Using classical molecular dynamics simulation, we have studied the effect of
edge-passivation by hydrogen (H-passivation) and isotope mixture (with random
or supperlattice distributions) on the thermal conductivity of rectangular
graphene nanoribbons (GNRs) (of several nanometers in size). We found that the
thermal conductivity is considerably reduced by the edge H-passivation. We also
find that the isotope mixing can reduce the thermal conductivities, with the
supperlattice distribution giving rise to more reduction than the random
distribution. These results can be useful in nanoscale engineering of thermal
transport and heat management using GNRs.Comment: 4 pages, 4 figure

Ajit Vallabhaneni

Ashcroft N. W.

Jiuning Hu

Stephen Schiffli

Xiulin Ruan

Yong P. Chen

English

arXiv

Crossref

Applied Physics Letters

Tuning the thermal conductivity of graphene nanoribbons by edge passivation and isotope engineering: A molecular dynamics study

Using classical molecular dynamics simulation, we have studied the effect of                 edge-passivation by hydrogen (H-passivation) and isotope mixture (with random or                 superlattice distributions) on the thermal conductivity of rectangular graphene                 nanoribbons (GNRs) (of several nanometers in size). We find that the thermal                 conductivity is considerably reduced by the edge H-passivation. We also find that                 the isotope mixing can reduce the thermal conductivities, with the superlattice                 distribution giving rise to more reduction than the random distribution. These                 results can be useful in nanoscale engineering of thermal transport and heat                 management using GNRs. (C) 2010 American Institute of Physics. [doi:                 10.1063/1.3491267

Hu, J. N.

Schiffli, S.

Vallabhaneni, A.

Ruan, X. L.

Chen, Y. P.

Purdue E-Pubs

PhysicsPhysics Research PublicationsPurdue University Year Tuning the thermal conductivity ofgraphene nanoribbons by edgepassivation and isotope engineering: Amolecular dynamics studyJ. N. Hu S. Schiffli A. VallabhaneniX. L. Ruan Y. P. ChenThis paper is posted at Purdue e-Pubs.http://docs.lib.purdue.edu/physics articles/1244Tuning the thermal conductivity of graphene nanoribbons by edgepassivation and isotope engineering: A molecular dynamics studyJiuning Hu,1,a Stephen Schiffli,2 Ajit Vallabhaneni,3 Xiulin Ruan,4 and Yong P. Chen5,b1School of Electrical and Computer Engineering, Birck Nanotechnology Center, Purdue University,West Lafayette, Indiana 47907, USA2School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA3School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA4School of Mechanical Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette,Indiana 47907, USA5Department of Physics, Birck Nanotechnology Center, School of Electrical and Computer Engineering,Purdue University, West Lafayette, Indiana 47907, USAReceived 13 July 2010; accepted 30 August 2010; published online 28 September 2010Using classical molecular dynamics simulation, we have studied the effect of edge-passivation byhydrogen H-passivation and isotope mixture with random or superlattice distributions on thethermal conductivity of rectangular graphene nanoribbons GNRs of several nanometers in size.We find that the thermal conductivity is considerably reduced by the edge H-passivation. We alsofind that the isotope mixing can reduce the thermal conductivities, with the superlattice distributiongiving rise to more reduction than the random distribution. These results can be useful in nanoscaleengineering of thermal transport and heat management using GNRs. © 2010 American Institute ofPhysics. doi:10.1063/1.3491267Graphene1,2 is a monolayer of graphite with a honey-comb lattice structure. It exhibits many unique properties andhas drawn intense attention in the past few years. The un-usual electronic properties of graphene are promising inmany fundamental studies and applications, e.g., the ultra-high electron mobility2 and the tunable band gap and mag-netic properties by the size and edge chirality of graphenenanoribbons GNRs.3–6 Graphene also has remarkable ther-mal properties. The measured value of thermal conductivityof graphene reaches as high as several thousand of watt permeter Kelvin,7–10 among the highest values of known mate-rials. Previous studies11–13 show that the thermal transport inGNRs depends on the edge chirality of GNRs. In realisticgraphene samples, the edges are often passivated14–16 and theisotope composition can be controlled.17 Motivated by these,we study the effect of the edge H-passivation and variousisotope distributions on the thermal transport in GNRs. Wefind that the thermal conductivity can be reduced by the edgeH-passivation and tuned by the isotope distributions. Ourstudy is useful in nanoscale control and management of ther-mal transport by engineering the chemical composition ofGNRs.In this work, we employ the classical molecular dynam-ics MD, similar to the method in Ref. 11 to calculate thethermal conductivities of GNRs. We use the Brennerpotential,18 which incorporates the many-body carbon-carbon and carbon-hydrogen interactions by introducing afractional number of covalent bonds. This method has beenapplied to many carbon-based systems,19,20 especially tographene.11,21,22 The structures of GNRs are shown in Fig. 1with edge H-passivation and the insets of Fig. 3 with iso-tope mixtures. We use fixed boundary conditions, i.e., theatoms denoted by squares are fixed at their equilibrium po-sitions. The atoms denoted by left- and right-pointing tri-angles are placed in two Nosé–Hoover23,24 thermostats atdifferent temperatures. The thermal conductivity can be cal-culated from the Fourier law =Jd / Twh, where T is thetemperature difference chosen to be in the linear responseregime25 between two thermostats, J is the resulting thermalcurrent, d is the length, w is the width, and h=0.335 nm isthe thickness of GNRs, respectively. Calculations presentedbelow are performed for representative GNRs with d6 nm and w1.5 nm. All the calculated thermal conduc-tivities are normalized by 0670 W /m K which is thethermal conductivity calculated at 100 K for the pure 12CGNR with armchair edge and without H-passivation shownin Fig. 1a in Ref. 26. Although the specific value of 0depends on the GNR size,25 the choice of thermostat andboundary condition in MD simulation,12,27 we have checkedthat our conclusions and the qualitative behavior of  dis-cussed below do not. The equations of motion for atomsaElectronic mail: hu49@purdue.edu.bElectronic mail: yongchen@purdue.edu.0 1 2 3 4 5−0.500.5nm(a) Armchair, H−passivatednm0 1 2 3 4 5−0.500.5nmnm(b) Zigzag, H−passivatedFIG. 1. Color online Structure of hydrogen-passivated armchair a andzigzag b GNRs. The hydrogen atoms are denoted by smaller symbolswhile the 12C atoms are denoted by larger ones.  denotes fixed boundaryatoms.   denotes atoms in the left right thermostat.  denotes theremaining atoms in the bulk.APPLIED PHYSICS LETTERS 97, 133107 20100003-6951/2010/9713/133107/3/$30.00 © 2010 American Institute of Physics97, 133107-1Downloaded 21 Apr 2011 to 128.211.161.17. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionslabeled by triangles in either left or right Nosé–Hoover ther-mostat are the following:ddtpi = Fi − pi,ddt =Tt − T02T0, 1where i runs over all the atoms in the thermostat, pi is themomentum of the i-th atom, Fi is the total force acting on thei-th atom,  is the dynamic parameter of the thermostat withinitial value of zero,  is the relaxation time of the thermo-stat, Tt2 /3NkBipi22miis the actual temperature of atoms inthe thermostat at time instant t, T0=TL or TR is the desiredtemperature of the left or right thermostat, N is the numberof atoms in the thermostat, kB is the Boltzmann constant andmi is the mass of the i-th atom. The atoms labeled by circlesobey the Newton’s law of motion with =0. The carbon-carbon potential is the same for all carbon isotopes.We study the temperature dependent thermal conductiv-ity of H-passivated GNRs. All of our simulation results indi-cate that the thermal conductivity increases with tempera-ture. This behavior is consistent with our previous work11and the recent prediction about the size-dependent behaviorof thermal conductivities in graphene flakes.28 Figure 1shows the armchair and zigzag GNRs with top and bottomedges H-passivated. As shown in Fig. 2, the edgeH-passivation significantly reduces the thermal conductivity,compared to the nonpassivated GNRs. A recent study29 usingequilibrium MD has obtained similar conclusions. We notethat the error bars related to MD fluctuations forH-passivated GNRs are considerably larger than that for thenonpassivated GNRs, probably due to the much smaller massof hydrogen atoms.We also study the effect of the mixture of carbon iso-topes 12C and 13C on the thermal conductivity of GNRs.Here, we demonstrate the results in the case of armchairGNRs qualitatively similar results are obtained for zigzagGNRs. The concentration of 13C is N13 / N12+N13, whereN12/13 is the number of12/13C atoms. The thermal conductiv-ity is seen to be reduced by introducing 13C, and the thermalconductivity of pure 13C GNRs is lower than that of pure 12CGNRs because 13C atoms have larger mass and thus givelower phonon frequency.30 The inset of Fig. 3a shows atypical random isotope distribution. Another isotope distribu-tion pattern we study is the isotopic superlattice structureshown in the inset of Fig. 3b. Here, the whole GNR iscomposed of four slices with equal length and the same iso-tope composition. Within each slice such as the dashed boxin the inset of Fig. 3b, the number L of vertical 13Catomic chains with zigzag shape e.g., L=4 for the inset ofFig. 3b can vary from 0 to 7 see details in Ref. 26. L=0L=7 corresponds to the pure 12C 13C GNR. The tem-perature dependent thermal conductivity in Fig. 3 shows thatthe isotope effect becomes more evident at higher tempera-tures. We show the thermal conductivity as a function of theconcentration of 13C calculated at the temperature of 500 Kin Fig. 4. In the case of the random distributions, the calcu-lated thermal conductivity is an average of 10 different dis-tributions with the same isotope concentration. For randomisotope distributions, the isotope concentration dependentthermal conductivity dashed line in Fig. 4 shows a panshape and is relatively flat in the concentration range of20%–90%. The thermal conductivity is reduced by 10%around the isotope concentration of 50%. The error barsare determined from the deviations of the thermal conduc-tivities for the ten different distributions from their averagevalue. In contrast, the conical shape of the solid line in Fig. 4shows much stronger dependence of the thermal conductivityon the isotope concentration for the superlattice structures,with 30% reduction in the thermal conductivity at 50%of the isotope concentration. We have also obtained similarresults using velocity exchange MD Ref. 31 in the LAMMPSpackage.32It has been previously demonstrated that the thermalconductivity depends on the edge chirality11–13 in the ab-100 150 200 250 3000.511.522.53T (K)κ/κ 0Armchair, H−passivatedArmchair, not passivatedZigzag, H−passivatedZigzag, not passivatedFIG. 2. Color online Temperature dependent thermal conductivity ofGNRs with and without edge H-passivation.100 200 300 400 500 600 700123T (K)0%13C30%13C50%13C70%13C100%13C100 200 300 400 500 600 7000123T (K)κ/κ 0L=0L=2L=4L=60 10 20 30 40 50−6−4−2024657%13C0 10 20 30 40 50−6−4−2024630%13C(b)(a)L=4FIG. 3. Color online Temperature dependent thermal conductivity ofGNRs with 13C isotopes distributed a randomly and b in a superlatticestructure. The insets show the corresponding typical structures of GNRswith the same meaning of symbols as that in Fig. 1. The larger smallersymbols denote 13C 12C atoms.0 0.2 0.4 0.6 0.8 12.22.42.62.833.2N13/(N12+N13)κ/κ 0SuperlatticeRandom distributionFIG. 4. Color online Thermal conductivity as a function of the 13C con-centration for superlattice solid line and random dashed line isotopedistributions.133107-2 Hu et al. Appl. Phys. Lett. 97, 133107 2010Downloaded 21 Apr 2011 to 128.211.161.17. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionssence of H-passivation, i.e., the thermal conductivity of thezigzag GNR is larger than that of the armchair GNR. How-ever, as shown in Fig. 2, their thermal conductivities becomeclose to each other within the MD error bars after theH-passivation, suggesting that phonon scattering with the hy-drogenated edges dominates over the contribution from thechirality effect. We have suggested that the smaller thermalconductivity of armchair GNRs is due to the stronger phononscattering at the armchair edges.11 It is interesting to note thatthe H-passivated zigzag GNR in Fig. 1b resembles the arm-chair GNRs at the edges. We suggest that the thermal trans-port in small GNRs several nanometers in size in our studyis strongly affected by the edge configuration.Recently, it has been experimentally demonstrated thatdifferent carbon isotopes can be controllably introduced ingraphene, such as 13C, in the chemical vapor depositiongrowth of graphene on metals. Both random and segregationby domains of different isotopes distributions have beenobserved.17 This opens possibilities of engineering the ther-mal properties of graphene by isotope distributions. Theisotope effect on the thermal transport has been studied inseveral nanomaterials, such as carbon nanotubes,33,34 boronnitride nanotubes,35,36 and silicon nanowires.37 The panshape of the dashed line in Fig. 4 is consistent with thereduction of the thermal conductivity in the “alloy limit.”38 Asimilar pan shape is found in GNRs Ref. 39 and SiGenanowires40 by tuning the composition. By keeping the iso-tope concentration a constant of 50%, it has been shown41that the thermal conductivity as a function of the slice lengthwhich is kept constant in our simulations gives similarconical shaped dependence as we see in Fig. 4 for the super-lattice structures.In conclusion, the classical MD is applied to calculatethe thermal conductivities of rectangular GNRs. We find thatthe edge H-passivation can reduce the thermal conductivitysignificantly. We also show that the thermal conductivity de-pends on the concentrations of isotopic atoms and their dis-tribution patterns. The isotopic superlattice distributions canreduce the thermal conductivity much more than random dis-tributions. These findings can be useful in controlling heattransfer in nanoscale using GNR-based thermal devices.This work is partially supported by the SemiconductorResearch Corporation SRC—Nanoelectronics ResearchInitiative NRI via Midwest Institute for NanoelectronicsDiscovery MIND and by Cooling Technologies ResearchCenter CTRC at Purdue University.1A. K. Geim and K. S. Novoselov, Nature Mater. 6, 183 2007.2A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K.Geim, Rev. Mod. Phys. 81, 109 2009.3K. Nakada, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev.B 54, 17954 1996.4Y. W. Son, M. L. Cohen, and S. G. Louie, Nature London 444, 3472006.5M. Y. Han, B. Ozyilmaz, Y. Zhang, and P. Kim, Phys. Rev. Lett. 98,206805 2007.6Z. Chen, Y. M. Lin, M. J. Rooks, and P. Avouris, Physica E 40, 2282007.7A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. 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Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

Tuning the thermal conductivity of graphene nanoribbons by edge passivation and
            isotope engineering: A molecular dynamics study

https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=3031&amp;context=physics_articles

Tuning the thermal conductivity of graphene nanoribbons by edge
  passivation and isotope engineering: a molecular dynamics study

Tuning the thermal conductivity of graphene nanoribbons by edge passivation and isotope engineering: a molecular dynamics study

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