A Facile Synthesis of Novel Amorphous TiO₂ Nanorods Decorated rGO Hybrid Composites with Wide Band Microwave Absorption

Abstract

Amorphous structures may play important roles in achieving highly efficient microwave absorption performance due to the polarization losses induced by the disorders, vacancies and other functional groups existed in them. Herein, a kind of amorphous TiO₂/rGO composite (a-TiO₂/rGO) was successfully fabricated via a facile one-step solvothermal method. The complex permittivity of the composites can be regulated by adjusting the addition of precursor solution. The minimum reflection loss of a-TiO₂/rGO composites reached −42.8 dB at 8.72 GHz with a thickness of 3.25 mm, and the widest efficient absorption bandwidth (EAB) was up to 6.2 GHz (11.8 to 18 GHz) with a thickness of only 2.15 mm, which achieved the full absorption in Ku band (12 to 18 GHz). Furthermore, the EAB was achieved ranging from 3.97 to 18 GHz by adjusting the thickness of the absorber, covering 87.7% of the whole radar frequency band. It is considered that the well-matched impedance, various polarization processes, capacitor-like structure and conductive networks all contributed to the excellent microwave absorption of a-TiO₂/rGO. This study provides reference on constructing amorphous structures for future microwave absorber researches and the as-prepared a-TiO₂/rGO composites also have great potential owing to its facile synthesis and highly efficient microwave absorption.

1. Introduction

Nowadays, with the rapid development of electronic information technology, electromagnetic radiation and pollution originating from electronic devices pose a threat to human health and information safety [1,2,3,4,5,6] and consequently the design and fabrication of microwave absorption materials which can dissipate microwave energy efficiently has become an urgent requirement [7,8,9]. In recent years, extensive efforts on the design of microwave absorbers have been focused on strengthening reflection loss (RL), broadening absorption bandwidth and reducing weight as well as thickness. Various microwave absorption materials based on carbon nanotubes (CNTs) [10,11,12], graphene [13,14,15], magnetic nanoparticles [16,17,18], conductive polymer [19,20], MXene [21,22,23], etc., have been developed, exhibiting promising microwave absorption performance.

Among these materials, graphene is expected to be one of the most promising candidates owing to its advantages of light weight, stable physical and chemical properties, low density, high specific surface area and remarkable electron mobility [24,25,26]. Unfortunately, the excessively high electrical conductivity of graphene always leads to a high reflection toward the incident microwave, which further results in the poor impedance matching [14,27,28]. On the other hand, the limited loss mechanism also leads to the weak microwave absorption of graphene [29,30]. To solve these drawbacks, many studies have combined graphene with other nanomaterials such as metals/alloys [31,32], ferrites [6,33,34], metal oxides/sulfide [35,36,37] and so on, which could achieve high magnetic or dielectric losses and thus add more loss mechanisms to improve their microwave absorption performance. These results indicate that their microwave absorption properties were indeed improved after introducing these materials. However, the addition of loss mechanism inevitably increases the complexity and difficulties of synthesis process, which limits the further practical applications of these materials. Meanwhile some shortcomings such as the poor physical or chemical stability, aggregation and high density of the introduced particles also become new challenges for the design of microwave absorption materials. Furthermore, compared with graphene, reduced graphene oxide (rGO) possesses more defects and functional groups which would achieve the synergistic effects of polarization loss and conduction loss. The rGO also exhibits relatively low electrical conductivity which would facilitate the impedance matching of the absorber. Therefore, it is feasible to choose rGO to add more loss mechanisms for achieving efficient microwave absorption.

Recently, dielectric materials have attracted considerable attention in microwave absorption owing to their thermal and chemical stabilities and high dielectric losses. For example, Chen et al. fabricated polyoxometalate-based materials [38] and Cu₉S₅ nanonets [39], both of which achieved excellent microwave absorption performance. As a typical dielectric material, titanium dioxide (TiO₂) has been reasonably considered to be a promising candidate for microwave absorption materials. Mo et al. [40] have fabricated a porous CNT@TiO₂ sponge, achieving a minimum RL value of −31.8 dB with the widest efficient absorption bandwidth (EAB) of 2.76 GHz. However, the microwave absorption performance of pure TiO₂ seems not as good as expected because of the single dielectric loss mechanism. Thus, many studies were performed to add extra materials to TiO₂ or to treat TiO₂ with an additional hydrogenation process to achieve more loss mechanisms, which complicated the fabrication of the absorber and made it harder to obtain a lightweight material. Recently, constructing an amorphous structure with multiple defects have been proved to be an effective method to induce various polarizations by microwaves [41]. For example, Shen et al. [42] have developed a kind of amorphous FeCo nanowires, which showed a minimum reflection value of −25.88 dB with an EAB of 5.40 GHz. It is thought that amorphous structures would be an effective way to enhance the microwave absorption performance of TiO₂. Moreover, amorphous TiO₂ (a-TiO₂) exhibits poor electric conductivity compared with graphene, further inspiring the strategy that a-TiO₂ can be combined with graphene to adjust the excessively high electric conductivity of graphene. Therefore, the impedance matching property of the composite could also be controlled easily via changing the proportion of two components. In addition, considering the morphology of the nanomaterials, 1D nanostructures including nanowires, nanotubes and nanorods possess higher aspect ratio as well as shape anisotropy, which increases their interfacial polarization area and improves charge transportation along the axial direction, further enhancing the microwave absorption performance. Consequently, designing a 1D nanostructure with a-TiO₂ would be a promising strategy for microwave absorption.

In this work, a-TiO₂ nanorods were uniformly implanted in reduced graphene oxidize (rGO) nanosheets via a facile one-pot solvothermal method. The impedance matching properties of the composites could be easily adjusted by changing the proportion of a-TiO₂ components. It was found that the as-prepared a-TiO₂/rGO composites exhibited excellent microwave absorption performance with light weight, thin thickness, strong microwave absorption and wide EAB. Significantly, the microwave absorption performance became weaker after converting the a-TiO₂ into crystalline TiO₂ (c-TiO₂) in the composites, indicating the superiority of amorphous structure in the high-performance microwave absorbers.

2. Materials and Methods

2.1. Materials

Graphene oxide (GO) was purchased from XFNANO (Nanjing, China). Tetrabutyltitanate (TBT), glycerol (C₃H₈O₃), and ethyl alcohol absolute (C₂H₅OH, wt% ≥ 99.7%) were purchased from Tianjin Kermel Chemical Reagent Co., Ltd. (Tianjin, China). All reagents were analytical grade and not further purified. All water used in experiments was deionized water.

2.2. Synthesis of a-TiO₂/rGO Composites

The schematic illustration of formation process for a-TiO₂/rGO and c-TiO₂/rGO composites is shown in Figure 1. The a-TiO₂/rGO composites were prepared via a facile one-pot solvothermal method. Initially, 75 mg GO was dispersed in 25 mL ethyl alcohol, followed by a 2 h sonication treatment to form a homogeneous dispersion. Then 5 mL glycerol and 0.25 mL TBT were added into the dispersion in sequence. After another sonication treatment for 30 min, the mixture was transferred into a 50 mL Teflon-lined autoclave and heated at 180 °C for 15 h. The precipitate in the resulting product was collected with suction filtration, washed with ethanol for 4–5 times and then was freezedried for 24 h. Finally, the a-TiO₂/rGO composite was obtained. Repeatedly, the similar composites were prepared by using different TBT contents of 0.25, 0.5, and 1 mL, denoted by a-T1, a-T2, and a-T3, respectively.

2.3. Synthesis of c-TiO₂/rGO Composites

As a comparison, the as prepared a-TiO₂/rGO composites were converted into c-TiO₂/rGO composites by an annealing method. The a-TiO₂/rGO powders were heated to 500 °C with a ramping rate of 5 °C/min and maintained at 500 °C for 2 h under a high purity argon gas (Ar, 350 sccm, purity ≥ 99.999%) atmosphere. After the annealing treatment, the samples of a-T1, a-T2, and a-T3 were relabeled as c-T1, c-T2, and c-T3, respectively.

2.4. Characterizations

The morphologies of as-prepared samples were observed by a field emission scanning electron microscopy (SEM, NanoSEM450, FEI, Hillsboro, OR, USA) equipped with an energy dispersive X-ray spectroscopy (EDS). Besides, transmission electron microscopy (TEM, Tecnai F30, FEI, Hillsboro, OR, USA) was also used to examine the microstructural features. X-ray diffraction (XRD, Lab XRD-7000s, Shimadzu, Kyoto, Japan) was performed to characterize the amorphous and crystalline components in these composites with a Cu Kα radiation source. The banding energy was measured by X-ray photoelectron spectroscopy (XPS, ESCALAB250Xi, Thermo Fisher Scientific, Waltham, MA, USA) with an Al Kα radiation. For electromagnetic characterizations, the as-prepared composites (20 wt%) were uniformly mixed with melted paraffin (80 wt%) and then pressed into a toroidal shape with dimensions of external diameter of 7.00 mm, inner diameter of 3.04 mm and thickness of 2.0 mm. Then the complex permittivity and relative complex permeability of the composites were measured via a network analyzer (8720B, Agilent, Santa Clara, CA, USA) in the band of 2 to 18 GHz. For the sample of a-T2, we prepared another two paraffin composites containing a-T2 of 10 wt% and 15 wt% to investigate the best mass ratio for microwave absorption.

3. Results and Discussion

3.1. Morphological and Structural Analysis

Figure 2 shows the SEM images of a-TiO₂/rGO and c-TiO₂/rGO. The as-prepared TiO₂/rGO composites consist of TiO₂ nanorods with diameters of 20–50 nm and lengths up to 100–300 nm, which are uniformly implanted on rGO nanosheets. In Figure 2a, the density of TiO₂ nanorods is relatively low because of the low amount of TBT added. It should be noted that most of the TiO₂ nanorods attach parallel to the rGO nanosheets to add more interface polarization sites, which is conductive to microwave absorption. From Figure 2a–c, the increase in density of TiO₂ nanorods on rGO nanosheets can be clearly observed with the increase of addition amount of TBT, suggesting that the density of TiO₂ nanorods can be well controlled by adjusting the addition amount of TBT. As shown in Figure 2d,h, the rGO nanosheets undergo no apparent changes while the diameter of TiO₂ nanorods decreases after the annealing treatment, which might be explained as the volume contraction of TiO₂ nanorods caused by the decrease of disorders and vacancies [43]. TEM images in Figure 2 show the microstructures of a-TiO₂/rGO and c-TiO₂/rGO. It is observed from Figure 2i,m that the TiO₂ nanorods are uniformly dispersed on the rGO nanosheets, which further confirms the results of the SEM observations. The HRTEM images shown in Figure 2j reveal no distinct lattice fringe, confirming the amorphous structure of a-TiO₂/rGO, while Figure 2n presents the crystal structure of TiO₂. The interplanar spacing is 0.32 nm, which corresponds to the (110) crystal plane of TiO₂. Moreover, the selected-area electron diffraction (SEAD) patterns in Figure 2k,o show a blurred image for a-TiO₂/rGO and clear diffraction rings for c-TiO₂/rGO, respectively, which is consistent with the HRTEM results.

Figure 2l shows the XRD spectra of a-TiO₂/ rGO and c-TiO₂/ rGO. A main broad diffraction peak at around 26.0° is observed in all samples, which corresponds to the (002) crystal plane of graphite carbon. However, no other obvious characteristic diffraction peak from the a-T2 sample, indicating an amorphous TiO₂ structure. After an annealing treatment, a series of clearer diffraction peaks appears at 27.4°, 36.1°, 41.3°, 54.3° and 56.7°, which were well matched with (110), (101), (111), (211) and (220) crystal planes of rutile phase TiO₂ (PDF file #01-086-0147, P42/mnm, a = b = 4.594 Å and c = 2.958 Å), respectively. As shown in the XRD patterns, both a-T2 and c-T2 shows no obvious peak around 10°, indicating that most of the GO is reduced. Moreover, the diffraction rings in Figure 2o also agree well with the XRD pattern of c-T2. These results reveal that amorphous TiO₂ has been transformed into crystalline TiO₂ via the annealing treatment.

Changes in the graphitization degree of GO by annealing treatment are also demonstrated by Raman spectroscopy. As shown in Figure 2p, both a-T2 and c-T2 present two prominent peaks around 1575 cm⁻¹(G band) and 1340 cm⁻¹(D band), which denote the vibrations of sp2 hybridization, and the vibration of disordered graphitic lattice [44]. Herein, the G band and D band signals mainly originated from the graphite carbon atoms as well as the disordered structures, and a small part of signals were derived from the organic materials synthesizing TiO₂ such as TBT and glycerol. Thus, the intensity ratio (I_D/I_G) was calculated to demonstrate the disorder degree of the carbon materials. It is observed that the pure GO possesses the highest I_D/I_G value of 2.35, indicating that a large number of defects and oxygen-containing functional groups exist in pure GO [45]. In addition, the I_D/I_G value of a-T2 is 1.76 while the I_D/I_G value of c-T2 is 1.50. Therefore, we believe that the rGO existing in a-T2 is partially reduced. That is to say, the partially reduced rGO not only provides enough conduction loss due to the improvement of graphitization degree, but also retains some defects and oxygen-containing functional groups to add more polarization loss, which is exactly what we expected to achieve.

The X-ray photoelectron spectroscopy (XPS) spectra of a-T2 and c-T2 are shown in Figure 3, where the Ti 2p spectra are similar for a-T2 and c-T2, as they both showed almost identical pattern from lattice Ti⁴⁺ ions with peaks centering at 458.6, 464.4, and 471.6 eV (Figure 3a,b). The O 1s spectra (Figure 3c,d) reveal that the c-T2 has less content of chemisorbed oxygen and some oxygen-containing functional groups such as OH, because its intensity around 532.5 eV is smaller than that of a-T2. It should be noticed that the O 1s peaks at 530–531 eV could be attributed to the lattice oxygen for TiO₂ [46]. After annealing treatment, this peak tended to shift by approximately 1 eV to the lower energy side due to crystallization. In addition, it is observed from the C 1s XPS spectra (Figure 3e,f) that a sharp decrease in the relative intensity of the C-O peak around 285.9 eV after annealing, indicating the reduction of oxidized carbon atoms. The lack of oxygen-containing functional groups and the reduction of oxidized carbon atoms in c-T2 can be confirmed further with Fourier transform infrared spectroscopy (FTIR) results (Figure S1). Compared with the clear peaks in a-T2, the vibration intensities of -OH (~3390 cm⁻¹, ~1038 cm⁻¹), C-O (~1117 cm⁻¹, ~810 cm⁻¹), and C=O (~1730 cm⁻¹, ~605 cm⁻¹) bonds in c-T2 all become smaller. Thus, it is reasonable to conclude that both oxygen-containing functional groups and defects are decreased by the annealing treatment, and the polarization losses induced by these groups and defects are decreased sequentially [47,48,49].

3.2. Microwave Absorption Properties

Generally, the RL represents the microwave absorbing efficiency of materials. A RL value less than −10 dB indicates that more than 90% of the incident wave have been absorbed and the corresponding absorption frequency range with RL less than −10 dB is considered as effective bandwidth. According to the transmission line theory [50,51,52], the RL value of an absorber is expressed as follows:

$$Z_{in}=Z_0\sqrt{\frac{{\mu }_r}{{\epsilon }_r}}\tan \mathrm{h}\left(j\frac{2\pi fd\sqrt{{\mu }_r{\epsilon }_r}}{c}\right)$$

(1)

$$\mathrm{RL}\left(\mathrm{dB}\right)=20\log \left|\frac{Z_{in}-Z_0}{Z_{in}+Z_0}\right|$$

(2)

where ε_r and μ_r are the complex permittivity and permeability, respectively; f is the frequency of incident microwave; d is the thickness of absorber; c is the velocity of light; Z₀ refers to the input impedance of the free space; and Z_in is the input impedance of absorber. Firstly, in view of the possible influence of different filler loading ratios on microwave absorption performance, we measured the electromagnetic parameters and calculated the frequency-dependent RL values of a-T2 with filler loading ratios of 10 wt%, 15 wt% and 20 wt%. From Figure S2, it is observed that a-T2 with the loading ratio of 20 wt% has the minimum reflection loss (RL) value, indicating its best microwave absorption performance. Therefore, filler loading of 20 wt% is selected as the optimal value in the following measurements. Figure 4 and Figure S3 illustrate the 3D RL with projection plots of a-T1, a-T2, a-T3, c-T1 and c-T2. The minimum RL value for a-T1 (Figure 4a,d) reaches −17.1 dB at 11.6 GHz when the thickness is 3 mm and the widest EAB is 4.7 GHz, which is much better than pure rGO. For a-T2 (Figure 4b,e), the minimum RL value reaches −42.8 dB at 8.72 GHz when the thickness is 3.25 mm and the widest EAB is 6.2 GHz, showing the best microwave absorption properties. However, it is observed from Figure 4c,f that the RL of a-T3 does not reach −10 dB in all frequency range of 2 to 18 GHz. These results suggest that the microwave absorption properties of a-TiO₂/rGO composites can be easily adjusted by changing the amorphous TiO₂ ratios. In Figure S3a,b, the widest EAB of c-T1 declines obviously compared with a-T1, indicating that the c-TiO₂ has weaker capability to adjust the impedance matching effectively. The little-changed RL values are possibly because that the TiO₂ ratio in c-T1 is so small that the polarization loss induced by the defects of a-TiO₂ is negligible. Figure S3c,d demonstrate that both the minimum RL value and the widest EAB of c-T2 decline sharply compared with a-T2, because the decrease of polarization sites and the impedance mismatching lead to the degradation of microwave absorption performance. As shown in Figure 4g, a-T2 obtains the widest EAB of 6.2GHz among all the TiO₂/rGO composites, achieving the full absorption of Ku band, which should be credited to its excellent impedance matching. What is more, Figure 4h,i and Table S1 show that the a-T2 not only possesses the minimum RL value and wide EAB, but also exhibits the advantages of less filler loading and less matching thickness compared with the graphene- and TiO₂-based absorbers reported in other researches [40,53,54,55,56,57,58,59,60,61,62].

3.3. Analysis of Electromagnetic Parameters

It is widely accepted that the microwave absorption properties of an absorber are strongly determined by its electromagnetic parameters including complex permittivity (ε_r = ε′ − jε″) and complex permeability (μ_r = μ′ − jμ″). The measured electromagnetic parameters for a-T1, a-T2, a-T3 and c-T2 are shown in Figure 5 and Figure S4. The real parts of complex permittivity (ε′) and complex permeability (μ′) represent the storage capability of electric and magnetic energies, while the imaginary parts (ε″ and μ″) stand for the loss capability of electric and magnetic energies [63]. Figure S4a,b show that the μ′ and μ″ values range from 0.96 to 1.10 and 0 to 0.06, respectively, indicating their weak magnetic properties. This means that the complex permittivity dominates the microwave absorption. From Figure 5a, it is observed that the real part of complex permittivity for all the samples decrease with the increase of microwave frequency. However, the imaginary parts shown in Figure 5b have multiple peaks, which are ascribed to polarizations. Both ε′ and ε″ values first increase then decrease with the increase of TiO₂ component, indicating that moderate TiO₂ nanorods prevent the stacking of rGO nanosheets and thus improve the electron transfer capability of the composite [64,65,66]. Furthermore, a-T2 processes larger ε′ and ε″ values than a-T1 and a-T3, revealing that the a-T2 absorbs more electric energy from the electromagnetic field, possibly owing to its more polarizable groups [67]. These mean that a-T2 is more efficient in dissipating the electric field energy. However, excessive TiO₂ would nearly wrap the rGO nanosheets and thus decline the electron transfer capability of the composite, resulting in the smallest ε′ and ε″ value of a-T3.

However, it is observed from Figure 5a,b that both ε′ and ε″ values of c-T2 increase compared with a-T2. The electromagnetic parameters for c-T1 and c-T3 shown in Figure S5 also demonstrate the similar changes compared with c-T2. These changes are mainly caused by that the annealing treatment not only improves the crystalline degrees of TiO₂ and rGO, but also removes the oxygen-containing functional groups and defects which are barriers or traps for the transport of electrons. On one hand, the improvement of crystalline degrees makes it hard to adjust the impedance matching of the composites. On the other hand, the removement of functional groups and defects also decrease the polarization process, which leads to the recession of microwave absorption performance.

Furthermore, these results are confirmed by Cole-Cole semicircles according to the Debye theory [68], from which the ε′ and ε″ can be expressed as:

$${\mathit{\epsilon }}^{\mathit{\prime }}={\epsilon }_{\infty }+\left({\epsilon }_s-{\epsilon }_{\infty }\right)/\left(1+{\omega }^2{\tau }^2\right),$$

(3)

$${\mathit{\epsilon }}^{\mathit{″}}=\mathit{\omega }\mathit{\tau }\left({\epsilon }_s-{\epsilon }_{\infty }\right)/\left(1+{\omega }^2{\tau }^2\right),$$

(4)

$$\mathit{\omega }=2\mathsf{\pi }f$$

(5)

where f represents the frequency of the microwave, ω represents the circular frequency of the microwave, τ is the polarization relaxation time, ε_s stands for the static permittivity, and ${\epsilon }_{\infty }$ is the optical dielectric permittivity. According to these two equations, the relationship between ε′ and ε″ is deduced as:

$${\left({\epsilon }^{\prime }-\frac{{\epsilon }_s+{\epsilon }_{\infty }}{2}\right)}^2+{\left({\epsilon }^{″}\right)}^2={\left(\frac{{\epsilon }_s+{\epsilon }_{\infty }}{2}\right)}^2$$

(6)

Thus, it can be concluded that the plot of ${\epsilon }^{\prime }$ versus ${\epsilon }^{″}$ is a single semicircle called Cole-Cole semicircle, each of which represents a Debye relaxation process. Figure 5c–f shows the ${\epsilon }^{\prime }$-${\epsilon }^{″}$ curves for a-T1, a-T2, c-T1 and c-T2. In Figure 5c,d, both a-T1 and a-T2 have three Cole-Cole semicircles corresponding to three Debye relaxation processes [69]. In a composite microwave absorber, interfacial polarization is generally considered to be the dominant polarization mechanism. With the additive amounts of a-TiO₂, more free charges accumulate at the interfaces between rGO and TiO₂, resulting in the Debye relaxation to transform electromagnetic energy to thermal energy. In addition, as shown in Figure 5e,f, not only does the amount of the Cole-Cole semicircles decrease, but also the size of the Cole-Cole semicircles becomes much smaller after the annealing treatment, which demonstrates less and weaker Debye relaxation processes because of the reduction of the defects and oxygen-containing functional groups. In addition, the straight-line part is related to the conduction loss, further confirming that annealing treatment improves the crystalline degrees of TiO₂ and rGO.

To further investigate the microwave absorption properties of the composites, the dielectric and magnetic dissipation factors of $\mathrm{tg}{\delta }_{\epsilon }={\epsilon }^{″}/{\epsilon }^{\prime }$ and $\mathrm{tg}{\delta }_{\mu }={\mu }^{″}/{\mu }^{\prime }$ are calculated, which provides a measure of how much power is dissipated in a material versus how much power is stored. And the value of attenuation constant $\mathsf{\alpha }$ which determines the attenuation properties is also calculated via the following Equation [70]:

$$\mathsf{\alpha }=\frac{\sqrt{2}\pi f}{c}\sqrt{\left({\mu }^{″}{\epsilon }^{″}-{\mu }^{\prime }{\epsilon }^{\prime }\right)+\sqrt{{\left({\mu }^{″}{\epsilon }^{″}-{\mu }^{\prime }{\epsilon }^{\prime }\right)}^2+{\left({\mu }^{″}{\epsilon }^{\prime }+{\mu }^{\prime }{\epsilon }^{″}\right)}^2}}$$

(7)

In addition, another key factor which affects the microwave absorption performance is the impedance matching of the materials. Impedance matching ($\mathrm{Z}=Z_{in}/Z_0$) represents the ability of the incident wave to enter into the internal parts of absorbers. Theoretically, when the Z value is 1, all the incident waves are penetrating into the absorber without reflection, which is hard to realize for the whole frequency range of the microwave. Consequently, it is beneficial for improving microwave absorption performance to adjust the Z value close to 1.

As shown in Figure S6, the magnetic dissipation factor $\mathrm{tg}{\delta }_{\mu }$ for all the samples is around 0 with slight fluctuation, demonstrating the low magnetic losses of the composites. Furthermore, in Figure 6a, b, the a-T1 possesses smaller dielectric dissipation factor $\mathrm{tg}{\delta }_{\epsilon }$ and attenuation constant α because of the lower content of TiO₂. With the increase of TiO₂ component, both the $\mathrm{tg}{\delta }_{\epsilon }$ and $\mathsf{\alpha }$ values increase initially then decrease, confirming that reasonable TiO₂ content is beneficial to dissipate electromagnetic energy. However, compared with a-T2, the c-T2 exhibits lower $\mathrm{tg}{\delta }_{\epsilon }$ value at most region from 2 to 18 GHz because the decrease of the polarization process while processes the highest $\mathsf{\alpha }$ value due to the enhanced conductive loss. However, this effect also brings a negative influence on the impedance matching property. Figure 6c to f depict the frequency-dependent Z values of a-T1, a-T2, a-T3 and c-T2. It is well known that pure rGO possesses poor impedance matching because of its excessive permittivity. In Figure 6c, the Z value of a-T1 is around 1.5 at each impedance matching peak frequency (f_z). Compared with pure rGO [71], the impedance matching becomes much better after the addition of TiO₂. Especially, the a-T2 exhibits an optimal Z value of around 1.1 at each f_z (Figure 6d), which is much closer to 1.

From Figure 6e, it is found that the Z value of a-T3 at each f_z far deviates from 1 because of the excessive addition of TiO₂, indicating a poor impedance matching and poor microwave absorption performance. Furthermore, in Figure 6f, the Z values of c-T2 at all microwave frequency bands of 2 to 18 GHz deviate from 1, confirming that c-TiO₂ could not do better in adjusting the impedance matching property compared with the a-TiO₂. Therefore, it is concluded that a-T2 balances the relation between attenuation properties and impedance matching property excellently, implying its better microwave absorption properties.

To better understand the microwave absorption performance of the a-T2, the quarter-wavelength matching model [72,73,74] is proposed to analyze the absorption mechanism of a-T2. In this model, the relationship between matching thickness (t_m) and absorption peak frequency (f_m) can be described by the following equation:

$$t_m=\frac{nc}{4f_m}\frac{1}{\sqrt{\left|{\epsilon }_r\right|\left|{\mu }_r\right|}};n=1,3,5,\dots$$

(8)

where $\left|{\epsilon }_r\right|$ and $\left|{\mu }_r\right|$ represent the modulus of complex permittivity and complex permeability respectively at matching frequency, and $c$ is the velocity of light. Generally speaking, if the calculated t_m value coincides with the experimental matching thickness, the phase cancellation effect will contribute to the microwave absorption. On one hand, it is clearly observed in Figure 7a that the absorption peaks of a-T2 shift to lower frequencies with the increase of thickness, which fits well to the quarter-wavelength matching model.

On the other hand, it is also noticed from Figure 4 and Figure S3 that the absorption peaks of all the samples at the same matching thickness also shift to lower frequency regions after annealing treatment due to the increase of ${\epsilon }_r$ values, which further confirms that the microwave absorption of the composites agrees well with the quarter-wavelength matching model. In addition, Figure 7c displays the relationship between t_m and frequency for a-T2, in which the black line stands for the $t_m$ values calculated from the electromagnetic parameters (denoted as t_m^cal) and the pentagrams represent the experimental t_m values (denoted as t_m^exp). Obviously, nearly all the t_m^exp values accord well with the calculated quarter-wavelength curve, further proving that the quarter-wavelength matching model dominates the relationship between t_m and frequency for a-T2. Moreover, it is shown in Figure 7d that for each frequency where the impedance matching value equals 1, there is a corresponding thickness which also accords well with the calculated quarter-wavelength curve. Figure S7 shows the quarter wavelength matching model of several other samples, which indicates that the a-T2 model matches better among amorphous samples. In Figure S7c,d, although the practical matching thicknesses of crystalline samples are consistent with the simulated thicknesses, a lack of polarization and impedance mismatching restrict their microwave absorption. Figure 7b shows the Cole-Cole plot of a-T2, where three distinct semicircles are found around 2.9, 8.7 and 14.7 GHz, corresponding to the three peaks around 3, 8 and 14 GHz in ε″ curve of a-T2 in Figure 5b, indicating the existence of Debye relaxation process. In a word, the highly consistent thickness-frequency relationship among the RL values, quarter-wavelength curve and impedance matching properties determine the excellent performance of microwave absorption in a-T2.

3.4. Microwave Absorption Mechanisms

The overall results show that the a-T2 has the best microwave absorption performance. Firstly, a highly efficient microwave absorber should guarantee that the microwave irradiated on its surface can infiltrate into its internal parts as much as possible. As previously discussed, a-T2 balances the relation between electrically conductive rGO and dielectric TiO₂ to achieve the best impedance matching, which extremely reduces the reflection of the incident microwave. Besides, as shown in Figure 7, the peak frequency of RL, the frequency where Z value equals to 1 and the frequency calculated from quarter-wavelength matching model accord well with each other, indicating a highly efficient absorption of incident microwave. It is certified that the quarter-wavelength matching is a crucial mechanism to determine the position of absorption peaks. Then the excellent $\mathrm{tg}{\delta }_{\epsilon }$ value around the same peak frequency position guarantees the further dissipation of the incident microwave effectively. Figure 8 illustrates the possible dielectric loss mechanisms present in a-T2, which can be summarized as follows:

• Multiscattering loss: When the microwave propagates in the internal part of the absorber, it would be repeatedly scattered by the rGO nanosheets. Particularly, the TiO₂ nanorods implanted in the rGO nanosheets further increase the scattering area and thus improve the multiscattering loss.
• Polarizations loss: On one hand, the defects and oxygen-containing functional groups in a-T2 would induce defect and dipole polarizations to improve the relaxation losses [75]. On the other hand, the accumulation of charges at the boundary between rGO and TiO₂ would induce the interfacial polarizations and thus promotes the microwave absorption [76,77].
• Conductive loss: The adjacent rGO nanosheets contacting with each other establish an interconnected conductive network for electron transport. These electrons could migrate not only from one side of a rGO nanosheet to another, but also from one rGO nanosheet to another, which leads to significant conduction loss.
• Capacitor-like loss: Significantly, the capacitor-like structures [78,79] at the interfaces between non-contact rGO nanosheets could generate the induced charges, further enhancing the microwave absorption performance [80,81].

4. Conclusions

Amorphous TiO₂/rGO (a-TiO₂/rGO) composites have been successfully prepared via a facile one-step solvothermal method whereby the electromagnetic parameters of the composites can be adjusted easily by changing the TiO₂ contents. The a-T2 balances the relation between conductive rGO and dielectric TiO₂ excellently and thus exhibits the best microwave absorption performance with the minimum reflection loss of –42.8 dB achieved at 8.72 GHz. More importantly, the widest EAB of a-T2 reaches 6.2 GHz at 2.15 mm with the filler loading ratio of 20 wt%, which covers the full Ku band (12 to 18 GHz). The crystalline TiO₂ composites show weaker microwave attenuation because of the less defects and oxygen-containing functional groups which induce the polarization losses. It is evidenced that the excellent impedance matching, the quarter-wavelength matching and superior dielectric losses coordinating around a same frequency are the main reasons for the excellent microwave absorption performance. This work would not only bring more inspiration that amorphous structures have better microwave absorption performance in designing high efficient microwave absorbers, but also provide a facile method in constructing and synthesizing high performance microwave absorption materials.