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Thermal Conductivity of Graphene Wrinkles: A Molecular Dynamics Simulation Liu Cui, Xiao-Ze Du, Gaosheng Wei, and Yanhui Feng J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07162 • Publication Date (Web): 27 Sep 2016 Downloaded from http://pubs.acs.org on October 2, 2016
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Thermal Conductivity of Graphene Wrinkles: A Molecular Dynamics Simulation Liu Cui 1, Xiaoze Du 1, *, Gaosheng Wei 1 and Yanhui Feng2, ** 1
Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of
Ministry of Education, School of Energy Power and Mechanical Engineering, North China Electric Power University, Chang Ping, Beijing 102206, China 2
School of Energy and Environmental Engineering, University of Science and
Technology Beijing, Haidian, Beijing 100083, China
*To whom correspondence should be addressed. E-mail: a)
[email protected] (Xiaoze Du); b)
[email protected] (Yanhui Feng)
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Abstract Based on the non-equilibrium molecular dynamics simulations, the heat conduction in a novel deformation of graphene, named graphene wrinkle (GW), is investigated. Distinct from pristine graphene, the GW exhibits a relatively low thermal conductivity. We observe that the low thermal conductivity stems from the strong phonon localizations, which are concentrated on the joint regions between crests and troughs of wrinkles. The suppression in GW thermal conductivity could be further attributed to the enhanced phonon scatterings, as evidenced by the vibrational density of states (VDOS) attenuation in the low frequency region, the G-band redshift of VDOS due to the flattened phonon dispersion curves (low phonon group velocities), and the decreased phonon lifetime. In addition, we find that the thermal conductivity of GW is almost insensitive to temperature in the range between 200 and 600 K. It is induced by the significant contribution of low frequency phonon modes, which are more influential in the direction perpendicular to the wrinkle texture. This study provides physical insight into the mechanisms of thermal transport in GWs, and offers design guidelines for applications of GW related devices.
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1. Introduction Graphene 1, a monolayer of graphite with hexagonal lattice structure, has attracted great attention over the past decade. The unusually high intrinsic thermal conductivity of graphene
2-4
makes it an excellent candidate for heat dissipation and thermal
management material. The rapid development in synthesis of graphene
5-8
have
motivated many efforts to tune graphene thermal properties by designing and changing its 2D structure, to meet the requirements of specific applications. For instance, the trapezium-shaped graphene nanoribbons have been found to act as thermal diodes
9-10
, which can control the heat flow along a specific direction.
Graphene nanomesh, a graphene sheet with periodically arranged nanopores, presents promising practical use as thermoelectrics
11-12
, which could convert heat energy
directly into electrical energy. Recently, a novel deformation of graphene, named graphene wrinkle (GW) has attract investors' attention. The GWs can be considered as the wrinkles that go across the entire graphene sheet with a well-defined direction. Their characteristics including amplitude and wavelength, for now, could be intentionally manipulated by various thermal and mechanical methods, such as thermally generated compression 13-14, atomic force microscopy (AFM) probe induced shear and compression 15, and cooperating with substrate morphology 16. Although some research has been done to understand the wrinkle effect on graphene properties, most of these studies focused mainly on their electronic transportation 17-20. Few efforts have been devoted to the studies on the heat conduction of GWs. Wang et al.
21
in their non-equilibrium molecular dynamics (NEMD) study reported that 3 ACS Paragon Plus Environment
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wrinkles could significantly degrade the thermal properties of graphene along the texture direction, but had little effect on the thermal conductivity along the wrinkling direction. Shen
22
used equilibrium molecular dynamics (EMD) to calculate the GW
thermal conductivity and studied its dependence on shear and temperature. Their results indicated that the GW thermal conductance became worse, with the increase of temperature and shear deformation. To date, the heat transport mechanisms of GW are not fully understood yet. The remainder of this paper is organized as follows. Section 2 introduces briefly the model and simulation methodology, which consist basically in using the NEMD technique to obtain the thermal conductivity. The results of NEMD simulation of thermal transport are presented in Section 3. The thermal conductivity of GW as a function of temperature is determined. In particular, the physical insight of thermal conductivity suppression in GWs is discussed by analyzing the phonon participation ratio, spatial energy distribution, vibrational density of states, phonon lifetime and thermal conductivity accumulation. Finally, the conclusion is proposed in Section 4. This study is expected to pave the way for manipulating the thermal transport properties of graphenes for future emerging applications. 2. Model structures and calculation methods We used the deformation-control method
23-24
to achieve the structure of GW. For a
10-nm-long and 10-nm-wide rectangular graphene as shown in Fig.1(a), one array of atoms denoted in violet were fixed, and another atomic array denoted in green were subjected to shear strain. After the structure optimization via the energy minimization, 4 ACS Paragon Plus Environment
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the dynamic shear strain was generated by applying gradual deformation increment to certain atoms. The green atoms were displaced along the x-axis in steps of 0.1 Å (shear strain 0.003). And the displacement was applied every 1000 time steps. The bigger accumulated increment for displacement means higher shear strain applied to the graphene. The wrinkle pattern of GW under 0.213 shear strain is presented in Fig.1(b), which includes mainly two crests and one trough. The mean wrinkle amplitude and wavelength are 5.440 Å and 15.199 Å, respectively.
(a)
(b)
Figure 1. Models of pristine graphene (a) and graphene wrinkle (b). Different colors of atoms in figure (b) indicate different normalized magnitudes of z coordinates.
To predict the thermal transport properties of GWs, the NEMD simulations were performed. The optimized Tersoff potential
25
was adopted to describe the C-C
interactions. Free boundary conditions were used in all directions. In the heat flow direction, the atoms at the two GW ends were fixed to avoid them from sublimating. All the NEMD simulations were carried out using LAMMPS 26 with a time step of 0.5 fs. The system was firstly relaxed in NVT ensemble using the Nosé-Hoover 5 ACS Paragon Plus Environment
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thermostat
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for 1.5 ns, and continued to another 3 ns for the relaxation in NVE
ensemble. Heat source and sink as shown in Fig.1(b) were established by adding/removing non-translational kinetic energy to the atoms in the heat source/sink. After the system reached equilibrium, the temperature gradient ∂T/∂L can be obtained. The thermal conductivity (k) was then calculated by Fourier 's law k
q hw T / L
(1)
where q represents the heat flux. h (=3.35 Å) and w are the thickness and width of graphene, respectively. It should be noted that w is taken as one half of the largest width in calculating the thermal conductivity of asymmetric GWs. 3. Results and discussion 3.1 Comparison between pristine graphene and graphene wrinkle The thermal conductivity of pristine graphene and GW under shear strain 0.213 was calculated in the temperature range of 200-600 K. For comparison, the heat conduction in different GW directions, such as perpendicular or parallel to the wrinkle texture orientation, were studied for each temperature. The results are summarized in Fig. 2. The thermal conductivity of pristine graphene given by NEMD is about 152 W/m·K at 300 K, which is in good agreement with the molecular dynamics (MD) results reported in previous papers
28-29
. Fig. 2 also shows that the thermal
conductivity of GW is smaller than that of pristine graphene, which is up to 36% decrease in the parallel direction and 52% in the perpendicular direction at 300 K. This conclusion is quantitatively distinct from that of Wang et al. 21. It is attributed to the different simulation details we used. Wang et al. employed AIREBO potential to 6 ACS Paragon Plus Environment
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describe the C-C interactions. Especially, they selected a specific wrinkle strip (a crest or trough of the wrinkle) as a model to study the GW thermal conductivity. However, our results have shown that the joint regions between crests and troughs of wrinkles have important effect on GW heat transfer (details in Fig. 4(b)). Parallel direction
300
Prinstine graphene Graphene wrinkle -parallel direction Graphene wrinkle -perpendicular direction
240
Thermal conductivity [W/mK]
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180
Heat flux
Perpendicular direction 120
Heat flux 60 200
300
400
500
600
Temperature [K]
Figure 2. Thermal conductivity of graphene wrinkle under different temperature.
It is known that the calculated values of thermal conductivity are quite small in comparison with experimental data (about 600-5000 W/m·K
30
) because of the
differences in the system scales between MD simulations (in the order of tens of nanometer) and experiments (in the order of a few micrometers). One should note here that phonon mean free path (MFP) in graphene is in the range of 700-800 nm 4. The size effect could arise if the system scale is not significantly longer than the phonon MFP
31-32
. The size dependent values of thermal conductivity have been
observed in previous studies
33-34
. However, MD results are qualitatively consistent
with experimental measurements. For instance, Lee et al. 35 and Yang 36 et al. studied the thermal conductivity of graphene using Raman scattering spectroscopy and MD, respectively. Both the results shown that the thermal conductivity of graphene 7 ACS Paragon Plus Environment
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decreased as the temperature increased. Chen et al.
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explored the isotope effects on
the thermal properties of graphene by optothermal Raman technique. They found that the isotope caused a reduction in thermal conductivity, which was consistent with the MD results reported by Zhang et al.
38
. The focus of this paper is on the new heat
transfer phenomena in GWs and the underlying mechanisms. 3.2 Participation ratio The mechanisms of reduction in the thermal conductivity of GWs, compared with pristine graphenes, can be discussed via participation ratios (PRs)
39-40
. The PR for
each mode λ is defined as 1
p
N i* , i , i
2
(2)
where εiα, λ is the i-th vibrational eigenvector component corresponding to the mode λ in the α direction, with α representing a Cartesian direction (i.e. x, y and z). Superscript * denotes the complex conjugate. N is the total number of atoms. The PR is a very useful quantity to characterize the phonon mode localization
41-42
. For
example, PR is 1/N if only one atom participates in the motion. When all atoms participate in the motion, PR is calculated out as 1. That is, the bigger the PR, the less localized the phonon modes. Accordingly, the thermal conductivity will be higher. The PRs of pristine graphene and GW are compared in Fig. 3. The presence of wrinkles leads to the PR decrease over the entire range of frequency. That is, phonon modes in GWs tend to be localized and less atoms participate in the motion. The localized phonons cannot transport thermal energy as efficiently as the delocalized ones in pristine graphenes, which results in a reduction in GW thermal conductivity, 8 ACS Paragon Plus Environment
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relative to pristine graphenes. 1
Pristine graphene
Graphene wrinkle
0.1
Participation ratio
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0.01
1E-3
1E-4 0
10
20
30
40
50
60
Frequency [THz]
Figure 3. Participation ratios for pristine graphene and graphene wrinkle.
3.3 Energy distribution Although the PR can indicate mode localizations quantitatively, it cannot offer information about the spatial distribution of a specific mode. The spatial localization for strongly localized modes (i.e. PR
