Retracted Article: A versatile strategy for alternately arranging the foam ratio layers of multilayer graphene/thermoplastic polyurethane composite foams towards lightweight and broadband electromagnetic wave absorption

Abstract

A broadband electromagnetic wave (EW) absorbing material should possess both wider effective absorption bandwidth and lower minimum reflection loss, depending on good impedance matching between the absorber and air and strong attenuation of EW. In this study, single-layer graphene/thermoplastic polyurethane (TPU) composite foams with different foam ratios and alternating multilayer graphene/TPU composite foams with different numbers of layers were prepared. Not only was the EW-absorbing mechanism of these composite foams examined, but also the relationship between the EW-absorbing properties and the number of layers were investigated. The single-layer sample S-5 with good impedance matching characteristics and S-3 with strong EW attenuation characteristics were selected as the constituent layers to design alternating multilayer graphene/TPU composite foams. Compared to the single-layer sample 4L-C (4L-C is defined as the monolayer sample S-4 with a thickness of 9 mm), the 4L alternating multilayer graphene/TPU composite foams could achieve more than 90% EW absorption in a wide frequency band of 8.5 GHz, and its minimum reflection loss was as low as −37.67 dB, which are very beneficial for its use as a lightweight, flexible electromagnetic wave absorbing material (EWAM) for broadband absorption. More importantly, the absorption of the obtained alternating multilayer composite foams could be simply modulated not only by the absorber thickness, but also by the number of layers to satisfy the applications in different frequency bands.

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1. Introduction

Electromagnetic wave (EW) irradiation generated during the use of electronic equipment increasingly causes serious electromagnetic wave pollution and can seriously endanger the ecological environment and human physical and mental health.^1–3 Therefore, the research and development of electromagnetic wave-absorbing materials (EWAMs) is of great significance and has aroused great interest in both academic and industrial fields. Polymeric composites, owing to their flexibilities for structure design and property modulation, light weight, and good processability, have been widely used in the design and implementation of EWAMs.^4–6

Dielectric absorbents, such as carbon nanotubes (CNTs),^7–9 carbon fibers (CFs),^10,11 and graphene and its derivatives,^12–14 due to their light weight, high conductivity, high aspect ratio, good resistance against corrosion, and excellent mechanical properties^15–18 have been added into polymer matrixes to achieve EW-absorbing properties. The most important features of these absorbents are their strong absorption capacity (reflection loss, RL) and broad effective absorption bandwidth (EB, RL < −10 dB, for 90% energy absorption).¹⁹ To obtain a lower reflection loss, numerous absorbents are generally required. However, employing a large amount of absorbents into polymer matrices will increase the fabrication cost and also is not conducive to the lightening of the EWAMs. Furthermore, the raised dielectric constant caused by the increased absorbent content narrows the effective bandwidth, limiting the use of these materials as EWAMs.²⁰ Therefore, enhancing the EW-absorbing efficiency of EWAMs at the lower absorbent addition rate has been the focus of many researchers.

Methods to cut down the absorbent addition, such as by modification with magnetic fillers^21–24 and the employment of multiple absorbents,^25–27 have been studied extensively. For example, He et al.²⁸ coupled flaky carbonyl iron (FCI) and reduced graphene oxide nanosheets in a homogenous composite to optimize characteristic impedance matching. Zhou et al.²⁹ designed hierarchical metal–organic framework (MOF)-derived Co/C@V₂O₃ hollow spheres to endow the composites with large dielectric and magnetic losses. Zhou et al.³⁰ explored porous heterogeneous Fe₇Co₃/ZnO nanosheets with tunable dielectric loss and magnetic loss for enhanced absorption over a wide frequency range (7.92 GHz). Nevertheless, the complicated preparation processes and high costs restrict the application of these techniques. The distribution of absorbents in the polymer matrix has a significant effect on reducing the content of absorbents and enhancing the EW-absorbing performance.^31–34 Therefore, the relationship between the dispersion of absorbents and the EW-absorbing performance has been investigated extensively.^35–37 Some researchers have found that preferentially distributed absorbents are good for the absorption of EW radiation.^38–42 Gao et al. found that selectively dispersing graphene in porous graphene/TPU composites helps the formation of electrically conductive pathways in cell walls to obtain high dielectric loss. Moreover, the plenty of air contained in cells makes the characteristic impedance of the polymer-based composites close to air, reducing the reflection of electromagnetic waves on the surface of the EWAMs.⁴³

Among various dielectric absorbents, graphene, which has many excellent properties such as light weight, admirable thermal conductivity and satisfactory corrosion resistance, has the potential to be employed in a polymer matrix to obtain EWAMs based on its excellent electrical conductivity and dielectric property, which can contribute to the dissipation of absorbed electromagnetic energy.^43–45 However, graphene easily forms a conductive network structure in a polymer matrix due to its large specific surface area and aspect ratio, which prevents electromagnetic waves from propagating the interior of the polymeric composites. Therefore, most publicly reported articles are usually based on modified graphene^46,47 or added magnetic absorbing agents, such as carbonyl iron and ferrite,^48,49 to obtain matching impedance for realizing efficient EW-absorption. However, to their practical applications are limited due the large amount of additives, high cost, complex preparation process, and long production cycle. If graphene could be selectively distributed in a polymer matrix by means of foaming, the adverse factors during the preparation process could be cleverly eliminated and the fantastic EW-absorbing properties could be realized.⁴³

On account of the merits, such as ease of processing and low cost, structure design has gradually become a widely accepted method to reduce the amount of the absorbent without damaging the EW-absorbing properties.^50–53 As a special morphology, the laminar structure with absorbents preferentially distributed in each layer can be regarded as an effective way of reducing the absorbent content.⁴⁰ Multilayered structure design has a great effect on adjusting impedance matching and enhancing the ability of EWAMs to attenuate electromagnetic waves,^39,54,55 thus obtaining high-efficiency EW-absorbance and reducing the addition of absorbents. Particularly, the alternating multilayer structure, as a co-continuous morphology, can lead to EWAMs with excellent EW-absorbing properties.⁴¹ For example, Liu et al.⁵⁶ found that the CoFe₂O₄/carbonyl iron composite with a double layer could broaden the effective absorption bandwidth to 9.4 GHz. Although researchers have found that the alternating multilayer structure shows great potential in the manufacture of EWAMs, to the best our knowledge, polymer-based composite foams with different foam ratios—obtained by foaming to selectively distribute graphene in a polymer matrix—that are alternately arranged in multilayers to meet the principle of impedance matching and strong attenuation capacity have rarely been studied and the relationship between the EW-absorbing properties and layer number is still ambiguous.

In this study, alternating multilayer EWAMs made by alternately arranging polymer-based composite foams with different foam ratios in the multilayer structure were designed and fabricated. The balance between impedance matching and a strong attenuation capacity was achieved by alternately arranging an impedance matching layer with a high foam ratio and a strong attenuation layer with a low foam ratio. Moreover, these well-defined cell structures containing plenty of air are beneficial for reducing the reflection of EWs on the surface of the EWAMs. Simultaneously, a low-density porous structure contributes to the use of alternating multilayer polymer-based composite foams as lightweight EWAMs. In addition, the multiple reflections of EWs between the layer interfaces facilitate the dissipation of EW energy inside the material. Thermoplastic polyurethane (TPU) was used as the polymer matrix owing to its satisfactory properties, such as flexibility, excellent compressible recovery, weathering, good processability, and low temperature resistance.^57–60 Graphene was selected as the dielectric absorbent because of its excellent electrical conductivity, and it can easily form electrically conductive pathways in cell walls to obtain high dielectric loss.⁴³ The effects of the layer number on the EW-absorbing property and the mechanism of the alternating multilayer structure to improve the EW-absorbing properties were investigated.

2. Experimental section

2.1 Materials

All the chemical reagents were commercially available and were used without further purification. A polyester-based TPU elastomer (Elastogran S85A) was obtained from BASF (Germany). Graphene (XTG-P-0762) was supplied by the Deyang Carbonene Co. Ltd (China). N,N′-Dimethyl formamide (DMF) and 1,4-dioxane were purchased from Kelong Reagent Co. Ltd (China).

2.2 Specimen preparation

Solution mixing was used to prepare graphene/TPU composites. Here, 2 g of graphene was first added into a beaker with 300 mL of DMF and the mixture was then sonicated (1000 W) for 40 min. Then, 700 mL of the TPU/DMF solution was added to the mixture and was magnetically stirred for 5 h at 25 °C. The resultant solution was integrated with excess deionized water, and the precipitate obtained after filtration was dried at 80 °C for 48 h to wipe off the epibiotic solvent.

Graphene/TPU composite foams were obtained by a thermally induced phase separation (TIPS) process.^60–64 The as-prepared graphene/TPU composites were dissolved in 1,4-dioxane and stirred for 5 h at 60 °C. The dispersed solutions with different concentrations, shown in Table 1, were poured into an undefiled metal mold with a length and width of 200 mm, and then placed in a low temperature test chamber at a constant temperature of −60 °C for 1 h. The frozen mixture was then transferred into a vacuum freeze dryer (LGJ-10FD, Yaxing Instrument Science and Technology Development Co., Ltd.) for 36 h at 0 °C. The resultant foam was then dried at 80 °C for 24 h to remove the residual 1,4-dioxane. The single-layer graphene/TPU composite foams with different foam ratios (samples S-1, S-2, S-3, S-4, and S-5) were obtained by changing the concentration of the pouring solution. The higher the pouring solution concentration, the larger the volume fraction of the graphene/TPU composite, resulting in a larger constraint effect of the cell wall composed of these composites on the cell growth. Thus, the composite foam obtained by pouring a higher concentration exhibited a smaller cell size and smaller expansion ratio. The alternating multilayer graphene/TPU composite foams with layer numbers of 2, 4, 6, 8, and 10 (samples 2L, 4L, 6L, 8L, and 10L, respectively) were obtained by bonding a plurality of single-layer samples of different foam ratios with commercial glue. Because the foam ratio was regulated by the pouring solution concentration, the foam ratio of the monolayer sample S-4 should be the same as the average foam ratio of the 2L and 4L multilayer samples obtained by alternately arranging samples S-3 and S-5. Therefore, the samples constituting the single-layer contrast sample S-4 with the same average foaming rate as the multilayer samples 2L and 4L were defined as 2L-C and 4L-C with the thicknesses of 7 mm and 9 mm, respectively. The pouring concentration, density, graphene content, electrical conductivity, foam ratio, and porosity of the single-layer graphene/TPU composite foams are presented in Table 1.

Table 1 The pouring concentration, densities, graphene content, electrical conductivity, foam ratio, and porosity of single-layer graphene/TPU composite foams with different foam ratios

Sample	S-1	S-2	S-3	S-4	S-5
Pouring concentration (g ml^−1)	12	10	8	6	4
Density (g cm^−3)	0.24	0.20	0.16	0.14	0.09
Graphene content (vol%)	2.3	2.3	2.3	2.3	2.3
Conductivity (10^−9 S cm^−1)	602.8	268	35.8	0.56	0.17
Foam ratio	3.3	4.0	4.9	5.6	8.6
Porosity	70%	75%	80%	82%	88%

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2.3 Characterization and testing

The morphology of the samples was determined using a scanning electron microscope (SEM, JEOL JSM-5900LV) under an accelerating voltage of 20 kV. The samples were cryo-fractured in liquid nitrogen, and the fractured surfaces were coated with a layer of gold in a vacuum chamber prior to visualization by SEM.

The expansion ratio ϕ of the foams was calculated using the eqn (1).⁶⁵

where ρ and ρ_f are the densities of the nonfoamed and foamed graphene/TPU composites, respectively, and was tested using a MDMDY-350 automatic density instrument (Meidi Analytical Co., Ltd., China).

The porosity P of single-layer foams was calculated using the eqn (2).⁶⁶

The electrical resistivities of S-1, S-2, S-3, S-4, and S-5 were obtained using a programmable insulation resistance tester (YD9820A). The sizes of all the samples were 10 mm in length (l), 10 mm in width (w), and 2 mm in thickness (t). A constant voltage of 1 V was applied to the samples, unless otherwise specified. The electrical conductivity, σ, was calculated by the following equation:

where R_V is the trial electrical resistance. At least five samples were tested in each case, and the average values were calculated. Conductive silver glue was used to enhance the electrical contact between the electrodes and samples.

The electromagnetic parameters, complex relative permittivity (ε_r = ε′ − jε′′) and permeability (μ_r = μ′ − jμ′′) of the five single-layer graphene/TPU composite foams with different foam ratios, which were processed into a concentric annular shape with an outer diameter of 7 mm, an inner diameter of 3.04 mm, and a fixed thickness of 3 mm, as measured by a vector network analyzer using the coaxial-line method (N5230A, Agilent Technologies Co., LTD) in the range of 2–18 GHz. The electromagnetic wave absorbing properties of all the multilayer samples were calculated according to the transmission line theory described in Section 3.1.

3. Results and discussion

3.1 Theory of EW absorption

Fig. 1 reveals a multilayer model containing n layers of different materials, while a metal plate was used as its reflective backing. The parameter d_i is the thickness of the ith layer, η_r is the complex intrinsic impedance of the ith layer, γ_i is the propagation constants of the ith layer (i = 1, 2, 3…, n), and ε₀ and μ₀ are the permittivity and permeability of the free space, respectively.

Fig. 1 Schematic of a multilayer model with a normally incident wave (d_i, ε_ri, and μ_ri are the thickness, complex permittivity, and permeability of the ith layer, respectively.).

According to the transmission-line theory,^67,68 the wave impedance, Z_i, of the ith layer can be calculated using the equation:

where η_i and γ_i are given as:where ε_ri and μ_ri are the complex relative permittivity and permeability of the ith layer, respectively, and η₀ is the characteristic impedance of free space. Based on the use of a metal conductor as the reflective backing, the characteristic impedance of the first layer is given by the following equation:

Z₁ = η₁ tanh(γ₁d₁) (7)

where η₁ is the intrinsic impedance of the first layer. The reflection loss (RL) of the incident EW can be obtained using the following equation:

In which the input impedance of the EW absorbing layer, Z_ri, is given by:

where ε_r and μ_r are the complex relative permittivity and permeability of the EWAMs, respectively, c is the velocity of light in free space, and f and d are the frequency and sample thickness, respectively.

As a result, the EW-absorbing properties of the alternating multilayer composite foams containing n layers of materials with different foam ratios can be calculated using the eqn (4)–(9).

3.2 EW-absorbing properties of single-layer graphene/TPU composite foams

Single-layer graphene/TPU composite foams with the same graphene content but different foam ratios were prepared via the TIPS method. The well-defined closed cells, which can be observed in Fig. 2a–e, gradually changed from spherical to a polygonal shape with the increase in foam ratio. The physical barrier action of graphene on the cell growth causes a deformation of the cell wall.⁶⁹ In addition, Fig. 2f–j indicate that the mean pore sizes increased with the increment in foam ratio.

Fig. 2 SEM images (a–e) and pore size distribution (f–j) of single-layer graphene/TPU composite foams with different foam ratios: a and f: (S-1); b and g: (S-2); c and h: (S-3); d and i: (S-4); e and j: (S-5).

Fig. 3 shows SEM images of a brittle fracture cross-section of sample S-3 etched by DMF. As illustrated in the figure, after the polymeric matrix TPU was etched by DMF, the selective distribution of graphene sheets along the cell walls can be seen clearly. Compared with the graphene/TPU composite foams without etching in Fig. 2c, it can be seen that the graphene skeleton was encapsulated into the TPU matrix. Owing to this admirable selective distribution of graphene sheets and integrated encapsulation structure, a good three-dimensional (3D) conductive network structure and favorable mechanical properties were simultaneously achieved by the graphene/TPU composite foams.

Fig. 3 SEM images of the brittle fracture cross-section of sample S-3 etched by DMF.

Fig. 4a–c show the frequency dependence of ε′ and ε′′ and tan δ of the single-layer samples S-1, S-2, S-3, S-4, and S-5. In Fig. 4a, the ε′ values of all the single-layer samples slightly decreased in the range of 2–18 GHz. Furthermore, the ε′ value of S-3 outclassed the other samples, indicating that a good conductive network was formed by the interaction with the bound charges, which is good for the dissipation of electromagnetic energy. As demonstrated in Fig. 4b, we can observe that the ε′′ values of S-1, S-2, and S-5 are almost constant, while those of S-3 and S-4 are dependent on the frequency. The imaginary part of the permittivity (ε′′) of S-3 was the highest among all single-layer samples, attributed to the conduction current arising from free electrons in the excellent conductive path according to the free electron theory.⁷⁰ On the basis of the data in Fig. 4c, the tan δ values of S-1, S-2, and S-5 showed a little fluctuation, while those of S-3 and S-4 were significantly higher than those of S-1, S-2, and S-5, suggesting that S-3 and S-4 have a strong dissipation ability for electromagnetic energy.

Fig. 4 Real parts (ε′), imaginary parts (ε′′) of the complex permittivity (a, b) and tan δ (c) spectra of single-layer graphene/TPU composite foams with different foam ratios in the frequency range of 2–18 GHz.

It is known that the tan δ is the quotient of the real and imaginary parts of relative permittivity, which is demonstrated by the following equation:

Also, ε′ and ε′′ are given by the following equations:

where ω is the angular frequency, τ is the polarization relaxation time, ε_s is the static permittivity, ε_∞ is the relative dielectric permittivity at the high frequency limit, σ is the conductivity, and ε₀ is the dielectric constant in a vacuum (ε₀ = 8.851 × 10⁻¹² F m⁻¹).^4,71

According to eqn (10)–(12), a higher tan δ can be obtained by increasing the conductivity. When the foam ratio was increased from 3.3 to 8.6, as shown in Fig. 5, the conductivity decreased significantly. The high conductivity was produced by the three-dimensional conductive network structure, which was induced by graphene's selective dispersion and alignment in the pore struts,^72,73 as can be observed in Fig. 5b. Sample S-5 exhibited a very low conductivity of 1.7 × 10⁻¹⁰ S cm⁻¹, indicating that the incident electromagnetic wave can enter into sample S-5 on account of the good impedance matching with air. Samples S-1, S-2, and S-3 with higher conductivity had larger dielectric loss constants, tan δ, which means they have a higher ability to dissipate electromagnetic energy.

Fig. 5 (a) The electrical conductivity of single-layer graphene/TPU composite foams with different foam ratios. (b) The three-dimensional conductive network structure of sample S-3.

The characteristic impedance η_r can be calculated using the following equation:^74,75

The attenuation constant α is introduced to describe the integral attenuation ability based on the following equation:^76,77

Therefore, the values of η_r and α for the single-layer foamed graphene/TPU composites with different foam ratios were calculated by eqn (13) and (14) and the results are demonstrated in Fig. 6a and b. As shown in the figures, the increment in the foam ratio leads to an increase in the characteristic impedance η_r, except for S-3, which could be ascribed to the large amount of air filled inside the cells and as increasing the foam ratio leads to an increment of the cell size, shown in Fig. 2, so more air is filled in the foamed graphene/TPU composites with higher foam ratios. Among these, S-5 possessed a characteristic impedance closer to air, indicating that more electromagnetic waves will penetrate the surface of the sample and enter the interior of the material, which will facilitate the use of S-5 as an impedance matching layer for multilayer EWAMs. As for the case of S-3, this may be attributed to the formation of a good three-dimensional conductive network structure after foaming, which will be detrimental to impedance matching. Fortunately, based on the formation of this good three-dimensional conductive network, the attenuation constant α of S-3 was much larger than that of the other four single-layer samples, as illustrated in Fig. 6b, giving rise to the incident electromagnetic wave energy being greatly dissipated, which is significant for using S-3 as a strong electromagnetic wave attenuation layer in multilayer EWAMs.

Fig. 6 Characteristic impedance (a) and attenuation constant (b) of single-layer graphene/TPU composite foams with different foam ratios in the frequency range of 2–18 GHz.

According to the transmission-line theory, the RL of the single-layer samples S-1, S-2, S-3, S-4 and S-5 could be calculated using the eqn (8) and (9). Fig. 7a–e show the frequency dependence of the reflection loss (RL) of the single-layer samples S-1, S-2, S-3, S-4, and S-5 when the thickness increases from 5 to 10 mm. It turned out that the minimum reflection loss RL_min of the samples S-1, S-2, S-3, S-4, and S-5 were −35.38, −25.05, −36.55, −15.70, and −29.97 dB at thicknesses of 8, 8, 5, 10, and 9 mm, respectively. However, the EB values of the single-layer samples as described above were only 1.3, 2.2, 3.6, 2.1, and 2.7 GHz at the corresponding thicknesses, respectively. These unsatisfactory EB values mean it is still difficult to meet the requirements for use as broadband EWAMs.

Fig. 7 Three-dimensional reflection loss plots of single-layer graphene/TPU composite foams with different foam ratios when the thickness increases from 5 to 10 mm: a: (S-1); b: (S-2); c: (S-3); d: (S-4); and e: (S-5).

In summary, sample S-5 with a relatively higher characteristic impedance proved to have good impedance matching with air, while sample S-3 with a relatively higher attenuation constant exhibited the best EW-absorbing properties. Therefore, to achieve satisfactory EW-absorbing properties, samples S-3 and S-5 were selected as component layers to prepare alternating multilayer EWAMs.

3.3 EW-absorbing properties of alternating multilayer graphene/TPU composite foams

In this study, we designed an alternating multilayer model composed of S-3 and S-5 layers, the schematic of which is shown in Fig. 1. The layer number for the research models 2, 4, 6, 8, and 10 were denoted as 2L, 4L, 6L, 8L, and 10L, respectively. The cross-sectional morphologies of the 2L, 4L, and 6L alternating multilayer graphene/TPU composite foams are shown in Fig. 8. As shown in Fig. 8a–c, the layer interface can be easily observed. Also, the difference in cell size between adjacent layers was relatively large, and the cells in the S-5 layer were much larger than in the S-3 layer with the increase in foam ratio. The thickness of each layer of the alternating multilayer sample was also basically the same, avoiding the problem that the input impedance was not uniformly changed by the uneven thickness of the layer.

Fig. 8 Cross-sectional morphologies of 2L, 4L, and 6L alternating multilayer graphene/TPU composite foams: (a): 2L; (b): 4L; (c): 6L.

The RL of the models with different layer numbers was calculated by eqn (4)–(8). Fig. 9 shows the relationship of RL and the frequency of the alternating multilayer models. It can be seen from the figure that the 2L, 4L, 6L, 8L, and 10L samples achieved the minimum reflection loss RL_min at thicknesses of 7, 9, 9, 10, and 10 mm, respectively. We calculated the RL_min and EB values for all the multilayer samples at the optimal thickness, as shown in Table 2. As can be seen from Table 2, sample 4L with the thickness of 9 mm possessed the lowest RL_min of −37.67 dB, and its EB value was as wide as 8.5 GHz and it produced a three-peak absorption, with the quarter-wavelength cancellation model applied to decipher its mechanism. In the quarter-wavelength cancellation model, the relationship between the absorber thickness (t_m) and the matching frequency (f_m) can be described by the following equation:^78,79

Fig. 9 Calculated reflection loss plots of alternating multilayer models when the thickness was increased from 5 to 10 mm: (a): 2L; (b): 4L; (c): 6L; (d): 8L; (e): 10L.

Table 2 EW-absorbing properties of alternating multilayer graphene/thermoplastic polyurethane composite foams consisting of S-3 and S-5 layers

Sample	2L (7 mm)	4L (9 mm)	6L (9 mm)	8L (10 mm)	10L (10 mm)
Average foam ratio	5.6	5.6	5.6	5.6	5.6
EB (GHz)	4.9	8.5	2.4	3.3	3.5
RLmin (dB)	−35.66	−37.67	−23.00	−23.17	−23.18

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Based on eqn (15), when the EW reflected from the layer interface and the absorber–metal reflective backing interface are out of phase by 180°, EW interference elimination occurs.^80,81 Also, the quarter-wavelength cancellation model can be applied to illustrate why RL_min shifted toward the lower frequency band with the increment in absorber thickness. On the basis of the above theory, the three-peak absorption, produced by sample 4L, may be due to the interference cancellation, resulting from matching the thickness and frequency.^79,82–84 However, when the number of layers reached 6 or more, the RL–frequency curves under the different layer numbers were almost the same, which means that at higher layers, the increasing number of layers is almost negligible for the improvement in the EW-absorbing properties. The reason for this phenomenon may be due to the effect of ambiguity of the interface becoming increasingly obvious with the increment in the layer number.⁸⁵ As for sample 2L, it exhibited good EW-absorbing properties at lower layers and lower thicknesses, compared to the 6L, 8L, and 10L samples, with a minimum reflection loss of −35.66 dB at 7 mm thickness and an EB value of 4.9 GHz. Therefore, samples 2L and 4L with better EW-absorbing properties were selected for further study.

The 2L and 4L alternating multilayer graphene/TPU composite foams were compared with the corresponding single-layer samples (2L-C and 4L-C) with the same average foam ratio at the thicknesses of 7 and 9 mm, as shown in Fig. 10, respectively. As can be seen from Fig. 10 and Table 3, all the RL_min values of the alternating multilayer samples are much lower than those of the corresponding single-layer samples, so S-3 and S-5 were selected as the strong EW attenuation layer and the impedance matching layer, respectively, to design an alternate multilayer structure, which is very beneficial for enhancing the EW-absorbing capability. Moreover, the EB value of the alternating multilayer sample 4L (8.5 GHz) was also much wider than that of the single-layer sample 4L-C (4.6 GHz), which was due to the introduction of the impedance matching layer S-5, reducing the reflection of the incident EW on the surface of the absorber, and the increased percentage of the electromagnetic wave propagated into the absorber inside by the strong attenuation layer S-3. Simultaneously, the interference cancellation caused by multiple reflections at the layer interface also fortified the electromagnetic energy dissipation.

Fig. 10 Reflection loss (RL) spectra of alternating multilayer EWAMs and the corresponding single-layer samples of the same average foam ratio at the thicknesses of 7 and 9 mm, respectively: (a): 2L (7 mm); (b): 4L (9 mm).

Table 3 EW-absorbing properties of 2L, 2L-C, 4L, and 4L-C

Sample	2L (7 mm)	2L-C (7 mm)	4L (9 mm)	4L-C (9 mm)
Average foam ratio	5.6	5.6	5.6	5.6
EB (GHz)	4.9	5.9	8.5	4.6
RLmin (dB)	−35.66	−13.87	−37.67	−15.07

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Fig. 11 shows the EW-absorbing mechanism of the alternating multilayer EWAMs. As shown in Fig. 11a, the mechanism of the alternating multilayer structure to effectively enhance EW-absorbing performance lies in the following three aspects: first, the introduction of the impedance matching layer (S-5) reduces the reflection of electromagnetic waves on the surface of the EWAMs, aggrandizing the percentage of incident electromagnetic waves entering the interior of the absorber, which is beneficial for increasing the dissipation of electromagnetic energy inside the absorber. Second, the multilayer structure increases the multiple reflection of electromagnetic waves at the layer interface, which facilitates the interference cancellation of electromagnetic waves. Moreover, this multiple reflection prolongs the transmission path of the electromagnetic waves inside the absorber, increasing its decay time. Third, the abrupt change in the cell size alters the transmission path of the electromagnetic wave inside the EWAMs: when the EW propagates into the interior of the EWAMs, it actually passes through not only the cell wall composed of the graphene/TPU composites but also the cells whose size is changed from large to small in the alternating multilayer structure. The skin depth of electromagnetic waves in the graphene/TPU mixture is small, but it is extremely high inside the cells.⁴³ Due to the presence of cells whose size abruptly changes, the EW actually only penetrates the thin cell wall, so the EW can still propagate into the multilayer EWAMs well and be attenuated.

Fig. 11 (a) EW-absorbing mechanism diagram of alternating multilayer graphene/TPU composite foams; (b) microscopic mechanism of the three-dimensional conductive path in EW energy dissipation.

In Fig. 11b, the microscopic mechanism of EW energy dissipation is discussed: first, the cell structure existing in the system augments the interface inside the material, so that EWs can generate multiple reflections inside these cells, which is then gradually dissipated; second, the closed loop formed by the graphene distributed along the cell wall generates an induced current to further dissipate the EW energy under the alternating electric field of the EW; third, the parallel distributed conductive graphene and the insulated TPU substrate between them form a microcapacitor structure called a “plate-dielectric-plate.” The hysteresis effect of these miniature capacitors when interacting with EWs also consumes part of the EWs.

According to the transmission-line theory, the characteristic impedances (Z_ri) of alternating multilayer EWAMs were calculated using the eqn (5)–(7), and the characteristic impedance (Z_ri) of the single-layer EWAMs can be given by eqn (9). The normalized impedance, Z = Z_ri/Z₀, was used to estimate the impedance matching characteristic. If the absorber possesses a better impedance matching characteristic, the modulus of Z should be infinitely close to 1.⁸⁶ Fig. 12 shows the |Z| versus frequency curves for the 2L and 4L alternating multilayer graphene/TPU composite foams and the corresponding single-layer samples 2L-C and 4L-C at the thicknesses of 7 and 9 mm, respectively. It is pretty clear that the |Z| values for 2L, 2L-C, 4L, and 4L-C are in the ranges of 0.06–1.67, 0.15–0.89, 0.16–1.26, and 0.15–0.81, respectively. It can clearly seen that the |Z| values of the alternating multilayer samples 2L and 4L are significantly closer to 1 than the corresponding single-layer samples 2L-C and 4L-C, especially at a higher frequency band. Good impedance matching, as shown in Fig. 12, between the multilayer samples and air explains why lower minimum reflection losses and wider effective absorption bandwidth occur.

Fig. 12 The |Z| versus frequency curves for the 2L and 4L alternating multilayer graphene/TPU composite foams and for the corresponding single-layer samples 2L-C and 4L-C at the thicknesses of 7 and 9 mm, respectively.

4. Conclusion

In this study, single-layer graphene/TPU composite foams with different foam ratios and alternating multilayer graphene/TPU composite foams with different numbers of layers were prepared. Not only were the EW-absorbing mechanisms of these composite foams examined, but the relationship between the EW-absorbing properties and the number of layers were also investigated. The obtained results are as follows:

(1) Among all the single-layer graphene/TPU composite foams with different foam ratios, the characteristic impedance of sample S-5 with a foam ratio of 8.6 was closest to air, indicating that S-5 was best to use as an impedance matching layer. Sample S-3 with a higher dielectric loss and attenuation constant was optimal for achieving the best EW-absorbing performance, meaning sample S-3 can serve as a candidate for a strong EW attenuation layer.

(2) The 2L and 4L alternating multilayer samples obtained by alternately arranging S-3 and S-5 to realize excellent impedance matching characteristics and strong attenuation capacity exhibited excellent EW-absorbing properties at the thicknesses of 7 and 9 mm, respectively. Compared to the single-layer samples 2L-C and 4L-C, the alternating multilayer samples exhibited lower RL_min and wider EB values.

(3) The absorption of the obtained alternating multilayer composite foams could be simply modulated not only by the absorber thickness, but also by the number of layers to satisfy applications in different frequency bands. More importantly, the 4L alternating multilayer graphene/TPU composite foams could achieve more than 90% EW absorption in a wide frequency band of 8.5 GHz and had a minimum reflection loss as low as −37.67 dB, which is beneficial for its use as a lightweight, flexible EWAM for broadband absorption.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors are grateful to the National Natural Science Foundation of China (51473103 and 51873112) for financial support for this work.

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