Characterization of Dielectric Properties of Graphene and Graphite Using the Resonant Cavity in 5G Test Band

Abstract This paper presents a study about the dielectric constant εr, dielectric loss tangent tan g(δ) and effective electrical conductivity σe of graphene, graphite and graphene-bakelite combination using the resonant cavity method. For this purpose, cylindrical samples with diameter of 30 mm and thickness of 4.5 mm were analyzed taking into account the central frequency f0 = 3.5 GHz, according to 5G technology standards. The constants εr and tan g(δ) were obtained from the resonance frequency fa of measured scattering parameters (S-parameters), when the cavity was loaded with the samples. An empirical equation was developed to model the relation between fa and εr. With this empirical equation it was found εr = 9.3203 and tan g(δ) = 0.7000 for graphene and εr = 17.1508 and tan g(δ) = 0.2700 for graphite. The addition of bakelite in combination with graphene allowed controlling the dielectric properties of these composites. The results, obtained in this macroscale characterization, are interesting for Telecommunications Engineering, especially in the development of radiation-absorbent material, which is suitable for mitigation of interference between different wireless communication systems.

e , dielectric loss tangent tan ( ) g d and effective electrical conductivity e s of graphene, graphite and graphene-bakelite combination using the resonant cavity method.For this purpose, cylindrical samples with diameter of 30 mm and thickness of 4.5 mm were analyzed taking into account the central frequency

I. INTRODUCTION
The investigation of dielectric properties of materials is particularly interesting for Telecommunications Engineering, especially in Microwave Engineering, Antenna Theory and industry of devices for communication systems.Among these properties, the relative electrical permittivity ( r e ) and the dielectric loss tangent ( tan ( ) g d ) can be considered the most relevant ones [1], [2].In the last years, graphene has become the most interesting carbon allotrope for the development of new materials, because of its promising possibilities in terms of technological Characterization of Dielectric Properties of Graphene and Graphite Using the Resonant Cavity in 5G Test Band observed that the variation of graphene oxide inserted into the matrix controls its dielectric constant and dielectric loss tangent values.Bispo et al. described a study about the different polymeric composites production based on polystyrene matrix [7].The composites produced with xerogel, carbon-graphene and graphite presented the most efficient results in terms of electromagnetic absorption in X-band (8.2 -12.4 GHz), where about 87% of the incident electromagnetic power was absorbed by these samples.These analyses were performed considering the macroscale effects of graphene interacting with electromagnetic fields.
The use of resonant cavities is a classic approach for the determination of the properties r e and tan ( ) g d of dielectric materials.This device is typically hollow, with metallic walls composing a cylindrical or a rectangular shape.When a dielectric sample with 1 r e > is inserted into the cavity, its resonance frequency 0 f decreases, due to perturbation of the internal electromagnetic field.From this frequency shift, the r e constant of the sample can be derived [8]- [10].The reports by Rubinger and Costa [11] and Zhang et al. [12] used the resonant cavity method for characterization of dielectric constants of polymeric samples.These parameters were mathematically obtained with specific equations, proposed by the authors, so as to link the measured frequency (for each sample) to the r e constant.In general, up to now, there are several studies about the dielectric properties characterization of graphene and graphite at different frequencies [13]- [15], but not at 3.5 GHz using the resonant cavity method.
Therefore, taking into account the previous comments, in this work, an experimental study for the macroscale characterization of dielectric and loss tangent constants of graphite, graphene and graphene-bakelite combinations using a cylindrical resonant cavity is presented.Initially, the technical details of the design and fabrication of the cavity are presented.Then, a mathematical modeling of this experimental setup is derived and empirical equations for r e and tan ( ) proposed.This approach is validated by the characterization of samples in macroscale, whereby graphene and graphite demonstrated to have large loss constants in the 5G test frequency 3.5 GHz.
This feature indicates that both are potential candidates to be used in the development and production of new radiation-absorbent materials (RAMs).This property is very interesting to mitigate inference between different wireless communication systems.
The next section presents the methodology used in this study.In section 3, the procedure for preparation of the samples and the used materials are described.The measured data (in terms of resonance frequency for each sample) and estimations for r e , tan ( ) g d and s are presented and discussed in section 4. Finally, the conclusions of this work are drawn.

A. Design of the resonant cavity
The design frequency ( 0 f ) was defined as 3.5 GHz, because this is the testing frequency for the development of new technologies for the 5G systems [16] [17].Next, the cavity geometry has been defined to be cylindrical, due to fabrication issues.The cavity dimensions have been optimized using the electromagnetic simulator ANSYS HFSS ® software and are summarized in Table 1, where a is the inner radius, d is the inner height and l is the length of the excitation elements (copper wires).The prototype of this resonant cavity was divided in two parts: the hollow main body and the cover.
The excitation elements have been attached to the latter.Both parts were produced with aluminum, with the dimensions a and d as listed in Table I, and are shown in Fig. 1   A vector network analyzer (VNA) model E5071C (Agilent Technologies) was used for the measurements of the S-parameters for the resonant cavity loaded with graphene, graphite and graphene-bakelite samples.The resonance frequency of the loaded cavity a f can be obtained with this setup and is determined by assessing the frequency for which the lowest value of 11 S is verified.The dielectric constants, of each sample can be estimated from a f with an empirical mathematical equation formulated for r e , whereas the loss tangent can be assessed by parametric simulations with ANSYS HFSS ® .The tan ( ) g d parameter is varied in the simulation model, and its experimental value can be inferred since that, the simulated value of 21 S approaches the magnitude of the measured 21 S in the pass-band.

B. Mathematical Modeling for the r e and tan ( ) g d calculation
The dielectric constant of the samples is calculated from a f , obtained from the measured 11 Sparameter, when the sample is placed inside the resonant cavity.For the r e calculation, a parametric study was performed in ANSYS HFSS ® software, by varying r e from 2 to 20, with a step of 1, in order to assess the resulting a f values and to allow estimating the most appropriate equation for the modeling of the proposed experimental setup.
The mathematical representation is based on the literature for the generalized equations for modeling the perturbation in the resonant cavity [18] and experimental studies presented by Rubinger and Costa [11] and Costa et al. [19].In these papers, the authors show that r e is related to ratio through an empirical equation, which holds exclusively for a given setup (in terms of geometry and dimensions of the cavity and of the samples).The general representation of this relation is given by [18].
From the most suitable function ( ) F x (with 1 r x e = -) that describes the relation between r e and a f , the argument x can be isolated and estimated according to the measured a f for each characterized sample.Finally, considering 1 r x e = + , the dielectric constant for each sample can be calculated.
From the generalized representation given by Eq. ( 1), the mathematical modeling of the present study is developed.In the present study, the samples exhibit cylindrical shape with diameter of 30 mm and thickness of 4.5 mm.The obtained data in parametric analysis with ANSYS HFSS ® simulator are listed in Table II.In Fig. 2, the graphical representation of this "calibration curve" for 0 The mathematical representation that adequately describes the calibration curve in Fig. 2 is given by: Isolating the term r e , the final form of the mathematical representation for this experimental setup is given by

C. Calculation of Effective Electrical Conductivity
The general mathematical representation of tan ( ) g d relates to electrical conductivity as '' 0 ' tan ( ) g s we d we Where, 0 s denotes the static electrical conductivity (S/m), is the angular frequency, in rad/s, ' e and '' e are the real and imaginary components of the electrical permittivity, given in F/m [20].
The term '' we can be also identified as the component of effective electrical conductivity ( e s ) due to the imaginary part of the electrical permittivity.Thereby, '' a s we Finally, replacing (5) With this equation, one can estimate the effective electrical conductivity from the calculated tan ( ) g d for each sample [20].

D. Samples Specifications
The commercial graphene and graphite used in this work were provided by the Brazilian companies Amazonas Grafeno and Nacional Grafite, respectively.Fig. 3 shows an image MEV (a), where it is possible to see the graphene layers, and an average Raman spectrum (~14 spectra taken at different places of one sample) (b) with its characteristic Raman bands (D, G, 2D e 2D ' ), of the graphene 69 powder used to prepare the samples.For these measurements the powder was placed on a SiO2 substrate using the micromechanical method.In order to verify the number of graphene layers the integrated intensity ratio I2D/IG was calculated, finding the value of ~0.6.It is well known that, for free-defect graphene, the I2D/IG is dependent on the number of graphene layers [21].The ratio I2D/IG ∼ 2-3.5 is for monolayer graphene, 1 < I2D/IG <2 for bilayer graphene and I2D/IG < 1 for few layers graphene (FL) as shonw on Fig. 3(a).The samples were produced using the embedding process.The zoomed pictures of the samples gn100 and gt100 (shown in Fig. 4(a) and (b)) are homogeneous and uniform, with some clusters of the material (white dots), indicating that the embedding process was effective in compacting the powder materials.
Samples based on the mixture of three different combinations of graphene and bakelite (powdered polymer that becomes solid) with the procedure described above were also produced for the verification of dielectric properties.The concentration (in %) of graphene and bakelite and their respective masses (g) are shown in Table III.The resulting bakelite-graphene samples are shown in Figs. 4 (c) -(e).The addition of bakelite in these mixtures results in the hardest samples to handle and are more suitable for experimental characterization.As seen for the samples gn100 and gt100 (Fig. 4 (a) and (b)), the zoomed pictures of the samples gn40, gn50 and gn60 (shown Fig. 4 (c -e)), taken with a x10 objective lens of an optical microscope, are also homogeneous and uniform to investigate the dielectric properties at the frequency of 3.5 GHz.It is worth to emphasize that, this frequency can be still considered as low frequency, and then the sample surface does not show significant irregularities that compromise the results at this frequency.

III. EXPERIMENTAL RESULTS
The samples described in the previous section were inserted, one at a time, into the resonant cavity and the S -parameters were measured.This behavior indicates that the dielectric constant of graphite is higher than that of graphene.
According to Fig. 5 (a), the resonance frequency of the cavity loaded with the sample gn100 is  Their analyzed the effects of the microscopic structure of the material and the interactions between the two graphene layers, reporting a dielectric constant of 6.0000 r e = , for BLG.However, Cismaru et al.
[23] obtained a different experimental result using a different characterization method.In their study, a single layer graphene (SLG) was deposited on a gold substrate to compose a coplanar waveguide (CPW) structure.Their samples were characterized from 5 to 40 GHz, obtaining 16.00 r e » at the frequency of 5 GHz.The difference between our results with those reported by other authors is attributed to the use of different characterization techniques applied at different frequencies.The cited studies developed graphene characterization in microscale, while this work considers the characterization of graphene in macroscale and at a lower frequency than the reported by the authors.
According to this, we can argue that different characterization methods and frequencies of analysis will give different responses of the dielectric properties.
For instance, Hotta et al. [24] has presented the characterization of dielectric properties of carbonaceous materials, considering frequencies from 1 GHz to 10 GHz, using the rectangular section waveguide method.In this study, the measured r e constant for the graphite sample is equal to 17.00 in the frequency of 3.5 GHz.Additionally, the authors report that the r e constant of graphite change as the frequency characterization changes.Therefore, we can infer that the characterization methodology adopted in this work is able to provide reliable estimation for r e .According to this procedure, the gn100 sample has tan ( ) 0.7000 g d = and the gt100 sample has tan ( ) 0.2700 g d = .These dielectric loss tangent values are very high and the characterized materials can be considered as very good electromagnetic absorbers at the frequency of interest.These materials have the capability to dissipate energy in its structure, hence producing large attenuation of the electromagnetic waves.For instance, for the gn100 sample, 68.45% of the power coupled to the cavity is dissipated by the sample, and, for gt100, this reduces to 45.32%.Hotta et al. [24] verified that tan ( ) 0.5294 g d » for graphite.This difference can be explained because the authors did not directly characterized this property, but estimated with theoretical equations.4 shows the r e constants calculated for these analyzed samples along with the obtained tan ( ) g d constant in the parametric simulations in ANSYS HFSS ® software.Therefore, the combination of two materials with different characteristics results in a composite with properties that can be controlled based on their concentrations: higher graphene concentrations result in composites with higher tan ( ) g d and r e values, whereas higher bakelite concentrations result in composites with lower tan ( ) g d and r e constants.between r e and the bakelite concentration (in %).The variation of r e and tan ( ) g d is inversely

As shown in
proportional to the bakelite concentration, as shown in Fig. 7(a) and (b).Therefore, the parameters r e and tan ( ) g d on the graphene composites tend to decrease accordingly as the concentration of a material with lower constants r e and tan ( ) g d increases.The effect of increasing r e constant with the addition of higher concentrations of graphene in the samples was also reported by others authors, considering different frequencies of analysis and matrix materials, but their results indicates the same deportment related in the present work.For instance, Bispo et al. [7] produced and characterized the dielectric properties of samples based in a polymeric matrix (polystyrene) with insertion of 10% of Carbon-Graphene Xerogel (CGX).The resulting measured dielectric constant (considering X-band, 8.2 -12.4 GHz) was r e (CGX) = 4.00.However, the reference sample (100% polystyrene) had a dielectric constant r e (matrix) = 2.99.And, Liu et al.
[23] also verified that the insertion of different concentrations of graphene oxide in a polyimide matrix resulted in different r e constants.For the highest concentration of graphene oxide (1%) the measured dielectric constant was 8.00 and the dielectric constant of the reference sample (100% polyimide resin) was r e (matrix) = 3.50.These experimental results were obtained at 1 MHz.
The increase of tan ( ) g d for higher concentrations of graphene in the samples was also observed by Liu et al. [25] even though considering different conditions of frequencies of analysis and matrix material.The authors verified that the insertion of different concentrations of graphene oxide in a polyimide resin matrix resulted in samples with different dielectric-loss constants.For the highest concentration of graphene oxide (1%) the measured tan ( ) g d was 0.12 with tan ( ) g d (matrix)= 0.02 for the reference sample (100% polyimide resin).These experimental parameters were also obtained at 1 MHz.
According to these experimental results, it is convenient to state that the insertion of controlled concentrations of graphene into a specified matrix causes the increase of their dielectric properties r e and tan ( ) g d .It is worth also to emphasize that different authors have determined the dielectric properties of graphene oxide mixing them with different materials and at different frequencies, but as mentioned in the introduction section so far there are not studies of these properties on graphene in the 5G test band (3.5 GHz).These results can contribute for making use these dielectric properties for the development of new RAMs.Marinho et al. [27] also reported that the e s constant of compact graphite structures present values varying to the pressure applied in the samples.In this analysis, the authors showed that, for minimal values of pressure applied in the compression of the samples, the resultant estimated electrical conductivity of sample based in graphite with density equal to 0.8600 g/cm³ is 900.0000 e s » S/mm.This specific result is comparable to the obtained in the present work for gt100 sample.

Finally, in
In addition, the mixture of bakelite with graphene causes a great reduction in e s .This fact can be explained because bakelite has tan ( ) g d lower than and, consequently, its electrical conductivity is also smaller.Then, its combination with graphene yields a composite with reduced electrical conducting capacity.In this work, we reported the characterization of dielectric properties of graphene, graphite and different combinations of bakelite-graphene, considering the test band of 5G (3.5 GHz), and compared these obtained data with previous works found in the literature.Samples entirely produced from graphene and graphite, and samples produced from three different combinations of graphene and bakelite, were analyzed.The high experimental values obtained suggest that these carbonaceous materials are very interesting for the development of technologies for electromagnetic radiation absorbing materials in the radiofrequency spectrum.It was demonstrated in the analysis of bakelitegraphene samples that it is possible to control the dielectric properties of the composites according to the adequate choice of the proportional concentrations of graphene and the matrix material (bakelite, in this work) in the same way as described in the literature.This is very interesting for different applications such as Stealth devices and absorbers materials for anechoic chambers.In addition, the optimal characteristic of electrical conductivity for graphene and graphite also was verified by means of the estimates for e s constant from the tan ( ) g d data.These values are in agreement with other studies previously reported in the literature.

e
and tan ( ) g d were obtained from the resonance frequency a f of measured scattering parameters (S-parameters), when the cavity was loaded with the samples.An empirical equation was developed to model the relation between a f and r e .especially in the development of radiation-absorbent material, which is suitable for mitigation of interference between different wireless communication systems.
(a) an (b).The excitation elements, which consist of two female SMA connectors with inner conductors extended with copper wires coated with nylon polymer, are shown in Fig. 1 (c).

Fig. 2 .
Fig. 2. Calibration curve for the experimental setup designed in this work.

Fig. 4
Fig. 4 shows samples of graphene (gn100) (a) and graphite (gt100) (b) produced from powdered materials (5.5251 g for graphene, and 5.8939 g for graphite), which were singly entered in a hydraulic piston at a constant pressure of 1000 lb/inch² and by applying a heating ramp from 25 o C to 145 o C during 7 minutes.The top temperature (145 o C) was then kept during additional 8 minutes.The final result is a pastille formed by the aggregation of powdered particles.
Fig. 5 shows a comparison of the 11 S (a) and 21 S (b) parameters for gn100 and gt100 samples with the measured parameters considering the unloaded cavity (UC, blue curves of 11 S and 21 S ).In both cases, the minimum values of 11 S and maximum of 21 S .The results obtained are plotted in Fig. 5 for samples gn100 and gt100.These measured values for the graphite sample exhibit larger shifts to lower frequencies when compared to the graphene sample.
Fig 5 (b), the peak magnitude of the measured 21 S is -5.8510 dB.For gt100 sample, it is -3.4430 dB at 3.3300 a f = GHz.The peak magnitude of the measured 21 S -parameter for the unloaded cavity is -0.8210 dB.This reduction in the peak magnitude for the loaded cavity demonstrates the influence of the tan ( ) g d constant on the analyzed materials.For the determination of dielectric loss tangents of the samples, some parametric simulations in ANSYS HFSS ® software, considering the calculated r e constant for each sample, were performed.The correct value of tan ( ) g d is the one where the simulated 21 S -parameter curve approaches the corresponding measured 21 S -parameter curve.

Fig. 6 (
Fig. 6 (a) and (b) show the 11 S and 21 S -parameters for samples manufactured by bakelite-graphene combinations.Measured 11 S -parameters for the loaded cavity with 40% graphene and 50% graphene samples (gn40 and gn50) resulted in a f values very close to each other, resulting in r e values slightly different, as shown in Table IV.However, the sample gn60 (with 60% graphene) presented the same result obtained with sample gn100, i.e. 3.3550 a f = GHz and 9.3203 r e = .Table4shows the r

Fig. 7 .
Fig. 7. Effect of different bakelite concentration on (a) dielectric constant and (b) dielectric loss tangent.

TABLE II .
VALUES OF a f (GHZ) OBTAINED WITH THE PARAMETRIC ANALYSES WITH ANSYS HFSS ® test frequency 3.5 GHz.For other cases, e.g.other frequency of interest, a new calibration curve must be obtained using the methodology explained here.

TABLE IV
These experimental data demonstrate the linear relation (region between dashed red lines) existing Table V the estimated values of electrical conductivity, obtained with Eq. (6), for

TABLE V .
CALCULATED VALUES OF ELECTRICAL CONDUCTIVITY OF SAMPLES FROM GRAPHITE, GRAPHENE AND GRAPHENE-