We have investigated the lattice thermal transport across the asymmetric tilt grain boundary between armchair and zigzag graphene by nonequilibrium molecular dynamics (NEMD). We have observed significant temperature drop and ultra-low temperature-dependent thermal boundary resistance. More importantly, we find an unexpected thermal rectification phenomenon. The thermal conductivity and Kapitza conductance is direction-dependent. The effect of thermal rectification could be amplified by increasing the difference of temperature imposed on two sides. Our results propose a promising kind of thermal rectifier and phonon diodes based on polycrystalline graphene without delicate manipulation of the atomic structure.
cial influence on the mechanical and electronic properties. For the mechanical property, the grain boundaries with high density of topological defects show anomalous characteristics of mechanical strength [12]. In the case of charge transportation, the charge mobility depends on the grain size which is determined by the grain boundaries [9]. Furthermore, the transmission of the charge carrier across the grain boundary depends on the symmetry of the atomic structure. The charge transport of the symmetric grain boundary reveals high transparency while that of the asymmetric grain boundary emerges almost perfect reflection [13]. Experiments have shown that the line defects like grain boundary can be one of the most powerful ways to manipulate electronic properties at nanoscale [14,15,16]. For the thermal transport, although there have been many studies on the point defects including vacancies [17], Stone-Wales defects [18] and isotope defects [19], the effect of line defects like grain boundary on thermal conductivity is still far from well-understood. In a recent work [20], thermal transport across the tilt grain boundaries with simplest symmetric atomic structure has been considered. Sudden temperature drop at the grain boundary and superior boundary conductance has been observed in that system [20]. There is still a long way for us to further explore and understand the impact of onedimensional global defects on the thermal transport of graphene. Similar to the charge transport, it is reasonable to expect that the asymmetric grain boundary would exhibit different property of thermal transport from that of the symmetric grain boundary.
In this paper, we adopt the nonequilibrium molecular dynamics (NEMD) method [21,22,23] to simulate the heat transport across the asymmetric grain boundary between armchair graphene and zigzag graphene. We show that the Kapitza conductance and the thermal conductivity have strong dependence on the temperature. Furthermore, surprising thermal rectification phenomenon has been observed in the graphene with such asymmetric grain boundary. Our results provide a practical choice for designing thermal rectifier in polycrystalline graphene without delicate atomic engineering.
Figure 1 shows the atomic structure of the asymmetric grain boundary connecting the armchair and the zigzag regions. This structure has been denoted as a boundary structure between the armchair graphene and the zigzag graphene [24] while the electronic transport across that has been studied [13,25]. This structure is composed of a periodic array of 5-pentagon and 7-heptagon topological defects. According to the mismatch of the period of the zigzag part and the armchair part, this asymmetric grain boundary shows peculiar 7-5-7 structure while the standard pentagon-heptagon dislocation cores would flip their orientations from 5-7 to 7-5 [24]. In spite of the lattice mismatch, the formation energy of this asymmetric grain boundary is much smaller than the typical energy of the bare edges in graphene [26].
In all simulations, velocity Verlet algorithm is used to integrate the equation of motions [27]. Periodic boundary condition is imposed on the direction parallel to the grain boundary. Along the direction perpendicular to the grain boundary, fixed boundary condition is applied on the green atoms in the Figure 1. The brown atoms in Figure 1 are coupled to N osé -Hoover heat baths [28], whose temperatures are set to T high and T low , respectively, to generate the temperature gradient. The length of heat bath used in our simulation is around 1 nm. We have carefully tested the effect of the heat bath length on our results. The quantity of the calculated thermal rectification is only slightly affected by the length of heat bath. A recent parameter-modified Tersoff potential is used to describe the atomic interaction [29], which has been verified to give the right velocities of the acoustic-phonon which is crucial in thermal transport. The new parametrized potential considerably improves the computational values of the lattice thermal conductivity and makes them in good agreement with the experimental results [18,30]. After the system reaches to the steady state, the heat flux could be calculated by the energy flowing from the heat bath to the system [31]. The thermal conductivity could be obtained according to the Fourier’s law
In the equation, J represents the heat flux, d is the length of sample, ∆T 1 is the temperature difference between T high and T low , w and h is the width and height of the monolayer graphene, respectively. The temperature usually shows significant temperature jump at the grain boundary region, the boundary conductance is defined as:
J is the heat flux and ∆T 2 is the temperature jump at the boundary [20]. Before starting the simulation, the atomic structure has been fully optimized in a microcanonical ensemble by conjugate gradient method for ensuring the forces on each atom being less than
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