2.1 Materials

The raw materials used in this research are outlined in Table 1. The materials have been used without purification.

2.2 Synthesis of graphene aerogel/barium ferrite nanoparticle composites

For synthesizing the nanocomposite, 0.25 g graphene oxide was added to 70 ml deionized water and homogenized via ultrasound device (Toposonic model, Iran) for 30 min. Next, 0.8 g of barium ferrite nanoparticles was added to the mixture and ultrasonicated for 30 min. The mixture was immediately transferred into the Teflon-lined autoclave, and the autoclave was placed in the oven at 150 °C for 5 h. Once the autoclave cooled down to room temperature, the graphene hydrogel/barium ferrite nanoparticles were placed inside a freeze drier(Dena Company, Iran) for 24 h. Fig. 1 shows a schematic of the synthesis steps of graphene oxide aerogel nanocomposites with the addition of barium ferrite nanoparticles.

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Fig. 1

Schematic of the synthesis step of graphene oxide/barium ferrite aerogels composite.

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For the synthesis of 3D nanocomposite samples, the amount of graphene oxide was kept constant, while the amount of barium ferrite nanoparticles was changed at 0.125 g, 0.166 g, 0.375 g, and 0.5 g. The aim was to investigate the effect of different weight percentages of barium ferrite nanoparticles on graphene oxide sheets on the EM wave absorption. The samples are named according to Table 2.

2.3 Test methods

For phase characterization of the composites, in this research, an XRD device (ASENWARE, AW-XDM300) (Sadeghi et al., 2022; Sivaraman et al., 2022; Jalil et al., 2021; Radjehi et al., 2023; Ghasemvand et al., 2023) was used with an X-ray wavelength of CuK_α = 0.15140 nm.

To detect functional groups in the synthesized nanoparticles, an FTIR device (Infralum ft-08, LUMEX Co., Russia) (Suanto et al., 2022) was used within the wavenumber of 400–4000 cm⁻¹. The bulk density of the sample was measured in paraffin solution (density of 0.775 g/cm³) according to Archimedes' principle.

Raman spectra were carried out on a LabRam HR laser confocal Raman Spectroscopy (Made by HORIBA, Japan) with a laser wavelength of 532 nm.

X-ray photoelectron spectroscopy (XPS) was performed under a very high vacuum on the model ESCALAB 250 (USA). The XPS peaks were calibrated regarding C and O elements.

Thermal stability using thermal gravimetric analysis (TGA) of Labsys Evo device at room temperature up to 800 °C with a rate of 10 °C/min under argon atmosphere (Shi et al., 2023). Differential scanning calorimetry (DSC, DSC131 evo) device was applied from room temperature to 600 °C at a rate of 10 °C/min under air atmosphere.

The magnetic properties of the samples, including hysteresis curves, saturation magnetization, and coercive field were evaluated using a vibrating sample magnetometer (Meghntis Daghigh Kavir, made in Iran) device in a 1.5 Tesla field (Khorshidi et al., 2022; Marras et al., 2008; Song et al., 2023; Xu and Liu, 2023; Ngafwan et al., 2021).

PVAN5222A device (Malaysia) was used with a frequency range of 0–26 GHz to measure the dielectric constant and magnetic permittivity of the samples.

Field emission scanning electron microscope (FE-SEM) (MIRA3, TESCAN Co.) was used with a resolution of 1.5 nm at a voltage of 15 kV (Fu et al., 2020; Suanto et al., 2022) to explore the morphology (Raya et al., 2022; Jasim et al., 2022; Guo et al., 2022; Fu et al., 2020; Bokov et al., 2021) of the barium ferrite nanoparticles, graphene oxide sheets, and distribution of barium ferrite nanoparticles onto the graphene oxide sheets.

3.1 Examining the XRD Patterns

Fig. 2a indicates the XRD pattern of graphene oxide (GO) powder. Two peaks at 2θ of 12° and 43° represent the (0 0 1) and (1 0 0) planes of GO sheets, respectively (Kumar et al., 2019; Ain et al., 2019). Also, Fig. 2a depicts the XRD pattern of graphene oxide aerogel. GO aerogel has two reflections at 23.98° and 42.92°, being related to (0 0 2) and (1 0 0) planes, respectively (Pavithra et al., 2017; Jiao et al., 2017). Since the structure of GO aerogel differs from that of GO powder in terms of inter-plane distance, and the distance between the GO aerogel planes is lower than that of GO powder due to the reduction of C⚌C functional groups, the diffraction angle of GO aerogel grows; accordingly, the diffraction at 12° of GO nanopowders is transferred to 24° in GO aerogel (Fig. 2a), but the diffraction of (1 0 0) plane does not change in the aerogel process (Jiao et al., 2017).

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Fig. 2

XRD pattern of (a) graphene oxide (GO) and graphene oxide aerogel (GA) (b) Barium ferrite nanoparticles, graphene oxide aerogel (GA) and, composite of graphene oxide aerogel /barium ferrite nanoparticles.

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Fig. 2b displays the XRD pattern of barium ferrite nanoparticles. The XRD pattern indicates the presence of a barium ferrite phase with a hexagonal crystalline system matching the reference code of 078-0.133 and iron oxide impurity matching the JCPDS No. 013-0534.

The diffraction emerging at angles of 30.485, 32.326, 37.252, 40.501, 42.614, 55.318, 56.847, 60.282, 63.384, 67.662, 72.961, and 77.971° are related to planes of (1 1 0), (1 0 7), (1 1 4), (2 0 3), (2 0 5), (2 0 6), (2 1 7), (2011), (2012), (2 2 0), (2014), (3 1 7), and (4 0 5) for the barium ferrite nanoparticles structure. The peaks observed at 2θ of 24.299, 33.280, 35.744, 40.972, 49.555, 62.540, 64.080, 72.033, and 75.515° are attributed to (0 1 2), (1 0 4), (1 1 0), (1 1 3), (0 2 4), (2 1 4), (3 0 0), (1 0 1 0), and (2 2 0) planes of iron oxide phase (Fe₂O₃).

To determine the crystallite size, the Scherrer equation was used. The crystallite size of the barium ferrite nanoparticles, using this relation, was found at 15–48 nm. Also, the crystallite size of iron oxide was achieved by 28–60 nm.

Also, Fig. 2b reveals the XRD pattern of the GO/2BF graphene oxide aerogel composite sample. As seen, most diffractions of barium ferrite nanoparticles, as explained earlier, exist in this XRD pattern. Also, the presence of the wide diffraction within the 2θ range of 20° confirms the presence of GO aerogel. The XRD pattern of other synthesized samples is also similar to that of the GO/2BF sample, with the difference that in some samples, the intensity of the barium ferrite nanoparticles peaks has diminished. This can be attributed to less separation of GO planes from each other as well as the low BF nanoparticles to GO ratio. In Fig. S1 of the appendix, the XRD patterns of all samples, including GO/2BF, 2GO/3BF, GO/BF, 3GO/2BF, 2GO/BF, and 3GO/BF are shown.

3.2 Fourier transform infrared (FTIR) spectroscopy

Fig. 3 displays the results of FTIR of the pure barium ferrite nanoparticles, GO, and GO/BF nanocomposites. In the FTIR analysis of barium ferrite nanoparticles, the presence of two bands at 578 cm⁻¹ and 432 cm⁻¹ is related to oxygen-metal (M—O) bonds (Feng et al., 2017). Based on Fig. 3, the band at 432 cm⁻¹ is related to Fe—O bonds at octahedral sites in ferrite lattice (Forushani et al., 2023a), while the wavenumber of 578 cm⁻¹ is associated with the M—O bonds at tetrahedral sites in the hexagonal structure of the barium ferrite. Thus, FTIR analysis confirms the presence of hexagonal barium ferrite nanoparticles (Vinay et al., 2018; Ghzaiel et al., 2016).

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Fig. 3

FTIR spectroscopy of the GO nanopowders, graphene oxide aerogel (GA) and GO/barium nanocomposites.

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In the FTIR analysis related to GO and GO aerogel, the presence of a wide peak at 3422 cm⁻¹ is related to stretching vibrations of O—H in the GO sheets (Gong et al., 2015). Also, the band at 2920 cm⁻¹ indicates aliphatic stretching vibrations of C—H₂ bonds (Zhao et al., 2023; Marras et al., 2008; Zhang et al., 2016; Wang et al., 2021; Zhang et al., 2022). The band at 1716 cm⁻¹ confirms the presence of C⚌O stretching vibrations of the carboxylic group, while the peak at 1650 cm⁻¹ originates from the bending modes of water molecules integrated into the GO structure (Fig. 3). In the FTIR spectrum of GO/BF nanocomposite, the wavenumber of 1211 cm⁻¹ is related to the C—O stretching vibrations of GO nanosheets. FTIR diagrams of all samples are shown in Fig. S2 of the Appendix.

3.3 X-ray photoelectron spectroscopy (XPS) analysis

Fig. 4 shows the XPS analysis of a graphene oxide/barium ferrite aerogel composite (3GO/2BF sample). Based on these curves, the peaks that originate from constituents of this composite, namely carbon, oxygen, iron, and barium, are observed. Fig. 4a is related to the full XPS spectrum of graphene oxide/barium ferrite aerogel composite and the elements in it are specified. In Fig. 4b, the peak of 779.35 eV corresponds to Ba 3d and Ba 3d_5/2 and the peak of 793.45 eV is related to Ba 3d_3/2 of the barium element. Fig. 4c is related to the iron element (in BF nanoparticles), which has two peaks of 709.75 eV and 723.25 eV corresponding to Fe 2p_3/2 and Fe 2p_1/2, respectively (Anand et al., 2020; He et al., 2023).

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Fig. 4

Full XPS spectra (a) 3GO/2BF Aerogel, (b) Barium (Ba 3d) element, (c) iron element, (d) Oxygen (O 1s) element, (e) Carbon (C 1s) element, (f) Barium (Ba 4d and Ba 5p) element.

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Fig. 4d shows the spectrum of oxygen (O 1s) at the binding energy of 530.55 eV, which can be quantitatively distinguished into three different parts. The oxygen is related to metal oxides with a binding energy of 528.91 eV, metal carbonates with a binding energy of 530.98 eV and C—O located at 535.38 eV. Fig. 4e shows the C 1s peaks with a binding energy of 283.55 eV, which can be quantitatively divided into two species, which are C—C peak at 283.47 eV and C—O—C with the binding energy of 286.01 eV (Anand et al., 2020; He et al., 2023). Fig. 4f shows other peaks of barium elements corresponding to the 4d, 5s, and 5p orbitals transition. More information, including the surface area and content of each element, is listed in Table 3.

3.4 Raman spectrum analysis

Fig. 5 illustrates the Raman spectra obtained using a laser wavelength of 532 nm for barium ferrite nanoparticles, graphene oxide sheets, and graphene oxide nanoparticles/barium ferrite composite aerogel (sample 3GO.2BF). For a strong Raman signal, a shorter wavelength (532 nm) is more advantageous as the intensity of the Raman band is inversely proportional to the fourth power of the excitation wavelength (Hanson et al., 2016).

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Fig. 5

Raman spectrum of BaFe₁₂O₁₉ (BF) nanoparticle (red), pure graphene oxide (GO) (black), and graphene oxide aerogel composite (3GO.2BF) (blue).

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Two distinct bands at 1353 cm⁻¹ (D-band) and 1586 cm⁻¹ (G-band) (Budi et al., 2022; Salahdin et al., 2022) for graphene oxide (GO) indicate that after the fabrication of the graphene oxide composite aerogel, the D band remains unchanged while the peak of the G-band shifts to 1598 cm⁻¹ (Boruah et al., 2017). The relative intensity ratio of I_D/I_G was calculated to be 0.89 for graphene oxide and 1.04 for the graphene oxide composite aerogel, representing an increase from 0.89 to 1.04, indicating the augmentation of defect points and structural changes (Hanson et al., 2016; Feng et al., 2022; Sun, 2023).

Furthermore, the peaks of the barium ferrite nanoparticles (red curve in Fig. 5) used in the fabrication of the graphene aerogel composite match the peaks of the 3GO.2BF aerogel composite sample (blue curve in Fig. 5).

3.5 Thermal stability analysis using TGA and DSC

Fig. 6 shows TGA and DSC analysis of pure graphene oxide aerogel and graphene oxide aerogel/barium ferrite (3GO.2BF) composite. By examining the thermal analysis (TGA) in the GA sample, it can be seen that from the temperature of 180 to 280 °C, a weight loss of 3.93% is seen due to the release of CO, CO₂ gas (Sun, 2023) and evaporation of adsorbed water (Kim et al., 2017). After that, the decomposition of the graphite substructure begins, which results in a greater weight loss for GO aerogel at temperatures higher than 400 °C (Du et al., 2023). Graphene oxide aerogel lost 11.4% of its weight up to a temperature of 800 °C (Fig. 6a), but, the 3GO.2BF sample shows a weight loss of 3.36%. thus, 3GO.2BF aerogel nanocomposite has higher thermal stability than pure GO aerogel (Fig. 6b).

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Fig. 6

TGA curves for (a) aerogel graphene oxide (b) sample 3GO.2BF. DSC curves for (c) aerogel graphene oxide (d) sample 3GO.2BF.

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Fig. 6(c,d) is related to DSC analysis from room temperatures to 600 °C for GA and 3GO.2BF samples. As indicated in both graphs, the endothermic part is related to the evaporation of water and the exothermic part is related to the oxidation of carbon in the samples. (Sun, 2023; Kim et al., 2017; Du et al., 2023; Gonçalves et al., 2020; Mazaheri Forushani et al., 2023; Zhang et al., 2022; Du et al., 2023; He et al., 2023).

3.6 Morphological examination

Fig. 7a reveals the FESEM image of the purchased GO powder. As seen in this figure, the GO morphology is planar. Expectedly, GO has a layered structure, where the thickness of the planes is 40–50 nm. Fig. 7b shows a FESEM image of barium ferrite nanoparticles. As observed, the structure of barium ferrite nanoparticles is hexagonal planar. Based on the images, the length of the planes is around 250 nm and its thickness is about 50 nm.

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Fig. 7

SEM images of (a) GO, (b) barium ferrite nanoparticles, and (c) schematic of the hexagonal barium ferrite nanoparticles.

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Based on the microscopic images in Fig. 8, the 3D structure of GO has been formed as interlinked twisted layers. According to Fig. 8a and b, the pores present in the aerogel are micrometric. Also, the pores are nonuniform, which may have happened due to drying the GO hydrogel method.

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Fig. 8

(a–d) images of graphene oxide aerogel (GA) with different magnifications, (e–h) images of graphene oxide aerogel/ barium ferrite nanoparticles composite (3GO/2BF) as well as arrangement of nanoparticles onto the GO planes with different magnifications, (i) SEM and EDS mapping of GO/ barium ferrite aerogel.

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Fig. 8e-h reveals the FESEM images of GO aerogel /barium ferrite nanoparticles composite (3GO/2BF) with different magnifications. As observed, barium ferrite nanoparticles have been bonded to the GO planes randomly and due to van der Waals force. Barium ferrite nanoparticles have been attached and at some points agglomerated due to intrinsic magnetic properties, the small size of nanoparticles, and the use of a high weight percentage of BF nanoparticles.

It is expected that this agglomeration and nonuniform distribution on GO planes would not be useful for the absorption of electromagnetic waves since these conditions cause a reduction of magnetic loss on GO planes. Carefully inspecting these images, it is seen that in addition to GO planes, ferrite nanoparticles have also been linked at the edges of the planes, which is useful for enhancing the magnetism of aerogel composites. Also, the use of a very high percentage of barium ferrite nanoparticles causes the size of pores to diminish and the separation of GO planes to decline compared to previous samples. This elevation of weight percentage will be useful for the enhancement of saturation magnetization and the absorption of electromagnetic waves.

Fig. 8i reveals FESEM images and its EDS mapping of the graphene multiplanar surrounded by barium ferrite nanoparticles. This analysis shows the homogenous distribution of Fe and Ba elements from BF nanoparticles on the C element from GO sheets.

Fig. 9 shows the EDS diagrams of GO aerogel and GO aerogel/ barium ferrite nanoparticles composite. As seen, the level of carbon and oxygen indicates the presence of GO, while the existence of Fe and Ba elements reveals the presence of barium ferrite nanoparticles on the surface of GO nanosheets.

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Fig. 9

EDS analysis of (a) graphene oxide aerogel, (b) GO aerogel composite with barium ferrite nanoparticles additives.

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3.7 Magnetic behavior

The magnetic behavior of the samples was studied via a vibrational magnetometer. The main factors affecting the magnetic Hysteresis curve include ferrite phase content and the quality of the relationship between the magnetic phase and GO aerogel. Saturation magnetization can be associated with the fact that the distribution of barium ferrite nanoparticles within the homogeneous aerogel structure and at considerable distances from each other change the bipolar-bipolar interaction between BF nanoparticles affects the saturation magnetization. With the increase in the amount of barium ferrite nanoparticles in the sample, the saturation magnetization increases (bipolar-bipolar interaction functions) (He et al., 2023; Su et al., 2023; Zhao, 2022; Wang et al., 2020; Sharma et al., 2017).

According to Fig. 10 and Table 4, barium hexaferrite nanoparticles have hard ferrimagnetic properties. GO and GO aerogel does not have magnetic properties. With the increasing amount of barium ferrite nanoparticles in the samples, the magnetism of the samples grew due to the dense distribution of nanoparticles on the GO nanosheets with an increase in the dipole–dipole bonds. Meanwhile, in the samples, with an increase in the barium ferrite nanoparticles, as previously observed in the XRD pattern, there is an iron oxide impurity phase. This impurity has led to reduced saturation magnetization of barium ferrite nanoparticles compared to the pure state. In the GO aerogels/ barium ferrite nanoparticles composite, the saturation magnetization depends on the amount of barium ferrite nanoparticles. The lower the percentage of barium ferrite nanoparticles, the less saturation magnetization would become in proportion with the percentage. The magnetization of 3GO/BF, 2GO/BF, and 3GO/2BF samples is close to each other, where an increase in the barium ferrite nanoparticles does not have much effect on their saturation magnetization. In the GO/BF, 2GO/BF, and GO/2BF samples, with increasing the amount of barium ferrite nanoparticles, the magnetization grows from 5–7 emu/g to 13–29 emu/g. These results suggest that with a 50 wt% increase in the barium ferrite nanoparticles, the effects of magnetization on aerogel composite become evident, and gradually with an increase in the weight percentage of nanoparticles, the magnetic properties of the composite have also been enhanced.

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Fig. 10

Hysteresis loop of (a) pure go,graphene oxide aerogel (GA) and GO/BF nanocomposites, (b) the utilized barium ferrite nanoparticles.

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According to Table 4 and Fig. 10, the most coercivity of nanocomposite (H_c = 3795.16–4091.55 Oe) was enhanced as compared to pure BF nanoparticles (H_c = 3360.46 Oe). The reduction in the Hc of 3GO/2BF can be due to the separation of BaFe₁₂O₁₉ nanoparticles by GO nanosheets (He et al., 2023; Su et al., 2023; Zhao, 2022; Wang et al., 2020; Sharma et al., 2017).

3.8 EM wave behavior

In the absorption of electromagnetic waves in GO/BF composite, the most important part is examining the magnetic losses and dielectric losses of the material. If these losses are high and their values get close to each other, the maximum absorption would occur in the electromagnetic absorbent.

According to Relation (1) (Nanni and Valentini, 2011):

In Eq. (2), the real part, indicated by ${\mathrm{\epsilon }}^{\prime }$ , is called the dielectric coefficient, and determines the amount of electrostatic energy stored in the volume unit of the material at the applied field. The imaginary part, represented by ${\mathrm{\epsilon }}^{″}$ , characterizes th losses of the energy controlled through a delay in the polarization as soon as the wave propagates at the time of crossing the material (Vinay et al., 2018). The tangent of the magnetic losses is also defined as follows (Vinay et al., 2018):

In this definition, $\mathrm{t}\mathrm{a}\mathrm{n}{\mathrm{\delta }}_{\mathrm{h}}$ represents the tangent of hysteresis losses, and $\mathrm{t}\mathrm{a}\mathrm{n}{\mathrm{\delta }}_{\mathrm{e}}$ denotes the residual losses (severe losses are often prevailing at high frequencies), while $\mathrm{t}\mathrm{a}\mathrm{n}{\mathrm{\delta }}_{\mathrm{r}}$ is the tangent of vortexed flow losses (Vinay et al., 2018).

Also, to express the dielectric losses from the dielectric loss tangent, Relation (5) is used (Ghzaiel et al., 2016, Yusof, 2004).

The larger the imaginary part of the magnetic permittivity and the imaginary part of the dielectric constant, and the lower their real parts, the greater the magnetic and dielectric losses will be in that material, which is more suitable. According to impedance matching principles, when the magnetic permittivity becomes equal to the dielectric constant of a material, there would be no reflection, and the absorption is in the best state. Also, if the tangent of magnetic losses as well as the tangent of dielectric losses is close to each other, impedance matching occurs and the material has good absorption.

To explore the absorptivity of the electromagnetic waves by the GO aerogel nanocomposites containing magnetic nanoparticles, the schematics of the input electromagnetic wave and its processes were drawn in Fig. 11.

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Fig. 11

Schematic of the mechanism of interactions of incident electromagnetic waves with the nanocomposites.

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When the input wave hits the nanocomposite, three states occur reflection, absorption, and transmission. Since the samples have GO aerogel and GO planes in them are three-dimensional and have pores, when the electromagnetic wave enters and hits the surface of the sample, due to the presence of pores in aerogel, it penetrates the sample. Then, with a frequent strike to the GO planes, the electromagnetic wave energy changes into heat energy, whereby the electromagnetic wave is absorbed into the sample.

At the impact of electromagnetic waves on the GO planes, to which barium ferrite nanoparticles have been bonded, as previously observed in FESEM images, two states occur so that the electromagnetic wave would be absorbed. The first state is dielectric losses on the GO planes due to having electric conductivity and electric permittivity, which causes absorption of EM waves with the movement of electrons on the planes and their transfer to other graphene planes. Also, due to the occurrence of superficial polarization processes as well as the dipole polarization on the GO planes, EM wave absorption occurs.

The barium ferrite nanoparticles linked to GO planes cause the development of magnetic losses at the time of hitting the electromagnetic wave to them, whereby wave absorption occurs in this state. Losses of vortexed flow are one of the three parts of magnetic loss that cause the absorption of electromagnetic waves (Mazaheri Forushani et al., 2023; Sharma et al., 2017).

In the GO aerogel nanocomposites containing barium ferrite nanoparticles, due to the 3D state of graphene planes and the separation that had occurred in the graphene planes (confirmed by a wide peak at 2theta of 24° in the XRD pattern of GO aerogel) and observed in the FESEM micrograph, the dielectric losses resulting from this planar structure will be high. The presence of pores in nanocomposites causes multiple impacts of EM waves onto the graphene planes and enhances the role of dielectric losses in the absorption of electromagnetic waves.

Nevertheless, the conditions are different for magnetic losses. This is because the random and nonuniform distribution of barium ferrite nanoparticles (according to Fig. 8) causes a reduction of magnetic losses. Meanwhile, based on the XRD pattern, the detected impure phase (α-Fe₂O₃) causes a reduction of magnetic losses. These aforementioned factors affect the magnetic losses and cause a reduction of these losses compared to the dielectric losses.

According to Fig. 12, the imaginary part of the magnetic permittivity of all samples is close to zero, while the real part of the magnetic permittivity is larger than that. Thus, in the samples, the magnetic losses are not greater. The imaginary part of the dielectric constant is close to the real part of the dielectric constant; so in the composite samples, dielectric losses are better than magnetic losses. The values of the tangent of the magnetic losses are close to each other. Thus, some samples can be used as electromagnetic wave absorbents.

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Fig. 12

A) imaginary part of magnetic permittivity, b) real part of magnetic permittivity, c) imaginary part of dielectric constant, d) real part of the dielectric constant, e) tangent of magnetic losses, and f) tangent of the dielectric losses. go and sample 1 is graphene oxide nanopowders and graphene oxide aerogel.

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Adjustment of electric conductivity is one of the important parameters in creating EM wave absorbent materials. Increase in electric conductivity results in increased losses in the vortexed flow and conductivity. Meanwhile, with an elevation of electric conductivity, the extent of apparent resistance coupling between the environment and absorbent decreases. Thus, the depth of shells will be very small, and almost all electromagnetic waves will be reflected by the surface (Forushani et al., 2023b; Nanni and Valentini, 2011; Wang, 2015).

An increase in the electric conductivity leads to an enhancement in the losses of vortexed flow and conductivity. If a conductive material is placed in an alternating magnetic field, an induction current would be created in it. This current, which scatters the energy, is called eddy current loss. The extent of eddy current losses can be shown at frequencies with low magnetic current density with eddy current loss coefficient. For a sheet with “d” thickness and electric conductivity of σ, the eddy current loss coefficient (e) is expressed by Eq. (6) (Yang et al., 2016).

Also, if magnetic losses are only a result of eddy current loss, the C₀ constant, which is defined in Relation (7), should remain constant (Zhang and Cao, 2012).

Using real electric permittivity data (έ), determined based on the output of the VNA device, the conductivity values (σ_AC) can be calculated using Eqs. (8) and (9):

Here, ω represents the frequency and ε₀ denotes the electric permittivity constant in vacuum, which is equal to 8.854 × 10⁻¹² F/m, and e is the Neper number which is equal to 2.718 (Feher, 2009).

Also, to calculate the electromagnetic wave absorptivity in an absorbent, it is common to use the reflection loss parameter, which is obtained from Relation (10) (Ellwood and Legg, 1937).

Where the relative dielectric constant “ε_A” and relative magnetic permittivity “μ_A” is frequency dependent.

Also, to calculate the absorbent impedance in the normalized state, an absorbent model with a metal background is used in which case the absorbent impedance will be expressed as an Eq. (13)

Based on Fig. 13a, the conductivity of the GA sample is higher than that of other samples due to the 3D state of GO planes in the GO aerogel. In the GO aerogel composites, due to the addition of non-conductive barium ferrite nanoparticles, the electric conductivity is lower than that of GO aerogel. Nevertheless, overall the conductivity of the samples has grown slightly with the frequency elevation.

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Fig. 13

A) conductivity, b) eddy current effect, c) attenuation coefficient and, d) impedance. go and sample 1 is graphene oxide nanopowders and graphene oxide aerogel.

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According to Fig. 13b, for an increase in the eddy current losses, the absorbent should have a high thickness and electric conductivity. Nevertheless, materials with high electric conductivity have a tendency to create unstable magnetic permittivity at high frequencies, which limits their usage at high frequencies such as X-band. If the magnetic losses are only due to eddy current losses, C₀ should remain constant in Eq. (7). The eddy current effect in all samples has the same trend.

Based on Fig. 13c, the minimization of the reflection coefficient is related to the attenuation of wave amplitude at the time of transmission through the absorbent medium. In other words, the higher the attenuation coefficient, the greater the absorption will be. According to the mentioned diagram, the attenuation coefficient of the EM waves has diminished with an increase in the amount of barium ferrite nanoparticles. In Fig. 13d, the impedance of the samples has had the same trend, where the minimum value is related to GO aerogel and the maximum to the barium ferrite nanoparticles.

According to Fig. 14, it is observed that in most samples, the most internal impedance reaches one in a region of the frequency range 0–18 GHz. If the internal impedance is equal to one, the impedance matching has occurred for the samples. When we have impedance matching, absorption of electromagnetic waves occurs with a high content.

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Fig. 14

Internal impedance of the samples with varying thicknesses.

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The Em wave absorptivity in an absorbent is usually expressed through the reflection loss (RL) characteristic. At this stage, after examining the samples regarding the absorption of electromagnetic waves and all effective mechanisms, including magnetic losses, dielectric losses, an increase of electric conductivity, and impedance matching for every single sample, their RLs are shown in Table 4. Also, Fig. 15 has drawn the RL curve for all samples.

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Fig. 15

RL curve of all samples with varying thicknesses.

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GO, barium ferrite nanoparticles, and GO aerogel do not have much RL value since within the frequency range 0–19 GHz, dielectric losses in GO and GO aerogel alone cannot be a factor for electromagnetic wave absorption. These conditions also apply to barium ferrite nanoparticles by having magnetic losses alone. Nevertheless, barium ferrite nanoparticles at higher frequencies can be absorbent of electromagnetic waves, and for this absorption by barium ferrite nanoparticles at X-band, either some elements should be doped in barium ferrite.

The 3GO/BF, 2GO/BF, and 3GO/2BF samples have three RL values above 10 dB at a thickness of 1–5 mm. The high saturation magnetization of the samples, as well as the high weight percentage of the barium ferrite nanoparticles compared to the GO sample, can explain the three RL peaks.

By investigating the RL curves of all samples, the best RL with −43 dB has occurred at a frequency of 12.1 GHz with a frequency range of 11–13.4 GHz at a thickness of 4 mm related to the 3GO/2BF sample. As shown in Table 4, 3GO/2BF aerogel composite show less coercivity than other samples due to the good separation of BF nanoparticles by GO nanosheets. The GO aerogel nanocomposite containing 40 wt% barium ferrite nanoparticles with a thickness of 4 can be used as an absorbent of electromagnetic waves. Other absorption properties of the electromagnetic waves of the samples are presented in Table 5.

Comparing the results of the present research with other studies (Table 6), it is seen that the best RL value obtained in this research is −43 dB as bicomponent aerogel; considering the bicomponent nature of the final product, it has had suitable RL compared to other aerogels with three components (Zhao et al., 2017; Zhang et al., 2018; Gupta et al., 2019; Feng et al., 2016; Wang et al., 2020; Ding et al., 2016; Wang et al., 2013; Zhang et al., 2016; Xu et al., 2018; Zhang et al., 2014; Zhang et al., 2016; Huang et al., 2018; Gordani et al., 2022; Wang et al., 2015; Liu et al., 2019). The bulk density of 3GO/2BF aerogels (Table 6) was 8.4 mg/cm³, which was lower than the 3 components of EM wave aerogels (∼10–14 mg/cm³) (Zhao et al., 2017; Zhang et al., 2018; Zhang et al., 2016; Zhang et al., 2016).

Due to the high specific surface area of graphene oxide nanosheets and its good wettability, their loading capacity for metal oxide nanoparticles such as barium ferrite is high. However, very large amounts of magnetic nanoparticles may increase the magnetic and dielectric parameters too much and decrease the impedance matching with the free space. Therefore, different amounts of different concentrations of barium ferrite nanoparticles (from 25 wt% to 67 wt%) were used in this research (see loading ratio in Table 2). Results show that the sample with loading 40% BF nanoparticle on GO nanosheets show the highest reflection loss value (RL = −43 dB).