1 Introduction

The rapid development of electronic information technology makes the application of electronic equipment more and more widely [1,2,3,4]. As a result, electromagnetic (EM) pollution has become an increasingly serious problem, which not only interferes with the use of satellite communication and communication equipment, but also endangers human health and safety [5, 6]. With the increasing demand for military safety and healthy life, electromagnetic wave (EMW) absorbing materials have attracted extensive attention. Electromagnetic absorbing material can convert electromagnetic energy into heat energy and other forms of energy [7,8,9]. However, the preparation of ideal EMW absorbing material with the characteristics of low weight, thin matching thickness, strong absorption capacity, and wide absorption bandwidth is still a challenge [10,11,12,13].

According to the absorbing mechanism, EMW absorbing materials are mainly divided into two categories: magnetic loss materials and dielectric loss materials. Among them, Fe3O4 [14], Co3O4 [15], and other magnetic loss materials are often limited due to their high density. In contrast, carbon fibers, carbon nanotubes, graphene oxide, porous carbon, and other carbon materials that belong to dielectric loss materials are considered ideal EMW absorbing candidates [16, 17]. Noticeably, porous carbon has attracted more and more attention due to its excellent electrical conductivity, large specific surface area, large pore size, and low density. Specifically, porous materials with nanopores or micropores can be considered effective media, which could be considered a mixture of solid and air. Hence, the existence of pore structure can reduce the dielectric constant and improve the impedance matching and make more EM waves enter the absorber [18,19,20,21]. At the same time, micropores increase the scattering and reflection of electromagnetic waves, which increases the transmission path of incident electromagnetic waves and provides more opportunities for the medium to attenuate EM wave energy. However, complex synthesis processes and certain environmental pollution limit the application of porous carbon materials. Therefore, it is necessary to investigate carbon materials with simple processes and environment-friendly and easily available raw materials [22,23,24,25,26].

In recent years, due to the rich source and environmental friendliness, biomass materials have attracted more attention [27,28,29]. According to previous studies, many biomass materials can be used to prepare porous carbon materials as EMW absorbing materials. For example, rice [30], eggshell membrane [31], walnut shells [32], and Spinach stem [33]. Through a simple carbonization process, biomass materials can be directly transformed into carbon materials [30]. In this paper, the porous carbon is synthesized by using pinecone as raw material, which is not only environmentally friendly but also low cost. The porous structure of carbon material is helpful to reduce its density and make the microwave absorbing material achieve the purpose of lightweight [34, 35]. However, according to previous reports, single-component carbon materials have high conductivity, which will lead to impedance mismatching. Besides, due to the dual loss mechanism, porous carbon materials are difficult to meet the requirements of wide bandwidth, lightweight, and thin thickness at the same time [36]. Therefore, the improvement of EMW absorption performance could be achieved by improving the impedance matching and the multiple loss of composites. Combining different materials with complementary characteristics to composite materials has become the research hotspot to prepare EMW absorbing materials [37,38,39,40,41].

Ceria is a common rare-earth compound, which is used in fuel cells, solar cells [42], photocatalysis [43], and other fields. Due to its poor electrical conductivity and high density, little research is about the application of CeO2 on the EMW absorption field. However, with the advantages of good chemical stability, easy synthesis, low cost, and oxygen vacancy defects, CeO2 shows huge potential in the field of EMW field. Previous studies have shown that the oxygen vacancy defects in CeO2 crystal are mainly caused by the transformation from Ce4+ to Ce3+, and with the increase of defects, the electrical conductivity and dielectric constant of CeO2 increase obviously, which is conducive to the attenuation of incident EMW. It is reported that the chemical and physical properties of CeO2 can be adjusted by recombination and doping, and the electronic structure can be optimized and the EMW absorption properties can be improved [44,45,46]. Therefore, it is feasible to synthesize multi-component composites composed of ceria for electromagnetic wave attenuation applications. For example, Wang et al. [47] prepared CeO2 doped multi-walled carbon nanotubes hybrid materials by a hydrothermal method. The nanocomposites exhibited the minimum reflection loss (RLmin) of − 40.95 dB with a thickness of 3.5 mm. Li et al. [48] successfully synthesized a 3D accordion-like CeO2/RGO composite by solvothermal and hydrothermal methods. The RLmin of the prepared material was − 50.6 dB with a thickness of 1.5 mm, and the effective absorption bandwidth (EAB) is 4.4 GHz; Li et al. [49] successfully synthesized 3D conductive network wrapped CeO2−x Yolk@Shell hybrid microspheres by solvothermal method. The RLmin of composites was − 52.4 dB when the thickness was 4.0 mm and the EAB was 5.5 GHz. In addition, when the size of CeO2 crystal is reduced to nanometer, the attenuation ability of electromagnetic wave will be enhanced due to quantum effect and interface effect. Therefore, ceria can be used as a candidate for EMW absorber [50].

However, the composite of porous carbon and ceria as electromagnetic wave absorbing material has not been reported. In this paper, CeO2/porous carbon composites with three-dimensional structure were prepared by a hydrothermal method using porous carbon as the template. The relationship among morphology, structure, and EMW absorption performance of CeO2/porous carbon composites was further investigated. In addition, the effects of CeO2 content on the microstructure, EMW absorption performance, and EM parameters of the composites were studied. When the filler content is 20 wt%, the material shows excellent EMW absorption performance with the RLmin of − 56.04 dB when the thickness is 1.9 mm, and the EAB is 5.28 GHz at a thickness of 2.1 mm. Moreover, the EMW absorption mechanism of the composites was illustrated. The CeO2/porous carbon composites prepared in this study have wide bandwidth, thin thickness, and excellent electromagnetic wave absorption performance, which is a candidate material for EMW absorption.

2 Experimental

2.1 Raw materials

The pinecone was obtained from the Pinus tabuliformis Carr in compass. Potassium hydroxide (KOH, 99.99%), cerium nitrate hexahydrate (Ce(NO3)3∙6H2O, 99.0%), NH3∙H2O (25 wt%), and paraffin were bought from Aladdin, and anhydrous ethanol was purchased from Sinopharm Chemical Reagent Co., Ltd (Shanghai, China). All the chemical reagents were analytical grade and used without further purification. Water was the deionized water (DI, 18.25 MΩ).

2.2 Experiment section

2.2.1 Pretreatment of pinecone

First of all, the pinecone was cleaned with deionized water to remove impurities and dust on its surface. Then, the cleaned pinecone was dried at 80 °C. Finally, the pineal gland was cut as raw material.

2.2.2 Synthesis of porous carbon materials

Firstly, the homogeneous solution was obtained by dissolving 2 g KOH in 30 mL deionized water. Then, 2 g pinecones were added into the solution and treated with ultrasonic for 30 min to make the pinecone fully soaked. Then, the pinecone was dried at 80 °C overnight. The dried pinecone was carbonized in an Ar flow tubular furnace at 650 °C for 1 h with a heating rate of 2 °C/min. After cooling to room temperature naturally, the intermediate products were ground into powder in an agate mortar. The by-product and excess KOH were removed by deionized water, and the final sample was obtained after drying at 80 °C. The porous carbon materials were named as S0.

2.2.3 Synthesis of CeO2/porous carbon composites

Typically, 200 mg synthesized porous carbon was dispersed into 60 mL deionized water under continuous stirring for 10 min. Then, a certain amount of cerium nitrate hexahydrate was dispersed in the uniform solution under magnetic stirring until completely dissolved. The NH3·H2O (25 wt%) was gradually added to the solution until the pH value became 11. Then, the system was transferred into a Teflon-lined autoclave at 160 °C for 12 h. After cooling down to room temperature naturally, the prepared samples were washed with deionized water and ethanol and dried overnight at 80 °C. After drying, the final sample was obtained after heat-treatment at 500 °C for 1 h under Ar atmosphere (heating rate 2 °C/min). As-prepared composites were named by the additional amount of Ce(NO3)3∙6H2O as S1 (0.2 mmol), S2 (0.4 mmol), S3 (0.6 mmol), S4 (0.8 mmol), and S5 (1.0 mmol), respectively.

2.3 Characterization

The crystalline structure of samples was determined by powder X-ray diffraction (Rigaku Ultima IV with Cu–Ka radiation (λ = 0.15418)). The Raman spectra of samples were collected by using a Renishaw inVia Plus Micro-Raman spectroscopy system equipped with a 50-mW DPSS laser at 532 mm. The FTIR spectrum was recorded on PerkinElmer, and Spectrum 100 was selected to study the surface structure of the sample. The thermogravimetric analysis (TGA) was carried out from room temperature to 800 °C on an SDT Q600 analyzer with a heating rate of 10 °C/min. The stage of elements in the surface of composites was characterized by X-ray photoelectron spectroscopy (XPS) on Thermo Fisher ESCALAB 250 Xi spectrometer with an Al Ka X-ray source (1486.6 eV). The morphology and element mapping of samples were obtained by field emission scanning electron microscope (SEM, JEOL JSM-7800 F), and lattice spacing was observed on transmission electron microscope (TEM, JEOL JEM-2100).

2.4 Electromagnetic parameter measurement

The composites were pressed into a toroidal-shaped pipe by mixing with the paraffin. The height, outer diameter, and inner diameter of the pipe were about 2.00 mm, 7.00 mm, and 3.04 mm, respectively. The weight ratio of composites to paraffin was 1:4. Based on the coaxial-line method, the electromagnetic parameters (\({\varepsilon }_{r}\) and \({\mu }_{r}\)) of composites were obtained on a vector network analyzer (VNA, Agilent N5222A). The reflection loss (RL) values of composites in the frequency from 2 to 18 GHz at 0.1–10 mm were worked out by transmission line theory as follows [51,52,53,54]:

$${\mathrm{Z}}_{\mathrm{in}}={Z}_{0}\sqrt{\frac{{\mu }_{r}}{{\varepsilon }_{r}}}\mathrm{tanh}\left|j(\frac{2\pi fd}{c})\sqrt{{\varepsilon }_{r}{\mu }_{r}}\right|$$
(1)
$$\mathrm{RL}\left(dB\right)=20\mathrm{log}\left|\frac{{Z}_{\mathrm{in}}-{Z}_{0}}{{Z}_{\mathrm{in}}+{Z}_{0}}\right|$$
(2)

where \({\varepsilon }_{r}\) and \({\mu }_{r}\) are the complex permittivity and permeability, f is the frequency, d is the thickness of the sample, c is the light speed in a vacuum, and Zin and Z0 are the input impedance and free space impedance, respectively. When the RL value lower than − 10 dB, it means that more than 90% EM waves would be absorbed and consumed by the absorber.

3 Results and discussion

The crystal structures of S0 to S5 are recorded by XRD. Figure 1b displays that the X-ray diffraction peaks at 2θ = 28.5°, 33.1°, 47.5°, 56.3°, 69.4°, 76.7°, and 79.1° are consistent with the (111), (200), (220), (311), (400), (331), and (420) crystal planes of cubic fluorite CeO2, indicating that CeO2 is successfully anchored onto porous carbon [55]. However, the diffraction peaks of porous carbon are difficult to distinguish in S1 to S5. This phenomenon occurs because porous carbon is amorphous and has no obvious diffraction peak, which can be confirmed by TEM.

Fig. 1
figure 1

(a) Schematic illustration of the synthesis process of CeO2/porous carbon composites. (b) XRD patterns of the samples of S0–S5. (c) Raman spectra of the samples of S0–S5

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The graphitization degree of S0–S5 is detected by Raman spectroscopy. Figure 1c shows that two typical peaks of CeO2/porous carbon composites located at around 1350 cm−1 and 1580 cm−1 can be assigned to the D and G bands. Generally, the D band represents the defects, limited size crystal, or disorder of graphite, while the G band is the in-plane vibration of sp2 C atom, which represents the ordered structure of graphite carbon [56]. Therefore, the degree of graphitization can be reflected by the intensity ratio of D peak to G peak (ID/IG). By comparing the ID/IG value of S0–S5, it is found that the graphitization degree of the samples shows little change after adding ceria, indicating that ceria addition has little effect on the graphitization degree of the samples.

The molecular structures of the C, O, and Ce elements are characterized by FT-IR. As is shown in Fig. 2a, the absorption peak at 3435 cm−1 corresponds to the O–H group in H2O, which is adsorbed on the sample surface. While the absorption peak at 2360 cm−1 comes from C = O. In addition, the absorption peak at 1623 cm−1 could confirm the existence of O–C = O, the absorption peak at 1100 cm−1 is C–O. According to previous studies, the presence of oxygen-containing groups will cause the charge asymmetric distributions, inducing the formation of dipoles. These dipoles could rotate toward the alternating electromagnetic field, converting electromagnetic energy to thermal energy through relaxation loss, which increases the ability to consume the energy of electromagnetic waves.

Fig. 2
figure 2

(a) FT-IR of S0-S5. (b) TGA of S0–S5

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The content of CeO2 in S1–S5 samples is determined by thermogravimetric analysis (TGA). As depicted in Fig. 2b, the thermal decomposition of S1–S5 is mainly divided into two stages. Firstly, a little weight loss (~ 4 wt%) is caused by the loss of water adsorbed on the sample surface below 100 °C, corresponding to the O–H bond in the FT-IR. Secondly, in the range of 350 to 580 °C, all the samples have obvious weight loss, which may be ascribed to the decomposition of porous carbon in the air. Then, the proportion of CeO2 was deduced from the residual products. Therefore, the contents of CeO2 in S1–S5 are estimated as 17.5 wt%, 26.9 wt%, 31.2 wt%, 37.8 wt%, and 41.9 wt% respectively. With the increase of molar amount of cerium salt, the proportion of cerium dioxide in the sample is increasing. The XRD of the residue of composites is shown in Fig. S1 (Supporting Information), which shows the CeO2 phase.

The surface chemical composition and valence state are analyzed by XPS. According to Fig. 3a, the presence of C, O, and Ce elements is confirmed. Figure 3b illustrates the groups corresponding to C–C/C = C, C–O, C = O, and O–-C = O at 284.2, 285.1, 286.0, and 289.0 eV in the C 1 s peak, respectively [45]. Figure 3c shows that groups corresponding to Ce–O, O–H, and O2− at 529.3, 531.2, and 532.1 eV in the O 1 s peak [57]. Figure 3d depicts the Ce 3d spectrum. Ce4+ in CeO2 is labeled as U, U″, U″′, V, V″, and V″′, and Ce3+ in CeO2 is labeled as V′ and U′ [45]. Therefore, the existence of Ce4+ and Ce3+ in the Ce 3d spectrum of S3 indicates the existence of oxygen vacancies [57]. Specifically, oxygen vacancies are generated to compensate for the negative charge generated by the increase of Ce3+ in CeO2. When the oxygen vacancy increases, the electrical conductivity increases, booming the conduction loss [58].

Fig. 3
figure 3

(a) Full XPS spectrum and high-resolution. (b) C 1 s. (c) O 1 s. (d) Ce 3d

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Figure 4 shows the surface morphology, structure, and element diagram of the samples. Figure 4(a1 and a2) depict the morphology and structure of porous carbon material, which is a three-dimensional porous framework with pore structure distributed on its surface. As is shown in Fig. 4(b1–f2), compared with the pure porous carbon material, the CeO2/porous carbon composites could show that CeO2 nanoparticles are anchored on the porous carbon material clearly. Figure 4(b1–f2) illustrate that, with the increase of CeO2 content in the sample, from CeO2 nanoparticles cannot completely wrap the porous carbon to uniformly wrap the porous carbon, and then, CeO2 nanoparticles are closely packed and gathered on the porous carbon material. As is shown in Fig. 4g, the O and Ce were uniformly distributed on the outer surface of S3, which further verifies the existence of CeO2 nanoparticles on porous carbon.

Fig. 4
figure 4

(a–f) SEM images of S0–S5. (g) Elements mapping of a selected area of S3

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Figure 5a and b show that the porous carbon is amorphous, which is the same as the conclusion obtained by XRD. As is shown in Fig. 5c, the porous carbon and CeO2 nanoparticles are closely combined to form a nanoscale heterogeneous interface. Figure 5d shows that the size of CeO2 nanoparticles was about 6–10 nm, and the CeO2 nanoparticles were uniformly anchored on the surface of porous carbon. As is shown in Fig. 5e, the crystal plane spacing of 0.27 and 0.31 nm corresponds to the (200) and (111) crystal plane of CeO2, which is consistent with the XRD spectrum. Figure 5f depicts the selected-area electron diffraction image of composites. Four diffraction rings correspond to (311), (111), (220), and (200) crystal planes of CeO2. From the above observation, it could be indicated that the CeO2/porous carbon composites are successfully synthesized.

Fig. 5
figure 5

(a) TEM, (b) HR-TEM images of S0, (c) TEM, (d–e) HR-TEM images, and (f) SAED patterns of S3

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The value of reflection loss (RL) is a key indicator to evaluate EMW absorption performance. In addition, when the RL value is less than − 10 dB, the EM absorber can absorb more than 90% of the electromagnetic wave. Figure 6 shows the 3D reflection loss of pure porous carbon and CeO2/porous carbon composites with different loadings. From Fig. 6a, the minimum RL value (RLmin) of S0 is − 22.24 dB at the thickness of 3.1 mm, confirming poor EMW absorption performance. Figure 6b shows that, after decorating porous carbon with CeO2 nanoparticles, S1 exhibits much better EMW absorption performance with RLmin of − 67.05 dB at a thickness of 4.4 mm than that of S0, and the S2 shows the RLmin of − 53.68 dB when the thickness is 3.4 mm. As for the S3, the RLmin is up to − 56.04 dB when the thickness is 1.9 mm, the RLmin of S4 dropped to − 51.04 dB with a thickness of 5.2 mm, and the S5 shows the RLmin of − 35.56 dB at the matching thickness increase of 9.4 mm. According to Fig. 6a–f, with the increasing proportion of CeO2 in composites, the RLmin of the samples shows an increasing process with the thickness decreases. Consequently, it could be found that the S3 shows the optimal absorption performance among as-obtained composites.

Fig. 6
figure 6

Reflection Loss in the frequency of 2–18 GHz for the S0 (a), S1 (b), S2 (c), S3 (d), S4 (e), and S5 (f), respectively

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Figure 7a–f show the effective absorption bandwidth (EAB) of S0–S5. From Fig. 7a–f, S1, S2, and S3 possess wide bandwidth with thin matching thickness. However, S0, S4, and S5 show a relatively thick thickness when the maximum EAB is obtained. Specifically, when the thickness of S1 is 2.0 mm, the EAB is 5.52 GHz. The bandwidth of S2 and S3 is 5.04 GHz and 5.28 GHz, respectively.

Fig. 7
figure 7

Contour map of absolute values of S0 (a), S1 (b), S2 (c), S3 (d), S4 (e), and S5 (f)

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The complex permittivity (\(\varepsilon_r=\varepsilon'-j\varepsilon''\)) and complex permeability (\(\mu_r=\mu'-j\mu''\)) of composites are measured. As is shown in Fig. 8a, the \({\varepsilon }^{^{\prime}}\) value of S0–S4 decreases with the increase of frequency, which is called dispersion behavior [59]. However, the \({\varepsilon }^{^{\prime}}\) of S5 remains at a stable value of 6 and that is lower than that of S0–S4, implying poor dielectric loss ability. As is shown in Fig. 8b, when the frequency increases, the \({\varepsilon }\) curve of samples firstly shows a downward trend, and multiple relaxation peaks appear with the increase of frequency, which indicates the existence of dielectric loss behavior. From the previous reports, the dielectric loss could be divided into polarization loss and conductive loss [60]. Generally speaking, electron polarization and ion polarization can be excluded, because they usually occur in the THz and PHz ranges. Then, as the frequency continues to increase, the \({\varepsilon }\) values of S0–S5 show an increasing trend, which means that, when the frequency of EMW increases, the dipole can quickly reorient and respond to the external electric field, which means that the effect of dipole polarization is also very small. In this case, multiple interfaces between CeO2 and porous carbon, CeO2 and CeO2, CeO2, and paraffin lead to interfacial polarization. In addition, porous carbon can provide a conductive path for the transmission of electrons. Based on the free-electron theory [58]:

Fig. 8
figure 8

(a) Real part and (b) imaginary part of complex permittivity of S0–S5. (c) Dielectric loss tangent of S0–S5, (d) real part, and (e) imaginary part of complex permeability of S0-S5. (f) Magnetic loss tangent of S0–S5

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$$\varepsilon''=1/2\varepsilon_0\pi\rho f$$
(3)

where \({\varepsilon }_{0}\), ρ, and f are permittivity of the vacuum, resistivity, and frequency of the EMW, respectively. As is shown in Fig. 8b, the maximum value of \(\varepsilon''\) of S0 is mainly caused by the high electrical conductivity of porous carbon, which will cause poor impedance matching and cause EM waves to be reflected from the absorber interface rather than absorbed, resulting in poor performance.

\(\mathrm{tan}{\delta }_{E}\) represents the dielectric loss capacity of the sample [60]. As is shown in Fig. 8c, the \(\mathrm{tan}{\delta }_{E}\) value of S0 shows more obvious fluctuation than that of S1–S5 at 2–18 GHz, and the \(\mathrm{tan}{\delta }_{E}\) value of S1–S5 tends to be a constant and less than S0. The explanation of this phenomenon can be found in some previous studies; pure porous carbon will have enough charge to reverse the traditional dielectric behavior under external electromagnetic wave. In this case, the conductive loss is dominant in the dielectric loss. When porous carbon is modified with CeO2, the interface between CeO2 and porous carbon polarizes and accumulates a lot of charges. When the ceria content reaches a higher level, the insulating properties of CeO2 will hinder this process, resulting in relatively poor dielectric properties. Therefore, the \(\mathrm{tan}{\delta }_{E}\) value of S1–S5 is lower than that of S0. The trends of \(\mathrm{tan}{\delta }_{\mu }\) and \(\mu''\) of all samples are similar with the increase of frequency. According to Fig. 8c and f, by comparing \(\mathrm{tan}{\delta }_{E}\) and \(\mathrm{tan}{\delta }_{\mu }\), the dielectric loss and magnetic loss both play an important role in EM loss.

The impedance matching diagram of S0–S5 is shown in Fig. 9. The impedance value (Z = Zin/Z0) is calculated as 0.1–10 mm at 2–18 GHz. The calculation formula is as follows [51,52,53,54]:

Fig. 9
figure 9

Normalized input impendence (Zin/Z0) of S0 (a), S1 (b), S2 (c), S3 (d), S4 (e), and S5 (f)

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$$Z=\frac{{\mathrm{Z}}_{in}}{{Z}_{0}}=\sqrt{\frac{{\mu }_{r}}{{\varepsilon }_{r}}}\mathrm{tanh}\left|j(\frac{2\pi fd}{c})\sqrt{{\varepsilon }_{r}{\mu }_{r}}\right|$$
(4)

As is shown in Fig. 9, the area between 0.9 and 1.1 is drawn with black lines, and the impedance matching degree of the samples can be expressed by calculating the area between the two black lines. Large area proves good impedance matching. It can be inferred that S3 has the best impedance matching, which is consistent with the conclusion that S3 shows the best absorbing performance.

Generally speaking, dielectric conductivity is an important index that affects the response of EMW absorbing materials to EM field. The dielectric conductivity could be expressed by the following formulate [61]:

$$\sigma=\omega\varepsilon_0\varepsilon''$$
(5)

where \(\omega\) (\(\omega =2\pi f\)) is the angular frequency, \({\upvarepsilon }_{0}\) (\({\varepsilon }_{0}\) = 8.854 × 10−12 F/m) represents the permittivity of free space, and \(\varepsilon''\) is the imaginary of complex permittivity. The dielectric conductivity of S0–S5 is shown in Fig. 10a. The S0 shows the maximum dielectric conductivity, which means that the influence of its conductive loss on the electromagnetic wave attenuation is more apparent in as-obtained samples. However, high dielectric conductivity will cause impedance mismatch, which leads to more electromagnetic waves reflected from the surface of the absorber rather than absorbed.

Fig. 10
figure 10

(a) Dielectric conductivity of S0–S5. (b) Attenuation constants of S0–S5

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In addition to the impedance matching index, the attenuation constant α is also a key indicator, which reflects the attenuation ability of the S0–S5. The α can be expressed as [62,63,64]:

$$\alpha=\frac{\sqrt2\pi f}c\times\sqrt{\left(\mu''\varepsilon''-\mu'\varepsilon'\right)+\sqrt{{(\mu'\varepsilon''+\mu''\varepsilon')}^2+{(\mu''\varepsilon''-\mu'\varepsilon')}^2}}$$
(6)

Figure 10b displays the α values of S0–S5. The S5 has the lowest α value and the worst performance. It is worth noting that S0 and S4 have higher α value, but they show poor electromagnetic wave absorption performance. On the contrary, S3 with low attenuation constant has the best absorption performance. This phenomenon could be explained that the impedance matching value of S3 is higher than that of S0 and S4, which indicates that more EMW can enter S3 and have more chances to be attenuated. Therefore, compared with the attenuation constant, the impedance matching is the main factor affecting the EMW absorption performance.

According to the Debye theory, the \(\varepsilon'\) and \(\varepsilon''\) could be calculated by the following formula [65, 66]:

$$\varepsilon'=\varepsilon_\infty+\frac{\varepsilon_s-\varepsilon_\infty}{1+{(2\pi f)}^2\tau^2}$$
(7)
$$\varepsilon''=\frac{2\pi f\tau(\varepsilon_s-\varepsilon_\infty)}{1+{(2\pi f)}^2\tau^2}$$
(8)

where the \({\varepsilon }_{s}\) represents the static dielectric constant, \({\varepsilon }_{\infty }\) represents the optimal dielectric constant, f represents the matching frequency, and \(\tau\) is the polarization relaxation time. Therefore, the Cole–Cole equation could be expressed by the following formula [65, 66]:

$${(\varepsilon'-\frac{\varepsilon_s+\varepsilon_\infty}2)}^2+{(\varepsilon'')}^2={(\frac{\varepsilon_s-\varepsilon_\infty}2)}^2$$
(9)

Figure 11 shows the Cole–Cole semicircles of the samples with different CeO2 loadings. Figure 11a–c present that the Cole–Cole curves in these three images show similar trends, with several Cole–Cole semicircles and an upward long tail. Through previous studies, the upward long tail indicates the conduction loss in S0–S2, and the Cole–Cole semicircle indicates the existence of polarization relaxation in S0–S5. According to the Cole–Cole semicircle curves, S3 processes the most Cole–Cole semicircles, which means that outstanding polarization relaxation occurs in S3.

Fig. 11
figure 11

Cole–Cole semicircle curves of S0 (a), S1 (b), S2 (c), S3 (d), S4 (e), and S5 (f)

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Based on Eqs. (7) and (8), the \(\varepsilon'\) could be expressed as follows [67]:

$$\varepsilon'=\frac1{2\pi\tau}\frac{\varepsilon''}f+\varepsilon_\infty$$
(10)

Theoretically, if the dielectric loss is related to the polarization relaxation, the functional relationship between \(\varepsilon'\) and \(\varepsilon''/f\) will be linear. The relaxation time is expressed by the slope of the linear function. The fitting lines are obtained by means of linear regression method, and the relaxation time is obtained by calculation. The relaxation time can be calculated by the formula [67]:

$$\tau =\frac{1}{2\pi k}$$
(11)

where the k is the slope of the linear function. Figure 12 shows the functional relationship between \(\varepsilon'\) and \(\varepsilon''/f\) of S0–S5. As is shown in Fig. 12, not all curves fit into a single straight line, which means that the multiple polarization relaxation process. Based on the previous reports, this phenomenon could be explicated as follows: (1) the dipoles are not all in the same environment. Therefore, the response of dipoles to EM field is distinct. Hence, the as-obtained samples showed different slopes. (2) Different polarization processes possess various relaxation time and provide different contributions to the dielectric loss.

Fig. 12
figure 12

The relationship between \(\varepsilon'\) and \(\varepsilon''/f\) of S0 (a), S1 (b), S2 (c), S3 (d), S4 (e), and S5 (f)

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The matching thickness (tm) and absorption peak frequency (fm) are two key factors affecting the application of EMW absorber. According to the quarter-wavelength matching theory, the relationship between tm and fm is as follows [68,69,70]:

$${t}_{m}=\frac{n\lambda }{4}=\frac{nc}{4{f}_{m}\sqrt{\left|{\mu }_{r}\right|\left|{\varepsilon }_{r}\right|}}\left(n=\mathrm{1,3},5\dots \right)$$
(12)

where tm and fm represent the matching thickness and the frequency of the RLmin value, c is the light speed in free space. \(\left|{\mu }_{r}\right|\) and \(\left|{\varepsilon }_{r}\right|\) are the modulus of the \({\mu }_{r}\) and \({\varepsilon }_{r}\), respectively. From Fig. 13, with the increase of matching thickness, the reflection loss peak of S0–S5 gradually moves to low frequency. The black hearts are the best matching thickness obtained from the RL diagram, and the purple line is calculated from the above equation. In Fig. 13, the black hearts are almost on the purple line. The results show that the quarter-wavelength theory can explain the EMW absorption characteristics of S0–S5.

Fig. 13
figure 13

Dependence of matching thickness (tm) on matching frequency (fm) of S0–S5 at a wavelength of λ/4

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The electromagnetic wave absorption mechanism of CeO2/porous carbon composites can be summarized as shown in Scheme 1. Firstly, the porous structure could be regarded as the solid-air composites, which improves the impedance matching and electromagnetic wave absorption capacity. Moreover, the porous carbon framework forms a conductive network to improve the conductive loss and O atom defects on porous carbon can act as dipoles to enhance the attenuation of electromagnetic waves. Secondly, the introduction of CeO2 nanoparticles into the porous carbon structure produces rich interfaces (such as CeO2–CeO2, CeO2-porous carbon). The interface polarization generated by the heterogeneous interface and the conductive loss generated by the conductive network of porous carbon has a synergistic effect, which transforms the EMW energy into heat and other forms of energy. Thirdly, multiple reflection scattering increases the dissipation of electromagnetic wave. Moreover, Ce4+ transforms into Ce3+ in CeO2 to produce a large number of oxygen vacancies, which can be used as dipoles, which is conducive to electron migration, enhanced charge relaxation, and increased electromagnetic wave attenuation. All the loss mechanisms mentioned work together to attenuate incident EMW energy.

Scheme 1
scheme 1

Schematic illustration of the electromagnetic wave absorption performance of composites

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4 Conclusions

In summary, CeO2/porous carbon composites were successfully fabricated by a simple hydrothermal method and subsequent pyrolysis method. Porous carbon materials were prepared by using pinecone as the precursor, and then, CeO2 nanoparticles were anchored on the surface of porous carbon by subsequent hydrothermal and pyrolysis methods. In addition, the effects of cerium addition on the morphology, EM parameters, and EMW absorption performance of all the samples were also studied. Through the characterization, it can be concluded that, when the cerium salt content is 0.6 mmol, the RLmin of − 56.04 dB is obtained with a thickness of 1.9 mm, and the EAB is 5.28 GHz with a thickness of 2.1 mm. Multiple interface polarization along with conductive loss and dipolar polarization is contributed to excellent electromagnetic wave absorption performance of the CeO2/porous carbon composites and multiple reflection and scattering enhance the dissipation of electromagnetic waves. Therefore, the as-obtained composites can be regarded as a potential candidate absorber to deal with the electromagnetic interference and pollution.