Dielectric Characteristics and Microwave Absorption of Graphene Composite Materials

materials

Article Dielectric Characteristics and Microwave Absorption of Graphene Composite Materials

Kevin Rubrice 1,2,*, Xavier Castel 2, Mohamed Himdi 2 and Patrick Parneix 1

1 DCNS Research Technocampus Océan, 5 rue de l’Halbrane, 44340 Bouguenais, France; [email protected] 2 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 www.mdpi.com/journal/materials Materials 2016, 9, 825 2 of 10

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 Section2, 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 Section4.

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 (Table1). 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) Graphene Size (µm) Weight Ratio (%) (Length × Width × Thickness) 150 × 150 × 10 0 0 150 × 150 × 5 3 10/20/25 150 × 150 × 5 6–8 10/15 150 × 150 × 5 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 0 00 imaginary parts of the complex permittivity ε*(ε* = ε + jε ) 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. Materials 2016, 9, 825 3 of 10 Materials 2016, 9, 825 3 of 10

Tocharacterizations. restrict any implementation To restrict any error implementation and microwave cableerror effect,and microwave a homemade cable bench-test effect, wasa homemade fabricated (Figurebench-test1a). was At leastfabricated 4 measuring (Figure 1a). points At least were 4 checked measuring on eachpoints sample. were checked The average on each of sample. the values The providedaverage of the the dielectric values provided characteristics the dielectric of the sample. characteristics The standard of thedeviation sample. The of the standard 4 measuring deviation points of 0 0 wasthe 4ε measuring= 1.0 and tanpointsδ = 0.05.was Theε’ = accuracy1.0 and tan wasδ = then 0.05. equal The toaccuracy±5% for was the then dielectric equal constantto ±5% forε andthe 00 0 ±dielectric0.05 for theconstant loss tangent ε’ and (tan±0.05δ =forε the/ε ).loss A smoothtangent sample (tanδ = surface ε”/ε’). withoutA smooth any sample porosity surface is essential without to theany reliabilityporosity is of essential the measurement, to the reliability due to theof th closee measurement, contact requirement due to the between close thecontact kit probe requirement and the samplebetween under the kit test. 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 Table1). 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 (Figure1b). 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]): || + |2| + |2 | =1 ; (1) |S11| + |S21| + |absorption| = 1; (1) =10log(1−|| ) −10log2 (|| ). 2 (2) αdB = 10 log 1 − |S11| − 10 log |S21| . (2) Using the sample thickness (Table 1), the material absorption was normalized in dB/cm, namely Using the sample thickness (Table1), 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.Samples Figure loaded2a presents with graphene the variation particles of the of dielectric different constant sizes at up a fixed to 18 weight GHz. At ratio a constant (10%) were working first frequency,studied. Figure the more 2a presents particle sizethe increases,variation theof morethe dielectric dielectric constant constant up increases. to 18 GHz. Increasing At a workingconstant 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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Materials 2016, 9, 825 4 of 10 frequency leads to a decrease of the dielectric constant due to relaxation phenomena, such as rotational andphenomena, vibrational such transitions, as rotational electronic, and vibrational and atomic tran polarizations,sitions, electronic, as mentioned and atomic by Grifﬁthspolarizations, [12] and as Materials 2016, 9, 825 4 of 10 Atwatermentioned et al.by [Griffiths13]. [12] and Atwater et al. [13]. Figure2b shows the nonlinear variation of the loss tangent parameter versus frequency. phenomena,Figure 2b suchshows as the rotational nonlinear and variation vibrational of tranthe sitions,loss tangent electronic, parameter and atomic versus polarizations, frequency. Lossas Loss tangent increases up to 8–10 GHz, behavior also noted from composite materials loaded with tangentmentioned increases by Griffiths up to [12]8–10 and GHz, Atwater behavior et al. [13]. also noted from composite materials loaded with grapheneFigure or carbon 2b shows nanotubes the nonlinear without variation any satisfactorysatisfac of thetory loss explanation tangent parameter [[14–16].14–16]. versus Sample frequency. loaded with Loss the 3-3-µmµtangentm particle increases size exhibits up to the8–10 highest GHz, lossbehavior tangenttangent also value.value. 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 loadedFigure with 2. Variation different of graphene dielectric particleconstant sizes ε’ (a) atand a constantloss tangent weight tanδ ratio(b) vs. (10%). frequency Pristine of epoxy epoxy resin resin values are given for reference. valuesloaded are with given different for reference. graphene particle sizes at a constant weight ratio (10%). Pristine epoxy resin values are given for reference. 3.1.2. Influence Inﬂuence of the Weight Ratio 3.1.2. Influence of the Weight Ratio Other samples fabricated with different weight ratios and the three particle sizes sizes (3 (3 µm,µm, 6–8 6–8 µm,µm, and 15 Otherµm)µm) were samples studied fabricated (Figure with3 3).). MaximumdifferentMaximum weight weightweight ratios ratioratio and achievedachieved the three dependsdepends particle sizes onon thethe (3 graphenegrapheneµm, 6–8 µm, size. Forand example,example, 15 µm) epoxy wereepoxy studied resin resin loaded loaded(Figure with with3). Maximum the the 3- µ3-µmm graphene weight graphene ratio particle achievedparticle size sizedepends cannot cannot exceed on theexceed 25% graphene weight25% weightsize. ratio, whileratio,For while thatexample, loaded that epoxyloaded with resin thewith 15-loaded theµm 15-µm particle with particlethe size 3-µm achieves size gr apheneachieves a maximum particle a maximum size of 10%.cannot of For10%. exceed higher For higher25% weight weight weight ratio values,ratioratio, values, thewhile mixture the that mixture loaded becomes withbecomes extremely the 15-µm extremely viscous particle viscou and size lumped achievess and lumped in a consistency.maximum in consistency. of Accordingly,10%. For Accordingly, higher the weight supplier the ratio values, the mixture becomes extremely viscous and lumped in consistency. Accordingly, the cannotsupplier insure cannot the insure mixture the quality.mixture quality. Figure3 a,bFigure present 3a,b thepresent complex the complex permittivity permittivity variation variation versus supplier cannot insure the mixture quality. Figure 3a,b present the complex permittivity variation theversus frequency the frequency of samples of samples loaded withloaded the with 3-µm the graphene 3-µm graphene particle size.particle Results size. showResults the show increase the versus the frequency of samples loaded with the 3-µm graphene particle size. Results show the ofincrease the dielectric of the dielectric constant constant (Figure3 (Figurea) and of3a) the and loss of the tangent loss tangent (Figure 3(Figureb) values 3b) with values respect with torespect the increase of the dielectric constant (Figure 3a) and of the loss tangent (Figure 3b) values with respect weightto the weight ratio. Furthermore,ratio. Furthermore, the maximum the maximum loss tangent loss tangent value ofvalue this of study this wasstudy reached was reached and set and at 0.36 set to the weight ratio. Furthermore, the maximum loss tangent value of this study was reached and set inat 0.36 the 8–10in the GHz 8–10 frequencyGHz frequency band. band. The weightThe weight ratio ratio variation variation versus versus frequency frequency is similar is similar to thatto that of of theat 0.36 particle in the size 8–10 variation GHz frequency (see Section band. The3.1.1): weight with ratio increasing variation frequency versus frequency at a constant is similar weight to that ratio, theof particle the particle size size variation variation (see (see Section Section 3.1.1 3.1.1):): with with increasing increasing frequency at at a aconstant constant weight weight ratio, ratio, the dielectric constant decreases, while the loss tangent increases up to 8–10 GHz and decreases thethe dielectric dielectric constant constant decreases, decreases, whilewhile thethe lossloss tangent increases increases up up to to 8–10 8–10 GHz GHz and and decreases decreases afterwards. Dielectric constant values of composite materials loaded with the largest particle sizes afterwards.afterwards. Dielectric Dielectric constant constant valuesvalues ofof compositecomposite materials loaded loaded with with the the largest largest particle particle sizes sizes (Figure 3c,e) remain higher than ~9. The related loss tangent does not improve much, even at higher (Figure(Figure3c,e) 3c,e) remain remain higher higher than than ~9. ~9. The The related related lossloss tangenttangent does not improve improve much, much, even even at at higher higher weight ratios (Figure 3d,f). weightweight ratios ratios (Figure (Figure3d,f). 3d,f).

Figure 3. Cont.

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FigureFigure 3.3. Variation3. Variation ofof ofdielectricdielectric dielectric constantconstant constant εε 0ε’ and’and and lossloss loss tangenttangent tangent tantanδδ vs.vs. frequency frequency of of epoxy epoxy resin resin loaded loaded withwithwith aa 3- 3-µmµa m3-µm graphene graphene graphene particle particle particle size size (sizea,b );( a( a,ab, 6–8-b);); aaµ 6–8-µmm6–8-µm graphene graphenegraphene particle particleparticle size (c , dsizesize); and (c(c,d a,d); 15-); and andµm a graphene a15-µm 15-µm particlegraphenegraphene size particle particle (e,f) withsize size ( variouse ,(fe), fwith) with weight various various ratios, weight weight respectively. ratios,ratios, respectirespecti Pristinevely. PristinePristine epoxy epoxy resinepoxy valuesresin resin values values are given are are given for reference. forgiven reference. for reference.

3.1.3. Particle Size and Weight Ratio Twofold Influence 3.1.3. Particle Size and Weight RatioRatio TwofoldTwofold InﬂuenceInfluence Samples loaded with the largest particle sizes at the maximum weight ratio exhibit closer Samples loadedloaded with with the the largest largest particle particle sizes size at thes at maximum the maximum weight ratioweight exhibit ratio closer exhibit dielectric closer dielectric constant and loss tangent values (Figure 4). The use of the smallest graphene particles constant and loss tangent values (Figure4). The use of the smallest graphene particles (3 µm) promotes dielectric(3 µm) promotesconstant higherand loss loss tangent tangent valuesvalues (Figure(Figure 4b). 4). AccordingThe use of to the Chung smallest [17], an graphene electromagnetic particles higher loss tangent values (Figure4b). According to Chung [ 17], an electromagnetic absorption (3 µm)absorption promotes mechanism higher loss can tang resultent from values the (Figureelectric 4b).dipoles According of materials to Chung with high[17], dielectrican electromagnetic constant mechanism can result from the electric dipoles of materials with high dielectric constant values. absorptionvalues. Themechanism interaction can betweenresult from the theelectromagne electric dipolestic field of materialsand the materialwith high induces dielectric molecular constant Thevalues.movements, interaction The interaction charge between relaxation, thebetween electromagnetic or theboth, electromagne leading ﬁeld to andenergytic thefield dissipation material and the induces[18,19]. material The molecular useinduces of the movements, molecularsmallest chargemovements,graphene relaxation, particlescharge or relaxation, with both, the leading highes or both, tot weight energy leading ratio dissipation to increases energy dissipation [ 18the,19 interaction]. The [18,19]. use surface of The the between smallestuse of the graphene graphene smallest particlesgrapheneand the withparticles matrix the and highestwith enhances the weighthighes the absorptiont ratioweight increases ratio mechanism increases the interaction by the the interaction composite surface materialsurface between betweenand graphenethus thegraphene loss. and theandThis matrixthe behaviormatrix and and enhanceshas enhances also been the thehighlighted absorption absorption by mechanism Cranemechanism et al. by through by the the composite composite their study material material on the metal and and thusparticlethus the size loss. ThisThiseffect behaviorbehavior on microwave hashas alsoalso beenbeenabsorption highlightedhighlighted [19]. byby CraneCrane etet al.al. through their study on the metal particle size effect onon microwavemicrowave absorptionabsorption [[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 Figurevalues 4.4. VariationVariationare given forofof dielectric dielreference.ectric constantconstant εε0’ ((aa)) andand lossloss tangenttangent tantanδδ ((bb)) vs.vs. frequencyfrequency ofof epoxyepoxy resinresin loadedloaded withwith thethe maximummaximum weightweight ratioratio ofof thethe relatedrelated graphenegraphene particleparticle sizes.sizes. PristinePristine epoxyepoxy resinresin valuesvalues areare givengiven forfor reference.reference.

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Materials 2016, 9, 825 6 of 10 3.2. Electromagnetic Absorption 3.2. ElectromagneticThe assessment Absorption 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 |S |2 and the electromagnetic transmitted power |S |2 by and through the free-space bench as described11 in Section 2.2. S-parameter measurements provide21 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 3.2.1.electromagnetic Influence of absorption the Particle α Sizeof the composite material.

3.2.1.Electromagnetic Influence of the absorption Particle Size of the graphene composite materials depends on different parameters. The influence of the graphene particle size in epoxy resin was first investigated. Figure5 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 loaded2 with 3 µm, 6–82 µm, and a perfect reflector (a metal plate). Compared with a perfect reflector (|S11| ≈ 0 dB), |S11| 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) 2 applied with a normal incident electromagnetic p 0 wave in air strikingq 0 a dielectric slab, as follows [20]: ε (1 − tanδ) − ε (1 − tanδair) 2 −2jβd air |S11|dB = 10 log  e ×  , (3) p 0 ()q0 () || = 10 log ε×(1 − tanδ) + ε (1 − tanδair, ) (3) ()air() 0 where β == 2π 2π/λ/ λis isthe the wavenumber, wavenumber, (ε’air (ε =air 1, =tan 1,δair tan = δ0)air is= the 0) dielectric is the dielectric characteristics characteristics of air, and of ( air,ε’, 0 andtanδ ()ε is, the tan δdielectric) is the dielectric characteristics characteristics of the composite of the composite material material with thickness with thickness d. d.

Figure 5. Reflected power |S11|²2 (a) and electromagnetic absorption α (b) vs. frequency of epoxy Figure 5. Reﬂected power |S11| (a) and electromagnetic absorption α (b) vs. frequency of epoxy resin loadedresin loaded with differentwith different graphene graphene particle particle sizes atsizes a constant at a constant weight weight ratio (10%).ratio (10%). Pristine Pristine epoxy epoxy resin valuesresin values are given are given for reference. 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 (Figure2a) and tan δ between 0.05 and 0.22 (Figure2b) induces a variation of |S11|² 2between −0.8 dB and −6.4 dB, as observed in Figure 5a. Observation of induces a variation of |S11| between −0.8 dB and −6.4 dB, as observed in Figure5a. 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 (λg0 = λ/ε’) satisfying the following Equation (4) [20]: (λg = λ/ ε ) satisfying the following Equation (4) [20]: × =dλg , (4) n × = d, (4) 2 where n is a positive integer (d = 5 mm for the composite materials and d = 10 mm for the pristine whereepoxy nresin,is a positive see Table integer 1). The (d =pristine 5 mm for epoxy the composite resin sample materials shows and a resonance d = 10 mm at for ~9 the GHz pristine (n = 1); epoxy the resin,sample see loaded Table 1with). The a pristine3-µm graphene epoxy resin particle sample size shows presents a resonance a resonance at ~9 peak GHz at ( n11.7= 1 );GHz the sample(n = 1); loadedthose with with 6-8-µm a 3-µm graphene graphene particle particle size size at presents 7.6 GHz a(n resonance = 1) and 15.0 peak GHz at 11.7 (n = GHz 2); those (n = with 1); those 15 µm with 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 0 (Materialsn = 1) and 2016 11.4, 9, 825 GHz (n = 2)—in agreement with the increase of the ε value when the graphene particle7 of 10 size increases (Figure2a). Figure5 b5b presents presents the the electromagnetic electromagnetic absorption absorp trendtion curvestrend curves of the samples of the oversamples the 4–18-GHz over the frequency4–18-GHz frequency band extracted band fromextracted the near from ﬁeld the free-spacenear field free-space bench measurements. bench measurements. Absorption Absorption variation followsvariation the follows same trendthe same for alltrend samples: for all weaksamples: values we atak lowvalues frequency at low frequency (1 dB/cm for(1 dB/cm the 3-µ form graphenethe 3-µm particlegraphene size particle and 4 size dB/cm and for4 dB/cm the 15- forµm the graphene 15-µm graphene particle sizeparticle at 4 size GHz) at and4 GHz) stronger and stronger ones at highones frequencyat high frequency (7 dB/cm (7 for dB/cm the 3-µ mfor graphene the 3-µm particle graphene size andparticle 16 dB/cm size forand the 16 15- dB/cmµm graphene for the particle15-µm sizegraphene at 18 GHz).particle Note size that at 18 the GHz). pristine Note epoxy that resinthe pristine exhibits epoxy a constant resin absorption exhibits a valueconstant (~0.1 absorption dB) over thevalue full (~0.1 working dB) over frequency the full band. working frequency band.

3.2.2. Influence Influence of the Weight RatioRatio The secondsecond investigated investigated parameter parameter is theis the graphene graphe weightne weight ratio inratio epoxy in resin.epoxy Figure resin.6 aFigure presents 6a thepresents reflected the powerreflected of thepower 3-µ mof graphenethe 3-µm compositegraphene materialscomposite loaded materials with loaded 10%, 20%, with and 10%, 25% 20%, weight and ratio.25% weight The perfect ratio. The reflector perfect and reflector pristine and epoxy pristine resin epoxy curves resin have curves also beenhave plottedalso been for plotted reference. for Thereference. behavior The of behavior the reflected of the power reflected is similarpower tois simi thatlar studied to that in studied Section in 3.2.1 Section, in agreement 3.2.1, in agreement with the relatedwith the complex related permittivitycomplex permittivity values. The values. 10% weight The 10% ratio weight sample ratio shows sample a resonance shows a peak resonance at 11.7 peak GHz (atn =11.7 1); GHz those ( withn = 1); 20% those weight with ratio 20% at weight 10.8 GHz ratio (n at= 10.8 1). The GHz magnitude (n = 1). The peak magnitude is damped peak by the is damped increase ofby thethe grapheneincrease of weight the graphene ratio, due weight to the ra risingtio, due of theto the related rising tan ofδ thevalue related (Figure tan3δb). value It is worth(Figure noting 3b). It thatis worth the resonance noting that peak the is resonance invisible for peak the is 25% invisi weightble for ratio the sample, 25% weight exhibiting ratio thesample, highest exhibiting loss tangent the ofhighest the present loss tangent study (tanof theδ = present 0.36). study (tanδ = 0.36). Figure6 6bb presentspresents thethe electromagneticelectromagnetic absorptionabsorption trendtrend curvescurves ofof thethe samplessamples overover thethe 4–18-GHz4–18-GHz frequency band.band. Absorption variation followsfollows thethe samesame trendtrend asas thatthat observedobserved inin FigureFigure5 b:5b: 1 1 dB/cm dB/cm for 10%10% weightweight ratioratio samplesample andand 55 dB/cmdB/cm for 25% weight ratio sample at 44 GHz;GHz; 77 dB/cmdB/cm for for 10% weight ratio sample andand 1616 dB/cmdB/cm for for 25% 25% weight weight ratio ratio sample sample at at 18 18 GHz.

Figure 6. Reflected power |S11|²2 (a) and electromagnetic absorption α (b) vs. frequency of epoxy Figure 6. Reﬂected power |S11| (a) and electromagnetic absorption α (b) vs. frequency of epoxy resin loadedresin loaded with a with 3-µm agraphene 3-µm graphene particle particle size with size various with weightvarious ratios. weight Pristine ratios. epoxy Pristine resin epoxy values resin are givenvalues for are reference. given for reference.

As expected, high dielectric constant and loss tangent values promote highhigh electromagneticelectromagnetic absorption α, as described by Equation (5)(5) fromfrom [[20]:20]:

ɛ = × r × 1+s () −1, (5) ω µ0ε0 q 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 of the composite material; A is where ω is the working pulsation; c is the speed of light in vacuum; µ0 is the relative permeability an adjustment factor (A = 8.68/100 dB·Np−1) to convert α in dB/cm. In order to check the relevance of of the composite material (µ = 1); (ε0, 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 (Figure3a,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.

Materials 2016, 9, 825 8 of 10 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) (Figure7), 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

EquationMaterials (5)2016 also, 9, 825 explains the linear variation of α versus the working frequency. 8 of 10 Materials 2016, 9, 825 8 of 10

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. variousFigure weight 7. Electromagnetic ratios. absorption α vs. epoxy resin loaded with a 3-µm graphene particle size with various weight ratios. 3.2.3.3.2.3. Particle Particle Size Size and and Weight Weight Ratio Ratio Twofold Twofold Influence Influence 3.2.3. Particle Size and Weight Ratio Twofold Influence TheseThese parameters parameters also also have have an influence an influence on the reflectedon the powerreflected (Figure power8a) and(Figure the electromagnetic8a) and the electromagneticThese parameters absorption also (Figurehave an8b). influence The first on relevant the reflected point concernspower (Figurethe resonance 8a)2 and peaks the absorption (Figure8b). The first relevant point concerns the resonance peaks (|S 11| ≤ −10 dB). electromagnetic(|S11|² ≤ −10 dB). absorption Samples with (Figure a 6–8-µm 8b). The graphene first relevant particle sizepoint and concerns 10% weight the resonance ratio shows peaks two Samples with a 6–8-µm graphene particle size and 10% weight ratio shows two resonance peaks at (|Sresonance11|² ≤ −10 peaks dB). at Samples 7.6 GHz with (n = 1)a 6–8-µmand 15.0 graphene GHz (n = particle2). With sizethe increaseand 10% in weight the weight ratio ratio shows to 15%,two 7.6 GHz (n = 1) and 15.0 GHz (n = 2). With the increase in the weight ratio to 15%, these peaks shift resonancethese peaks peaks shift at at 7.6 5.6 GHz GHz (n ( =n 1)= and1) and 15.0 10.5 GHz GHz (n = ( 2).n = With 2). This the increasebehavior in is the consistent weight ratiowith to that 15%, of at 5.6 GHz (n = 1) and 10.5 GHz (n = 2). This behavior is consistent with that of samples loaded thesesamples peaks loaded shift with at 5.6 a 15-µmGHz ( ngraphene = 1) and particle 10.5 GHz size ( nat = 5% 2). andThis 10% behavior weight is ratios. consistent The secondwith that point of with a 15-µm graphene particle size at 5% and 10% weight ratios. The second point is a behavior samplesis a behavior loaded similar with a to15-µm these graphene samples. particle The re sizeflected at 5%power and 10%of a weightsample ratios. loaded The with second a 6–8-µm point µ similarisgraphene a behavior to these particle samples.similar size towith Thethese a reflected10% samples. weight power The ratio re of andflected a samplethat power of a loaded sample of a with sampleloaded a 6–8- withloadedm a 15-µm graphenewith agraphene 6–8-µm particle µ sizegrapheneparticle with a size 10%particle with weight sizea 5% ratiowith weight anda 10% thatratio weight of are a sampleratioalike. and In loaded thethat same of with a sampleway, a 15- a loadedmsample graphene with loaded a particle15-µm with graphenea size 6-8-µm with a µ 5%particlegraphene weight size ratio particle with are alike.sizea 5% with Inweight the a 15% same ratio weight way, are alike. aratio sample presentsIn the loaded same a similar with way, a |S 6-8-a11 sample|² mto graphenethat loaded loaded particlewith with a a6-8-µm size15-µm with 2 µ a 15%graphenegraphene weight particleparticle ratio presents size size with with a a similar a15% 10% weight |Sweight11| ratio toratio. that presents We loaded attribute a similar with athese 15-|S11|² mresults to graphene that to loaded the particle close with dielectric sizea 15-µm with a 10%grapheneconstants weight and ratio.particle loss We sizetangents attribute with of a thesethe10% two weight results sets of toratio. samples the We close (Tableattribute dielectric 2). these constants results andto the loss close tangents dielectric of the twoconstants sets of samplesand loss (Tabletangents2). of the two sets of samples (Table 2).

Figure 8. Reflected power |S11|² (a) and electromagnetic absorption α (b) vs. frequency of epoxy

Figureresin loaded 8. Reflected with 6–8-µm power |Sand11|² 15-µm (a) and graphene electromagnetic particle sizesabsorption with various α (b) vs. weight frequency ratios. of Pristine epoxy Figure 8. Reﬂected power |S |2 (a) and electromagnetic absorption α (b) vs. frequency of epoxy resin resinepoxy loaded resin values with 6–8-µmare given 11and for 15-µm reference. 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. valuesTable are 2. givenDielectric for reference.constant and loss tangent of epoxy resin loaded with 6–8-µm and 15-µm graphene Tableparticle 2. sizesDielectric with constantvarious weight and loss ratios. tangent of epoxy resin loaded with 6–8-µm and 15-µm graphene Betweenparticle sizes 4 GHz with and various 18 GHz, weight the ratios. absorption α ranges from 3–4 dB/cm at 4 GHz to 8.7 dB/cm at 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 Particle(µm) Size Weight(%) Ratio @10ε GHz’ @10tan GHzδ @18ε GHz’ @18tan GHzδ (µm)6–8 (%)10 @1010.6 GHz @100.14 GHz @1810.2 GHz @180.11 GHz 6–815 105 10.69.5 0.140.15 10.29.2 0.110.10 6–815 155 18.59.5 0.150.18 17.89.2 0.100.18 6–815 1510 18.520.4 0.180.18 17.820.4 0.180.16 15 10 20.4 0.18 20.4 0.16

Materials 2016, 9, 825 9 of 10 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 9 of 10 Particle Size (µm) Weight Ratio (%) ε0 @10 GHz tanδ @10 GHz ε0 @18 GHz tanδ @18 GHz Between6–8 4 GHz and 18 GHz, 10 the absorption 10.6 α ranges from 0.14 3–4 dB/cm10.2 at 4 GHz to 8.7 0.11 dB/cm at 18 GHz 15for the 6–8-µm graphene 5 particle size 9.5 with 10% 0.15weight ratio and 9.2 the 15-µm 0.10graphene 6–8 15 18.5 0.18 17.8 0.18 particle size15 with 5% weight 10 ratio samples. 20.4After a relative 0.18 weight ratio 20.4increase, α ranges 0.16 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. Figure9 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 (Figure4a) with ratio for the three graphene sizes. The three samples exhibit high dielectric constants (Figure 4a) differing loss tangent values (Figure4b). 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 δ particlegraphene size particle with a 25%size with weight a 25% ratio weight sample ratio is compensatedsample is compensated by a higher by a tan highervalue, tanδ and value, therefore and explainstherefore the explains sameness the of sameness the three absorptionof the three responses.absorption Finally,responses. at 10 Finally, GHz, aat minimum 10 GHz, a absorption minimum of 9 dB/cmabsorption is reached of 9 dB/cm with is all reached samples. 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.

4.4. Conclusions Conclusions InIn this this study, study, graphene graphene particles particles were were usedused asas ﬁllerfiller in a thermosetting thermosetting resin, resin, namely namely an an epoxy epoxy resin,resin, in in view view of of microwave microwave absorption absorption and and electromagnetic electromagnetic shielding applications. applications. The The composite composite materialsmaterials produced produced have have thereby thereby been been evaluated evaluated in relation in relation to two to relevant two relevant parameters: parameters: the graphene the 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 µ δ graphene(tanδ = size0.36) (3 andm) a middle and the dielectric highest weight constant ratio value (25%) (ε’ ≃ exhibits12–14) the in the highest 8–10 lossGHz tangent frequency (tan range.= 0.36) 0 andFilling a middle the dielectricepoxy resin constant with valuethe smallest (ε ' 12–14) graphene in the 8–10particles GHz promotes frequency range.high loss Filling tangent the epoxy at resinmicrowaves with the smallestand thus graphenethe microwave particles absorption promotes of highthe electromagnetic loss tangent at waves microwaves by the andcomposite thus the microwavematerial. Moreover, absorption a oflower the dielectric electromagnetic constant waveswill be byfavored the composite to restrict the material. impedanceMoreover, mismatch a lower at dielectricthe interface constant between will be air favored and tosurface restrict samples the impedance and thus mismatch to restrict at thethe interfaceelectromagnetic between wave air and surfacereflectivity samples at andthis thusinterface. to restrict The thecomposite electromagnetic material then wave provides reflectivity a high at this absorption interface. level: The composite from 5 materialdB/cm then at 4 providesGHz to 16 a dB/cm high absorption at 18 GHz. level: from 5 dB/cm at 4 GHz to 16 dB/cm at 18 GHz.

Acknowledgments:Acknowledgments:The The Direction Direction Générale Généralede de l’Armementl’Armement (DGA, France) France) is is gratefully gratefully acknowledged acknowledged for for its its ﬁnancialfinancial support. support.

AuthorAuthor Contributions: Contributions:All All authors authors contributed contributed toto thethe workwork presente presentedd in in this this paper paper and and to to the the writing writing of ofthe the ﬁnal manuscript. final manuscript.

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

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Materials 2016, 9, 825 10 of 10

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

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