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  • KIM ET AL. VOL. 6 NO. 10 90509057 2012

    www.acsnano.org

    9050

    September 13, 2012

    C 2012 American Chemical Society

    Thermal Transport in FunctionalizedGrapheneJeong Yun Kim, Joo-Hyoung Lee, and Jeffrey C. Grossman,*

    Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States and School of MaterialsScience and Engineering, Gwangju Institute of Science and Technology, Gwangju, Republic of Korea

    Graphene has attracted intense atten-tion for both its superior carrier mo-bility at room temperature and its

    unique zero-gap band structure, which leadsto massless charge carriers.1,2 In addition tothese remarkable electronic properties, therehave been recent attempts to use graphenefor thermoelectric (TE) applications3,4 dueto its low-dimensional structure and ambi-polar nature, controlling the sign of theSeebeck coefficient (S) by changing thegate bias instead of doping. The efficiencyof a TE material is determined by its figure ofmerit, ZT = S2T/, where S is the Seebeckcoefficient, the electrical conductivity, the thermal conductivity, and T the tempera-ture. For a pristine graphene monolayer,the TE properties have been studied boththeoretically57 and experimentally,810 withreported values for S as high as 100 V/K,suggesting the potential of graphene as acandidatematerial for TE applications. How-ever, because of its extremely high ,1113

    bare graphene is overall a highly inefficientTE material.8 Thus, in order to create anefficient ZT material based on graphene, asignificant reduction in the thermal conduc-tivity is required.One way to suppress the thermal conduc-

    tivity of graphene, or nearly any material,would be to introduce point defects such asinterstitials, vacancies, or by alloying. How-ever, if the goal is to explore thermoelectricapplications, one must balance reducedthermal conductivity against the needfor a large power factor (S2). Unlike arange of other promising classes of thermo-electric materials that utilize controlled de-fects (phonon glass) as phonon scatteringsitesby takingadvantageof inherent electroncrystal properties in thematerials, includingskutterudites14 and clathrates,15 the intro-duction of controlled rattling structuresinto a graphene sheet would pose an en-ormous synthesis challenge. The use of lesscontrolled defects such as vacancies16 or

    substitutional impurities17 would of courselower the thermal conductivity, but theywould also lower the power factor by somuch that such an approach is unlikely tobe relevant to the case of graphene-basedthermoelectrics. Introduction of isotope dis-order and isotope patterns would be amethod of reducing thermal conductivityof graphene without degrading electrontransport; however, because of the relativelymarginal thermal conductivity reduction,by only a factor of 2,18 such approaches alsohave not led to significant increases in ZT.Another way to suppress the thermal

    conductivity of a material is to reduce itsdimensionality, for example,byusingquantum

    * Address correspondence tojcg@mit.edu.

    Received for review July 15, 2012and accepted September 13, 2012.

    Published online10.1021/nn3031595

    ABSTRACT

    We investigate the effects of two-dimensional (2D) periodic patterns of functional groups on

    the thermal transport in a graphene monolayer by employing molecular and lattice dynamics

    simulations. Our calculations show that the use of patterned 2D shapes on graphene reduces

    the room temperature thermal conductivity, by as much as 40 times lower than that of the

    pristine monolayer, due to a combination of boundary and clamping effects. Lattice dynamics

    calculations elucidate the correlation between this large reduction in thermal conductivity and

    two dynamical properties of the main heat carrying phonon modes: (1) decreased phonon

    lifetimes by an order of magnitude due to scattering, and (2) direction-dependent group

    velocities arising from phonon confinement. Taken together, these results suggest that

    patterned graphene nanoroads provide a method for tuning the thermal conductivity of

    graphene without the introduction of defects in the lattice, opening an important possibility

    for thermoelectric applications.

    KEYWORDS: thermal conductivity . graphene . chemical functionalization .thermoelectrics . molecular dynamics . lattice dynamics

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    wires or superlattices.1921 Recent theoretical studieshave shown that the thermal conductivity of a gra-phene nanoribbon (GNR) can be suppressed by severalorders of magnitude compared to graphene due toits edge disorder,3,2224 which is introduced duringfabrication. However, owing to several obstacles toproducing GNR-based devices, including the challengeof reliable production of GNRs with controlled widthdistributions and themanipulation required for assem-bling as-produced GNRs into devices,25 it would beadvantageous to develop approaches that reduce thethermal conductivity of graphene that do not rely onphysical cutting or etching. Toward this end, graphenesuperlattices made with chemical functionalizationare of great interest and have been explored recentlydue to the possibility of nanostructuring grapheneinto complex patterns.2529 Functionalization alsoleads to tunable electronic properties by opening theenergy gap of graphene, originating from the inducedchanges in the hybridization of carbon atoms from sp2

    to sp3.25,2729 It is therefore of great interest to furtherexplore the potential of graphene superlattices madewith chemical functionalization for TE applications, inparticular, the role of such functionalization on thermaltransport properties.Among various kinds of pattern shapes, we focus

    in this work on 2D periodic line patterns to producegraphene nanoroads,25 which are in a sense a mix-ture of pristine GNRs and GNRs with full functionaliza-tion within the same sheet. Such partial functionali-zation generates patterned sp3-hybridized carbon re-gions with well-defined boundaries between the sp2

    (pristine GNR) and sp3 (functionalized GNR) domains.The key question for suchmaterials regarding TE appli-cations is whether their thermal conductivity can beefficiently suppressed due to the phonon scatteringat these boundaries without severely degrading the

    electronic properties of the pristine monolayer. Here,we study the influence of 2D periodic patterns on thethermal transport of partially functionalized graphenewith different functional groups, employing a combi-nation of classical molecular dynamics and latticedynamics simulations. The thermal conductivity iscomputed as a function of a range of pattern widthsand functional groups (H and hydrocarbon chains). Ourcalculations demonstrate that the presence of hydro-genated regions leads to thermal conductivities up to7 times smaller than that of pristine graphene in thedirection perpendicular to the pattern boundary, dueto a combination of scattering at the interface andphonon confinement effects. Such a reduction alonewould not be sufficient to make graphene-based TEpractical. However, we find that an additional reduc-tion by a factor of more than 20 is obtained inpatterned graphene with hydrocarbon chains, due toa clamping effect of the chains arising from theirsteric repulsion, as well as scattering between sp2 andsp3 carbon. We show that combining both types offunctional groups further reduces the thermal conduc-tivity in both perpendicular and parallel directions tothe pattern boundary (by as much as 40 in ourcalculations for the perpendicular direction), implyingthat chemical functionalization could be an efficientroute to engineering the thermal transport in graphenemonolayers.

    RESULTS AND DISCUSSION

    In our simulations, patterned graphene nanoroadsare formed via partial functionalization of graphenesheets with the armchair-type of interface, which has ageometry that remains completely flat upon structuralrelaxation (see Figure 1a).25 Graphene is functionalizedwith H atoms and hydrocarbon chains (pentane C5H12,referred to as C5) on both sides of the sheet in an

    Figure 1. (a) Schematic representation of apatternedgraphene samplewith an armchair-typeboundary alongwith structuralvariables used in the calculations. Blue shaded area indicates the patterned region, and the black dotted square representsthe MD simulation unit cell. (b) Unit cell of H-functionalized graphene with graphane structure (inset). (c) C5-functionalizedgraphene. The inset shows the C sites of graphene where C5 chains are attached, arranged in a two-dimensional hexagonalclose-packed lattice, as well as the structure of C5 (pentane: C5H12).

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    alternating manner.30 While H atoms can be attachedto each C site of graphene to make graphane (seeFigure 1b),29 it is not possible to functionalize gra-phene with C5 chains in the same fashion as for Hatoms due to the steric repulsion between the chains(see Figure 1c).31 Thus, we model the densest packingof C5 chains on graphene possible, given the possiblebonding configurations available in the graphenelattice, namely, a close-packed array of C5 chainsseparated by 4.2 , as shown in Figure 1c.

    Molecular Dynamics Simulations. Molecular dynamics(MD) simulations are employed within the LAMMPSpackage32 to compute thermal conductivities for allof the systems considered in this work. We first com-pute the thermal conductivity of approximately squaregraphene sheets ranging in size from 20 to 500 (corresponding to 20092 000 atoms in the simula-tion cell) and find that converges to the value of350 W/mK for sizes larger than 50 (see SupportingInf