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The thermal conductivity (TC) of isolated graphene with different concentrations of isotope (C_{13}) is studied with equilibrium molecular dynamics method at 300 K. In the limit of pure C_{12} or C_{13} graphene, TC of graphene in zigzag and armchair directions are ~630 W/mK and ~1000W/mK, respectively. We find that the TC of graphene can be maximally reduced by ~80%, in both armchair and zigzag directions, when a random distribution of C_{12} and C_{13} is assumed at different doping concentrations. Therefore, our simulation results suggest an effective way to tune the TC of graphene without changing its atomic and electronic structure, thus yielding a promising application for nanoelectronics and thermoelectricity of graphene-based nano device.

Since it was fabricated in 2004 [

In addition to utilizing its high TC, another possible application of graphene has been investigated for thermoelectric energy conversion [

Modeling of thermal transport can be achieved by using Boltzmann transport equation (BTE) [

In Section

The Green-Kubo formula [_{B} is the Boltzmann constant, T is the system temperature, and _{m} is the time required to be longer than the time for current-current correlations to decay to zero [

In the equilibrium MD simulations, we used the second generation REBO carbon potential for its accuracy in describing bond strength and anharmonicity of carbon materials [

Structure of graphene unit cell with 112 carbon atoms.

We computed the TC of mass defect-free graphene as 630 W/mk and 1000 W/mk in armchair and zigzag direction, respectively. This is lower than the reported experimental data [

One primary test done before studying isotope effects on thermal transport is the convergence test for graphene with different unit cell periodic boundary lengths. As shown in Figure

Graphene TC convergence tests with different unit cell boundary lengths.

The first thing we learned from the simulations is that TC of pure

(a) Phonon dispersions for

Normalized Graphene TC as a function of

In the isotope effect study, we generated a wide range of graphene samples with different C_{13} concentrations randomly distributed, since it is a more realistic possible configuration after the synthesis of graphene. Recently, Mingo et al. have proposed a possible method to generate isotope clusters in graphene, and theoretically demonstrated TC reduction using nonequilibrium Green’s function method [

The explanation of the almost “parabolic” shape of TC in Figure _{i} and M_{i} represent the concentration and the mass of the constituent isotope atoms, respectively. Thus, the mean free path directly has to do with the g factor, which is the mass variation of isotope atoms. In our simulation, _{13}, so there we have the minimum phonon mean free path and the minimum TC. As

Among various methods that modulate the TC of graphene, the isotope-doping method provides an efficient way to improve thermoelectric efficiency, since isotope atoms do not change the electronic structure of graphene, the electric conductivity, and the Seebeck coefficient remains the same after the

In summary, we have studied isotope effect on TC of isolated graphene with equilibrium MD methods. Our simulation results suggest that TC of graphene can be effectively reduced by up to 80% in armchair and zigzag directions for isotope concentrations as low as 25%. The phenomenon that mass defect can reduce TC is explained with the relation between phonon mean free path and mass variation of the isotope mixtures [_{13} could be a practical way to reduce TC without changing its electric property, thus promoting thermoelectric coefficient.

The authors are grateful to support from Lockheed Martin. G. Lee acknowledges support from SWAN, and A. F. Fonseca acknowledges partial support from the Brazilian agency CNPq. We thank Rodney Ruoff for suggesting to study isotope effect in graphene. The authors also appreciate discussions with Davide Donadio and Giulia Galli.