Some Aspects of Thermal Transport across the Interface between

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Some Aspects on Thermal Transport across the Interface between Graphene and Epoxy in Nanocomposites Yu Wang, Chunhui Yang, Qing-Xiang Pei, and Yingyan Zhang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b00325 • Publication Date (Web): 09 Mar 2016 Downloaded from http://pubs.acs.org on March 12, 2016

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ACS Applied Materials & Interfaces

Some Aspects on Thermal Transport across the Interface between Graphene and Epoxy in Nanocomposites Yu Wang,† Chunhui Yang,† Qing-Xiang Pei,‡ and Yingyan Zhang*,† †

School of Computing, Engineering and Mathematics, Western Sydney University, Locked Bag 1797, Sydney NSW 2751, Australia ‡ Institute of High Performance Computing, A*STAR, Singapore 138632, Singapore

*Corresponding Author: Tel.:+61 2 47360606; Fax: +61 2 47360833; Email: [email protected]

ABSTRACT: Owing to the superior thermal properties of graphene, graphene-reinforced polymer nanocomposites hold great potentials as the thermal interface materials (TIMs) dissipating heat for electronic packages. However, this application is greatly hindered by the high thermal resistance at the interface between graphene and polymer. In this paper, some important aspects on the improvement of the thermal transport across the interface between graphene and epoxy in graphene-epoxy nanocomposites, including the effectiveness of covalent and non-covalent functionalisation, isotope doping and acetylenic linkage in graphene are systematically investigated using molecular dynamics (MD) simulations. The simulation results show that the covalent and non-covalent functionalisation techniques could considerably reduce the graphene-epoxy interfacial thermal resistance in the nanocomposites. Among different covalent functional groups, butyl is more effective than carboxyl and hydroxyl in reducing the interfacial thermal resistance. Different non-covalent functional molecules, including 1-pyrenebutyl, 1-pyrenebutyric acid and 1-pyrenebutylamine, yield a similar amount of reductions. Moreover, it is found that the graphene-epoxy interfacial thermal resistance is insensitive to the carbon isotope doping in graphene, while it can be reduced moderately by replacing the sp2 bonds in graphene with acetylenic linkages.

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KEYWORDS: graphene, epoxy, interfacial thermal resistance, functionalisation, isotope, acetylenic linkage, molecular dynamics.

1. INTRODUCTION Owing to the superior electronic, mechanical and thermal properties of graphene,1-4 nanocomposites with graphene fillers dispersed in hosting matrices have attracted significant attention in the past few years.5-7 A large amount of research has indicated that thermal properties of such nanocomposites could be greatly enhanced, and thus they hold a great potential in a wide range of practical applications.5-7 One of the most promising applications is in the thermal interface materials (TIMs) inside the packages for electronic devices.8 In modern electronic packages, the TIMs used for cooling the integrated circuit (IC) chips are mostly composites composed of polymer matrices and thermally conductive fillers.9 Polymers generally have a very low thermal conductivity in the range of 0.1-0.3 Wm-1K-1, which is not desired for heat dissipation. By contrast, graphene has an extremely high thermal conductivity in a range of 2,000-5,300 Wm-1K-1 near room temperature.4,10,11 Dispersing graphene fillers into polymers is a promising approach to increase the thermal conductivity of polymeric composite TIMs and improve the cooling efficiency of electronic devices.12,13 When graphene is dispersed in polymer, the resultant composite properties are influenced significantly by the interfacial interaction between graphene and polymer.7 The distinct thermal properties of the graphene and polymer lead to a temperature jump at the interface and the associated interfacial thermal resistance (also known as Kapitza resistance).14,15 It is well-known that the thermal conductivity (and the other properties) of graphene composites depends heavily on graphene dispersion, alignment and the interfacial properties between graphene and polymer. In particular, the interfacial properties are critically important.16 Great research efforts have been devoted to investigating the interfacial thermal transport between 2 ACS Paragon Plus Environment

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graphene and different matrix materials, including phenolic resin,14 octane,17-20 paraffin21-23 and polyethylene.24 Using molecular dynamics (MD) simulations, Konatham et al.17,18 found that the interfacial thermal resistance between graphene and octane could be reduced by up to 72% when the graphene is covalently functionalized by hydrocarbon chains. Lin and Buehler19 found that the graphene-octane interfacial thermal conductance can be enhanced by non-covalent functionalisation using C8-pyrene molecules by 18%. Hu et al.14 explored the interfacial thermal transport between graphene and phenolic resin by using MD simulations. It was reported that the interfacial thermal conductance is insensitive to the number of graphene layers and the low-frequency phonon modes dominate the thermal transport across the interface. Recently, Wang et al.22,23 found that the interfacial thermal resistance between graphene and paraffin can be modulated by the covalent functional groups (hydrogen and butyl, etc.) in graphene. The presence of the functional groups in graphene reduces the interfacial thermal resistance and consequently increases the thermal conductance of graphene-paraffin nanocomposites. Most recently, Wang et al.24 found that the interfacial thermal conductance between graphene and polyethylene can be enhanced by more than twice when the coverage of C15H31 chains reaches 0.0144 Å-2, compared to that without functionalisation. Epoxy (bisphenol A diglycidyl ether) is one of the most widely used matrix materials in composite TIMs for electronics thermal management applications,9,25 owing to its unique properties, including good electrical insulation, low shrinkage, good chemical resistance, and high adhesive bond strength with metals and silicon. These excellent properties of epoxy make it easy to implement during the packaging and assembly processes. These properties also ensure a long-term reliability of electronic devices.26,27 Pristine epoxy has a thermal conductivity of ~0.19-0.20 Wm-1K-1.8 A lot of TIMs based on epoxy matrix have been developed and commercialised in the modern electronic manufacturing industry. In recent 3 ACS Paragon Plus Environment


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research studies, epoxy has also been extensively used to synthesise graphene-epoxy nanocomposite TIMs.28-36 Therefore, it is of great significance to understand the thermal transport across the interface between graphene and epoxy. The present work aims to explore the graphene-epoxy interfacial thermal transport and know how it responses to various commonly-used engineering treatments for graphene. Based on the large-scale MD simulations, the roles of covalent functionalisation, non-covalent functionalisation,

13

C

isotope and acetylenic linkage (−C≡C−) in modulating the interfacial thermal resistance between graphene and epoxy are investigated systematically. A variety of covalent functional groups (i.e., butyl, carboxyl and hydroxyl) and non-covalent functional molecules (i.e., 1pyrenebutyl, 1-pyrenebutyric acid and 1-pyrenebutylamine) at different coverages are considered in this study.

2. COMPUTATIONAL METHODS MD simulation allows for an atomic-scale description of the interfaces between graphene and other materials. Hence, it has been broadly used for studying the interfacial thermal transport properties.17-24 In this work, the interfacial thermal resistance between graphene and epoxy was investigated by using the reverse non-equilibrium molecular dynamics (RNEMD) simulation method based on Muller-Plathe’s approach.37 The simulation model consists of three epoxy blocks separated by two graphene sheets (see Figure 1a). Periodic boundary conditions are imposed in all three directions. The cross section area of the composite model is 29 Å × 29 Å and the length is about 160 Å. The size effect on the interfacial thermal transport across graphene-paraffin interfaces has been studied thoroughly by Luo and Lloyd.21 It was found that the interfacial thermal transport is insensitive to the size when the polymer block length is greater than 35 Å and the cross-sectional width is larger than 19.68 Å, mainly due to short mean free paths of heat carriers in polymers. In present work, one single 4 ACS Paragon Plus Environment

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model size is used and the attention is focused to the effects of different engineering treatments. In the MD simulations, the interactions between the carbon atoms in graphene were described by the adapted intermolecular reactive-empirical bond order (AIREBO) potential.38 The consistent valence force field (CVFF)39,40 was used to simulate the epoxy matrix, functional groups and functional molecules. The epoxy matrix interacts with the graphene, functional groups or functional molecules via van der Waals (vdW) interactions, which were described by the Lenard-Jones (LJ) potential. The LJ potential is expressed as =

4 ⁄

− ⁄ , where is the distance between atoms i and j; and are the

energy and distance constants, respectively. The parameters ( and ) for carbon in graphene were adopted from previous research21 and those for other atom types were taken from the vdW term in the CVFF from the software Material Studio. The LJ potential parameters across different types of atoms were calculated by using the Lorentz-Berthelot mixing rules, i.e., = ; = + ⁄2. The details of LJ potential parameters used in this study are given in Table 1. A time step of 0.25 fs is used in the MD simulations. All the simulations were performed in the open-source large-scale atomic/molecular massively parallel simulator (LAMMPS).41 Table 1. LJ Potential Parameters Used in the Simulations atom types

energy constant ε (eV) distance constant σ (Å)

carbon in graphene

0.002390

3.412

aromatic carbon

0.006418

3.617

aliphatic carbon

0.001691

3.875

oxygen

0.009887

2.860

nitrogen

0.007242

3.501

hydrogen

0.001648

2.450



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In the simulations, the nanocomposite system was relaxed in two steps. Firstly, it was relaxed in a canonical NVT ensemble for 500 ps, during which the temperature was increased from 300 K to 1,000 K at a rate of 7 K/ps, kept at 1,000 K for 100 ps, and then cooled down to 300 K at the same rate. Secondly, the nanocomposite model was fully relaxed in an isothermal-isobaric NPT ensemble at 300 K and 1 atm for 500 ps. The essential idea of RNEMD is to apply a heat flux onto a system and measure the induced temperature gradient. The simulation model is divided into several slabs with equal width along the heat flux direction. Then the heat flux is generated by exchanging the kinetic energy of the hottest atom in the cold slab (heat sink) with the coldest atom in the hot slab (heat source). The heat sink and the heat source slabs are located at the end and middle of the model as illustrated in Figure 1. The heat swap was performed every 1,000 time steps in a microcanonical NVE ensemble. The resultant heat flux is given by =

∑!" #$"

(1)

where %$ is the number of exchange, $ is the summation time, & is the cross-section area that the heat energy passes through, subscripts ℎ and ( refer to the hottest and coldest atoms of which the kinetic energies are interchanged, respectively. A stable temperature gradient can be established between the heat source and heat sink slabs after a steady state is reached. A representative temperature profile of the composite model is shown in Figure 1b. It is clearly seen from Figure 1b that the graphene-epoxy interface experiences a temperature drop of ∆*, due to the distinct thermal properties of graphene and epoxy. The resultant interfacial thermal resistance +, is then calculated by using +, = ∆*⁄

(2)


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By averaging the data collected over a 4.5 ns period in the steady state, the final interfacial thermal resistance value was calculated. The error bars were determined using the block averaging approach with a block size of 0.5 ns.42 It is worth noting that the present work focused on single-layer graphene. In practical applications, graphene fillers in TIMs could be a mixture of single-layer and few-layer graphene. However, based on the previous MD simulation studies,14,22 the layer number has a negligible effect on the graphene-polymer interfacial thermal transport when the layer number changes from 1 to 5. Graphene

(a)

Heat source

Heat flux J

(b)

Epoxy

Heat sink

Heat flux J

400 380 360

Temperature (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


340 320 300

2∆T

2∆T

280 260 240 220 200 0

20

40

60

80

Position (Å)

100

120

140

160

Figure 1. (a) Nanocomposites composed of epoxy and graphene in RNEMD simulation (Blue balls are hydrogen atoms, red balls are oxygen atoms, grey balls are carbon atoms in epoxy and orange balls are carbon atoms in graphene, respectively); and (b) the resultant temperature gradient along the length of the nanocomposites.



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3. RESULTS AND DISCUSSION In order to validate the computational model, MD simulations were first performed on pure epoxy with a block size of 29 Å × 29 Å × 74 Å and a density of 1.1 g cm-3. By using the Fourier’s law of heat conduction - = ⁄./*⁄/0 1, where /*⁄/0 is the temperature gradient, the thermal conductivity - of pure epoxy was calculated as 0.197 ± 0.006 Wm-1K-1. This value is in excellent agreement with the experimental results, i.e., 0.19-0.20 Wm-1K-1.8,30,31 Simulations were then carried out for graphene-epoxy nanocomposites to find the interfacial thermal resistance between epoxy and pristine graphene. The interfacial thermal resistance between epoxy and pristine graphene was then calculated as (0.713 ± 0.036) ×10-8 m2KW-1. This value is in good agreement with (0.667-1.158) ×10-8 m2KW-1 as observed by other researchers.14,20,43 Using this value RK0 as a reference, all the interfacial thermal resistance values are normalised as RK/RK0 to identify the effects of covalent functionalisation, non-covalent functionalisation, isotope and acetylenic linkage on the graphene-epoxy interfacial thermal transport. 3.1. Effect of Covalent Functionalisation The effect of covalent functionalisation was examined through simulating the graphene with different covalent functional groups, including butyl (-C4H9), carboxyl (-COOH) and hydroxyl (-OH). The chosen functional groups are commonly used and they have been applied for functionalising the graphene in experimental studies in literature.44-46 For generality, the functional groups were randomly distributed on both sides of the graphene at different coverages varying from 1.19% to 9.52%. The coverage of functionalisation is defined as the total number of the functional groups divided by total number of carbon atoms in the graphene. Figure 2 displays the initial models of pristine graphene and graphene covalently bonded with different functional groups.


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Figure 2. Simulation models of (a) pristine graphene and graphene functionalised with (b) butyl, (c) carboxyl, and (d) hydroxyl (Blue balls are hydrogen atoms, red balls are oxygen atoms, orange balls are carbon atoms in graphene and green balls are carbon atoms in functional groups, respectively).

The relative interfacial thermal resistance RK/RK0 (where RK0 is the interfacial thermal resistance between pristine graphene and epoxy) with respect to the coverage is shown in Figure 3. It is readily seen that all the relative interfacial thermal resistances are smaller than 1, indicating that the presence of covalent functionalisation leads to a reduction of grapheneepoxy interfacial thermal resistance. In addition, this reduction increases with increasing coverages. Among the different covalent functional groups, butyl causes the most significant reduction. For instance, with a butyl coverage of 9.52%, the interfacial thermal resistance between graphene and epoxy is decreased by 76.7%, which is much higher than 54.8% and 31.2% produced by carboxyl and hydroxyl groups at the same coverage, respectively.



1.0 0.9 0.8 0.7 0.6

Rk/Rk0

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0.5 0.4

Butyl

0.3

Carboxyl

0.2

Hydroxyl

0.1 0.0

2.0

4.0

6.0

8.0

Functionalisation coverage (%)

Figure 3. Variation of the relative interfacial thermal resistance with respect to the coverage of different covalent functional groups.

It is well-known from the theoretical analysis15 that the thermal transport across the interface between two contacting materials is inherently governed by the overlap of their vibrational density of states (VDOS). In order to elucidate the underlying mechanisms of the reduced graphene-epoxy interfacial thermal resistance in the presence of different covalent functional groups, the VDOS for epoxy, pristine graphene and covalently functionalised graphene were calculated by taking the Fourier transform of the velocity autocorrelation functions of atoms in an equilibrium state. Figure 4a shows the VDOS of epoxy and pristine graphene. The VDOS peaks of pristine graphene appear at about 10-18 THz and 53 THz, which represent the out-of-plane and in-plane phonon modes, respectively. The frequency peaks of graphene are in agreement with the results obtained by other researchers.19,21 The peaks in the VDOS of epoxy are distributed at frequency ranges of about 23-45 THz and 88-


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90 THz. It is clearly shown in Figure 4a that the VDOS curves of pristine graphene and epoxy have a poor overlap with each other. The poor overlap indicates the inefficient heat transfer across the interface, thus leads to a high interfacial thermal resistance. When graphene is functionalised by covalent groups, the VDOS curve overlaps much better with that of epoxy as shown in Figure 4b for the case of butyl. The better overlap means a better heat conduction at the interface and the associated lower interfacial thermal resistance. This mechanism is consistent with the observations in a recent experimental research,47 which demonstrated that the thermal transport across a hard-soft material interface can be enhanced by functionalising the surface of the hard material. As shown in Figures 4c and 4d, the VDOS peaks of carboxyl and hydroxyl functionalised graphene have a less degree of overlap with epoxy compared to those of butyl. As a result, carboxyl and hydroxyl groups were found to be less effective in reducing the graphene-epoxy interfacial thermal resistance, as observed in Figure 3.



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Figure 4. Comparing VDOS of epoxy to that of (a) pristine graphene, (b) graphene with butyl, (c) graphene with carboxyl, and (d) graphene with hydroxyl.

3.2. Effect of Non-covalent Functionalisation Next, MD simulations were performed to investigate the effect of non-covalent functionalisation on the graphene-epoxy interfacial thermal transport. To effectively enhance


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interfacial thermal transport, the selected non-covalent functional molecules shall possess similar phonon spectral features as the filler and matrix materials. As proposed in earlier research,19,48,49 polycyclic aromatic hydrocarbons (particularly pyrene derivatives) could be promising non-covalent functional molecules for graphene, since they possess a similar benzene ring structure as graphene and have a strong π-π stacking interaction with graphene. Hence, in this study, 1-pyrenebutyl, 1-pyrenebutyric acid and 1-pyrenebutylamine (see Figures 5a-c) were chosen as the non-covalent functional molecules. These functional molecules have been used for functionalising graphene in previous simulations and experiments.19,48,49 Figure 5d illustrates a 1-pyrenebutyl molecule adsorbed onto a 29 Å × 29 Å graphene sheet used in the MD simulations. During the RNEMD simulations, the functional molecules were distributed onto both sides of the graphene. Here the coverage of functionalisation refers to the total number of functional molecules divided by the number of carbon atoms in the graphene. Using Eq. (2), the graphene-epoxy interfacial thermal resistance RK was obtained for different types and coverage of non-covalent functional molecules. The relative interfacial thermal resistance RK/RK0 with respect to the functionalisation coverage is given in Figure 6. It is clearly seen that the presence of noncovalent functional molecules leads to a reduced graphene-epoxy interfacial thermal resistance and this reduction increases with higher coverage of functionalisation. The different types of non-covalent functional molecules used in this study yield a similar amount of reduction in the interfacial thermal resistance. For instance, with a functionalisation coverage of 2.38%, the different functional molecules reduce the graphene-epoxy interfacial thermal resistance by 20.4-21.0%.



Figure 5. Simulation models of (a) 1-pyrenebutyl, (b) 1-pyrenebutyric acid, (c) 1pyrenebutylamine, and (d) graphene absorbed with a 1-pyrenebutyl molecule. (Blue balls are hydrogen atoms, red balls are oxygen atoms, orange balls are carbon atoms in graphene and green balls are carbon atoms in functional molecules, respectively).

1-pyrenebutyl 1-pyrenebutyric acid 1-pyrenebutylamine

1.0 0.9 0.8

Rk/Rk0

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0.7 0.6 0.5 0.0

0.5

1.0

1.5

2.0

Functionalisation coverage (%)

2.5

Figure 6. Variation of the relative interfacial thermal resistance with respect to the functionalisation ratio of different non-covalent functional molecules.


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The VDOS of epoxy, pristine graphene and non-covalently functionalised graphene were calculated and shown in Figure 7. Figure 7a shows the VDOS of independent 1-pyrenebutyl. It can be seen that the VDOS possess some peaks (i.e., 20-50 THz and 85-90 THz) that couple well with those of epoxy, and some other small peaks (i.e., 0-20 THz and 53 THz) that couple with those of graphene. As shown in Figure 7b, after absorbing the non-covalent functional molecules (i.e., 1-pyrenebutyl), the VDOS peaks of graphene are significantly redistributed, compared to that of pristine graphene. In addition to the existing peaks of graphene, extra VDOS peaks arise at about 87 THz and 20-50 THz. This redistribution leads to a better overlap between the VDOS of graphene and epoxy, which readily explains the reduced graphene-epoxy interfacial thermal resistance with the application of non-covalent functionalisation. Figure 7c shows the VDOS of graphene absorbed with 1-pyrenebutyl, 1pyrenebutyric acid and 1-pyrenebutylamine molecules, respectively. The graphene with these three types of non-covalent functional molecules has similar VDOS curves, which could be attributed to the same pyrene and hydrocarbon moieties in the different functional molecules. Therefore, it is evidenced from Figure 7c that the different non-covalent functional molecules lead to a similar interfacial thermal resistance between graphene and epoxy.



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Figure 7. (a) VDOS of 1-pyrenebutyl molecules; (b) VDOS of epoxy, pristine graphene and graphene absorbed with 1-pyrenebutyl molecules; and (c) VDOS of graphene absorbed with different types of non-covalent functional molecules.

Comparing the results obtained using non-covalent functionalisation (i.e., 2.38% functionalisation reduces the interfacial thermal resistance by about 20.4-21.0%) to those obtained using covalent functionalisation (i.e., 2.38% butyl reduces the interfacial thermal resistance by about 38.0%), it may suggest that the covalent functionalisation technique is more effective than non-covalent one in enhancing the thermal transport across the graphene16 ACS Paragon Plus Environment

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epoxy interface. This finding is consistent with those reported by other researchers on hydrocarbon-based matrix materials.19,24 Although covalent functionalisation is more effective in enhancing the interfacial thermal transport, the non-covalent functionalisation method involves less complicated synthesis processes and it also does not introduce defects into the graphene’s basal plane. Covalent functionalisation introduces defects into the graphene’s basal plane, which reduces the intrinsic thermal transport properties of graphene.50,51 Similar findings were reported in recent experimental studies.48,52,53

3.3. Effect of Isotope Doping Isotope impurities can be introduced in graphene during the fabrication process. It has been reported that the isotope composition can modify the thermal properties of graphene.54-56 In the following, the effect of

13

C isotope on the thermal transport across the graphene-epoxy

interface was investigated. By performing RNEMD simulations on graphene models with different percentages of 13C isotope, the corresponding interfacial thermal resistance RK was obtained. Figure 8 presents the relative interfacial thermal resistance RK/RK0 with respect to 13

C percentage. The MD simulation models of graphene with 13C isotope are displayed as the

inset of Figure 8. Interestingly, unlike the thermal conductivity of graphene which can be significantly modulated by up to 45% with the mixture of isotopes,54 the results here indicate that the graphene-epoxy interfacial thermal resistance remains almost unchanged as the percentage of 13C isotope varies.



1.1 1.0 0.9

Rk/Rk0

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0.8 0.7 0.6 0.5 0

13C

50

Percentage (%)

100

Figure 8. Relative interfacial thermal resistance with respect to the percentage of 13C isotope. Insets are the MD simulation models of graphene with 50% and 100% 13C, respectively. (Orange balls are 12C and yellow balls are 13C)

The VDOS for 13C modified graphene was calculated and shown in Figure 9. Comparing to the VDOS of graphene based on

12

C, it is found that the graphene based on

13

C has a

slightly weakened low-frequency peak and a slightly downshifted high-frequency peak, which is consistent with the research findings from other researchers.56 However, such small modulations on the VDOS of graphene have nearly no impact on its overlap with the VDOS of epoxy. Consequently, the graphene-epoxy interfacial thermal resistance was found to be insensitive to the presence of 13C isotope, as seen in Figure 8.


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Figure 9. VDOS of epoxy, graphene based on 12C and graphene based on 13C.

3.4. Effect of Acetylenic Linkage When a certain percentage of sp2 bonds in graphene are replaced by acetylenic linkages, various types of graphene allotropes, namely graphynes can be formed.57 Recently, there has been an increasing interest in the physical properties of graphynes.58,59 In this study, the interfacial thermal transport between the most typical graphyne, γ-graphyne and epoxy was explored. By performing RNEMD simulations, the interfacial thermal resistance between γgraphyne and epoxy was calculated to be (0.638 ± 0.020) ×10-8 m2KW-1, which is about 10.5% lower than that between graphene and epoxy. The VDOS of γ-graphyne was given in Figure 10. Comparing to the VDOS of graphene, the VDOS of γ-graphyne possesses more lowfrequency peaks at about 0-40 THz, which facilitate a better overlap with the VDOS peaks of epoxy. It could thus explain the lower thermal resistance observed between γ-graphyne and epoxy.

Figure 10. VDOS of epoxy, graphene and γ-graphyne. Inset is the MD simulation model of γ-graphyne.



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4. CONCLUSIONS In this study, MD simulations have been performed to investigate the thermal transport across the interface between graphene and epoxy in graphene-epoxy nanocomposites. The variation of the interfacial thermal resistance with respect to the functionalisation, isotope and acetylenic linkages in graphene is systematically examined. From the simulation results of the 29 Å × 29 Å × 160 Å sized composite model, it has been found that the graphene-epoxy interfacial thermal resistance can be greatly reduced by using the covalent and non-covalent functionalisation, and the reduction increases with higher coverage of functionalisation. Among the different functional groups, covalent butyl is the most effective one in reducing the interfacial thermal resistance whereas the non-covalent functional groups produce smaller but similar reduction. For other geometrical modification in graphene, including

13

C and

acetylenic linkages, merely no changes have been found in the interfacial thermal resistance. The present findings provide better understanding of the thermal transport across the graphene-epoxy interface, and offer a useful guidance for the future development of graphene-epoxy composites in the thermal management application.

ACKNOWLEDGEMENTS Y. Wang acknowledges the financial support on his PhD study from Australian Government via Australian Postgraduate Awards Scheme (APA). The computational support provided by Intersect Australia Ltd. (INTERSECT) and National Computing Infrastructure (NCI) is gratefully acknowledged.

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TABLE OF CONTENTS (TOC) GRAPHIC

J

J 400 350 T (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


300 250 200 0

20

40

60

80 100 Position (Å)

120

140

160


Some Aspects of Thermal Transport across the Interface between

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