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High-Temperature Electromagnetic and Thermal Characteristics of Graphene Composites

We describe a method for scalable synthesis of epoxy composites with graphene and few-layer graphene fillers, and report on the electromagnetic interference (EMI) shielding and thermal properties of such composites at elevated temperatures. The tested materials reveal excellent total EMI shielding of ~65 dB (~105 dB) at a thickness of 1 mm(~2 mm) in the X-band frequency range of f=8.2 GHz - 12.4 GHz. The room-temperature cross-plane thermal conductivity of the composite with ~19.5 vol.% of fillers was determined to be ~11.2 W/mK, which is a factor of x41 larger than that of the pristine epoxy. Interestingly, the EMI shielding efficiency improves further as the temperature increases to 520 K while the thermal conductivity remains approximately constant. The excellent EMI shielding and heat conduction characteristics of such multifunctional graphene composites at elevated temperatures are promising for packaging applications of microwave components where EMI shielding and thermal management are important design considerations.

In EMI shielding applications at elevated temperatures, a high thermal conductivity of composites is not only an advantage but a requirement. The absorbed portion of EM wave energy by the EMI shield coating goes to heat. The heat has to be conducted away and dissipated. The reflection property of the EMI shielding material reduces at elevated temperatures because the electrical conductivity of metals decreases with increasing temperature. The high thermal conductivity of the composites is also beneficial for composites, which are used both as EMI shielding materials and TIMs. TIMs are materials which are applied between two solid surfaces in order to fill the microscopic voids at the interface and enhance the thermal transport from a heat source to a heat sink. [87][88][89] The base materials for TIMs are also amorphous polymers, which have low thermal conductivity, typically in the range from 0.2 to 0.5 Wm −1 K −1 . 90 For this reason, the polymers used as base materials for TIM are filled with highly thermally conductive fillers to enhance its overall thermal transport. Among all fillers, mentioned previously, graphene and FLG have both high electrical conductivity and the highest thermal conductivity. [91][92][93][94][95][96] Composites filled with ceramics and other carbon allotropes exhibit lower thermal conductivity comparing to that of graphene. The in-plane thermal conductivity of MXene films is reported to be ~ 3 to ~4 Wm −1 K −1 , which is an order of magnitude less than that of ceramics. 97 The intrinsic thermal conductivity of graphene is in the range of 2000 − 5000 Wm −1 K −1 depending on its lateral dimensions, crystal quality, and defect concentration. [94][95][96] For practical thermal applications, a mixture of graphene and FLG is the most beneficial because FLG retains the excellent heat conduction properties while offering higher cross-section area for the heat flux.
Owing to their mechanical flexibility, graphene fillers facilitate the formation of the interconnected network of FLG fillers. Phonons are the main heat carriers in graphene and FLG. For this reason, large lateral dimensions of the fillers are required in order to preserve the heat conduction properties. 98 The phonon mean free path (MFP) in graphene is ~750 − 800 nm, suggesting that the fillers used in composites should have lateral dimensions exceeding the phonon MFP. 99 The thermal transport properties of FLG are expected to be less affected by the exposure to the matrix material. In our recent study, we reported an enhancement of the thermal conductivity by a factor of ×51 at = 45 vol% loading fraction of a mixture of graphene and FLG. 88 The thermal conductivity of ~15 Wm −1 K −1 can now be routinely reached by an addition of graphene fillers to polymer matrices. [100][101][102] The thermal conductivity enhancement factor depended on the quality of the filler, its average lateral dimension, and the composite synthesis procedure.
Despite the importance of knowing EMI shielding efficiency at elevated temperatures and thermal properties of EMI composites there have been few studies that provided such data. Here, we report on the EMI shielding properties and thermal characteristics of the multifunctional epoxy -based composites with FLG fillers. The composites exhibit room temperature cross-plane thermal conductivity of 11.2 ± 0.9 Wm −1 K −1 and the total shielding efficiency of 65 dB at a thickness of = 1 mm at the filler loading of = 19.5 vol% in the X-band frequency range. The EMI shielding and thermal properties of the samples were examined at the temperatures beyond 500 K.
The results show that the graphene -epoxy samples preserve their excellent heat conduction properties at high temperatures while the EMI shielding efficiency even improves. The excellent EMI shielding and thermal properties of the multi-functional graphene composites at elevated temperatures along with their thermal stability and light-weight are important for electronic packaging and airborne systems where efficient EMI shielding, low cost, and low weight are required at high temperatures and high power densities.

II. Material Synthesis and Characterization
The materials synthesis processes and quality control steps for epoxy-based composites with graphene and FLG fillers are illustrated in Figure 1 (a-e). The samples were synthesized with the commercially available graphene powder (xGnP, grade H, XG-Sciences, USA) and epoxy (Allied High-Tech Products, Inc.). It has been shown that graphene fillers with a larger aspect ratio provide the highest EMI shielding efficiency and thermal conductivity.  Figure S1 (a-b). In order to prepare composites with different filler concentrations, FLG powder was added to epoxy resin in certain amounts, followed by the addition of the hardener.
The compound was mixed using a high shear speed mixer (Flacktek Inc) in several steps to obtain a uniform dispersion. The mixture was vacuumed several times at least for 15 minutes at each step in order to remove any possible voids or air bubbles. The final mixture was poured into round molds, gently pressed, and left to solidify at RT for approximately 8 hours. After curing, the samples were placed to a furnace for ~1 hour at 120 ℃ (Figure 1 a-b). It should be noted that in the EMI shielding experiments, the thickness of the sample affects its absorption and thus, its total shielding efficiency. Therefore, for detailed comparison, all samples were polished down to the same thickness of ~1.00 mm. An optical image of the pristine epoxy and the composite with 11.4 vol% and 15.3 vol% of graphene fillers is shown in Figure 1 (c).
[ Figure 1] The quality of the samples was verified by the SEM inspection and Raman spectroscopy. Raman spectra of representative samples with different graphene loadings are shown in Figure 1 (d). The intensity of the characteristic Raman peaks of graphene, namely the G peak at ~1570 cm −1 and 2D band at 2700 cm −1 , increases as more graphene is loaded to the epoxy. These two peaks are not distinguishable in the samples with graphene loading less than ≤ 1.5 vol%. The variations in the graphene filler concentration and their overlap are clearly seen in the SEM image of the composite with 15.3 vol% of the fillers (see Figure 1 (e)). Additional data of SEM inspection of the samples are provided in the Supporting Information ( Figure S1 (c-f)). The data confirm that at high loadings, graphene fillers overlap forming the electrically percolated networks. The filler attachments and percolation strongly affects the electrical and thermal characteristics of the composites, and finally their EMI shielding performance at RT and above. The process of EM wave interaction with the graphene composite is illustrated in Figure 1 (f). Large hexagons indicate FLG fillers. A fraction of the incident EM wave is reflected at the air-composite interface. A part of the EM wave, which passes through the composite's interface, is absorbed directly or after multiple internal reflections inside the composite. Only a small fraction of the incident EM wave is transmitted through the samples. The absorption of EM waves results in the increase of the composite's temperature, which explains the need for high thermal conductivity of EMI shielding material. In the schematic, the red arrows indicate the highly conductive paths for heat dissipation through the fillers inside the epoxy polymer base. The EMI shielding efficiency and the crossplane thermal conductivity of the samples were measured using a programmable network analyzer (see Figure S2) and a "laser flash" instrument (see Figure S3). The schematic and operational principles of both systems are shown in Figures 1 (g-h). The details of the experimental setups and measurements are provided in the Methods and Supporting Information.

III. Results and Discussion
EMI Shielding: To determine EMI characteristics, we measured the scattering parameters, , using the two-port PNA system at RT and higher temperatures. The indices and represents the ports, which are receiving and emitting the EM waves. Each port can simultaneously emit and detect the EM waves and thus, the results of the measurements include four parameters of 11 , 12 , 21 , and 22 . Given that the samples are symmetric, one can expect that | 11 | = | 22 | and | 12 | = | 21 |. The scattering parameters are related to the coefficients of reflection, = | 11 | 2 , and transmission, = | 21 | 2 . 108 Knowing these two coefficients, one can obtain the coefficient of absorption, , according to = 1 − − . This is because for any EM wave incident on the sample, a fraction is reflected at the interface. A part of EM wave, which enters the composite, is absorbed and the rest is transmitted. The coefficient of absorption, which is defined as the power percentile of the absorbed EM way in the medium to the total power of incident wave, is not truly indicative of material's ability in absorbing the EM waves. This is because some part of the wave is reflected at the interface prior to entering the medium. For this reason, the effective absorption coefficient, , is defined as After determining , , and , the shielding efficiency of the material can be calculated. The calculated , , and as a function of the frequency for the samples with different FLG concentrations are presented in Supplementary Information Figure S4.
The attenuation of EM waves in a conductive medium is related to the skin depth, . 108 In good conductors, = ( ) 1/2 where , , and are the EM wave frequency, medium's permeability and electrical conductivity, respectively. Graphene and FLG are good conductors of electricity.
The sheet resistance of SLG and FLG vary from ~100 Ω up to 30 kΩ depending on the number of layers and quality. 91-93 Pristine epoxy, on the other hand, is an electrical insulator with the conductivity in the order of ~10 −16 Sm −1 . 109 Addition of FLG to the epoxy, increases the composite's electrical conductivity after the establishment of the percolation network of the fillers.
The results of the standard four-probe in-plane electrical conductivity measurements of the epoxy with FLG as a function of the filler loading are presented in Figure 2 (b). The details of the measurements are explained in the Methods and Supporting Information. The abrupt change in conductivity observed at = 2.5 vol% indicates the onset of the electrical percolation where the large FLG fillers inside the insulating polymer matrix create an electrically conductive network.
Electrical percolation is theoretically described by power scaling law, ~( − ℎ ) , where ℎ is the filler loading fraction at the electrical percolation threshold, and is the "universal" critical exponent. 103,110 The coincidence of the electrcial percolation threshold shown in Figure 2 (b) and the filler loading at which the abrupt change in the effective absorption and transmission is observed demonstrate the correlation among these parameters.
[ Figure 2] The total shielding efficiency, , describes the total attenuation of the incident EM wave as it hits and passes through the composite. This parameter determines the material's ability to block the EM waves and consists of two terms of reflection loss, or reflection shielding efficiency, , and absorption loss, or absorption shielding efficiency, . These parameters can be calculated in terms of , , and as follows 2,108 where , , , and are the power of incident, reflected, absorbed, and transmitted EM wave, respectively. Figure 3 (a-c) shows , , and of the samples as the functions of the graphene filler loading. As more fillers are loaded to the pristine epoxy polymer, rapidly increases ( Figure   3(a)). At ≥ 2.5 vol%, the enhancement in reflection becomes slower, and the saturates, i.e.
it does not increase significantly with more graphene loading. The reflection efficiency is directly related to the surface electrical conductivity or, in other words, the concentration of free charge carriers at or near the interface. The saturation behavior of indicates that the large graphene fillers are overlapping at the surface of the sample, increasing the overall electrical conductivity of the sample by orders of magnitude as compared to that of pristine epoxy or composites with low loading. Note that at = 2.5 vol%, ~73% indicating that most part of the incident EM wave is already reflected back at the interface. In contrast, increases with adding more fillers ( Figure 3 (b)). In samples with ≥ 2.5 vol%, the absorption loss becomes the dominant shielding mechanism. This can be seen clearly at higher filler loadings where approaches 52 dB at = 19.5 vol% meaning that almost all the remaining fraction of the EM wave, which passes through the medium after reflection, is being absorbed by the composites. Figure 3 (c) presents the total EMI shielding efficiency of the samples as a function of the graphene loading. The average reflection, absorption, and total shielding efficiency of composites over the complete X-band frequency range as a function of graphene loading are shown in Figure 3 (d). As it is seen and described previously, the reflection loss (red circles) initially increases but then saturates and becomes almost constant at ≥ 2.5 vol% whereas the absorption and thus, total shielding efficiency continue to increase with addition of more fillers. One can summaries the difference in behavior by noting that reflection is mostly a surface phenomenon while absorption happens ij the volume of the composite. The electrically conducting percolation network forms at the surface at lower graphene loading than in the volume of the material.
[ Figure 3] In Figure 4 (a-b)  at the level of the total 30 dB shielding efficiency. 2,23 Another advantage of the graphene-enhanced epoxy composites is that they provide higher EM shielding at much lower weights and with stable mechanical structure as compared to conventional metallic enclosures, which are widely used in electronic packaging.
[ Figure 4] Densely packed electronics, in addition to emitting undesirable EM waves to the environment, dissipate high amounts of heat, which leads to the increase in temperature of all components in the electronic package. A part of the EM wave, which turns into heat during the absorption process, can be described by the following equation: 20 Here, is the power, 0 and ′′ are the vacuum and imaginary part of medium's relative permittivity, and 0 and ′′ are the vacuum and imaginary part of medium's relative permeability.
The first, second, and the third terms in the right hand side correspond to the Joule heat loss, dielectric loss, and magnetic loss, where the latter is negligible for the epoxy composites with graphene. The temperature-rise in most cases adversely affect the ability of materials in blocking the EM waves. In this regard, the EM shield material must possess a high thermal stability, i.e.
preserving its EM shielding characteristics even at elevated temperatures at least up to 500 K, and relatively high thermal conductivity in order to dissipate heat to the environment. as the temperature increases from RT to ~520 K. In Figure 5 (d-f), we present color maps of as the function of temperature and frequency for composites with the low (3.5 vol%), medium (9.3 vol%), and high (17.1 vol%) graphene loadings. In contrast to some prior studies, we observed a continuous increase in the for all filler loadings. 30,111 The increase in the is originated mainly from the enhancement in absorption loss rather than increase in the reflection attenuation (see Figure S5). The epoxy composites reach the electrical percolation threshold at a rather low FLG concentration of ~2.5 vol%. In these samples, the absorption is defined by the electrical conductivity. In a disordered system of randomly dispersed FLG fillers in a polymer matrix, the conductivity by migrating electrons ( ) in the plane of FLG fillers and conductivity by hopping electrons ( ℎ ) among the different FLG fillers affect the bulk average electrical conductivity of the composite. The hopping conductance mechanism is generally described as ℎ ~ −( 0 ⁄ ) where 0 depends on the material's property and is a parameter defined by the type of hopping. As the temperature increases, the hopping conductivity strongly increases. One should note that it is known that the electrical conductivity in graphite and graphene also increases with rise. 111,112 For these reasons, both mechanisms of electrical conduction in epoxy-graphene composites enhance with increasing temperature. The latter explains the increase in the absorption and the EMI shielding efficiency at elevated temperatures.
The high thermal stability of epoxy composites laden with FLG fillers provides several advantages over other types of EM shielding materials and fillers, e.g. ceramics, ferromagnets, or MXenes.
Ceramic-based composites usually use SiC, which, although thermally stable, has rather poor High-Temperature Electromagnetic and Thermal Characteristics of Graphene Composites − UC Riverside 14 | P a g e absorption properties. The ferromagnetic fillers lose their magnetic properties as the temperature passes the Curie temperature, causing the drop in their magnetic shielding characteristics at elevated temperatures. The MXene fillers and films exhibit high shielding efficiencies but prone to formation of oxide layers and reveal poor thermal conductivity making them unsuitable for hightemperature EMI shielding applications. 26,27,97,113 [Figure5] Thermal Characteristics: The cross-plane thermal diffusivity and conductivity of the composites at RT and at elevated temperatures were measured using the "laser flash" analysis (LFA, 467 HyperFlash, NETZSCH, Germany). The schematic and operational principal of the measurements are shown in Figures 1 (i). The details of the experimental setup and measurements are provided in the Methods. The thermal diffusivity, , was measured directly while the thermal conductivity, , was calculated as = , where and are the mass density and the specific heat. Figure   6 (a-b) shows the cross-plane thermal diffusivity and thermal conductivity of the composites as the functions of the graphene loading. Both thermal characteristics, and , grow fast with increasing graphene loading. The super-linear, nearly of higher than quadratic, dependence of the thermal characteristics of the composites as the function of the filler loading is attributed to creation of the highly thermally conductive paths of the percolated FLG fillers. The mechanism of the thermal percolation in epoxy composites with graphene has been described by us previously. 88,100,114 One should note that epoxy composites with only 19.5 vol% FLG loading provide crossplane thermal conductivity of 11.2 ± 0.9 Wm −1 K −1 , which is comparable to that of the ceramic materials, widely used in high−temperature EMI shielding, specifically for their rather high thermal conductivity and thermal stability. The advantage of graphene composites over conventional ceramics is that their EMI shielding efficiency is much higher and their weigh is much lower than that of conventional ceramics.
In order to investigate the thermal stability of the composites, we carried out temperature dependent thermal diffusivity and conductivity experiments in the temperature range between RT to 460 K. the results of the measurements are presented in Figures 6 (c-d). The thermal diffusivity of the samples decreases with increasing the temperature. The rate of change is more significant for the composites with higher graphene loadings. However, the thermal conductivity is almost constant owing to the increase in the specific heat as the temperature increases. One should note that the reported data is for the thermal transport properties in the cross-plane direction. The inplane thermal conductivity of the samples is expected to be much higher because graphene flakes tend to align in the in-plane direction during the fabrication process. 102 The nearly constant high thermal conductivity of the composites over a wide temperature range demonstrates that epoxy with graphene fillers can serve as a multifunctional composite for applications in electronic systems, providing excellent EMI shielding, heat dissipation, mechanical support and adhesion even at elevated temperatures.

IV. Conclusions
We examined the EMI shielding efficiency and thermal conductivity of multi-functional epoxy composites with graphene fillers at elevated temperatures. It was found that graphene composites with the filler loading of = 19.5 vol% exhibit a high total shielding efficiency of 65 dB The PNA was calibrated for 2-port measurements of scattering parameters at input power = 3 dBm. A WR-90 commercial grade straight waveguide with two adapters at both ends with SMA coaxial ports was used as a sample holder. In order to carry out high-temperature RF measurements, the waveguide with the sample were heated using a hot-plate heater. The temperature of the waveguide and the samples were measured using 6 thermocouples attached at different points of the waveguide (see Figure 1 (g)). Prior to collecting the temperature dependent RF measurements, the waveguide without any samples was tested in the temperature range between RT and 520 K. The performance of the waveguide did not change with temperature rise. Figure S6 shows the of the bare waveguide without any samples as a function of temperature.
Special cables were used for high temperature RF measurements. The samples with diameter ≥      ) of the composite of 1 mm thickness in the frequency range from 8.0 GHz to 12.4 GHz at different graphene loading fractions. With the increasing graphene loading, the EMI shielding efficiency of the composites improves significantly. The total EMI shielding of the composites reaches to ~65 dB at 19.5 vol% of the graphene filler concentration.

Figure 4:
Total EMI shielding of epoxy composites with (a) 13.4 vol% and (b) 18.8 vol% graphene filler loading as a function of frequency at different thicknesses. Total EMI shielding of the epoxy composites with (c) 13.4 vol% and (d) 18.8 vol% loading of the filler versus thje thickness of the composites at frequencies of 8.5, 9.5, and 11.5 GHz. Note that the EM shielding increases linearly with increasing the thickness of the composite owing to the increase in shielding by absorption. The EMI efficiency increases with temperature in all samples. The color map of the total EMI shielding efficiency of the composites with (a) 3.5 vol% (b) 9.3 vol% and (c) 17.1 vol% of graphene filler loading as a function of frequency in the temperature range from 303 K to 523 K. The EMI attenuation for all samples increase as the temperature rises. The enhancement is more pronounced at higher frequencies. thermal conductivity of the composites as a function of graphene loading fraction at room temperature. The thermal conductivity exhibits a quadratic dependence on the filler loading except near the loading ~11.4 vol% where there is plateau-like dependence attributed to the formation of graphene clusters. (c) Thermal diffusivity and (d) thermal conductivity of three different composites with the low, medium, and high loading of graphene fillers as a function of temperature. The thermal diffusivity decreases with temperature. The thermal conductivity remains nearly constant because the increase in the specific heat compensates for the decrease in thermal diffusivity as the temperature rises.