Abstract
We present equilibrium and non-equilibrium molecular dynamics approaches to determine thermal transport properties in particular Helfand formulation and its modifications due to finite size encountered in nanoscale systems. Applications on carbon nanotubes, graphene and graphene nanoribbons, the influence of topological defects, and isotopic effect are discussed.
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References
D.A. McQuarrie, Statistical Mechanics (University Science Books, Sausalito, CA, 2000)
R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn. 12, 570 (1957)
R. Zwanzig, Time correlation functions and transport coefficients in statistical mechanics. Annu. Rev. Phys. Chem. 16, 67 (1965)
E. Helfand, Transport coefficients from dissipation in a canonical ensemble. Phys. Rev. 119, 1–9 (1960)
A. Kınacı, J.B. Haskins, T. Çağın, On calculation of thermal conductivity from Einstein relation in equilibrium MD. J. Chem. Phys. 137, 014106 (2012)
S. Viscardy, J. Servantie, Transport and Helfand moments in the Lennard-Jones fluid. II. Thermal conductivity. J. Chem. Phys. 126, 184513 (2007)
J.B. Haskins, A. Kınacı, C. Sevik, T. Çağın, Equilibrium limit of thermal conduction and boundary scattering in nanostructures. J. Chem. Phys. 137, 014106 (2014)
J.-W. Che, T. Cagin, W.A. Goddard III, Thermal conductivity of carbon nanotubes. Nanotechnology 11, 65–69 (2000)
J.-W. Che, T. Cagin, W. Deng, W.A. Goddard III, Thermal conductivity of diamond and related materials from molecular dynamics simulations. J. Chem. Phys. 113, 6888–6900 (2000)
F. Müller-Plathe, A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity. J. Chem. Phys. 106, 6082 (1997)
M. Zhang, E. Lussetti, L.E.S. de Souza, F. Müller-Plathe, Thermal conductivities of molecular liquids by reverse nonequilibrium molecular dynamics. J. Phys. Chem. B 109, 15060–15067 (2005)
D.P. Sellan, E.S. Landry, J.E. Turney, J.H. McGaughey, C.H. Amon, Size effects in molecular dynamics thermal conductivity predictions. Phys. Rev. B 81, 214305 (2010)
P. Schelling, S. Phillpot, P. Keblinski, Comparison of atomic-level simulation methods for computing thermal conductivity. Phys. Rev. B 65, 1–12 (2002)
D. Evans, Homogeneous NEMD algorithm for thermal conductivity—application of non-canonical linear response theory. Phys. Lett. A 91, 457–460 (1982)
S. Berber, Y.-K. Kwon, D. Tomanek, Unusually high thermal conductivity of carbon nanotubes. Phys. Rev. Lett. 84, 4613–4616 (2000)
C. Sevik, H. Sevinçli, G. Cuniberti, T. Çağın, Phonon engineering in carbon nanotubes by controlling defect concentration. Nano Lett. 11, 4971–4977 (2011)
J. Chen, G. Zhang, B. Li, Molecular dynamics simulations of heat conduction in nanostructures: effect of heat bath. J. Phys. Soc. Jpn. 79, 074604 (2010)
J. Hu, X. Ruan, Y. Chen, Thermal conductivity and thermal rectification in graphene nanoribbons: a molecular dynamics study. Nano Lett. 9, 2730–2735 (2009)
T. Tong, Y. Zhao, L. Delzeit, A. Kashani, M. Meyyappan, A. Majumdar, Dense vertically aligned multiwalled carbon nanotube arrays as thermal interface materials. IEEE. Trans. Compon. Packaging Technol. 30, 92 (2007)
M.A. Panzer, G. Zhang, D. Mann, X. Hu, E. Pop, H. Dai, K.E. Goodson, Thermal properties of metal-coated vertically aligned single-wall nanotube arrays. ASME J. Heat Trans. 130, 052401 (2008)
E. Pop, Energy dissipation and transport in nanoscale devices. Nano Res. 3, 147 (2010)
K. Kordas, G. Toth, P. Moilanen, M. Kumpumaki, J. Vahakangas, A. Uusimaki, R. Vajtai, P.M. Ajayan, Chip cooling with integrated carbon nanotube microfin architectures. Appl. Phys. Lett. 90, 123105 (2007)
O.F. Mohammed, P.C. Samartzis, A.H. Zewail, Heating and cooling dynamics of carbon nanotubes observed by temperature-jump spectroscopy and electron microscopy. J. Am. Chem. Soc. 131, 16010 (2009)
B.A. Cola, X. Xu, T.S. Fisher, Increased real contact in thermal interfaces: a carbon nanotube/foil material. Appl. Phys. Lett. 90, 093513 (2007)
K. Zhang, Y. Chai, M.M.F. Yuen, D.G.W. Xiao, P.C.H. Chan, Carbon nanotube thermal interface material for high-brightness light-emitting-diode cooling. Nanotechnology 19, 215706 (2008)
M. Biercuk, M. Llaguno, M. Radosavljevic, J. Hyun, A. Johnson, J. Fischer, Carbon nanotube composites for thermal management. Appl. Phys. Lett. 80, 2767 (2002)
H. Huang, C. Liu, Y. Wu, S. Fan, Aligned carbon nanotube composite films for thermal management. Adv. Mater. 17, 1652 (2005)
J. Xu, T.S. Fisher, Enhancement of thermal interface materials with carbon nanotube arrays. Int. J. Heat Mass Transfer 49, 1658 (2006)
A. Jorio, M. Dresselhaus, G. Dresselhaus, Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications (Springer, New York, 2008)
J. Haskins, A. Kinaci, C. Sevik, H. Sevinçli, G. Cuniberti, T. Çağın, Control of thermal and electronic transport in defect-engineered graphene nanoribbons. ACS Nano 5, 3779 (2011)
J. Hone, M. Whitney, C. Piskoti, A. Zettl, Thermal conductivity of single-walled carbon nanotubes. Phys. Rev. B 59, R2514 (1999)
C. Yu, L. Shi, Z. Yao, D. Li, A. Majumdar, Thermal conductance and thermopower of an individual single-wall carbon nanotube. Nano Lett. 5, 1842 (2005)
E. Pop, D. Mann, J. Cao, Q. Wang, K. Goodson, H. Dai, Negative differential conductance and hot phonons in suspended nanotube molecular wires. Phys. Rev. Lett. 95, 155505 (2005)
E. Pop, D. Mann, Q. Wang, K. Goodson, H. Dai, Thermal conductance of an individual single-wall carbon nanotube above room temperature. Nano Lett. 6, 96 (2006)
M.T. Pettes, L. Shi, Thermal and structural characterizations of individual single-, double-, and multi-walled carbon nanotubes. Adv. Funct. Mater. 19, 3918 (2009)
Q. Li, C. Liu, X. Wang, S. Fan, Measuring the thermal conductivity of individual carbon nanotubes by the Raman shift method. Nanotechnology 20, 145702 (2009)
T.Y. Choi, D. Poulikakos, J. Tharian, U. Sennhauser, Measurement of the thermal conductivity of individual carbon nanotubes by the four-point three-omega method. Nano Lett. 6, 1589 (2006)
T. Choi, D. Poulikakos, J. Tharian, U. Sennhauser, Measurement of thermal conductivity of individual multiwalled carbon nanotubes by the 3-omega method. Appl. Phys. Lett. 87, 013108 (2005)
M. Fujii, X. Zhang, H. Xie, H. Ago, K. Takahashi, T. Ikuta, H. Abe, T. Shimizu, Measuring the thermal conductivity of a single carbon nanotube. Phys. Rev. Lett. 95, 065502 (2005)
P. Kim, L. Shi, A. Majumdar, P. McEuen, Thermal transport measurements of individual multiwalled nanotubes. Phys. Rev. Lett. 87, 215502 (2001)
C.W. Chang, A.M. Fennimore, A. Afanasiev, D. Okawa, T. Ikuno, H. Garcia, D. Li, A. Majumdar, A. Zettl, Isotope effect on the thermal conductivity of boron nitride nanotubes. Phys. Rev. Lett. 97, 085901 (2006)
I.K. Hsu, R. Kumar, A. Bushmaker, S.B. Cronin, M.T. Pettes, L. Shi, T. Brintlinger, M.S. Fuhrer, J. Cumings, Optical measurement of thermal transport in suspended carbon nanotubes. Appl. Phys. Lett. 92, 063119 (2008)
R. Prasher, Thermal boundary resistance and thermal conductivity of multiwalled carbon nanotubes. Phys. Rev. 77, 075424 (2008)
S. Berber, Y. Kwon, D. Tomanek, Unusually high thermal conductivity of carbon nanotubes. Phys. Rev. Lett. 84, 4613 (2000)
Y. Gu, Y. Chen, Thermal conductivities of single-walled carbon nanotubes calculated from the complete phonon dispersion relations. Phys. Rev. B 76, 134110 (2007)
F. Nishimura, T. Takahashi, K. Watanabe, T. Yamamoto, Bending robustness of thermal conductance of carbon nanotubes: nonequilibrium molecular dynamics simulation. Appl. Phys. Exp. 2, 035003 (2009)
G. Zhang, B. Li, Thermal conductivity of nanotubes revisited: effects of chirality, isotope impurity, tube length, and temperature. J. Chem. Phys. 123, 114714 (2005)
M.A. Osman, D. Srivastava, Temperature dependence of the thermal conductivity of single-wall carbon nanotubes. Nanotechnology 12, 21 (2001)
D. Donadio, G. Galli, Thermal conductivity of isolated and interacting carbon nanotubes: comparing results from molecular dynamics and the Boltzmann transport equation. Phys. Rev. Lett. 99, 255502 (2007)
N. Mingo, D. Broido, Length dependence of carbon nanotube thermal conductivity and the problem of long waves. Nano Lett. 5, 1221 (2005)
M. Alaghemandi, E. Algaer, M.C. Boehm, F. Mueller-Plathe, The thermal conductivity and thermal rectification of carbon nanotubes studied using reverse non-equilibrium molecular dynamics simulations. Nanotechnology 20, 115704 (2009)
N. Mingo, D.A. Stewart, D.A. Broido, D. Srivastava, Phonon transmission through defects in carbon nanotubes from first principles. Phys. Rev. B 77, 033418 (2008)
S. Ghosh, I. Calizo, D. Teweldebrhan, E.P. Pokatilov, D.L. Nika, A.A. Balandin, W. Bao, F. Miao, C.N. Lau, Extremely high thermal conductivity of graphene: prospects for thermal management applications in nanoelectronic circuits. Appl. Phys. Lett. 92, 151911 (2008)
A.V. Savin, B. Hu, Y.S. Kivshar, Thermal conductivity of single-walled carbon nanotubes. Phys. Rev. B 80, 195423 (2009)
L. Lindsay, D.A. Broido, N. Mingo, Diameter dependence of carbon nanotube thermal conductivity and extension to the graphene limit. Phys. Rev. B 82, 161402 (2010)
L. Lindsay, D.A. Broido, Optimized Tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene. Phys. Rev. B 81, 205441 (2010)
C. Sevik, A. Kinaci, B.J. Haskins, T. Çağin, Characterization of thermal transport in low-dimensional boron nitride nanostructures. Phys. Rev. B 84, 085409 (2011)
J.H. Seol, I. Jo, A.L. Moore, L. Lindsay, Z.H. Aitken, M.T. Pettes, X. Li, Z. Yao, R. Huang, D. Broido et al., Two-dimensional phonon transport in supported graphene. Science 328, 213 (2010)
W. Cai, A.L. Moore, Y. Zhu, X. Li, S. Chen, L. Shi, R.S. Ruoff, thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition. Nano Lett. 10, 1645 (2010)
A.A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, C.N. Lau, Superior thermal conductivity of single-layer graphene. Nano Lett. 8, 902 (2008)
S. Ghosh, W. Bao, D.L. Nika, S. Subrina, E.P. Pokatilov, C.N. Lau, A.A. Balandin, Dimensional crossover of thermal transport in few-layer graphene. Nat. Mater. 9, 555–558 (2010)
B.D. Kong, S. Paul, M.B. Nardelli, K.W. Kim, First-principles analysis of lattice thermal conductivity in monolayer and bilayer graphene. Phys. Rev. B 80, 033406 (2009)
D.L. Nika, E.P. Pokatilov, A.S. Askerov, A.A. Balandin, Phonon thermal conduction in graphene: role of Umklapp and edge roughness scattering. Phys. Rev. B 79, 155413 (2009)
K. Saito, J. Nakamura, A. Natori, Ballistic thermal conductance of a graphene sheet. Phys. Rev. B 76, 115409 (2007)
W.J. Evans, L. Hu, P. Keblinski, Thermal conductivity of graphene ribbons from equilibrium molecular dynamics: effect of ribbon width, edge roughness, and hydrogen termination. Appl. Phys. Lett. 96, 203112–3 (2010)
J. Lan, J.S. Wang, C.K. Gan, S.K. Chin, Edge effects on quantum thermal transport in graphene nanoribbons: tight-binding calculations. Phys. Rev. B 79, 115401 (2009)
T. Ouyang, Y.P. Chen, K.K. Yang, J.X. Zhong, Thermal transport of isotopic-superlattice graphene nanoribbons with zigzag edge. EPL 88, 28002 (2009)
Z. Guo, D. Zhang, X.G. Gong, Thermal conductivity of graphene nanoribbons. Appl. Phys. Lett. 95, 163103 (2009)
E. Muñoz, J. Lu, B.I. Yakobson, Ballistic thermal conductance of graphene ribbons. Nano Lett. 10, 1652 (2010)
T. Yamamoto, K. Watanabe, K. Mii, Empirical-potential study of phonon transport in graphitic ribbons. Phys. Rev. B 70, 245402 (2004)
N. Yang, G. Zhang, B. Li, Thermal rectification in asymmetric graphene ribbons. Appl. Phys. Lett. 95, 033107 (2009)
W. Li, H. Sevinçli, G. Cuniberti, S. Roche, Phonon transport in large scale carbon-based disordered materials: implementation of an efficient order-\(n\) and real-space Kubo methodology. Phys. Rev. B 82, 041410 (2010)
Z.W. Tan, J.S. Wang, C.K. Gan, First-principles study of heat transport properties of graphene nanoribbons. Nano Lett. 11, 214 (2011)
X. Yong, C. Xiaobin, G. Bing-Lin, D. Wenhui, Intrinsic anisotropy of thermal conductance in graphene nanoribbons. Appl. Phys. Lett. 95, 233116 (2009)
L. Lindsay, D.A. Broido, N. Mingo, Flexural phonons and thermal transport in graphene. Phys. Rev. B 82, 115427 (2010)
Z.W. Tan, J.-S. Wang, C.K. Gan, First-principles study of heat transport properties of graphene nanoribbons. Nano Lett. 11, 214–219 (2011)
M.-H. Bae, Z. Li, Z. Aksamija, P.N. Martin, F. Xiong, Z.-Y. Ong, I. Knezevic, E. Pop, Ballistic to diffusive crossover of heat flow in graphene ribbons. Nat. Commun. 4, 1734 (2013)
M. Vandescuren, P. Hermet, V. Meuier, L. Henrard, Ph. Lambin, Theoretical study of the vibrational edge modes in graphene nanoribbons. Phys. Rev. B 78, 195401 (2008)
R. Gillen, M. Mohr, J. Maultzsch, Symmetry properties of vibrational modes in graphene nanoribbons. Phys. Rev. B 81, 205426 (2010)
M.S. Dresselhaus, P.C. Eklund, Phonons in carbon nanotubes. Adv. Phys. 49, 705–814 (2000)
X. Li, W. Cai, L. Colombo, R.S. Ruoff, Evolution of graphene growth on Ni and Cu by carbon isotope labeling. Nano Lett. 9(12), 4268–72 (2009b)
R. McLellan, The solubility of carbon in solid gold, copper, and silver. Scripta Metall. Mater. 3, 389–392 (1969)
K. Natesan, T. Kassner, Thermodynamics of carbon in nickel, iron-nickel and iron-chromium-nickel alloys. Metall. Mater. Trans. 4, 2557–2566 (1973)
M. Eizenberg, J. Blakely, Carbon monolayer phase condensation on Ni(111). Surf. Sci. 82(1), 228–236 (1979)
J. Shelton, H. Patil, J. Blakely, Equilibrium segregation of carbon to a nickel (111) surface: a surface phase transition. Surf. Sci. 43(2), 493–520 (1974)
X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S.K. Banerjee, L. Colombo, R.S. Ruoff, Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 324(5932), 1312–1314 (2009a)
S. Chen, Q. Wu, C. Mishra, J. Kang, H. Zhang, K. Cho, W. Cai, Balandin Aa, R.S. Ruoff, Thermal conductivity of isotopically modified graphene. Nat. Mater. 11(3), 203–7 (2012)
P.G. Klemens, The scattering of low-frequency lattice waves by static imperfections. Proc. Phys. Soc. Lond. Sect. A 68(12), 1113–1128 (1955)
C. Sevik, A. Kınacı, J.B. Haskins, T. Çağın, Influence of disorder on thermal transport properties of boron nitride nanostructures. Phys. Rev. B 86(075), 403 (2012)
P. Kim, L. Shi, A. Majumdar, P. McEuen, Thermal transport measurements of individual multiwalled nanotubes. Phys. Rev. Lett. 87(21), 215–502 (2001)
C. Yu, L. Shi, Z. Yao, D. Li, A. Majumdar, Thermal conductance and thermopower of an individual single-wall carbon nanotube. Nano Lett. 5(9), 1842–6 (2005)
A. Kınacı, J.B. Haskins, C. Sevik, T. Çağın, Thermal conductivity of BN-C nanostructures. Phys. Rev. B 86(115), 410 (2012)
N. Mingo, K. Esfarjani, D.A. Broido, D.A. Stewart, Cluster scattering effects on phonon conduction in graphene. Phys. Rev. B 81(045), 408 (2010)
Acknowledgements
Dedication: This work is a representation of how Professor Goddard influences on people over such a long research and education career. I (TC) have had the blessing to work with him at Materials and Process Simulation Center of Caltech over a 15 year period and continued getting inspired by him though from afar but always close. His wisdom, vision, and contribution to science and engineering is transferred through people he has mentored, we (TC, JBH, AK, and CS) wish him many many more years of being him.
The work is mainly conducted at Texas A&M University, with ample support from TAMU High Performance Computing Center. Parts of the research are supported by grants from DARPA—PROM project, NSF (IMI), DoE (LLNS).
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Çağın, T., Haskins, J.B., Kınacı, A., Sevik, C. (2021). Thermal Transport for Nanostructured Materials. In: Shankar, S., Muller, R., Dunning, T., Chen, G.H. (eds) Computational Materials, Chemistry, and Biochemistry: From Bold Initiatives to the Last Mile. Springer Series in Materials Science, vol 284. Springer, Cham. https://doi.org/10.1007/978-3-030-18778-1_20
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