势能模型对石墨烯导热性质分子动力学模拟的影响

摘要/Abstract

摘要： 针对常用的Tersoff势、Rebo势和Airebo势，系统性地分析势能模型对分子动力学模拟计算石墨烯色散关系、声子态密度、群速度和热导率的影响. 结果表明：Rebo势和Airebo势描述的声子色散关系接近实验值，Airebo势对应的声子态密度与第一性原理计算的结果较为符合，Rebo势和Airebo势计算的Γ点处声子群速度高于Tersoff势. 采用Airebo势得到石墨烯热导率约为1 150 W·（m·K）^-1，与实验值相近. 综合各种影响，相比于Tersoff势和Rebo势，Airebo势能模型更适合计算石墨烯的导热性质.

关键词: 石墨烯, 分子动力学模拟, 势能模型, 热导率

Abstract: We compare Tersoff, Rebo and Airebo models in calculating thermal properties of graphene, including phonon dispersion, density of states, group velocities and thermal conductivity. It is found that phonon dispersions derived from Rebo and Airebo models are in better agreement with experiments, and density of states derived from Airebo model is close to predictions of first-principles. As for group velocities around Γ point, Rebo and Airebo models provide higher values than Tersoff model. We also find that thermal conductivity of graphene provided by Airebo model is about 1150 W·m^-1·K^-1, which agrees with experimental results. Compromising various factors, compared with Rebo and Tersoff models Airebo model may be suitable for describing thermal properties of graphene.

Key words: graphene, molecular dynamics, potential model, thermal conductivity

中图分类号:

TK124

邹济杭, 叶振强, 曹炳阳. 势能模型对石墨烯导热性质分子动力学模拟的影响[J]. 计算物理, 2017, 34(2): 221-229.

ZOU Jihang, YE Zhenqiang, CAO Bingyang. Effects of Potential Models on Thermal Properties of Graphene in Molecular Dynamics Simulations[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(2): 221-229.

参考文献

[1] BOLOTIN K I, SIKES K J, JIANG Z, et al. Ultrahigh electron mobility in suspended graphene[J]. Solid State Communications, 2008, 146: 351-355.
[2] LEE G G, WEI X D, KYSAR J W, et al. Measurement of the elastic properties and intrinsic strength of monolayer graphene [J]. Science, 2008, 321: 385-388.
[3] BALANDIN A A, GHOSH S, BAO W, et al. Superior thermal conductivity of single-layer graphene [J]. Nano Letters, 2008, 8(3): 902-907.
[4] BAE S, KIM H, LEE Y, et al. Roll-to-roll production of 30-inch graphene films for transparent electrodes[J]. Nature Nanotechnology, 2010, 5(8): 574-578.
[5] GEIM A K, KIM P. Carbon wonderland [J]. Scientific American, 2008, 298(4): 90-97.
[6] GEIM A K. Graphene: Status and prospects [J]. Science, 2009, 324(5934): 1530-1534.
[7] ALLEN M J, TUNG V C, KANER R B. Honeycomb carbon: A review of graphene [J]. Chemical Reviews, 2009, 110(1): 132-145.
[8] STANKOVICH S, DIKIN D A, DOMMETT G H B, et al. Graphene-based composite materials [J]. Nature, 2006, 442(7100): 282-286.
[9] BU H, CHEN Y, ZOU M, et al. Atomistic simulations of mechanical properties of graphene nanoribbons [J]. Physics Letters A, 2009, 373(37): 3359-3362.
[10] BUNCH J S, VAN DER ZANDE A M, VERBRIDGE S S, et al. Electromechanical resonators from graphene sheets [J]. Science, 2007, 315(5811): 490-493.
[11] NETO A H C, GUINEAR F, PERES N M R, et al. The electronic properties of graphene [J]. Reviews of Modern Physics, 2009, 81(1): 109.
[12] ZHANG Y, TAN Y W, STORMER H L, et al. Experimental observation of the quantum Hall effect and Berry's phase in graphene [J]. Nature, 2005, 438(7065): 201-204.
[13] SHAO Q, LIU G, TEWELDEBRHAN D, et al. High-temperature quenching of electrical resistance in graphene interconnects [J]. Applied Physics Letters, 2008, 92(20): 202108.
[14] CAI W, MOORE A L, ZHU Y, et al. Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition [J]. Nano Letters, 2010, 10(5): 1645-1651.
[15] JAUREGUI L A, YUE Y, SIDOROV A N, et al. Thermal transport in graphene nanostructures: Experiments and simulations [J]. ECS, 2010, 28(5): 73-83.
[16] GHOSH S, BAO W, NIKA D L, et al. Dimensional crossover of thermal transport in few-layer graphene [J]. Nature Materials, 2010, 9(7): 555-558.
[17] CHEN S, WU Q, MISHRA C, et al. Thermal conductivity of isotopically modified graphene [J]. Nature Materials, 2012, 11:203-207.
[18] BALANDIN A A. Thermal properties of graphene and nanostructured carbon materials [J]. Nature Materials, 2011, 10(8): 569-581.
[19] NIKA D L, POKATILOV E P, ASKEROV A S, et al. Phonon thermal conduction in graphene: Role of Umklapp and edge roughness scattering [J]. Physical Review B, 2009, 79(15): 155413.
[20] NIKA D L, GHOSH S, POKATILOV E P, et al. Lattice thermal conductivity of graphene flakes: Comparison with bulk graphite [J]. Applied Physics Letters, 2009, 94(20): 203103.
[21] CEPELLOTTI A, FUGALLO G, PAULATTO L, et al. Phonon hydrodynamics in two-dimensional materials [J]. Nature Communications, 2015, 6.
[22] LEE S, BROIDO D, ESFARJANI K, et al. Hydrodynamic phonon transport in suspended graphene [J]. Nature Communications, 2015, 6.
[23] POP E, VARSHNEY V, ROY A K. Thermal properties of graphene: Fundamentals and applications [J]. MRS Bulletin, 2012, 37(12): 1273-1281.
[24] BANERJEE S K, REGISTER L F, TUTUC E, et al. Graphene for CMOS and beyond CMOS applications [J]. Proceedings of the IEEE, 2010, 98(12): 2032-2046.
[25] GHOSH S, CALIZO I, TEWELDEBRHAN D, et al. Extremely high thermal conductivity of graphene: Prospects for thermal management applications in nanoelectronic circuits [J]. Applied Physics Letters, 2008, 92(15): 151911.
[26] LEE J U, YOON D, KIM H, et al. Thermal conductivity of suspended pristine graphene measured by Raman spectroscopy [J]. Physical Review B, 2011, 83(8): 081419.
[27] FAUGERAS C, FAUGERAS B, ORLITA M, et al. Thermal conductivity of graphene in corbino membrane geometry [J]. ACS Nano, 2010, 4(4): 1889-1892.
[28] KLEMENS P G. Theory of thermal conduction in thin ceramic films [J]. International Journal of Thermophysics, 2001, 22(1): 265-275.
[29] SEOL J H, JO I, MOORE A L, et al. Two-dimensional phonon transport in supported graphene [J]. Science, 2010, 328(5975): 213-216.
[30] ZHONG W R, ZHANG M P, AI B Q, et al. Chirality and thickness-dependent thermal conductivity of few-layer graphene: A molecular dynamics study [J]. Applied Physics Letters, 2011, 98(11): 113107.
[31] HU J, RUAN X, CHEN Y P. Thermal conductivity and thermal rectification in graphene nanoribbons: A molecular dynamics study [J]. Nano Letters, 2009, 9(7): 2730-2735.
[32] CAO B Y, YAO W J, YE Z Q. Networked nanoconstrictions: An effective route to tuning the thermal transport properties of graphene [J]. Carbon, 2016, 96: 711-719.
[33] ZHANG H, LEE G, CHO K. Thermal transport in graphene and effects of vacancy defects [J]. Physical Review B, 2011, 84(11): 115460.
[34] ZHANG H, LEE G, FONSECA A F, et al. Isotope effect on the thermal conductivity of graphene [J]. Journal of Nanomaterials, 2010, 2010: 7.
[35] YE Z Q, CAO B Y, YAO W J, et al. Spectral phonon thermal properties in graphene nanoribbons [J]. Carbon, 2015, 93: 915-923.
[36] TERSOFF J. Empirical interatomic potential for carbon, with applications to amorphous carbon [J]. Physical Review Letters, 1988, 61(25): 2879.
[37] ERHART P, ALBE K. Analytical potential for atomistic simulations of silicon, carbon, and silicon carbide [J]. Physical Review B, 2005, 71(3): 035211.
[38] BRENNER D W. Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films [J]. Physical Review B, 1990, 42(15): 9458.
[39] BRENNER D W, SHENDEROVA O A, HARRISON J A, et al. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons [J]. Journal of Physics: Condensed Matter, 2002, 14(4): 783.
[40] STUART S J, TUTEIN A B, HARRISON J A. A reactive potential for hydrocarbons with intermolecular interactions [J]. The Journal of Chemical Physics, 2000, 112(14): 6472-6486.
[41] GUO Z, ZHANG D, GONG X G. Thermal conductivity of graphene nanoribbons [J]. Applied Physics Letters, 2009, 95(16): 163103.
[42] 姚文俊, 曹炳阳. 石墨烯中热波传递的分子动力学研究[J]. 科学通报, 2014, 59(25): 2528-2536.
[43] YAO W J, CAO B Y. Molecular dynamics studies on ballistic thermal resistance of graphene nano-junctions [J]. Communications in Theoretical Physics, 2015, 63(5): 619.
[44] 郑伯昱, 董慧龙, 陈非凡. 基于量子修正的石墨烯纳米带热导率分子动力学表征方法[J]. 物理学报, 2014, (7):76501-076501.
[45] QIU B, RUAN X. Reduction of spectral phonon relaxation times from suspended to supported graphene [J]. Applied Physics Letters, 2012, 100(19): 193101.
[46] 叶振强, 曹炳阳, 过增元. 石墨烯的声子热学性质研究[J]. 物理学报, 2014, 63(15): 154704-154704.
[47] EVANS W J, HU L, KEBLINSKI P. Thermal conductivity of graphene ribbons from equilibrium molecular dynamics: Effect of ribbon width, edge roughness, and hydrogen termination [J]. Applied Physics Letters, 2010, 96(20): 203112.
[48] LINDSAY L, BROIDO D A. Optimized Tersoff and Rebo empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene [J]. Physical Review B, 2010, 81(20): 205441.
[49] KONG L T. Phonon dispersion measured directly from molecular dynamics simulations [J]. Computer Physics Communications, 2011, 182(10): 2201-2207.
[50] KONG L T, BARTELS G, CAMPAÑÁ C, et al. Implementation of Green's function molecular dynamics: An extension to LAMMPS [J]. Computer Physics Communications, 2009, 180(6): 1004-1010.
[51] TEWARY V K, YANG B. Parametric interatomic potential for graphene [J]. Physical Review B, 2009, 79(7): 075442.
[52] LU Q, ARROYO M, HUANG R. Elastic bending modulus of monolayer graphene [J]. Journal of Physics D: Applied Physics, 2009, 42(10): 102002.
[53] KOUKARAS E N, KALOSAKAS G, GALIOTIS C, et al. Phonon properties of graphene derived from molecular dynamics simulations [J]. Scientific Reports, 2015, 5:12923.
[54] ZHANG J, HUANG X, YUE Y, et al. Dynamic response of graphene to thermal impulse [J]. Physical Review B, 2011, 84(23): 235416.
[55] LIU F, MING P, LI J. Ab initio calculation of ideal strength and phonon instability of graphene under tension [J]. Physical Review B, 2007, 76(6): 064120.
[56] MOHR M, MAULTZSCH J, DOBARDŽIĆ E, et al. Phonon dispersion of graphite by inelastic X-ray scattering [J]. Physical Review B, 2007, 76(3): 035439.
[57] NIKA D L, BALANDIN A A. Two-dimensional phonon transport in graphene [J]. Journal of Physics: Condensed Matter, 2012, 24(23): 233203.
[58] LINDSAY L, BROIDO D A, MINGO N. Flexural phonons and thermal transport in graphene [J]. Physical Review B, 2010, 82(11): 115427.
[59] KUBO R. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems [J]. Journal of the Physical Society of Japan, 1957, 12(6): 570-586.
[60] YE Z Q, CAO B Y, LI Y W. Heat current calculation in equilibrium molecular dynamics simulations of thermal conductivity [J]. Chinese J Comput Phys, 2015, 32(2): 186-194.
[61] LINDSAY L, BROIDO D A, MINGO N. Diameter dependence of carbon nanotube thermal conductivity and extension to the graphene limit [J]. Physical Review B, 2010, 82(16): 161402.