Thermal rectification in partially hydrogenated graphene with grain boundary, a non-equilibrium molecular dynamics study

Computational Materials Science 139 (2017) 330–334

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Thermal rectification in partially hydrogenated graphene with grain boundary, a non-equilibrium molecular dynamics study Masoumeh Shavikloo a,⇑, Salimeh Kimiagar b a b

Department of Physics, Islamic Azad University, Central Tehran Branch (IAUCTB), Tehran, Iran Nano Research Lab (NRL), Department of Physics, Islamic Azad University, Central Tehran Branch (IAUCTB), Tehran, Iran

a r t i c l e

i n f o

Article history: Received 8 April 2017 Received in revised form 15 August 2017 Accepted 16 August 2017

Keywords: Thermal rectification Molecular dynamics Grain boundary Graphene

a b s t r a c t In the present study, we have tried to investigate thermal conductivity and thermal rectification in the partially hydrogenated graphene sheet with grain boundary through non-equilibrium molecular dynamics simulation method. To this end, the 3-body Tersoff and the Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential were employed. The results revealed that the grain boundary plays an important role in phonon scattering, which flows to the other side of grain boundary. It was observed that temperature drops significantly across a grain boundary that leads to the thermal resistance. It has been also proved that thermal rectification depends on the temperature difference between two ends of the system. Also in such a system, a tuning factor for the tuning of the thermal rectification has been introduced by randomly removing hydrogen atoms of the partially hydrogenated graphene sheet with grain boundary. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction Graphene is a nano-sized molecule of carbon atoms in the form of a two-dimensional honeycomb lattice structure, in which carbon atoms have sp2 covalent bonds [1,2]. Much attention has been paid to the unique properties of graphene such as mechanical [2– 7], electronic [8–12] and thermal [13–21] properties in the past decade. In order to develop silicon-based micro-sized devices, we need to search for a new type of material with high thermal conductivity to manage and control the heat of the system. Due to its high thermal conductivity, graphene is an appropriate candidate to the thermal transport and heat management among nanoscale materials [22]. Another application of thermal conductivity of graphene is to generate a driving force to move molecules, utilizing the temperature gradient [23,24]. Shahil and others [15] have reviewed its thermal properties, heat management and the applications of graphene, as well as multilayer graphene of advanced electronics and optoelectronics. Several investigations have been conducted about thermal transport and thermal conductivity of graphene-based composites [25–28]. To modify thermal conductivity of polymers (which is about 0.1–1 W m
1 K
1) up to higher values, graphene is added to it [29]. Moreover, the graphene wrinkle (GW) is a novel molecule that its thermal conductivity was investigated [30]. The GW shows relatively low thermal conductiv⇑ Corresponding author. E-mail address: [email protected] (M. Shavikloo). http://dx.doi.org/10.1016/j.commatsci.2017.08.024 0927-0256/Ó 2017 Elsevier B.V. All rights reserved.

ity than that of pristine graphene. To manage heat conduction in the micro-electronic devices, telescopic silicon nanowire has been also suggested [31]. In the telescopic geometry of silicon nanowire, the thermal rectification was calculated by non-equilibrium molecular dynamics simulation (NEMD), and theoretically was studied for various temperature differences between two ends of nanowire. The thermal rectification indicates that there is a priority in direction for heat flow. Therefore, thermal conduction in one direction is greatly compared to the opposite one. Among the carbon-based nanostructures, Hydrogenated graphene (graphane), which assumes hydrogen atoms attached to both sides, has also remarkable thermal conductivity [32]. In the graphane, sp2 bond between carbon atoms transforms into sp3. All properties of graphene can be controlled through hydrogenation of graphene [33]. Therefore, the graphene and graphane open numerous properties, making it possible to use them for nanoscale thermal management. Recently, Ali Rajabpour and others [34] have investigated thermal transport in graphene-graphane nanoribbon or patterned hydrogen functionalized graphene, using NEMD simulation and consequently have found a thermal resistance at the interface of graphene-graphane. The thermal resistance can make this setup as the thermal rectifier with remarkable performance. In the structure discussed in [34] the interface includes no defect, and all rings are hexagonal in the interface and also direction of two sides is the armchair. Another system which is similar to graphene-graphane, that was discussed above, has been introduced by Yazyev and Louie, LAGBI [35]. LAGBI is a graphene with a grain boundary. A

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Fig. 1. (a) Atomic structure of the model which shows two misorientation graphene connected via grain boundary (colored by red) with 2h = 32.2° (LAGBI) and, (b) the full hydrogenated of right side of LAGBI (F-LAGBI), (c) cross-section view of selected portion. Carbon and hydrogen atoms are colored by gray and orange, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

grain boundary is introduced as an array of pentagon-heptagon defects along the y direction that its misorientation angle of two sides is 2h = 32.2° (see Fig. 1(a)). Lotfi and Neek-Amal [21] have studied temperature profile in LAGBI and revealed that there is a thermal resistance at the grain boundary. The observed temperature gap in grain boundary is 10 K while temperature difference was 20 K and the length of sheet was 30 nm. In the present work, we have intended to investigate the thermal conductivity of both sides of LAGBI nanoribbon and thermal rectification of patterned hydrogen functionalized LAGBI nanoribbon. The patterned hydrogen functionalized LAGBI, will be introduced as an appropriate apparatus for the thermal rectifier.

2. Computational method In this study, all of simulations were performed using the Largescale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [36,37], which is a classical molecular dynamic code. In this stage, a system of graphene sheet with dimensions 20 nm  10 nm containing a grain boundary with misorientation angle 2h = 32.2° (LAGBI) which has already been introduced in the [38] is considered, and also the right side of grain boundary is assumed to be full hydrogenated (F-LAGBI) the same as graphane, which is a form of hydrogenated graphene in both sides in an alternating manner. In fact, the grain boundary is the interface between domains of graphene with different crystallographic orientation. Moreover, to generate partially hydrogenated of right side of LAGBI, we randomly removed H atoms from the both sides of F-LAGBI (PLAGBI). In the F-LAGBI and P-LAGBI there is no symmetry, so that they can be an appropriate candidate for thermal rectifier. In order to model interactions between CAC and CAH atoms in the system, we considered AIREBO potential [39]. The Motion equation is integrated with time step 1 fs, by velocity Verlet algorithm. Also, we

have applied free boundary condition to all directions. First, whole of the system was coupled with the NVE ensemble, as well as Langevin thermostat [40] to reach thermal equilibrium for 500 ps. Then, to calculate the local temperature on the sheet, it was divided to regions with 1 nm width. So, two end regions, as illustrated in Fig. 1(a), were fixed during simulation time. Two other regions which have been specified as cold and hot regions are coupled with Nose-Hoover thermostat [41,42] to generate the temperature gradient across the sheet and also steady-state heat current for about 500 ps simulation time. The hot and the cold regions’ temperature were set to T + D and T
D, respectively, where T and 2D are the mean temperature of system and the temperature difference between the hot and the cold regions, respectively. The NVE ensemble was applied between the hot and the cold regions (middle region). After reaching to steady state, the heat flux was calculated as energy per time unit per area that is extracted from the hot region and enters to the cold region. The heat flux and the regions’ temperatures were averaged over 500 ps and presented as the results. To obtain thermal conductivity, we used Fourier’s law j ¼
jrT. Prior to rectification calculations, thermal conductivity j(T) for both graphene and graphane sheets was obtained with the same orientation as those domains in F-LAGBI. The sizes of sheets were considered 10 nm  10 nm. The thermal rectification is then calculated for F-LAGBI and P-LAGBI.

3. Results and discussions The non-equilibrium molecular dynamics simulations were carried out to obtain thermal conductivity and thermal rectification graphene-based nanostructures. As depicted in Fig. 2, thermal conductivity of graphane was obtained with the same orientation, which is approximately equal to half of graphene, that is due to the conversion of sp2 bondings in graphene to sp3 one’s in graphane

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Fig. 2. Thermal conductivity of the left and right sides of F-LAGBI, which increases with temperature for 2D = 50 K.

[34]. Furthermore, it can be observed that thermal conductivity of graphene and graphane increase with the mean temperature of the system whose behavior is in good agreement with other studies [43]. In both, temperature gradient is constant and 2D = 50 K. Next, in order to investigate thermal rectification of F-LAGBI, the F-LAGBI sheet was simulated with the length of 20 nm. We applied various temperature gradients to the system and its influence on the thermal rectification and temperature gap in the grain boundary line was investigated. As illustrated in Fig. 3, that the temperature profiles are plotted for two cases, when hot region is placed on the left side and when hot region is placed on the right side. Mean temperature and temperature difference 2D in this case are 500 and 300 K, respectively. As it is seen, for a case in which the hot region is in the left side, temperature decreases linearly in both sides but in the grain boundary the temperature falls sharply (temperature gap). The temperature gap can also be observed in the opposite direction (from the right side to the left side) in temperature profile. As it can be observed in Fig. 3, the amount of the

Fig. 3. Temperature profile in two directions, the hot region was placed on the left side (black symbol) and at the right side (red symbol). When heat flux flows from graphene into graphene, the temperature gap is higher than the opposite direction. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

gap depends upon the direction of the applied gradient, so that there are Tg = 35.54 and 28.86 K for the left side to the right side and the right side to the left-side directions, respectively. The temperature gap arises from asymmetric system and the presence of grain boundary that leads to the existence of a preferred direction for heat current. Because of this, we can setup an apparatus such as this system to rectify the heat current. The boundary resistance Rg for the mean temperatures 500 K, was obtained when the temperature difference 2D changes, as demonstrated in Fig. 4. The NEMD simulation results indicate that Rg increases as a function of 2D. This results show that when heat flux direction is from the left to the right side, thermal resistance (boundary resistance and Kapitza resistance [44]) is significantly large. Moreover, we studied thermal rectification in F-LAGBI with mean temperature throughout the system in two cases T = 300 K and 500 K. In order to evaluate the thermal rectification, we focus on it, by running a series of NEMD simulations for a given set of ±2D. The thermal rectification can easily be obtained as,

TR ¼

ðjR!L Þ
ðjL!R Þ  100 ðjL!R Þ

ð1Þ

where jR!L (jL!R ) is the heat current from the left to the right side (the right to the left side). The results of NEMD simulations for thermal rectification of F-LAGBI have been depicted in Fig. 5. As discussed above, the right side of F-LAGBI is full hydrogenated. Fig. 5 shows that by increasing 2D, we can see a descending behavior in thermal rectification when temperature difference 2D Located at the minimum, the maximum amount of thermal rectification can be obtained. Furthermore, we can see that the thermal rectification for the mean temperature 500 K is greater than other mean temperature 300 K. When the mean temperature increases, the ratio of scattered phonons moving from the right side to the left side over scattered phonons, move from the left to the right side decreases. The thermal conductance arises from phonon transport through graphene. when the phonons mean free path (MFP) in graphene is comparable with its length, phonons don’t scatter and easily pass through graphene. In this case, we called ballistic transport. The average MFP for phonons is a few hundred nanometers. When the length of LAGBI smaller than MFP the thermal conductance

Fig. 4. Boundary resistance Rg at the grain boundary with temperature difference 2D in F-LAGBI. As expected, the Rg in the case of left to right direction, is greater than the opposite direction. The mean temperature was 500 K.

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Fig. 5. Thermal rectification obtained from NEMD simulations from two different mean temperature T = 300 K and 500 K. As schematically depicted in the inset, heat current (phonons) can easily flow from the right side to the left side than opposite direction.

of grain boundary depends on the graphene sample length due to quasiballistic [14,45,46]. Moreover, once it gets interesting that we find a way for tuning thermal rectification in such a system. Tuning allowed us a possibility to use this system as a thermal rectifier in a wide range of applications at the specified mean temperature of the system. In order to achieve that goal, we considered the partially hydrogenated system with respect to the F-LAGBI (P-LAGBI), which is created by removing hydrogen atoms with a certain percentage from F-LAGBI. In this way, H atoms were removed randomly, then thermal rectification was estimated. Removing H atoms can impact on thermal rectification, so it can be assumed as the tuning factor. Therefore, we tune thermal rectification by changing the removed H atoms’ percentage. As demonstrated in Fig. 6, thermal rectification increases with removing the H atoms. The range of variation in thermal rectification is significant, up to 17%. In the that event, the thermal rectifier up to 17% is preferred to be utilized. This setup can be a suitable system.

Fig. 7. Phonon spectra for two groups of atoms near to and on both sides of grain boundary for F-LAGBI with T = 300 K and 2D = 50 K. Temperature gradient direction from (a) the left side to the right side, (b) the right side to the left side.

Another quantity which can also help to get more insightful results from the underlying mechanism of the thermal rectification, is phonon spectra of the F-LAGBI. Phonon spectra can be obtained from velocity autocorrelation function of the two groups of atoms, corresponding to the sides of grain boundary [34]. Phonon spectra was calculated from the following equation [47],

PðxÞ ¼

Z

0

1

v ð0Þ  v ðtÞe
ixt dt

ð2Þ

where x indicates the phonons frequency, in which there are specified groups of atoms. As depicted in Fig. 7, phonon spectra for those phonons that flow from the left to the right (the right to the left) for two groups near the grain boundary, there are remarkable mismatches. The mismatch between the spectrum shows that phonons scattered from grain boundary (interface) and some of them were not allowed to go through grain boundary and enter the other side. 4. Conclusion

Fig. 6. Thermal rectification for P-LAGBI in various percentages of removed H atoms at T = 300 for 2D = 50 and 100 K.

In the present study, a set of atomistic NEMD simulations were performed to explore thermal properties of F-LAGBI sheet. It was found that there is a temperature gap in the grain boundary line due to the boundary and Kapitza resistance. It was also concluded that the Tg increases as a function of temperature difference 2D between the hot and the cold regions. The NEMD results revealed

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the fact that thermal rectification decreases with 2D. The maximum of thermal rectification was obtained for the minimum of 2D. Moreover, a tuning factor was introduced for thermal rectification when removing hydrogen atoms from both sides of F-LAGBI. By utilizing the tuning factor, we can tune thermal rectification up to 17%. To understanding basic of changing thermal rectification in F-LAGBI, the phonon spectrum was obtained. It was obviously observed that there was a significant mismatch between the phonon spectrum on both sides of the grain boundary line, which means phonons are scattering from the grain boundary. Even though phonon’s scattering take place in the grain boundary, it also depends on the direction in which heat current flow so that this dependency generates the mentioned rectification.

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