We report compressive mechanical response of graphene foams (GFs) and the thermal resistance (RTIM) between copper (Cu) and GFs, where GFs were prepared by the chemical vapor deposition method. We observe that Young’s modulus (EGF) and compressive strength (σGF) of GFs have a power law dependence on increasing density (ρGF) of GFs. The maximum efficiency of absorbed energy (ηmax) for all GFs during the compression is larger than ∼0.39. We also find that a GF with a higher ρGF shows a larger ηmax. In addition, we observe that the measured RTIM of Cu/GFs at room temperature with a contact pressure of 0.25 MP applied increases from ∼50 to ∼90 mm2 K/W when ρGF increases from 4.7 to 31.9 mg/cm3.

Three-dimensional (3D) carbon structures have attracted much attention for the past decades due to unique structural properties (e.g., lightweight, flexibility) and excellent electrical and thermal properties. In particular, after the pioneering experiments on graphene,1 there are a lot of efforts to develop 3D graphene based structures by using chemically exfoliated graphene derivatives such as graphene oxide (GO) or reduced GO.2 It has been demonstrated that this approach (assembling graphene derivatives to 3D structures) can be useful for some applications.2 However, the quality of graphene derivatives is usually inferior to pristine graphene or graphite due to significant defects caused by the chemical exfoliation process. In addition, the 3D structures prepared by assembling graphene derivatives inevitably include many thermal or electrical interfaces (between graphene and graphene, or graphene and polymer matrices in their composites), causing deterioration of electrical and thermal transport in freestanding structures or their polymer composites.

On the other hand, 3D interconnected graphene structures grown by the chemical vapor deposition (CVD) method such as graphene (or graphitic) foams (GFs), in which the quality of graphene is comparable to pristine graphene or graphite, have been recently developed3 and enabled us to achieve continuous structures with less redundant interfaces, providing good electrical and thermal conduction paths in ultra-lightweight structures.3,4 GFs grown by CVD have been demonstrated to be useful for applications for elastic polymeric conductors, electromagnetic interference (EMI) shielding, gas sensors, electrochemical applications (e.g., biosensors, electrodes for batteries and supercapacitors), packaging, and thermal interface materials (TIMs).5–8 

In particular, 3D GFs or their composites are promising materials for TIM applications and packaging applications due to their excellent thermal and mechanical properties. One can achieve efficient heat conduction across thermal interfaces by filling in surface irregularities (e.g., air gaps) at the interfaces with TIMs. In general, many TIMs are composite materials consisting of fillers (e.g., metal, ceramic, or carbon based particles) and matrices (e.g., hydrocarbon oil, silicone oil, epoxy, or phase change materials). The thermal resistance (RTIM) of those composite TIMs at interfaces can be 2-60 mm2 K/W.9,10 On the other hand, the RTIM of a graphite paper or a carbon nanotube paper can be 20-170 mm2 K/W, which is usually higher than that of those composite types of TIMs by one order of magnitude.11–13 In this work, we studied the compressive mechanical response of GFs with various densities (ρGF), and the RTIM between copper (Cu) and compressed GFs, where GFs were prepared by the CVD method. Some studies on GFs prepared by the CVD method have been reported but most of these studies have focused on GFs with a limited range of ρGF. The ρGF-dependent mechanical response and RTIM for CVD-grown GFs (at the ρGF range of a few mg/cm3 to tens of mg/cm3) have not been reported, despite the promise of thermal interface applications and many mechanical applications. Such studies as reported in this work will provide insights into the mechanical response of GFs under compression and the RTIM for particular packaging applications or thermal interface applications.

We prepared GFs using a similar method as described in Ref. 3. Nickel (Ni) foams (70 pores/in. and 3 mm-thick) were cleaned with 20% acetic acid solution for 1 h and rinsed with deionized water. Pre-cleaned Ni foams were loaded into a horizontal CVD furnace chamber and annealed at 1050 °C for 1 h with a flow of H2 (30 sccm) and Ar (170 sccm). GF was grown on the Ni foam with a flow of CH4 (20 sccm), H2 (20 sccm), and Ar (210 sccm) for 8-120 min. After the growth, we coated the GF/Ni foam with polymethyl methacrylate (PMMA) to protect the GF from an etching process. The Ni foam was etched by 1M (molar concentration) iron nitrate nonahydrate (>98%, Sigma Aldrich) solution at 90 °C for 2 days and additionally etched by 1M hydrochloric acid solution at 90 °C for 2 days. After the etching process, we removed PMMA using acetone.

Microscopic structures of GFs were studied using a scanning electron microscope (SEM) (FEI Nova 200 NanoLab DualBeam SEM). X-ray diffraction spectra of GFs were collected using an X-ray diffractometer (Bruker D8 Focus) with a Cu Kα radiation source (wavelength ∼1.54 Å). We performed Raman spectroscopy on GFs using a confocal Raman microscope (Horiba Jobin Yvon Xplora) with a 100× objective lens and a 532 nm laser (∼1 mW of incident power on the sample). We conducted the compression test using a universal mechanical test system (Instron 3345) with a 50 N load cell. We prepared a square-shaped GF (10 mm × 10 mm × 3 mm) and placed the GF between two parallel metal plates (each metal plate is mechanically attached to the upper and lower anvil platens, respectively) as shown in the inset in Fig. 2(a). Before the compression test started, we performed calibration and zeroing of the system. The compression test was performed at a strain rate of 3 μm s−1. The data for displacement and force were recorded using the Bluehill software (provided by Instron). On average, four samples for each density were studied to extract the Young’s modulus (EGF) and compressive strength (σGF) of GFs, and we report average and standard deviation of the measured values. We measured the RTIM between Cu and compressed GFs while changing the contact pressure from 0.14 to 1 MPa, using a modified ASTM D5470 method described in Ref. 14. In short, GFs were placed between the upper and lower heat flux meters (Cu rods with a diameter of 19.05 mm), where each surface of the Cu rods was polished using 1 μm alumina particles (root mean square roughness of the Cu surface ∼300 nm). A heating power was supplied by a 50 Ω cartridge heater attached on the upper heat flux meter, and a cooling power was applied by flowing water with a controlled fluidic pressure. Temperatures along the heat flux direction were measured using six Pt resistance temperature detectors (RTDs) when a steady state condition is reached. The heat flux and temperature were controlled by a temperature controller (Lake Shore 340).

Figs. 1(a) and 1(b) show microscopic structures of GFs with different ρGF (density of the uncompressed and as-grown GFs unless otherwise noted), confirming 3D interconnected structures (consisting of interconnected graphitic ligaments) with a pore size of 100-500 μm. In general, we find that the surface morphology of low-density GFs is smoother than that of high-density GFs, as also observed in the previous studies.4 We studied the crystal structure of GFs using XRD as shown in Fig. 1(c). We observe two significant peaks at 2θ = 26.5° and 54.6°, originating from (002) and (004) planes in graphite, respectively (JCPDS 75-1621).15 The interplanar spacing is calculated to be ∼3.36 Å, similar to that of highly oriented pyrolytic graphite (HOPG).4 In addition, the representative Raman spectrum of a GF in Fig. 1(d) demonstrates a low defect density, as shown in the negligible intensity of the Raman “D” peak, indicating a high-quality graphitic structure.

FIG. 1.

((a) and (b)) SEM images of as-grown graphene foams (GFs) with a density (ρGF) of (a) 4 and (b) 13.5 mg/cm3. (c) Representative XRD spectrum of an as-grown GF. (d) Representative Raman spectrum of an as-grown GF.

FIG. 1.

((a) and (b)) SEM images of as-grown graphene foams (GFs) with a density (ρGF) of (a) 4 and (b) 13.5 mg/cm3. (c) Representative XRD spectrum of an as-grown GF. (d) Representative Raman spectrum of an as-grown GF.

Close modal

It is important to understand the mechanical response of GFs for some applications such as packaging or TIMs. We studied the stress (σ)-strain (ε) behavior of GFs as shown in Fig. 2(a), by applying the compressive load. The compressive mechanical response for GFs exhibits three distinct regions (labeled in Fig. 2(a)): a linear elastic region, a plateau region (plastic deformation region), and a densification region. We observe that the linear elastic region occurs below ε ∼ 0.1 for GFs with various ρGF, which is related to elastic bending of graphitic ligaments in GFs. Unlike the elastic region, the plateau region, where σ is almost independent of ε, originates from plastic collapses of graphitic ligaments. We also find noticeable peaks for high-density (e.g., 31.5 mg/cm3) GFs in the plateau regime, indicating multi-stage collapses of those graphitic ligaments, similar to the previous report.16 Above the plateau region, it is observed that σ sharply increases with increasing ε, suggesting that graphitic walls touch together and start to be packed. Thus, a higher σ is required to displace GFs, resulting in decreasing efficiency for the GFs to absorb energy during the further compression, as shown below.

FIG. 2.

(a) Compressive stress (σ)-strain (ε) curves of graphene foams (GFs) with various densities (ρGF). Inset: illustration of the compression test setup. (b) Compressive Young’s modulus (EGF) of GFs as a function of ρGF. Inset: ln(EGF) versus ln(ρGF/ρs), where ρs is the density of bulk graphite. (c) Compressive strength (σGF) of GFs as a function of ρGF. Inset: ln(σGF) versus ln(ρGF/ρs).

FIG. 2.

(a) Compressive stress (σ)-strain (ε) curves of graphene foams (GFs) with various densities (ρGF). Inset: illustration of the compression test setup. (b) Compressive Young’s modulus (EGF) of GFs as a function of ρGF. Inset: ln(EGF) versus ln(ρGF/ρs), where ρs is the density of bulk graphite. (c) Compressive strength (σGF) of GFs as a function of ρGF. Inset: ln(σGF) versus ln(ρGF/ρs).

Close modal

The compressive Young’s modulus (EGF, the slope of σ-ε in the elastic regime) of GFs increases from ∼16 kPa to ∼418 kPa with increasing ρGF of GFs from ∼4 to ∼32 mg/cm3, as shown in Fig. 2(b). The trend shows a power law dependence on ρGF (Fig. 2(b) inset). Similarly, the compressive strength (σGF, the stress at which the plastic deformation starts) of GFs as a function of ρGF also exhibits a power law dependence on ρGF as shown in Fig. 2(c). The ρGF-dependent EGF (or σGF) can be explained by the Gibson-Ashby (GA) model.17–19 For our GFs, which are similar to plastic open-cell structures, EGF and σGF follow (EGF/Es) = C1(ρGF/ρs)n and (σGFs) = C2(ρGF/ρs)m, respectively, where ρs, Es, and σs are the density (∼2.2 g/cm3), Young’s modulus (∼20 GPa),20,21 and compressive strength of CVD-grown bulk graphite, respectively, and C1 and C2 are constants. The fitting of data yields n ∼ 1.6 and m ∼ 1.3 (as shown in the insets in Figs. 2(b) and 2(c)), respectively, compared to the expected n = 2 and m = 1.5 for the theoretical GA model.18 Power law dependence of the Young’s modulus has been found in various carbon based 3D structures but the experimentally measured exponent n could vary from ∼1 to ∼5, indicating that the exponent strongly depends on structural details.22 

The energy absorption properties of GFs with various ρGF could provide fundamental information for designing proper cushion or packaging materials. Fig. 3(a) shows representative energy absorption diagrams (W/Es vs. σ/Es) for GFs with various ρGF, where W(=0εmσ(ε)dε) is the energy absorption capacity (absorbed energy per unit volume) up to a strain εm (which is varied from 0 to 0.9 to calculate W(εm) from the data in Fig. 2(a), and correspondingly σ = σ(εm)).18 For GFs with different ρGF, we observe that W/Es gradually increases with increasing σ/Es, and then the sharp increase (particularly pronounced in high-density GFs) of W/Es occurs in the plateau region (the plastic deformation region in σ-ε curves). Above the sharp increase, the saturation region of W/Es is observed, implying that the absorbed energy does not change significantly above the onset of densification. In general, to design cushion materials for packaging, it is believed that the optimal energy absorption can be achieved around the onset of the densification at a given density. In particular, around the onset of densification, W/Es of a GF with ρGF = 31.5 mg/cm3 is larger by one order of magnitude than that of a GF with ρGF = 4 mg/cm3, implying that a larger energy can be absorbed in GFs with a higher ρGF. It is observed that the densification for all GFs occurs around εm = 0.6-0.7.

FIG. 3.

(a) Energy absorption diagrams (W/Es versus σ/Es) for graphene foams (GFs) with various densities (ρGF), where W is the absorbed energy per unit volume, Es is the Young’s modulus of bulk graphite, and σ is the stress. (b) Energy absorption efficiency (η = W/σ) of GFs with various ρGF as a function of σ. (c) Ideality factor (β = W/(σεm), where εm is varied from 0 to 0.9) of GFs with various ρGF as a function of σ. (d) Maximum η (ηmax) and maximum β (βmax) of GFs as a function of ρGF. The red dashed line represents an ideal plastic foam (β = 1).

FIG. 3.

(a) Energy absorption diagrams (W/Es versus σ/Es) for graphene foams (GFs) with various densities (ρGF), where W is the absorbed energy per unit volume, Es is the Young’s modulus of bulk graphite, and σ is the stress. (b) Energy absorption efficiency (η = W/σ) of GFs with various ρGF as a function of σ. (c) Ideality factor (β = W/(σεm), where εm is varied from 0 to 0.9) of GFs with various ρGF as a function of σ. (d) Maximum η (ηmax) and maximum β (βmax) of GFs as a function of ρGF. The red dashed line represents an ideal plastic foam (β = 1).

Close modal

However, in order to make fair comparisons of the energy absorption properties for GFs with various ρGF, the efficiency of absorbed energy during compression should be considered. Figs. 3(b) and 3(c) show the energy absorption efficiency (η = W/σ, the ratio of the energy absorbed by GFs per unit volume to σ applied) and the ideality factor (β = W/(σεm), the ratio of the energy absorbed by GFs up to εm with σ = σ(εm) to that by an ideal plastic foam with constant σ), respectively.23 It is also found that η and β dramatically increase with increasing σ until GFs enter the densification regime and then more gradually decrease beyond this regime, showing that our GFs could be more suitable for applications requiring a low stress below ∼20 kPa. As shown in Fig. 3(d), for our GFs, the average values (among multiple samples tested) for ηmax and βmax are larger than 0.39 and 0.68, respectively, which are comparable to or higher than those of many polymeric foams.23 The highest ηmax (∼0.5) and βmax (∼0.98) are found at GFs with the highest ρGF (∼32 mg/cm3), implying that the compression response of GFs with a higher ρGF becomes close to an ideal plastic foam (β = 1).

In order to evaluate usefulness of GFs as TIMs, we investigate thermal resistance at interfaces (RTIM = 2Rint + t/κ, where Rint is the interfacial thermal resistance between Cu and compressed GFs, t is the thickness of the compressed GFs, and κ is the thermal conductivity of the compressed GFs) between Cu and GFs with various applied contact pressures. The detailed measurement setup and process can be found in Ref. 14. The measured RTIM of GFs as a function of ρGF at room temperature with a contact pressure of 0.25 MPa is shown in Fig. 4(a) and the inset shows a representative temperature profile along the upper heat flux meter (Cu)/GF(ρGF = 4.7 mg/cm3)/lower heat flux meter (Cu). We observe that RTIM of GFs increases from ∼50 to ∼90 mm2 K/W when ρGF increases from 4.7 to 31.9 mg/cm3. RTIM of our GF with 4.7 mg/cm3 is larger by at least a factor of 7–10 than that of GFs measured at 0.23 MPa in a previous report.8 We speculate that the portion of bulk contribution (t/κ) is more significant than that in Ref. 8, possibly due to our use of GFs with a higher ρGF giving a larger t at a given contact pressure (but a density information was not given in Ref. 8), or use of thicker pre-compressed GFs (3 mm-thick). We also studied RTIM of GFs with various ρGF as a function of the contact pressure applied, showing a decrease in RTIM with increasing the pressure applied, related to a decrease in thickness (t) of the compressed GFs and an increase in the real contact area between Cu and the compressed GFs at a higher contact pressure. In general, low-density GFs have larger compressibility, resulting in a larger contact area and a smaller t at a given contact pressure.

FIG. 4.

(a) Thermal resistance (RTIM) between graphene foams (GFs) and copper (Cu) as a function of density (ρGF) with a pressure of 0.25 MPa applied at 300 K. Inset figure shows a representative temperature profile along the upper heat flux meter (Cu)/GF(ρGF = 4.7 mg/cm3)/lower heat flux meter (Cu), and the temperatures (from T1 to T6) are read by RTDs in the heat flux meters (blue colored), where the black arrow represents the heat flux direction and the red line represents the compressed GF (the thickness (t) of the compressed GFs is usually less than 500 μm). (b) RTIM of GFs with various ρGF as a function of pressure applied at 300 K.

FIG. 4.

(a) Thermal resistance (RTIM) between graphene foams (GFs) and copper (Cu) as a function of density (ρGF) with a pressure of 0.25 MPa applied at 300 K. Inset figure shows a representative temperature profile along the upper heat flux meter (Cu)/GF(ρGF = 4.7 mg/cm3)/lower heat flux meter (Cu), and the temperatures (from T1 to T6) are read by RTDs in the heat flux meters (blue colored), where the black arrow represents the heat flux direction and the red line represents the compressed GF (the thickness (t) of the compressed GFs is usually less than 500 μm). (b) RTIM of GFs with various ρGF as a function of pressure applied at 300 K.

Close modal

In summary, we investigated the compressive mechanical response of GFs and thermal resistance (RTIM) at interfaces between GFs and Cu in order to evaluate usefulness of GFs for packaging or thermal interface application. We observe that Young’s modulus (EGF) and compressive strength (σGF) of GFs follow the power dependence on the density (ρGF) of GFs with the exponent n = ∼1.6 and m = ∼1.3, respectively. In addition, we find that the maximum efficiency of absorbed energy (ηmax) and the maximum ideality factor (βmax) of GFs during compression can be as high as ηmax ∼ 0.5 and βmax ∼ 0.98, which are comparable to or higher than those of many polymeric foams. We also characterized the RTIM at interfaces between Cu and GFs with various ρGF. We measure RTIM of a GF with ρGF = 4.7 mg/cm3 to be ∼50 mm2 K/W with 0.25 MPa applied and it can be ∼25 mm2 K/W with 1 MPa applied, which is comparable to commercial graphite papers (20-170 mm2 K/W).11,12 The measured RTIM is found to be larger than that of GFs in the previous report, possibly due to the significant bulk contribution (t/κ). However, with a proper selection of templates for the CVD process, a proper selection of ρGF, or a use of polymers, we believe that RTIM can be reduced further and the energy absorption property can be tunable as well, possibly making GFs a promising material for many applications including packaging and thermal interface materials.

We thank Dr. Rebecca Kramer at Purdue University for access to Instron 3345 and also thank Ms. Michelle Yuen at Purdue University for helping us with mechanical characterizations. This work was partly supported by the Purdue Cooling Technologies Research Center (CTRC, a National Science Foundation (NSF) industry/university cooperative research center), and NSF Civil, Mechanical, and Manufacturing Innovation (CMMI) Program (No. 1538360).

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