Vertically and compactly rolled-up reduced graphene oxide film/epoxy composites: a two-stage reduction method for graphene-based thermal interfacial materials

Abstract

Graphene-based thermal conductive composites have come into notice in recent years. A considerable number of works have been devoted to increasing their thermal conductivity by increasing the graphene loading. However, it is not practical for the fabrication process when the graphene content is too high. In this work, a novel fabrication method of graphene-based composites is proposed, by which a thermal-reduced vertically aligned reduced graphene oxide (TR-VArGO)/epoxy composite was obtained. This method mainly involves a two-step reduction of graphene oxide and a hand-rolling process of reduced graphene oxide film. The thermal conductivity of the TR-VArGO/epoxy composite is up to 2.645 W m⁻¹ K⁻¹, i.e. an enhancement of as high as 887% compared to pure epoxy. By contrast, a randomly distributed TR-rGO sheets/epoxy composite with the same rGO loading has a thermal conductivity of only 1.270 W m⁻¹ K⁻¹. This difference is attributed to the vertical alignment of TR-VArGO films, which provides a rapid and effective heat-transfer path. This mechanism of high thermal conductivity is further confirmed by theoretical prediction and finite element calculation. The results obtained indicate that the vertically aligned reduced graphene oxide/epoxy composite may become a good candidate for thermal interfacial materials.

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1. Introduction

With the continuous development of modern microelectronic devices packed with highly integrated circuits, their increasing power densities have caused higher operating temperature, resulting in a significant bottleneck of heat dissipation in various micro-devices.^1–6 Great efforts have been made for the development of high-performance thermal interfacial materials (TIMs) based on carbon materials (e.g., diamond powders, graphite nanoplatelets, carbon nanotubes and carbon fibers) in order to break this bottleneck.^4,7–10 Most of these works are devoted to improving the thermal conductivity of polymeric composites by increasing the carbon-fillers loading. However, the good dispersion of fillers and processability of high filler mixtures are always difficult to realize when the fillers content is too high.

Graphene, a surprising allotrope of carbon which is comprised of only one plain layer of atoms arranged in a two-dimensional hexagonal lattice, exhibits a number of intriguing unique properties, such as ultrafast electron mobility,¹¹ super high mechanical strength,¹² unusually good thermal conductivity^13–15 and ultralarge specific surface area.¹⁶ Compared to carbon nanotubes, carbon blacks and other nanofillers, these unique properties make graphene a peerless material, which has been used in chemical sensors,¹⁷ microelectronic devices,^18,19 transparent & flexible electrically conductive films²⁰ and micro-supercapacitors for energy storage,²¹ etc. Besides, it is noteworthy that two dimensional graphite, graphene or graphene oxide (GO) are often used as fillers for polymeric composites to improve certain properties, such as mechanical, electrical or thermal properties.^4,8,22–26 For instance, the thermal performance of graphite nanoplatelets/epoxy composites got better with increasing degree of graphite exfoliation.⁸ In some cases, it is necessary to assemble graphene into a specific architecture to implement certain features. A typical example is that graphene must be stacked in a 3-D porous structure in electrodes of electrical energy storage devices to promote rapid ion migration and make the most of its large specific surface area.¹⁶ Hence, it’s necessary to arrange graphene into particular structures so as to fulfill diverse functions. For TIMs, high thermal conductivity in the out-of-plane direction is expected,^27,28 so it’s essential to assemble graphene into a vertically aligned architecture to facilitate heat dissipation in the normal direction of contact solid interfaces. However, unlike carbon nanotube arrays,²⁸ it’s difficult or even impossible to grow vertically aligned graphene directly. On one hand, graphene is inclined to lean on substrates; on the other hand, the direct growth method has a low yield and is unavailable for large-scale applications. Therefore, novel and simple approaches to vertically align graphene or reduced graphene oxide (rGO) are desired to increase the out-of-plane thermal conductivity of TIMs.

Yoon et al.²⁹ reported a method to fabricate densely and vertically aligned reduced graphene oxide (VArGO). First, GO film was obtained by spontaneous evaporation overnight. Then the films were rolled manually to get a vertically aligned architecture. Finally, VArGO film was formed by thermal annealing at the temperature up to 1000 °C for 1 h (0.14 °C min⁻¹). Herein, we report a more efficient and simple method to fabricate a thermal-reduced VArGO (TR-VArGO)/epoxy composite, which has a high thermal conductivity of 2.645 W m⁻¹ K⁻¹, i.e. an enhancement of as high as 887% compared to pure epoxy. This value is more than 2 times that of a randomly distributed TR-rGO sheets/epoxy composite with the same rGO loading, indicating that the vertical alignment of continuous rGO film provides a rapid and effective heat-transfer path to facilitate the heat dissipation. Furthermore, the heat-transfer mechanism of the composite is confirmed by theoretical prediction and finite element calculation.

2. Experimental

2.1. Fabrication of rGO film and rGO sheets

Well-dispersed GO aqueous solution (6 mg mL⁻¹) was prepared from graphite powder (Sinopharm Chemical Reagent Co., Ltd) with NaNO₃, H₂SO₄ and KMnO₄ using a modified Hummers method according to previous reports.^21,30

rGO film was fabricated on a zinc foil template at ambient temperature by an interfacial-gel method.³¹ The GO dispersion was diluted to 3 mg mL⁻¹ with pre-made aqueous HCl solution (10⁻³ mol L⁻¹) and the mixture was ultrasonically agitated at a power of 100 W for 3 h. Zinc foil (Benchely) of 0.2 mm in thickness was immersed into the acidified GO dispersion for interfacial gelation for 3 h. Then interfacial gel grown on the zinc foil surface was completely washed with deionized water and then immersed in water for a period of 20–30 min so as to remove physically adsorbed GO platelets. Immediately following the washing step, the interfacial gel film was detached from the zinc foil surface in 20 fold diluted HCl solution. The free-standing gel film was then transferred into aqueous HCl solution for another 5 h to dissolve residual Zn impurities. Finally, the prepared gel (rGO) film was immersed in deionized water for more than 12 h to remove acidic impurities. Furthermore, by sonicating at a power of 100 W for 5 h in deionized water, some pieces of rGO films were exfoliated into rGO sheets which were collected for the thermal reduction process after further vacuum freeze-drying.

2.2. Fabrication of rGO/polyvinyl alcohol (PVA) composite film

Before fabrication of the rGO/PVA composite film, the rGO gel film was transferred from deionized water into 4 wt% aqueous solution of PVA (PVA-124, Sinopharm Chemical Reagent Co., Ltd, average molecular weight 105 000 g mol⁻¹). Then the rGO film was kept in aqueous PVA solution at 50 °C for 1 h so that the PVA molecules could fully diffuse into the porous architecture of the rGO film. Next, the rGO film was moved onto a piece of polyethylene glycol terephthalate (PET) membrane, hung up to remove redundant aqueous PVA solution, and dried at room temperature for 5 h. After thoroughly drying, it was easy to peel off the rGO/PVA composite film from the PET membrane, and the composite film was of sufficient strength to proceed with the rolling-up process.

2.3. Fabrication of vertically aligned rGO/PVA (VArGO/PVA) composite

As-fabricated rGO/PVA composite film was cut into narrow strips (3 mm in width) prior to the rolling-up process. Then, the surface of these strips was slightly wetted with aqueous PVA solution (4 wt%) to allow them to be tightly rolled. After vacuum freeze-drying, a strip was manually rolled up to get a VArGO/PVA composite disc sample with a diameter of 12.7 mm and thickness of 3 mm.

2.4. Fabrication of thermal-reduced VArGO (TR-VArGO) and TR-rGO sheets

TR-VArGO and TR-rGO sheets were formed by a thermal reduction treatment which included a three-stage temperature-rise period and a 30 min-holding stage. The staged heating process was determined by the thermogravimetric (TG) curve of the VArGO/PVA composite and was used to prevent excessive reduction of the VArGO/PVA composite into rGO powder. As shown in Fig. 1, the weight loss of the VArGO/PVA composite was divided into three stages as follows: (I) from room temperature to 200 °C, the physically absorbed water of the VArGO/PVA composite was evaporated;³² (II) from 200 to 400 °C, PVA was decomposed into abundant CO and CO₂. Besides, CO and CO₂ were also released from the decomposition of anhydrides and phenols of rGO;³³ (III) from 400 to 1000 °C, residual oxygen-containing functional groups in the VArGO/PVA composite were removed steadily.³⁴

Fig. 1 Thermogravimetric (TG) and derivative thermogravimetric (DTG) analysis of VArGO/PVA composite.

The thermal reduction process of the VArGO/PVA composite samples and rGO sheets is the same as follows: firstly, samples were put in a U-type quartz tube installed in a temperature programmable furnace (SGL-1200, Shanghai Daheng), then they were heated from room temperature to 200 °C at the rate of 0.5 °C min⁻¹ under an argon flow (100 sccm); secondly, the temperature was increased from 200 to 400 °C at a slower ramp rate of 0.2 °C min⁻¹; thirdly, the samples were heated up to 1000 °C at a rate of 2 °C min⁻¹, and then the specific temperature was kept for 30 min under the same argon flow; finally, the furnace was allowed to cool to room temperature to get pure TR-VArGO samples and TR-rGO sheets.

2.5. Fabrication of TR-VArGO/epoxy and TR-rGO sheets/epoxy composites

TR-VArGO/epoxy composite was prepared in suitable molds by infiltrating the as-fabricated TR-VArGO with liquid epoxy resin prepolymer and a viscous mixture of base and curing agent (diglycidyl ether of bisphenol A, E-51 and diethyltoluenediamine, 593#, Beijing Pulin Chemical Co., Ltd, base/curing agent = 4 : 1 in weight), followed by vacuum outgassing in a vacuum oven for 20 min and then thermal curing at 80 °C for 4 h to obtain the composite sample.

As for the TR-rGO sheets/epoxy composite, first, 0.188 g TR-rGO sheets were dispersed in acetone and the mixture was agitated by ultrasonic treatment at a power of 100 W for 3 h. Then 0.8 g epoxy base agent was added into the mixture and mechanically stirred for 1 h, followed by adding 0.2 g curing agent and continually stirring for another 30 min at 50 °C to remove excess acetone. The final curing process of the TR-rGO sheets/epoxy composite is identical to that of the TR-VArGO/epoxy composite. In order to realize accurate measurements of thermal conductivity, the top and bottom surfaces of the as-prepared TR-VArGO/epoxy and TR-rGO sheets/epoxy composite discs were slicked by slight and careful polishing and the final dimensions of the samples are 12.7 mm (diameter) × 2 mm (thickness).

2.6. Characterization of materials

The morphological and microstructural characterizations of as-obtained samples were performed using a field emission scanning electron microscope (FE-SEM, S-4800, HITACHI, Japan) operated at 10 kV. The detailed morphology of TR-rGO sheets was measured by a transmission electron microscope (TEM, JEM-2100F, JEOL, Japan) at 200 kV. Chemical composition and structure characterizations of GO, metal-reduced rGO (MR-rGO) and thermal-reduced rGO (TR-rGO) were performed. Energy dispersive spectroscopy (EDS) measurements were conducted on a Bruker X Flash Detector 5010 energy dispersive spectrometer. X-ray powder diffraction (XRD) measurements were performed on a D8/Advance X-ray diffractometer (BRUKER/AXS, Germany) with Cu Kα radiation in the range of 5–50°. Laser Raman spectroscopy was performed using a HORIBA Jobin Yvon LabRAM HR Evolution Raman spectrometer with He–Ne laser excitation at 514.5 nm with a power of 150 μW cm⁻². Fourier transform infrared spectroscopy (FT-IR) was measured on a VECTOR 22 Fourier transform infrared spectrometer (BRUKER/AXS, Germany). All X-ray photoelectron spectroscopy (XPS) measurements were conducted by an Axis Ultra imaging photoelectron spectrometer (Kratos Analytical Ltd., Japan) with a monochromatic Al Kα X-ray source at 225 W.

2.7. Thermal properties characterization

Values of thermal conductivity were calculated from the equation k = αρC_p, where k, α, ρ and C_p represent thermal conductivity, thermal diffusivity, material bulk density and specific heat capacity, respectively. Thermal diffusivity was measured by a laser flash apparatus (LFA 447 Nanoflash, NETSZCH, Germany). Bulk density was calculated from sample weight and volume. Specific heat capacity was obtained by a differential scanning calorimeter (DSC, Q2000, TA Instruments, America) with a heating rate of 10 °C min⁻¹ from 0 to 100 °C. Dynamic thermogravimetric analysis was performed on a thermogravimetric Analyzer (Q600 SDT, TA Instruments, America) with a heating rate of 10 °C min⁻¹ from room temperature to 900 °C in a nitrogen atmosphere.

3. Results and discussion

Generally, rGO film is formed by one-step thermal reduction of paper-like aligned GO film which is prepared by a vacuum assisted flow-filtration method.^35,36 In order to increase the efficiency in the film-forming process, we transformed the reduction procedure into a two-stage process. This two-stage reduction method is described in Fig. 2. Firstly, according to a metal-templated interfacial-gel method reported by Maiti et al.,³¹ we prepared metal-reduced rGO (MR-rGO) film instead of GO film on a zinc foil template. Meanwhile, to make sure that the as-prepared rGO film has sufficient strength to proceed into the rolling-up process, it was immersed into 4 wt% aqueous solution of PVA, and after thoroughly dried, rGO/PVA composite film was formed. Due to the addition of PVA, this composite film with sufficient tensile strength can be cut into strips and rolled into VArGO/PVA composite with a packing density of 0.36 g cm⁻³. In the following thermal reduction process, TR-VArGO was formed by a three-stage temperature-rise period and a 30 min-holding stage, yielding a packing density of 0.16 g cm⁻³. Finally, TR-VArGO/epoxy composite was fabricated in suitable molds by infiltrating the as-made TR-VArGO with epoxy resin. The prepared TR-VArGO/epoxy composites can be used as TIMs to fill the voids and grooves created by the imperfect surface finish of two mating surfaces, thus improving surface contact and ensuring a continuous path for heat-transfer. Fig. 2F shows two TIM layers used in an integrated circuit, TIM-1 is inserted between the chip and the integrated heat spreader (IHS) while TIM-2 is used between the IHS and the heat sink.

Fig. 2 Schematic of the fabrication procedure of the thermal-reduced vertically aligned reduced graphene oxide (TR-VArGO)/epoxy composite. (A) The free-standing rGO film was fabricated on a zinc foil template at ambient temperature by the interfacial-gel method.³¹ (B) As-prepared rGO film was immersed into 4 wt% aqueous solution of polyvinyl alcohol (PVA), and after thoroughly dried, it was cut into several narrow strips (3 mm in width). (C) Rolling process of thin rGO/PVA composite strips. (D) The VArGO/PVA composite was reduced by a thermal reduction process to give the TR-VArGO sample. (E) The TR-VArGO/epoxy composite was fabricated in suitable molds by infiltrating the as-prepared TR-VArGO with epoxy resin. (F) TR-VArGO/epoxy composites were used as TIMs in an integrated circuit (TIM-1 used between the chip and the integrated heat spreader (IHS), TIM-2 used between the IHS and the heat sink).

3.1. Morphologies and microstructures of TR-rGO sheets, VArGO/PVA composite and TR-VArGO

The morphologies and microstructures of TR-rGO sheets, VArGO/PVA composite and TR-VArGO samples are shown in Fig. 3. It is clearly seen in Fig. 3a and b that the TR-rGO sheet is on the order of 8–10 μm in size and 1.4–3.4 nm in thickness (about 4–10 layers), and is transparent with some ripples and wrinkles, indicating that the TR-rGO sheet is quite thin and flexible. Fig. 3c shows that the VArGO/PVA composite is densely piled after the simple hand rolling process and vertically aligned films are stuck tightly together due to the addition of PVA. The arrows in Fig. 3c point out some extended PVA filaments bridging a small amount of gaps between layers, resulting in a decreased packing density. Nevertheless, the gaps between layers can benefit the penetration of liquid polymer in the following fabrication of the composite. Because PVA can be completely decomposed at about 600 °C,³⁶ thus further thermal reduction of the VArGO/PVA composite via a staged heating process up to 1000 °C removed all the PVA adhered on the surface of VArGO, and pure TR-VArGO samples were obtained. From Fig. 3d and its inset, it can be seen that there is almost no difference between these two samples except for the decomposition of PVA, the vertically aligned architecture of VArGO was retained after high temperature thermal reduction. TR-VArGO is arranged densely and the thickness of a single layer is about 10–15 μm.

Fig. 3 (a and b) TEM images of TR-rGO sheet. (c and d) SEM images of top surfaces of VArGO/PVA composite and TR-VArGO, respectively. Insets show digital camera images of the samples.

3.2. Chemical composition and structure characterizations

Two-stage reduction of GO removed most oxygen functional groups to give highly reduced rGOs,^31,35–38 which is confirmed by the measurements of Fourier transform infrared spectroscopy (FT-IR), X-ray photoelectron spectroscopy (XPS), laser Raman spectroscopy and X-ray powder diffraction (XRD). The oxygen content of GO illustrated in Table 1, which was determined by low-resolution scanning XPS spectra, is as high as 54.70 at% and that of rGO was reduced gradually with the progress of reduction. Furthermore, the element content is also confirmed by EDS (Table 2). As shown in the FT-IR spectra (Fig. 4a), characteristic peaks appear for C=O (1730 cm⁻¹), aromatic C=C (1625 cm⁻¹), epoxy C–O–C (1224 cm⁻¹), and C–O (1054 cm⁻¹) in the GO spectrum,³⁹ demonstrating that the graphite powder has a high degree of oxidation. After the zinc reduction, the peaks for oxygen functional groups are partially reduced, and the peak at 1224 cm⁻¹ for epoxy C–O is nearly completely removed by zinc reduction for 3 h. Further thermal treatment of MR-rGO at a temperature up to 1000 °C removed most of the residual oxygen-containing functionalities to give higher reductive degree thermal-reduced rGO (TR-rGO), this can be verified by the fact that the peaks at 1730 cm⁻¹ for C=O and 1054 cm⁻¹ for C–O became almost invisible compared to the MR-rGO spectrum. The remaining strong δ C=C mode is ascribed to the effective repairing of conjugated C=C in sp² graphitic regions.⁴⁰ Furthermore, in the MR-rGO and TR-rGO spectra, a distinct new peak at 1568 cm⁻¹ appears and is attributed to the aromatic C=C group.⁴¹ XPS was used to further quantitatively analyze the element content (Table 1) and chemical structure of GO, MR-rGO and TR-rGO. The deconvoluted XPS C1s spectra of these samples (Fig. 4b) show three peaks for graphitic structure (C–C/C=C at 284.8 eV), hydroxyl/epoxy groups (C–O at 286.8 eV), and carbonyl groups (O–C=O at 288.5 eV), respectively. The C–O bands come from epoxy and hydroxyl groups in the basal plane.³⁵ The C=O compounds mainly arose from single ketones⁴² which decorate the edges of GO sheets but may also be bound to the basal plane as carbonyl groups.^43,44 Compared to the XPS C1s spectrum of GO (Fig. 4b), a sharp decrease of the peak intensities for oxygen functional groups in the XPS C1s spectra of MR-rGO and TR-rGO indicates a high degree of reduction of GO after the two-stage treatment. Moreover, the evolution of carbon bonds is also quantitated as shown in Table 3. It is obvious that the carbon sp² fraction increased with the progress of reduction, while the content of oxygen-containing functionalities (C–O and C=O) decreased.

Table 1 Summary of the elemental compositions of materials

Sample	C^a (%)	O^a (%)	d-spacing^b (Å)	ID/IG^c
a Determined by low-resolution scanning XPS spectra.b Determined by XRD.c Determined by Raman.
GO	45.31	54.69	7.81	0.92
MR-rGO	82.04	17.96	3.75	1.89
TR-rGO	92.94	7.06	3.43	1.29

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Table 2 EDS results of the elemental composition of samples

Sample	Mass ratio (wt%)		Atomic ratio (at%)
	C	O	C	O
GO	49.37	50.63	56.50	43.50
MR-rGO	87.89	12.11	90.63	9.37
TR-rGO	95.24	4.76	96.38	3.62

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Fig. 4 (a) FT-IR spectra, (b) XPS C1s spectra, (c) Raman spectra, (d) XRD patterns of GO, MR-rGO and TR-rGO.

Table 3 Fitted binding energy (B.E.) and atomic ratio (at%) of the C1s XPS spectra of samples

B.E. (eV)	C1 (284.8)	C2 (286.8)	C3 (288.5)
Assignment	C–C/C=C	C–O	O–C=O
GO	39.01	54.51	6.48
MR-rGO	64.49	28.48	7.03
TR-rGO	80.77	13.24	5.99

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Raman was performed to further investigate the texture of the samples. The Raman spectra of GO, MR-rGO and TR-rGO (Fig. 4c) show two characteristic peaks at ∼1352 cm⁻¹ and ∼1594 cm⁻¹, corresponding to D and G bands of graphene, respectively. As shown in Table 1, the ratio of I_D/I_G rises from 0.92 of GO to 1.89 of MR-rGO after the metal reduction, owing to an increase in structural defects which is attributable to the desorption of oxygen bonded saturated sp³ carbons as CO₂ and/or CO (especially from epoxy groups).⁴⁵ It is of vital importance to remove the oxygen contained in the GO during the reduction process, as sp² clusters in GO are isolated by oxygen atoms and a reduction by removal of O results in greater connectivity among the existing graphitic domains by the formation of new sp² domains.^45,46 Surprisingly, a significant decrease in the I_D/I_G ratio from 1.89 to 1.29 is observed after thermal annealing treatment, which is ascribed to the recovery of sp²-hybridized carbon–carbon bonds of the graphitic lattice and connection of new sp² clusters in the samples through thermal treatment.⁴⁷

XRD was conducted to study the structure evolution of the samples. As shown in Fig. 4d, a sharp peak appears at 2θ = 11.3° corresponding to the (001) lattice plane in the pattern of GO, while it is nearly invisible in the patterns of MR-rGO and TR-rGO. However, there are two characteristic peaks at 2θ = 23.7° and 26.0°, corresponding to the (002) plane in the other two rGO samples. According to the typical bulk graphite, presenting a diffraction peak at 2θ = 27.0°,⁴⁷ our final sample has a high graphitization degree. Additionally, from Table 1, it can be seen that the interlayer distance (d-spacing) of the samples decreased with the progress of reduction. The d-spacing ranges from 7.81 Å for GO to 3.43 Å for TR-rGO, which is attributed to the higher thermal exfoliation degree, higher reduction level, the decomposition of oxygen-containing functional groups and a better ordering of the two-dimensional sheets.³⁵ Compared to the d-spacing of pristine bulk graphite (3.40 Å),⁴⁷ it is slightly larger for TR-rGO, this can be ascribed to the presence of a small amount of residual oxygen-containing functional groups or other structural defects.⁴⁸ From the above results, it is obvious that the TR-VArGO is homogeneously and densely piled by simple hand rolling, and it is at a high reduction level after the two-stage reduction treatment. As a result, we deduce that the as-prepared TR-VArGO/epoxy composite has high thermal conductivity in the normal direction.

3.3. Morphology and microstructure of TR-VArGO/epoxy and TR-rGO sheets/epoxy composites

Fig. 5a and b show the morphologies of the top surface and a longitudinal section of the TR-VArGO/epoxy composite (the filler loading is 15.79 wt%). It can be clearly seen in Fig. 5a and the inset that the arc-shaped rGO layers are embedded in epoxy matrix, i.e. the gaps between rGO layers (Fig. 3b) are filled with epoxy, making TR-VArGO and epoxy be combined into a uniform bulk material. As expected, there exist few small crevices between the rGO layers and epoxy matrix, indicating a good interface-bonding between filler and matrix. The cryo-fractured longitudinal section in Fig. 5b also shows the layered and compact structure of this composite. Fig. 5c displays the microstructure of a cryo-fractured surface of the TR-rGO sheets/epoxy composite with the same TR-rGO loading. It is noted that the TR-rGO sheets distribute randomly and densely in the epoxy matrix. Furthermore, the aggregation of TR-rGO sheets occurred and large-sized TR-rGO sheets were formed due to the high filler content.

Fig. 5 SEM images of (a and b) top surface and longitudinal section of TR-VArGO/epoxy composite and (c) cryo-fractured surface of TR-rGO sheets/epoxy composite. The inset shows a digital camera image of the sample.

3.4. Thermal properties

The thermal diffusivity of the TR-VArGO/epoxy and TR-rGO sheets/epoxy composites was measured by a laser flash apparatus. To make a comparative analysis, the thermal diffusivity of pure epoxy was also measured. Quantitative values of thermal diffusivity are given in Table 4. Furthermore, specific heat capacity was measured by a differential scanning calorimeter and bulk density was calculated from sample weight and volume.

Table 4 Summary of detailed sample information and thermal properties

Sample	α (mm^2 s^−1)	ρ (g cm^−3)	Cp (J g^−1 K^−1)	k (W m^−1 K^−1)	Mass fraction (wt%)
Epoxy	0.164	1.152	1.456	0.275	—
TR-VArGO/epoxy	2.025	0.919	1.421	2.645	15.79
TR-rGO sheets/epoxy	1.004	0.897	1.410	1.270	15.80

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As detailed in Table 4, the values of thermal conductivity and thermal diffusivity of the as-prepared 15.79 wt% TR-VArGO/epoxy composite are 2.645 W m⁻¹ K⁻¹ and 2.025 mm² s⁻¹ (measured at 25 °C), i.e. 9.62 and 12.34 times that of pure epoxy, respectively. Meanwhile, the corresponding values for the randomly distributed TR-rGO sheets/epoxy composite are 1.270 W m⁻¹ K⁻¹ and 1.004 mm² s⁻¹, respectively, lower than half of the values of the TR-VArGO/epoxy composite. It is known that thermal conductivity is mainly determined by thermal diffusivity, which measures the ability of a material to conduct thermal energy relative to its ability to store thermal energy. To a large extent, the thermal conductivity enhancement of the TR-VArGO/epoxy composite is primarily contributed by the vertical alignment of the TR-rGO films.

In order to ascertain the thermal parameters of TR-VArGO, a parallel structure model determined by rule of mixture is proposed and combined with experimental results. Concerning the geometry shown in Fig. 6, the effective thermal conductivity of the composite is given by:⁴⁹

k_par = k₁f₁ + k₂(1 − f₁) (1)

where k_i and f_i are the thermal conductivity and volume fraction of the ith materials, respectively.

Fig. 6 Thermal conductivity first-order models for the TR-VArGO/polymer composite.

Due to the excellent surface polishing, it is apparent in the schematic diagram of Fig. 6 that the parallel structure model can be perfectly applied to TR-VArGO/epoxy composite. Hence, based on the experimental results of pure epoxy and the TR-VArGO/epoxy composite (Table 4), it’s fairly easy to obtain the thermal parameters of TR-VArGO using eqn (1), which are detailed in Table 5.

Table 5 Summary of density and thermal properties of TR-VArGO

Sample	Density^a (g cm^−3)	Specific heat capacity^a (J g^−1 K^−1)	Thermal diffusivity^b (mm^2 s^−1)	Thermal conductivity^c (W m^−1 K^−1)
a Calculated from experimental results.b Calculated from experimental and theoretical results.c Calculated by eqn (1).
TR-VArGO	0.442	1.147	14.786	7.496

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Based on the detailed thermal properties of TR-VArGO, the heat-transfer mechanism is quantitatively analyzed using the finite element method. As shown in Fig. 7a, a simple TR-VArGO/epoxy composite model is built. A strong anisotropy of the TR-VArGO/polymer composite is evidenced by a distinguished architectural difference between the in-plane and out-of-plane directions, here r represents the in-plane direction and Z represents the out-of-plane direction. According to Liang et al.,⁵⁰ aligned functionalized multilayer graphene sheets (fMGs) have high in-plane and low out-of-plane thermal conductivity. In real applications of TIMs, out-of-plane thermal conductivity is often required and so is measured in this work. In Fig. 7b, the TR-VArGO/epoxy composite is geometrically modeled to be composed of parallel TR-VArGO (red parts) embedded in epoxy matrix (blue parts). By using the finite element method, the heat flux density profile across the composite sample is obtained in Fig. 7b. Corresponding to the color bar, the heat flux density of TR-VArGO (red parts) is two orders of magnitude higher than that of epoxy (blue parts). So it’s quite clear that almost all the heat flux travels preferentially through the TR-VArGO without thermal interface resistance between the two different phases, which differs significantly from the heat-transfer mechanism of the TR-rGO sheets/epoxy composite. Compared with vertically aligned TR-VArGO film, the random distribution of TR-rGO sheets in the epoxy matrix causes two critical disadvantages. One is high thermal resistance at interfaces which are inclined at 0–90° angles to the heat flux direction. The other is the discontinuity of TR-rGO sheets which reduces the effectiveness of heat transfer in the material. Furthermore, Fig. 7c exhibits a well-distributed temperature gradient profile, demonstrating a stable, reliable and high-efficiency heat-transfer process.

Fig. 7 (a) An anisotropy schematic of the TR-VArGO/epoxy composite. Normal direction Z and radial direction r are shown by the red and blue arrows, respectively. (b) Longitudinal section and three-dimensional heat flux density and (c) temperature gradient profiles of the TR-VArGO/epoxy composite.

Since the higher thermal conductivity of the TR-VArGO/epoxy composite is primarily determined by the vertical alignment of TR-rGO films, the effect of TR-VArGO volume fraction on the thermal conductivity is further studied numerically and theoretically. As illustrated in Fig. 8, the thermal conductivity increases linearly with increasing volume fraction of TR-VArGO. Meanwhile, the two curves in Fig. 8 are partially overlapping and show almost the same variation trend, demonstrating the accordance of the parallel model and numerical simulation. Furthermore, the experimentally measured thermal conductivity values situate on or close to the theoretical curve, but are slightly smaller than the numerical ones. For example, the measured conductivity is 2.645 W m⁻¹ K⁻¹ at the TR-VArGO volume fraction of 32.8 vol%, i.e. 3% lower than the numerical value (2.725 W m⁻¹ K⁻¹). The difference comes from the existence of a small quantity of pores in the real composite, while the numerical calculation assumes a perfect microstructure of the composite. It is confirmed by the longitudinal section view in Fig. 5b that there are some irregular pores present in the composite, increasing thermal resistance and hindering heat conduction in the normal direction.

Fig. 8 Thermal conductivities of TR-VArGO/epoxy composites as a function of volume fraction of TR-VArGO.

From the theoretical and numerical results, it can be concluded that the TR-VArGO/epoxy composite has a simple heat-transfer mechanism dominated by the elements with high thermal conductivity (TR-VArGO). Furthermore, a revelation is that the elements with high thermal conductivity must be stacked compactly and parallel to the heat flow direction to get high thermal conductivity.

3.5. Comparison with reported results

Graphene is an optimal thermal conductive filler in polymeric composites due to its ultrahigh thermal conductivity (∼5300 W m⁻¹ K⁻¹ for a suspended single-layer graphene)¹⁴ and ease of assembly. However, efficient heat dissipation requires a heat transfer pathway established by a large number of interconnected graphene nanoplatelets. The loading of graphene nanoplatelets must reach a certain level in order to construct a three-dimensional interconnected heat-transfer network. Great efforts have been made in the preparation of graphene filled polymer composites by increasing the loading of graphene. However, the favorable dispersion of filler cannot be guaranteed when the filler loading is too high, which causes a sensible reduction in thermal conductivity. Moreover, the poor processability of high filler composite materials is unlikely to meet the requirements of real industrial production processes. This work gives a novel approach for the high-efficiency fabrication of TR-VArGO, as well as TR-VArGO/epoxy composites. High thermal conductivity (2.645 W m⁻¹ K⁻¹) and thermal conductivity enhancement (887%) of the TR-VArGO/epoxy composite are obtained at a moderate graphene weight fraction (15.79 wt%).

For the purpose of comparison, our results and those of state-of-the-art graphene filled polymer composites are illustrated together in Fig. 9. It is noticed that most of the graphene-based polymer composites reported in the literature show increasing thermal conductivity by increasing graphene loading as much as possible. Sun et al.⁵² obtained an effective thermal conductivity of ∼1.98 W m⁻¹ K⁻¹ at the optimum lateral dimensions (∼200–400 μm) of graphite nanoplatelets (loading 10 wt%). Song et al.⁵³ fabricated graphene-based epoxy composites at low cost and with environmentally friendly processing techniques and obtained a high thermal conductivity of 1.53 W m⁻¹ K⁻¹, as well as a large thermal conductivity enhancement of 670% at a low filler loading (10 wt%). Yu et al.⁸ improved the thermal conductivity of graphite nanoplatelet/epoxy composite to 6.44 W m⁻¹ K⁻¹ by increasing the filler loading to 40 wt%. Unlike other efforts, Ji et al.⁵¹ applied ultrathin-graphite foams with weight fractions as low as 4.8 wt% in a phase change material (wax) instead of dispersing a large-amount of high thermal conductivity graphene flakes or nanotubes to increase the thermal conductivity of composites and reported that the thermal conductivity of their ultrathin-graphite foams/wax composite measured by a self-electrical-heating steady state technique is ∼1.65 W m⁻¹ K⁻¹. As illustrated in Fig. 9, the TR-VArGO/epoxy composite has high thermal conductivity and thermal conductivity enhancement, elucidating that it’s especially necessary to arrange graphene or reduced graphene oxide into a particular architecture so as to take advantage of its high in-plane thermal conductivity. However, there still exist other graphene-based composites with higher thermal conductivity than the TR-VArGO/epoxy composite, which may result from their high thermal conductivity and weight fraction of additive graphene. Hence, we learn that it’s especially necessary to increase the fillers’ thermal conductivity and weight fraction in our future work.

Fig. 9 Comparison of weight fraction, thermal conductivity and its enhancement in graphene filled polymer composites from results in the literature and in this work.

4. Conclusions

In summary, a two-stage reduction method and a simple rolling process were proposed to prepare a vertically and compactly aligned reduced graphene oxide (VArGO)/epoxy composite. A high reduction level of thermal-reduced VArGO (TR-VArGO) is achieved using the two-stage method. The rolling process guarantees the vertical and compact alignment of TR-VArGO film in the composite. The thermal conductivity of the TR-VArGO/epoxy composite is up to 2.645 W m⁻¹ K⁻¹ and the thermal conductivity enhancement is as high as 887%. Meanwhile, a randomly distributed TR-rGO sheets/epoxy composite with the same TR-rGO loading has a thermal conductivity of 1.270 W m⁻¹ K⁻¹, lower than half of the value of the TR-VArGO/epoxy composite. This difference is attributed to the vertical alignment of TR-VArGO films. By theoretical modelling and finite element simulation, it is revealed that the alignment of continuous graphene film provides a rapid and effective heat-transfer path to facilitate heat dissipation. The high performance of the TR-VArGO/epoxy composite synthesized by a simple and facile process in this work shows promising potential in the thermal management of microelectronic devices and photonic applications.

Acknowledgements

The authors would like to thank the support by NSFC and NSFC-RGC Joint Research Scheme (No. 11272008, 11361161001, 11202005 and CUHK450/13).

Notes and references

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