VMS increases from 30 wt% to 50 wt%, the dielectric constant significantly rises. This is attributed to the increased conductivity resulting from the higher filling rate, which in turn enhances the \((\varepsilon)\). To evaluate the loss capacity of EM wave energy, the dielectric loss tangent value was examined, as shown in Figure 3b. Similar to the \((\varepsilon)\), the dielectric loss tangent (tan(\(\delta\varepsilon\))) value increases with the filling rate, indicating that the dielectric loss capacity also rises with the filling rate and is further improved after VMS annealing. In order to further elucidate the dielectric loss mechanism of the sample, a Cole-Cole relationship curve was plotted based on the Debye relaxation theory. The relationship in the Cole-Cole plot is defined as follows:  
\[\left[\varepsilon^{\prime}-\frac{1}{2}(\varepsilon_{s}+\varepsilon_{\infty}) \right]^{2}+(\varepsilon^{\prime\prime})^{2}=\frac{1}{4}(\varepsilon_{s}- \varepsilon_{\infty})^{2} \tag{4}\]  
In the formula, \(\varepsilon_{s}\) and \(\varepsilon_{\infty}\) represent the static dielectric constant and optical dielectric constant. The ideal Debye relaxation model predicts a Cole-Cole diagram featuring a perfect semicircle centered on the real axis of the complex dielectric constant plane. However, this ideal behavior is rarely observed in natural materials, with only a few exceptions like water.