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Dielectric Characteristics and Microwave Absorption of Graphene Composite Materials Kevin Rubrice 1,2, *, Xavier Castel 2 , Mohamed Himdi 2 and Patrick Parneix 1 1 2

*

DCNS Research Technocampus Océan, 5 rue de l’Halbrane, 44340 Bouguenais, France; [email protected] Institut d’Electronique et de Télécommunications de Rennes (IETR, UMR-6164)/Institut Universitaire de Technologie de Saint-Brieuc/Université de Rennes 1, 18 rue Henri Wallon, 22004 Saint-Brieuc & 263 avenue du Général Leclerc, 35042 Rennes, France; [email protected] (X.C.); [email protected] (M.H.) Correspondence: [email protected]; Tel.: +33-223-237-253

Academic Editors: Juergen Stampfl and Arne Berner Received: 12 September 2016; Accepted: 2 October 2016; Published: 13 October 2016

Abstract: Nowadays, many types of materials are elaborated for microwave absorption applications. Carbon-based nanoparticles belong to these types of materials. Among these, graphene presents some distinctive features for electromagnetic radiation absorption and thus microwave isolation applications. In this paper, the dielectric characteristics and microwave absorption properties of epoxy resin loaded with graphene particles are presented from 2 GHz to 18 GHz. The influence of various parameters such as particle size (3 µm, 6–8 µm, and 15 µm) and weight ratio (from 5% to 25%) are presented, studied, and discussed. The sample loaded with the smallest graphene size (3 µm) and the highest weight ratio (25%) exhibits high loss tangent (tanδ = 0.36) and a middle dielectric constant ε0 = 12–14 in the 8–10 GHz frequency range. As expected, this sample also provides the highest absorption level: from 5 dB/cm at 4 GHz to 16 dB/cm at 18 GHz. Keywords: multifunctional composite materials; graphene; physical properties; analytical modeling; electromagnetic absorption; complex dielectric constants

1. Introduction Graphene is made out of a two-dimensional carbon structure in hexagonal lattice with a nanosizing in the perpendicular direction. It presents interesting thermal, mechanical, and electrical properties [1] along with light weight and high electrical characteristics: electron mobility µ = 230,000 cm2 ·V−1 ·s−1 [2] and conductivity σ (σ = 400 S·m−1 in the powder form [3] and σ = 5 × 106 S·m−1 in thin layer form [4]). Another graphene characteristic has been highlighted in recent years: its microwave absorption and electromagnetic shielding abilities. Different materials with graphene particles have therefore been studied [5–8] and show interesting electromagnetic absorption feature. For example, the use of chemically reduced graphene oxide with residual defects improves the electromagnetic wave absorption through additional relaxation processes, namely dielectric, dipole, and polarization relaxations. Microwave reflection loss as much as −6.9 dB is then obtained at 7 GHz [5]. Graphene-polymethylmethacrylate nanocomposite microcellular foams present high electromagnetic interference shielding efficiency (13–19 dB at 8–12 GHz) by favoring multireflections and scattering of the incident microwaves into the foam samples [6]. Graphene sheets with polyaniline nanorods embedded in a paraffin matrix show microwave reflection loss below −20 dB from 7.0 GHz to 17.6 GHz by improving the Debye relaxation process [7]. Graphene nanoplatelets in epoxy resin exhibit −14.5 dB maximum reflection loss at 18.9 GHz, mainly attributed to the charge multipoles at the polarized interfaces into the composite material [8]. Materials 2016, 9, 825; doi:10.3390/ma9100825

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Materials 2016, 9, 825

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The present paper deals with graphene particles embedded into an epoxy resin for microwave absorption applications, and more specifically for the microwave isolation of closer antennas attached on the same composite panel and working between 2 GHz and 18 GHz. It is organized as follows. In Section 2, sample fabrication and the measuring process are described. In the following section, the composite materials loaded with graphene are investigated in light of two parameters: the graphene particle size and the weight ratio of graphene particles into the composite materials. For each material and parameter combination, the complex permittivity was measured from 2 GHz to 18 GHz, and the results are discussed. The microwave absorption ability of the composite materials from 4 GHz to 18 GHz is also investigated and related to the dielectric constant and loss tangent results. Finally, conclusions are drawn in Section 4. 2. Materials and Methods 2.1. Graphene Composite Material Fabrication Samples were fabricated from pre-dispersals of graphene particles in epoxy resin and a related hardener (masterbatch). The graphene particles consist of the agglomeration of single-layer graphene flakes, each about 0.34-nm-thick corresponding to the interlayer spacing of graphite from sp2 carbon chemistry [9]. Graphene is obtained through mechanical exfoliation of small pieces of graphite. Three different masterbatches were used, preloaded with 3-µm, 6–8-µm, and 15-µm graphene particle sizes with respective weight ratios of 25%, 15%, and 10% (masterbatches manufactured and supplied by the Nanovia company, Louargat, France, with Prime™ 27 epoxy resin and Prime™ 20 hardener from the Gurit company, Newport, UK). The final weight ratio of graphene in each sample is adjusted after the mixture of masterbatches (preloaded resin + preloaded hardener) with pristine epoxy resin and pristine hardener (dilution with 28:100 hardener/resin weight ratio). This process is particularly well adapted (I) to obtain fair particle dispersion; (II) to prevent any graphene aggregation; and finally (III) to produce a homogeneous material [10]. Epoxy resin has been selected for this study due to its low viscosity (480–510 cP for Prime™ 27 epoxy resin and 13–15 cP for Prime™ 20 hardener @ 25 ◦ C), allowing a high graphene ratio, its low exothermicity during the cross-linking reaction, and its low shrinkage characteristic. Numerous samples (a total of 24) with different particle sizes and weight ratios have been fabricated (Table 1). A standard 5-mm-thick sample dimension was selected. It promotes both measurements to assess the complex permittivity and the microwave absorption. The reference sample is a pristine epoxy resin free of graphene particles. Table 1. Sample details. Sample Size (mm3 ) (Length × Width × Thickness)

Graphene Size (µm)

Weight Ratio (%)

150 × 150 × 10 150 × 150 × 5 150 × 150 × 5 150 × 150 × 5

0 3 6–8 15

0 10/20/25 10/15 5/15

2.2. Measuring Process The samples were characterized over a large broadband frequency by assessing three parameters: the complex permittivity, the material reflection, and the material absorption factors. The real and imaginary parts of the complex permittivity ε* (ε* = ε0 + jε00 ) were retrieved from the S11 reflection coefficient measured via a commercial dielectric kit (High Temperature probe (19 mm in diameter) associated with the N1500A Material Measurement Suite software, both supplied by the Keysight Technologies company, Les Ulis, France). The set-up consisted in a probe in close contact with the surface sample. After an air/short/water probe calibration, results between 2 GHz and 18 GHz were presented to be consistent with the forthcoming reflection and absorption characterizations.


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To restrict any implementation errorimplementation and microwave cable a homemadecable bench-test fabricated characterizations. To restrict any erroreffect, and microwave effect,was a homemade (Figure 1a). At least 4 measuring points were checked on each sample. The average of the values bench-test was fabricated (Figure 1a). At least 4 measuring points were checked on each sample. The provided characteristics of the sample. The standard of the 4 measuring points average ofthe thedielectric values provided the dielectric characteristics of thedeviation sample. The standard deviation of 0 = 1.0 and tanδ = 0.05. The accuracy was then equal to ±5% for the dielectric constant ε0 and was ε the 4 measuring points was ε’ = 1.0 and tanδ = 0.05. The accuracy was then equal to ±5% for the ± 0.05 for the loss tangent ε00the /ε0 ).loss A smooth any porosity is essential to dielectric constant ε’ and (tanδ ±0.05 =for tangentsample (tanδ =surface ε”/ε’). without A smooth sample surface without the of essential the measurement, due to the close contact requirement between kit probe and the anyreliability porosity is to the reliability of the measurement, due to the close the contact requirement sample under test. between the kit probe and the sample under test.

Figure 1. Dielectric kit measurement (a) & free-space bench (b). Figure 1. Dielectric kit measurement (a) & free-space bench (b).

The second and third studied parameters here are the microwave reflection and absorption of The second and third studied parameters here are the microwave reflection and absorption of the materials. To this end, 3 pairs of high matching horn antennas (4.65–8 GHz // 8–12 GHz // 12.5–18 the materials. To this end, 3 pairs of high matching horn antennas (4.65–8 GHz // 8–12 GHz // GHz) were successively used to measure the S-parameters in a near-field setting. The largest 12.5–18 GHz) were successively used to measure the S-parameters in a near-field setting. The largest apertures of the horn antennas (109.25 mm × 79 mm) had imposed the sample dimensions (150 mm × apertures of the horn antennas (109.25 mm × 79 mm) had imposed the sample dimensions 150 mm, see Table 1). This choice was to be explained by the lack of lens to focus the electromagnetic (150 mm × 150 mm, see Table 1). This choice was to be explained by the lack of lens to focus the waves on the samples at frequencies as low as 4 GHz. Prior to sample measurements, a preliminary electromagnetic waves on the samples at frequencies as low as 4 GHz. Prior to sample measurements, transmission calibration between horn antennas in pairs was carried out. Then, each sample was a preliminary transmission calibration between horn antennas in pairs was carried out. Then, positioned in close contact between the two horn apertures to restrict diffraction phenomena from each sample was positioned in close contact between the two horn apertures to restrict diffraction the sample edges (Figure 1b). On the one hand, we considered the samples as infinite planes with a phenomena from the sample edges (Figure 1b). On the one hand, we considered the samples as infinite thickness d. On the other hand, S-parameters were affected by the near-field transmission setting, planes with a thickness d. On the other hand, S-parameters were affected by the near-field transmission which induced phase shift effects and then oscillations on such microwave measurements. Time setting, which induced phase shift effects and then oscillations on such microwave measurements. domain and gating techniques were applied to reduce unwanted reflections. It is worth noting too Time domain and gating techniques were applied to reduce unwanted reflections. It is worth noting too that the use of a single broadband antenna (2–18 GHz) must be avoided here because a that the use of a single broadband antenna (2–18 GHz) must be avoided here because a high-sensibility high-sensibility reflection was required to measure the material absorption with accuracy. reflection was required to measure the material absorption with accuracy. Recording the reflection S11 Recording the reflection S11 and the transmission S21 coefficients, the material absorption was and the transmission S21 coefficients, the material absorption was computed from the linear power computed from the linear power conservation Equation (1) expressed as follows (Equation (2) [11]): conservation Equation (1) expressed as follows (Equation (2) [11]): |=1 ; | | + | 2 | + | 2 (1) (1) |S11 | + |S21 | + | absorption| = 1; )− (2)(2) == 1010 log(1 αdB log −1|− ||S11 −log(| 10 log ||S).21 |2 . |2 10 Using the sample thickness (Table 1), the material absorption was normalized in dB/cm, namely Using the sample thickness (Table 1), the material absorption was normalized in dB/cm, namely α. α. This method is valuable for any kind of materials with reflectors, absorbers, or dielectric This method is valuable for any kind of materials with reflectors, absorbers, or dielectric behaviors. behaviors. 3. Results and Discussion 3. Results and Discussion 3.1. Complex Permittivity Results 3.1. Complex Permittivity Results 3.1.1. Influence of the Particle Size 3.1.1. Influence of the Particle Size Samples loaded with graphene particles of different sizes at a fixed weight ratio (10%) were first studied. Figure 2a presents the variation of theof dielectric to 18weight GHz. At a constant working Samples loaded with graphene particles differentconstant sizes atup a fixed ratio (10%) were first frequency, the more particle size dielectricconstant constantup increases. Increasing studied. Figure 2a presents the increases, variation the of more the dielectric to 18 GHz. At a working constant working frequency, the more particle size increases, the more dielectric constant increases. Increasing working frequency leads to a decrease of the dielectric constant due to relaxation


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frequency leads to a decrease of the dielectric constant due to relaxation phenomena, such as rotational and vibrational transitions, electronic, and atomic polarizations, as mentioned by Griffiths [12] and phenomena, such as rotational and vibrational transitions, electronic, and atomic polarizations, as Materials 2016, 9, 825 4 of 10 Atwater et al. mentioned by[13]. Griffiths [12] and Atwater et al. [13]. Figure 2b shows shows thenonlinear nonlinear variation of the tangent parameter versus frequency. Figure 2b of transitions, the lossloss tangent parameter versus frequency. Loss phenomena, such asthe rotational andvariation vibrational electronic, and atomic polarizations, as Loss tangent increases up to 8–10 GHz, behavior also noted from composite materials loaded with tangent increases up to 8–10 GHz, behavior also noted from composite materials loaded with mentioned by Griffiths [12] and Atwater et al. [13]. graphene or nanotubes without any [14–16]. Sample loaded with graphene or carbon carbon nanotubes without any satisfactory satisfactory explanation [14–16].versus Sample loaded with the Figure 2b shows the nonlinear variation of the lossexplanation tangent parameter frequency. Lossthe 3-µm particle size exhibits the highest loss tangent value. 3-µm particle size exhibits tangent tangent increases up to the 8–10highest GHz, loss behavior alsovalue. noted from composite materials loaded with graphene or carbon nanotubes without any satisfactory explanation [14–16]. Sample loaded with the 3-µm particle size exhibits the highest loss tangent value.

Figure 2. Variation of dielectric constant ε’ (a) and loss tangent tanδ (b) vs. frequency of epoxy resin Figure 2. Variation of dielectric constant ε0 (a) and loss tangent tanδ (b) vs. frequency of epoxy resin loaded with different graphene particle sizes at a constant weight ratio (10%). Pristine epoxy resin Figure 2. Variation dielectricparticle constantsizes ε’ (a)at and loss tangent tanδ ratio (b) vs.(10%). frequency of epoxy resin loaded with differentofgraphene a constant weight Pristine epoxy resin values are given for reference. loaded different graphene particle sizes at a constant weight ratio (10%). Pristine epoxy resin values arewith given for reference. values are given for reference.

3.1.2. Influence Ratio 3.1.2. Influence of of the the Weight Weight Ratio 3.1.2. Influence of the Weightwith Ratio Other samples Other samples fabricated fabricated with different different weight weight ratios ratios and and the the three three particle particle sizes sizes (3 (3 µm, µm, 6–8 6–8 µm, µm, and 15 µm) were studied (Figure 3). Maximum weight ratio achieved depends on the graphene size. samples fabricated with weight ratios and the threedepends particle sizes (3 µm, 6–8 µm, and 15 Other µm) were studied (Figure 3). different Maximum weight ratio achieved on the graphene size. Forand example, epoxystudied resinloaded loaded with 3-µm graphene particle cannot exceed 25% weight 15 µm)epoxy were (Figure 3). Maximum weight ratio achieved depends on the graphene size. For example, resin with thethe 3-µm graphene particle size size cannot exceed 25% weight ratio, ratio, while that loaded with the 15-µm particle size achieves a maximum of 10%. For higher weight For example, epoxy resin loaded with the 3-µm graphene particle size cannot exceed 25% weight while that loaded with the 15-µm particle size achieves a maximum of 10%. For higher weight ratio ratio, while thatmixture loaded with the 15-µm particle sizelumped achieves maximum ofAccordingly, 10%. ForAccordingly, higher ratio values, the becomes extremely viscous and lumped in consistency. the values, the mixture becomes extremely viscous and ina consistency. theweight supplier ratio values, the mixture becomes extremely viscous and lumped in consistency. Accordingly, the supplierinsure cannotthe insure the quality. mixture quality. Figure 3a,b present the complex permittivity variation cannot mixture Figure 3a,b present the complex permittivity variation versus supplier cannot insure the mixture quality. Figure 3a,b present the complex permittivity variation versus the frequency of samples loaded with the 3-µm graphene particle size. Results show the the frequency of samples loaded with the 3-µm graphene particle size. Results show the increase versusofthe frequency ofconstant samples(Figure loaded3a) with the 3-µm graphene particle size. Resultswith showrespect the increase the dielectric and of the loss tangent (Figure 3b) values of the dielectric constant (Figure 3a) and of the loss tangent (Figure 3b) values with respect to the increase of the dielectric constantthe (Figure 3a) and of tangent the loss tangent (Figure 3b) values with respect to the weight ratio. Furthermore, maximum loss value this was study was reached set weight ratio. Furthermore, the maximum loss tangent value of this of study reached and setand at 0.36 to the weight ratio. Furthermore, the maximum loss tangent value of this study was reached andtoset at 0.36 in the 8–10 GHz frequency band. The weight ratio variation versus frequency is similar that in at the0.36 8–10 GHz frequency band. band. The weight ratioratio variation versus frequency is issimilar totothat of in the 8–10 GHz frequency The weight variation versus frequency similar that of the particle size variation (see Section 3.1.1): with increasing frequency at a constant weight ratio, theofparticle size size variation (see(see Section 3.1.1): ataaconstant constantweight weight ratio, the particle variation Section 3.1.1):with withincreasing increasing frequency frequency at ratio, the dielectric dielectric constant constant decreases, while the loss tangent increases up to 8–10 GHz GHz and and decreases decreases the decreases, while the loss tangent increases up to 8–10 the dielectric constant decreases, while the loss tangent increases up to 8–10 GHz and decreases afterwards. Dielectric constant values of composite materials loaded with the largest particle particle sizes sizes afterwards. Dielectric materialsloaded loadedwith withthe thelargest largest afterwards. Dielectricconstant constantvalues values of of composite composite materials particle sizes (Figure 3c,e) 3c,e) remain remain higher higher than ~9. ~9. The related loss tangent does not improve much, even at higher (Figure tangent does doesnot notimprove improvemuch, much,even even higher (Figure 3c,e) remain higherthan than ~9.The The related related loss loss tangent at at higher weight ratios (Figure 3d,f). weight ratios (Figure 3d,f). weight ratios (Figure 3d,f).

Figure 3. Cont.

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Figure 3. Variation dielectric constantεε’0ε’and andloss losstangent tangent tanδ tanδ vs. vs. Figure 3. of dielectric constant frequencyof ofepoxy epoxyresin resinloaded loaded Figure 3. Variation Variation of of dielectric constant and loss tangent tanδ vs. frequency with a 3-µm graphene particle size (a,b); a 6–8-µm graphene particle size (c,d); and with particle sizesize (a,b);(a,b); a 6–8-µm graphene particleparticle size (c,d); and a 15-µm with aa3-µm 3-µmgraphene graphene particle a 6–8-µm graphene size (c,d); andagraphene a15-µm 15-µm graphene particle sizevarious (e,f) with various weight ratios, respectively. resin values are particle size (e,f) with ratios, respectively. PristinePristine epoxy epoxy resin are given graphene particle size (e,f) withweight various weight ratios, respectively. Pristine epoxyvalues resin values are given for reference. for reference. given for reference.

3.1.3. Particle Size and Weight Ratio Twofold Influence 3.1.3. Particle Size and Weight Weight Ratio Ratio Twofold TwofoldInfluence Influence Samples loaded with the largest particle sizes at the maximum weight ratio exhibit closer Samples thethe largest particle sizessizes at theat maximum weight ratio exhibit dielectric Samplesloaded loadedwith with largest particle the maximum weight ratiocloser exhibit closer dielectric constant and loss tangent values (Figure 4). The use of the smallest graphene particles constant and loss tangent values (Figure 4). The use of 4). the The smallest graphene particles (3 µm) promotes dielectric constant and loss tangent values (Figure use of the smallest graphene particles (3 µm) promotes higher loss tangent values (Figure 4b). According to Chung [17], an electromagnetic higher loss tangent values (Figure 4b). According4b). to According Chung [17], electromagnetic absorption (3 µm) promotes higher loss values to an Chung [17], dielectric an electromagnetic absorption mechanism cantangent result from the (Figure electric dipoles of materials with high constant mechanism can result from the electric dipoles of materials with high dielectric constant values. absorption mechanism can result from the electric dipoles of materials with high dielectric constant values. The interaction between the electromagnetic field and the material induces molecular The interaction between the electromagnetic field the material induces molecular movements, values. The interaction between field and the material induces molecular movements, charge relaxation, or the both,electromagnetic leading to and energy dissipation [18,19]. The use of the smallest charge relaxation, or both, leading to energy dissipation [18,19]. The use of the smallest graphene movements, charge relaxation, or both, leading to energy dissipation [18,19]. The use of the smallest graphene particles with the highest weight ratio increases the interaction surface between graphene particles with the highest weight ratio increases the interaction surface between graphene and graphene with the highest weight ratio increases surface between graphene and theparticles matrix and enhances the absorption mechanism bythe theinteraction composite material and thus the loss. the matrix andand enhances the the absorption mechanism the material and andThis the behavior matrix absorption mechanism by thecomposite composite material andthus thus thesize loss. hasenhances also been highlighted by Crane et al.by through their study on the metal particle This behavior has also been highlighted by Crane et al. through their study on the metal particle size This behavior has also been highlighted effect on microwave absorption [19]. by Crane et al. effect effect on on microwave microwave absorption absorption [19]. [19].

Figure 4. Variation of dielectric constant ε’ (a) and loss tangent tanδ (b) vs. frequency of epoxy resin loaded with the maximum weight ratio of the related graphene particle sizes. Pristine epoxy resin Figure 4. Variation Variation of dielectric dielectric constant εε’0 (a) (a) and and loss loss tangent tangent tanδ tanδ (b) (b) vs. vs. frequency frequency of of epoxy epoxy resin resin values are given for reference.constant Figure 4. of

loaded with with the the maximum maximum weight weight ratio ratio of of the the related related graphene graphene particle particle sizes. sizes. Pristine Pristine epoxy epoxy resin resin loaded values are given for reference. values are given for reference.


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3.2. Electromagnetic Absorption

3.2. Electromagnetic Absorption The assessment of the electromagnetic absorption was made using an homemade near field free-space bench as described in Section 2.2. S-parameter measurements provide the electromagnetic The assessment of the electromagnetic absorption was made using an homemade near field reflected power |S11 |2 and the electromagnetic transmitted power |S21 |2 by and through the free-space bench as described in Section 2.2. S-parameter measurements provide the electromagnetic composite material under test, respectively. With Equation (2), it is easy to compute the electromagnetic reflected power |S11|² and the electromagnetic transmitted power |S21|² by and through the absorption α of the composite material. composite material under test, respectively. With Equation (2), it is easy to compute the electromagnetic α Size of the composite material. 3.2.1. Influence ofabsorption the Particle of the graphene composite materials depends on different parameters. 3.2.1.Electromagnetic Influence of theabsorption Particle Size The influence of the graphene particle size in epoxy resin was first investigated. Figure 5 shows the Electromagnetic absorption of the graphene composite materials depends on different reflected power of the 10% weight ratio graphene composites loaded with 3 µm, 6–8 µm, and 15 µm parameters. The influence of the graphene particle size in epoxy resin was first investigated. Figure 5 particle sizes. Two additional curves have been plotted for reference: the pristine dielectric epoxy resin shows the reflected power of the 10% weight ratio graphene composites loaded with 3 µm, 6–8 µm, and a perfect reflector (a metal plate). Compared with a perfect reflector (|S11 |2 ≈ 0 dB), |S11 |2 values and 15 µm particle sizes. Two additional curves have been plotted for reference: the pristine of the composite materials remain lower than −3 dB in the 8–18 GHz frequency range, evidencing the dielectric epoxy resin and a perfect reflector (a metal plate). Compared with a perfect reflector penetration of the electromagnetic wave into the materials. Reflected power and complex permittivity (|S11|²  0 dB), |S11|² values of the composite materials remain lower than −3 dB in the 8–18 GHz are closely interrelated with respect to Equation (3) applied with a normal incident electromagnetic frequency range, evidencing the penetration of the electromagnetic wave into the materials. wave in air striking a dielectric slab, as follows [20]: Reflected power and complex permittivity are closely interrelated with respect to Equation (3) q 2  p wave in air striking applied with a normal incident electromagnetic dielectric ε0 (1 − tanδ) − ε0air (1a − tanδair ) slab, as follows [20]:  , q (3) |S11 |2dB = 10 log  e−2jβd × p ( ) ( ) 0 0 (3) | | = 10 log ε ×(1 − tanδ) + ε air (1 − tanδair, ) (

)

(

)

(ε0

where β β ==2π/λ 2π/λis is wavenumber, 1, air tanδ 0) dielectric is the dielectric characteristics of (ε’, air, tanδ = 0)airis=the characteristics of air, and thethe wavenumber, (ε’air =air1, = 0 and tanδ) is the dielectric characteristics of the composite with thickness d. tanδ)(εis, the dielectric characteristics of the composite materialmaterial with thickness d.

Figure 5. 5. Reflected Reflectedpower power|S|S11 |² 2 (a) and electromagnetic absorption α (b) vs. frequency of epoxy Figure 11 | (a) and electromagnetic absorption α (b) vs. frequency of epoxy resin resin loaded with different graphene particle sizes at a constant ratio (10%). Pristine loaded with different graphene particle sizes at a constant weightweight ratio (10%). Pristine epoxyepoxy resin resin values are given for reference. values are given for reference.

The variation of ε’ between 5 and 24 (Figure 2a) and tanδ between 0.05 and 0.22 (Figure 2b) The variation of ε0 between 5 and 24 (Figure 2a) and tanδ between 0.05 and 0.22 (Figure 2b) induces a variation of |S11|² between −0.8 dB and −6.4 dB, as observed in Figure 5a. Observation of induces a variation of |S11 |2 between −0.8 dB and −6.4 dB, as observed in Figure 5a. Observation resonance peaks close to 10 GHz with |S11|² 2≤ −10 dB is explained by the total reflection of the of resonance peaks close to 10 GHz with |S11 | ≤ −10 dB is explained by the total reflection of the electromagnetic waves by the composite material, the guide wavelength λg into the composite electromagnetic waves by the composite material, the guide wavelength λg into the composite material material√(λg = λ/ε’) satisfying the following Equation (4) [20]: (λg = λ/ ε0 ) satisfying the following Equation (4) [20]: (4) × =λ gd, n× = d, (4) 2 where n is a positive integer (d = 5 mm for the composite materials and d = 10 mm for the pristine where is a positive integer (d =pristine 5 mm for the composite materials d = 10 mmatfor~9the pristine epoxy epoxy nresin, see Table 1). The epoxy resin sample showsand a resonance GHz (n = 1); the resin, see Table 1). The pristine epoxy resin sample shows a resonance at ~9 GHz (n = 1); the sample sample loaded with a 3-µm graphene particle size presents a resonance peak at 11.7 GHz (n = 1); loaded with6-8-µm a 3-µmgraphene grapheneparticle particlesize sizeatpresents peakGHz at 11.7 (n = with 1); those with those with 7.6 GHza(nresonance = 1) and 15.0 (n =GHz 2); those 15 µm at 5.7 GHz (n = 1) and 11.4 GHz (n = 2)—in agreement with the increase of the ε’ value when the graphene particle size increases (Figure 2a).


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6-8-µm graphene particle size at 7.6 GHz (n = 1) and 15.0 GHz (n = 2); those with 15 µm at 5.7 GHz (n = 1) and GHz (n = 2)—in agreement with the increase of the ε0 value when the graphene particle Materials 2016,11.4 9, 825 7 of 10 size increases (Figure 2a). Figure thethe electromagnetic absorption trend trend curvescurves of the samples the 4–18-GHz Figure 5b 5bpresents presents electromagnetic absorption of the over samples over the frequency band extracted from the near field free-space bench measurements. Absorption variation 4–18-GHz frequency band extracted from the near field free-space bench measurements. Absorption follows the same trend for all samples: values at low frequency (1 dB/cm for the 3-µm variation follows the same trend for allweak samples: weak values at low frequency (1 dB/cm for graphene the 3-µm particle size and 4size dB/cm the 15-µm graphene particle size at 4 size GHz) stronger ones at high graphene particle and for 4 dB/cm for the 15-µm graphene particle at and 4 GHz) and stronger ones frequency (7 dB/cm (7 fordB/cm the 3-µm particle size and 16 dB/cm graphene at high frequency forgraphene the 3-µm graphene particle size for andthe 1615-µm dB/cm for the particle 15-µm size at 18 GHz). Note theGHz). pristine epoxy exhibitsepoxy a constant (~0.1 dB) over graphene particle sizethat at 18 Note thatresin the pristine resinabsorption exhibits a value constant absorption the full(~0.1 working frequency value dB) over the fullband. working frequency band. 3.2.2. Influence of 3.2.2. Influence of the the Weight Weight Ratio Ratio The is the graphene weight ratio in epoxy presents The second secondinvestigated investigatedparameter parameter is the graphene weight ratio in resin. epoxyFigure resin.6aFigure 6a the reflected power of the 3-µm graphene composite materials loaded with 10%, 20%, and 25% weight presents the reflected power of the 3-µm graphene composite materials loaded with 10%, 20%, and ratio. The perfect reflector and pristineand epoxy resinepoxy curves have also been forplotted reference. 25% weight ratio. The perfect reflector pristine resin curves have plotted also been for The behavior of the reflected power is similar to that studied in Section 3.2.1, in agreement with the reference. The behavior of the reflected power is similar to that studied in Section 3.2.1, in agreement related values. The 10% weight ratio sample shows a resonance at 11.7 peak GHz with thecomplex related permittivity complex permittivity values. The 10% weight ratio sample shows apeak resonance (n = 1); those with 20% weight ratio at 10.8 GHz (n = 1). The magnitude peak is damped by the increase at 11.7 GHz (n = 1); those with 20% weight ratio at 10.8 GHz (n = 1). The magnitude peak is damped of weight ratio, due to theratio, risingdue of the related tanδ value (Figure 3b). It is (Figure worth noting bythe thegraphene increase of the graphene weight to the rising of the related tanδ value 3b). It that the resonance peak invisible for theis25% weightfor ratio exhibiting highest loss tangent is worth noting that theisresonance peak invisible thesample, 25% weight ratiothe sample, exhibiting the of the present study (tanδ = 0.36). highest loss tangent of the present study (tanδ = 0.36). Figure Figure 6b 6b presents presents the the electromagnetic electromagnetic absorption absorption trend trend curves curves of of the the samples samples over over the the 4–18-GHz 4–18-GHz frequency frequency band. band. Absorption Absorption variation variation follows follows the the same same trend trendas asthat thatobserved observedin inFigure Figure5b: 5b:11dB/cm dB/cm for 10% weight ratio sample and 5 dB/cm for 25% weight ratio sample at 4 GHz; 7 dB/cm for 10% for 10% weight ratio sample and 5 dB/cm for 25% weight ratio sample at 4 GHz; 7 dB/cm for 10% weight for 25% 25% weight weight ratio ratio sample sample at at 18 18 GHz. GHz. weight ratio ratio sample sample and and 16 16 dB/cm dB/cm for

Figure 6. 6. Reflected Reflectedpower power|S|S11||² (a)and andelectromagnetic electromagnetic absorption α vs. (b) frequency vs. frequency of epoxy 2 (a) Figure absorption α (b) of epoxy resin 11 resin loaded with a 3-µm graphene particle size with various weight ratios. Pristine epoxy resin loaded with a 3-µm graphene particle size with various weight ratios. Pristine epoxy resin values are valuesfor arereference. given for reference. given

As expected, expected, high high dielectric dielectric constant constant and and loss loss tangent tangent values values promote promote high high electromagnetic electromagnetic As absorption α, α, as as described described by by Equation Equation (5) (5) from from [20]: [20]: absorption s ɛ r (5) ( ) −1 , × 1 +q = × ω µ0 ε0 α = A× × 1 + (tanδ)2 − 1 , (5) c 2 where ω is the working pulsation; c is the speed of light in vacuum; µ’ is the relative permeability of the composite material (µ = 1); (ε’, tanδ) is the dielectric characteristics of0 the composite material; A is where ω is the working pulsation; c is the speed of light in vacuum; µ is the relative permeability −1) to convert α in dB/cm. In order to check the relevance of an adjustment factor (A = 8.68/100 dB·Np 0 of the composite material (µ = 1); (ε , tanδ) is the dielectric characteristics of the composite material; the ε’ and tanδ values provided by the dielectric kit method (Figure 3a,b), α values have been A is an adjustment factor (A = 8.68/100 dB·Np−1 ) to convert α in dB/cm. In order to check the computed from Equation (5) and compared with the measured values deduced from Equation (2). relevance of the ε0 and tanδ values provided by the dielectric kit method (Figure 3a,b), α values have The satisfactory fit between the measured and computed α values confirms the reliability of the dielectric characteristics (ε’, tanδ) (Figure 7), despite a drift between the trend curve and the measured values for the 20% weight ratio sample at the frequency band edge. The frequency dependence of Equation (5) also explains the linear variation of α versus the working frequency.


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been computed from Equation (5) and compared with the measured values deduced from Equation (2). The satisfactory fit between the measured and computed α values confirms the reliability of the dielectric characteristics (ε0 , tanδ) (Figure 7), despite a drift between the trend curve and the measured values for the 20% weight ratio sample at the frequency band edge. The frequency dependence of Equation also explains the linear variation of α versus the working frequency. Materials (5) 2016, 9, 825 8 of 10 Materials 2016, 9, 825

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Figure 7. Electromagnetic absorption α vs. epoxy resin loaded with a 3-µm graphene particle size Figure 7. Electromagnetic absorption α vs. epoxy resin loaded with a 3-µm graphene particle size with with various weight ratios.absorption α vs. epoxy resin loaded with a 3-µm graphene particle size Figure 7. Electromagnetic various weight ratios. with various weight ratios.

3.2.3. Particle Size andWeight WeightRatio RatioTwofold TwofoldInfluence Influence 3.2.3. Particle Size and 3.2.3. Particle Size and Weight Ratio Twofold Influence These parameters also have an influence on the reflected power (Figure 8a) and the These parameters also have an influence on the reflected power (Figure 8a) and the electromagnetic electromagnetic absorption (Figure 8b).influence The firstonrelevant point concerns the resonance peaks These parameters alsofirst have an the the reflected power (Figure and absorption (Figure 8b). The relevant point concerns resonance peaks (|S118a) |2 ≤ dB). −10the (|S11|² ≤ −10 dB).absorption Samples with a 6–8-µm graphene particle size 10% weight ratio shows two electromagnetic (Figure 8b). The first relevant pointand concerns the resonance peaks Samples with a 6–8-µm graphene particle size and 10% weight ratio shows two resonance peaks at resonance peaks 7.6 GHzwith (n = 1) and 15.0graphene GHz (n = particle 2). With size the increase the weight to 15%, (|S 11|² ≤ −10 dB).atSamples a 6–8-µm and 10%inweight ratioratio shows two 7.6 GHz (n = 1) and 15.0 GHz (n = 2). With the increase in the weight ratio to 15%, these peaks shift these peaks shift at 5.6 GHz (n = 1) and 10.5 GHz (n = 2). This behavior is consistent with of resonance peaks at 7.6 GHz (n = 1) and 15.0 GHz (n = 2). With the increase in the weight ratio tothat 15%, at 5.6 GHz (n = 1) and 10.5 GHz (n = 2). This behavior is consistent with that of samples loaded samples loaded a 15-µm size(nat=5% weightisratios. The second point these peaks shiftwith at 5.6 GHz (ngraphene = 1) andparticle 10.5 GHz 2). and This10% behavior consistent with that of with graphene to particle size at 5%The andreflected 10% weight ratios. The second point isaa 6–8-µm behavior is aa 15-µm behavior thesegraphene samples. power of a weight sample loaded with samples loadedsimilar with a 15-µm particle size at 5% and 10% ratios. The second point similar to these samples. The power ofand a sample a 6–8-µm graphene particle graphene particle size to with areflected 10% weight ratioreflected thatpower of aloaded sample loaded with a 15-µm is a behavior similar these samples. The of a with sample loaded with agraphene 6–8-µm size with asize 10% weight ratio and that ofare a sample a 15-µm graphene with a particle with a 5% weight ratio alike.and Inloaded the way, a loaded sample loaded with graphene asize 6-8-µm graphene particle size with a 10% weight ratio thatsame ofwith a sample with a particle 15-µm 5%particle weight ratio are alike. In the same way, a sample loaded with a 6-8-µm graphene particle size with graphene particle a 15% weight ratio presents a similar |² to that loadedwith witha a6-8-µm 15-µm size with size a 5%with weight ratio are alike. In the same way,|Sa11sample loaded 2 to that loaded with a 15-µm graphene particle size with a a 15% weight ratio presents a similar |S | 11 ratio graphene particle particlesize sizewith witha a15% 10% weight ratio. We attribute the close graphene weight presents a similarthese |S11|²results to thatto loaded withdielectric a 15-µm 10% weight and ratio. Wesize attribute results the We close dielectric constants loss tangents of the constants loss tangents the sets ofto samples (Table 2). these graphene particle withofathese 10%two weight ratio. attribute results and to the close dielectric two sets of samples 2).of the two sets of samples (Table 2). constants and loss (Table tangents

Figure 8. Reflected power |S11|² (a) and electromagnetic absorption α (b) vs. frequency of epoxy resin loaded with 6–8-µm and graphene particle sizes with various weight ratios.ofPristine Figure 8. Reflected power |S 11|²15-µm (a) and electromagnetic absorption α (b) vs. frequency epoxy Figure 8. resin Reflected power |S11 for |2 (a) and electromagnetic absorption α (b) vs. frequency of epoxy resin epoxyloaded values are given reference. resin with 6–8-µm and 15-µm graphene particle sizes with various weight ratios. Pristine loaded with 6–8-µm and 15-µm graphene particle sizes with various weight ratios. Pristine epoxy resin epoxy resin values are given for reference. values are2. given for reference. Table Dielectric constant and loss tangent of epoxy resin loaded with 6–8-µm and 15-µm graphene particle with constant various weight ratios. Table 2. sizes Dielectric and loss tangent of epoxy resin loaded with 6–8-µm and 15-µm graphene

Between 4 GHz and 18 GHz, theratios. absorption α ranges from 3–4 dB/cm at 4 GHz to 8.7 dB/cm at particle sizes with various weight Particle Size Weight Ratio ε’ tanδ ε’ tanδ 18 GHz for the 6–8-µm graphene particle size with 10% weight ratio and the 15-µm graphene particle (µm)Size Particle 6–8 (µm) 15 6–8 6–8 15 15 6–8 15

(%)Ratio Weight 10 (%) 5 10 15 5 10 15 10

@10ε’GHz @1010.6 GHz 9.5 10.6 18.5 9.5 20.4 18.5

@10 GHz tanδ 0.14 @10 GHz 0.15 0.14 0.18 0.15 0.18 0.18

@18ε’GHz @1810.2 GHz 9.2 10.2 17.8 9.2 20.4 17.8

@18 GHz tanδ 0.11 @18 GHz 0.10 0.11 0.18 0.10 0.16 0.18

20.4

0.18

20.4

0.16


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size with 5% weight ratio samples. After a relative weight ratio increase, α ranges from 4–5 dB/cm at 4 GHz to achieve 15–16 dB/cm at 18 GHz for the 6–8-µm graphene particle size with 15% weight ratio and the 15-µm graphene particle size with 10% weight ratio samples. Table 2. Dielectric constant and loss tangent of epoxy resin loaded with 6–8-µm and 15-µm graphene particle sizes with various weight ratios. Materials 2016, 9, 825

Particle Size (µm)

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Weight Ratio (%)

ε0 @10 GHz

tanδ @10 GHz

ε0 @18 GHz

tanδ @18 GHz

Between the absorption at 4 GHz to 8.70.11 dB/cm at 6–8 4 GHz and 18 GHz, 10 10.6 α ranges from 0.14 3–4 dB/cm10.2 5 9.5 with 10% 0.15 9.2 the 15-µm 0.10 18 GHz 15 for the 6–8-µm graphene particle size weight ratio and graphene 15 18.5 0.18 17.8 0.18 particle 6–8 size with 5% weight10 ratio samples.20.4 After a relative weight ratio20.4 increase, α ranges from 15 0.18 0.16 4–5 dB/cm at 4 GHz to achieve 15–16 dB/cm at 18 GHz for the 6–8-µm graphene particle size with 15% weight ratio and the 15-µm graphene particle size with 10% weight ratio samples. Figure 9 presents the absorption responses of the samples loaded with the maximum weight Figure 9 presents the absorption responses of the samples loaded with the maximum weight ratio for the three graphene sizes. The three samples exhibit high dielectric constants (Figure 4a) with ratio for the three graphene sizes. The three samples exhibit high dielectric constants (Figure 4a) differing loss tangent values (Figure 4b). It is worth noting that the lower ε0 value of the 3-µm graphene with differing loss tangent values (Figure 4b). It is worth noting that the lower ε’ value of the 3-µm particle size particle with a 25% weight ratio sample is compensated by a higher value, therefore graphene size with a 25% weight ratio sample is compensated by atanδ higher tanδand value, and explains the explains samenessthe of sameness the three absorption at 10Finally, GHz, aatminimum therefore of the threeresponses. absorptionFinally, responses. 10 GHz, aabsorption minimum of 9 dB/cm is reached withisall samples. absorption of 9 dB/cm reached with all samples.

Figure 9. Electromagnetic absorption α vs. frequency of samples loaded with the maximum weight Figure 9. Electromagnetic absorption α vs. frequency of samples loaded with the maximum weight ratio of the related graphene particle sizes. Pristine epoxy resin values are given for reference. ratio of the related graphene particle sizes. Pristine epoxy resin values are given for reference.

Conclusions 4. 4. Conclusions this study, grapheneparticles particleswere wereused used as as filler filler in anan epoxy In In this study, graphene in aa thermosetting thermosettingresin, resin,namely namely epoxy resin, in view of microwave absorption and electromagnetic shielding applications. The composite resin, in view of microwave absorption and electromagnetic shielding applications. The composite materials produced have thereby been evaluated in relation to two relevant parameters: the materials produced have thereby been evaluated in relation to two relevant parameters: the graphene graphene particle size (3 µm, 6–8 µm, and 15 µm) and the graphene weight ratio (ranging from 5% to particle size (3 µm, 6–8 µm, and 15 µm) and the graphene weight ratio (ranging from 5% to 25%). 25%). For these, the dielectric constant and loss tangent (ε’, tanδ), and the microwave absorption α of For these, the dielectric constant and loss tangent (ε0 , tanδ), and the microwave absorption α of each each sample, were measured using a dielectric kit (from 2 GHz to 18 GHz) and a homemade near sample, were measured using a dielectric kit (from 2 GHz to 18 GHz) and a homemade near field field free-space bench (from 4 GHz to 18 GHz), respectively. The epoxy resin loaded with the free-space bench (from 4 GHz to 18 GHz), respectively. The epoxy resin loaded with the smallest smallest graphene size (3 µm) and the highest weight ratio (25%) exhibits the highest loss tangent graphene µm) and thedielectric highest weight ratio (25%) exhibits highest (tanδ = 0.36) (tanδ = size 0.36)(3and a middle constant value (ε’ ≃ 12–14)the in the 8–10loss GHztangent frequency range. 0 andFilling a middle constant (ε ' 12–14) in the 8–10 GHz promotes frequency range. Filling the epoxy the dielectric epoxy resin withvalue the smallest graphene particles high loss tangent at resin with the smallest graphene particles promotes high loss tangent at microwaves and thus the microwaves and thus the microwave absorption of the electromagnetic waves by the composite microwave absorptiona of the dielectric electromagnetic the composite material. Moreover, a lower material. Moreover, lower constant waves will be by favored to restrict the impedance mismatch at dielectric constant will be air favored restrictsamples the impedance mismatch at the between wave air and the interface between and to surface and thus to restrict theinterface electromagnetic surface samples to restrict electromagnetic waveprovides reflectivity at this interface. level: The composite reflectivity at and this thus interface. The the composite material then a high absorption from 5 material high absorption dB/cmthen at 4 provides GHz to 16adB/cm at 18 GHz.level: from 5 dB/cm at 4 GHz to 16 dB/cm at 18 GHz. Acknowledgments: The Direction France)isisgratefully gratefullyacknowledged acknowledged Acknowledgments: The DirectionGénérale Généralede del’Armement l’Armement (DGA, (DGA, France) forfor its its financial support. financial support. Author Contributions: All presentedin inthis thispaper paperand andtotothe thewriting writing Author Contributions: Allauthors authorscontributed contributed to to the the work work presented of of thethe final manuscript. final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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Conflicts of Interest: The authors declare no conflict of interest.

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