| 研究生: |
鄭大印 Cheng, Ta-Yin |
|---|---|
| 論文名稱: |
利用分子動力學研究不同效應對石墨烯熱傳導係數的影響 Investigating the Impact of Various Effects on the Thermal Conductivity of Graphene Using Molecular Dynamics |
| 指導教授: |
温昌達
Wen, Chang-Da |
| 學位類別: |
碩士 Master |
| 系所名稱: |
工學院 - 機械工程學系 Department of Mechanical Engineering |
| 論文出版年: | 2023 |
| 畢業學年度: | 111 |
| 語文別: | 中文 |
| 論文頁數: | 108 |
| 中文關鍵詞: | 石墨烯 、分子動力學 、聲子狀態密度 、熱傳導係數 、多層石墨烯 |
| 外文關鍵詞: | graphene, molecular dynamics, phonon density of states, thermal conductivity, multilayer graphene |
| 相關次數: | 點閱:87 下載:0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
由於現代電子零件需要在有限的晶片內集成更多的功能,會產生更多的熱量。因此,散熱能力成為了一個重要的課題。石墨烯是一種輕薄、強韌、高導電、高導熱的材料,其單層厚度約為0.345納米。由於石墨烯原子之間的鍵結穩定且非常強,所以它具有極高的機械強度,甚至比鋼鐵還要堅韌,可以承受高強度的拉伸,拉伸性能也超越了許多金屬,石墨烯還具有優異的導電性和導熱性,甚至超越了傳統金屬銀。是非常特殊的材料,可解決現代電子設備中面臨的導熱問題。
本研究通過LAMMPS分子動力學進行模擬,條件建立在傅立葉定律和Green-Kubo公式,計算石墨烯的熱傳導係數,以及尺度、溫度、空位缺陷、同位素摻雜效應對其熱傳導係數的影響,吾人還透過將速度自相關函數進行傅立葉轉換,直接觀察熱傳下聲子的傳輸行為,並畫出聲子狀態密度圖,瞭解上述效應影響熱傳導係數的原因,並做深入的研究,這將有助於深入研究石墨烯的熱傳機制。
研究發現單層石墨烯的熱傳導係數嚴重受到缺陷率的影響,下降幅到高達驚人的94%,缺陷率增大對熱傳導係數具有顯著的降低作用。隨著石墨烯層數增加到六層,其熱傳導係數下降約57%,而在旋轉石墨烯中,層間扭轉角度的改變也對熱傳導係數造成了下降四成左右的影響。多層石墨烯進行實際應用時,其熱傳導性能將不如單層石墨烯。在多層旋轉石墨烯的旋轉效應下,只有在無旋轉的情況下才能獲得最高的熱導率。儘管目前單層無缺陷石墨烯的科技應用仍然有待發展,但它已成為了未來科技發展的一個熱門研究領域。
Modern electronic components require more functions within limited chip space, making heat dissipation crucial. Graphene, a lightweight, thin, strong, highly electrically conductive material with a thickness of only 0.345 nanometers. It also offers excellent thermal conductivity and promises to solve heat dissipation problems in modern electronic devices.
In this study, we employed LAMMPS molecular dynamics simulations to calculate graphene's thermal conductivity based on Fourier's law and the Green-Kubo formula. We investigated the effects of scale, temperature, vacancy defects, and isotope doping on the thermal conductivity coefficient. We also used the velocity autocorrelation function for Fourier transformation to observe phonon transport behavior under heat conduction. We generated a phonon density of states plot, providing an in-depth analysis of the factors influencing the thermal conductivity coefficient.
Research revealed that the thermal conductivity coefficient of monolayer graphene was significantly affected by defect density, leading to a decrease of up to 94%. As defect density increased, the thermal conductivity coefficient decreased. When the number of graphene layers increased to six, the thermal conductivity coefficient decreased by approximately 57%. In rotated graphene, changes in interlayer twist angles also resulted in a reduction of the thermal conductivity coefficient by about 40%. In practical applications, multilayer graphene exhibited lower thermal conductivity performance than monolayer graphene. In multilayer rotated graphene, the highest thermal conductivity could only be achieved without a twist angle. Although defect-free monolayer graphene was still under development, it became a hot research area for future technology advancements.
[1] J. Emsley, Nature's building blocks: an AZ guide to the elements. Oxford University Press, 2011.
[2] H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, and R. E. Smalley, "C60: Buckminsterfullerene," nature, vol. 318, no. 6042, pp. 162-163, 1985.
[3] S. Iijima, "Helical microtubules of graphitic carbon," nature, vol. 354, no. 6348, pp. 56-58, 1991.
[4] J. D. Bernal, "The structure of graphite," Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 106, no. 740, pp. 749-773, 1924.
[5] K. S. Novoselov et al., "Electric field effect in atomically thin carbon films," Science, vol. 306, no. 5696, pp. 666-9, Oct 22 2004, doi: 10.1126/science.1102896.
[6] C. Lee, X. Wei, J. W. Kysar, and J. Hone, "Measurement of the elastic properties and intrinsic strength of monolayer graphene," Science, vol. 321, no. 5887, pp. 385-388, 2008.
[7] A. K. Geim, "Graphene: status and prospects," Science, vol. 324, no. 5934, pp. 1530-1534, 2009.
[8] A. A. Balandin et al., "Superior thermal conductivity of single-layer graphene," Nano Lett., vol. 8, no. 3, pp. 902-907, 2008.
[9] S. Plimpton, "Fast parallel algorithms for short-range molecular dynamics," J. Comput. Phys., vol. 117, no. 1, pp. 1-19, 1995.
[10] F. Banhart, "Elemental carbon in the sp1 hybridization," ChemTexts, vol. 6, p. 3, 12/12 2019, doi: 10.1007/s40828-019-0098-z.
[11] L. Pauling, "The nature of the chemical bond. II. The one-electron bond and the three-electron bond," Journal of the American Chemical Society, vol. 53, no. 9, pp. 3225-3237, 1931.
[12] Y.-W. Son, M. L. Cohen, and S. G. Louie, "Energy gaps in graphene nanoribbons," Phys. Rev. Lett., vol. 97, no. 21, p. 216803, 2006.
[13] D. Ghosh et al., "Extremely high thermal conductivity of graphene: Prospects for thermal management applications in nanoelectronic circuits," Appl. Phys. Lett., vol. 92, no. 15, p. 151911, 2008.
[14] J. Hone, "Phonons and thermal properties of carbon nanotubes," in Carbon nanotubes: synthesis, structure, properties, and applications: Springer, 2001, pp. 273-286.
[15] A. I. Cocemasov, D. L. Nika, and A. A. Balandin, "Engineering of the thermodynamic properties of bilayer graphene by atomic plane rotations: the role of the out-of-plane phonons," Nanoscale, vol. 7, no. 30, pp. 12851-12859, 2015.
[16] S. Shin, Q. Wang, J. Luo, and R. Chen, "Advanced materials for high‐temperature thermal transport," Adv. Funct. Mater., vol. 30, no. 8, p. 1904815, 2020.
[17] B. Latour and Y. Chalopin, "Distinguishing between spatial coherence and temporal coherence of phonons," Physical Review B, vol. 95, no. 21, p. 214310, 2017.
[18] F. Giustino, "Electron-phonon interactions from first principles," Rev. Mod. Phys., vol. 89, no. 1, p. 015003, 2017.
[19] R. Pawula, "Approximation of the linear Boltzmann equation by the Fokker-Planck equation," Phys. Rev., vol. 162, no. 1, p. 186, 1967.
[20] J. H. Seol et al., "Two-dimensional phonon transport in supported graphene," Science, vol. 328, no. 5975, pp. 213-216, 2010.
[21] W. Cai et al., "Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition," Nano Lett., vol. 10, no. 5, pp. 1645-1651, 2010.
[22] S. Chen et al., "Raman measurements of thermal transport in suspended monolayer graphene of variable sizes in vacuum and gaseous environments," ACS nano, vol. 5, no. 1, pp. 321-328, 2011.
[23] D. Nika, E. Pokatilov, A. Askerov, and A. Balandin, "Phonon thermal conduction in graphene: Role of Umklapp and edge roughness scattering," Physical Review B, vol. 79, no. 15, p. 155413, 2009.
[24] D. Singh, J. Y. Murthy, and T. S. Fisher, "Mechanism of thermal conductivity reduction in few-layer graphene," J. Appl. Phys., vol. 110, no. 4, p. 044317, 2011.
[25] Z. Wei, Z. Ni, K. Bi, M. Chen, and Y. Chen, "In-plane lattice thermal conductivities of multilayer graphene films," Carbon, vol. 49, no. 8, pp. 2653-2658, 2011.
[26] C.-W. Wu, "The Study on Thermal Conductivity of Perfect and Defective Silicon Carbide Nanofilms and the Influence of Phonon Transport Behavior Using Non-Equilibrium Molecular Dynamics," master, Department of Mechanical Engineering, National Cheng Kung University, Tainan, 2020.
[27] J. M. Ziman, Electrons and phonons: the theory of transport phenomena in solids. Oxford university press, 2001.
[28] S. Ghosh et al., "Dimensional crossover of thermal transport in few-layer graphene," Nature materials, vol. 9, no. 7, pp. 555-558, 2010.
[29] J. Hu, X. Ruan, and Y. P. Chen, "Thermal conductivity and thermal rectification in graphene nanoribbons: a molecular dynamics study," Nano Lett., vol. 9, no. 7, pp. 2730-2735, 2009.
[30] Y. Cao et al., "Correlated insulator behaviour at half-filling in magic-angle graphene superlattices," Nature, vol. 556, no. 7699, pp. 80-84, 2018.
[31] Y. Cao et al., "Unconventional superconductivity in magic-angle graphene superlattices," Nature, vol. 556, no. 7699, pp. 43-50, 2018.
[32] M. Yankowitz et al., "Tuning superconductivity in twisted bilayer graphene," Science, vol. 363, no. 6431, pp. 1059-1064, 2019.
[33] T. B. Limbu et al., "Grain size-dependent thermal conductivity of polycrystalline twisted bilayer graphene," Carbon, vol. 117, pp. 367-375, 2017.
[34] J. Oh et al., "Significantly reduced thermal conductivity and enhanced thermoelectric properties of single-and bi-layer graphene nanomeshes with sub-10 nm neck-width," Nano Energy, vol. 35, pp. 26-35, 2017.
[35] X. Nie, L. Zhao, S. Deng, Y. Zhang, and Z. Du, "How interlayer twist angles affect in-plane and cross-plane thermal conduction of multilayer graphene: A non-equilibrium molecular dynamics study," Int. J. Heat Mass Transfer, vol. 137, pp. 161-173, 2019.
[36] H. Zhan, Y. Zhang, J. M. Bell, and Y. Gu, "Suppressed thermal conductivity of bilayer graphene with vacancy-initiated linkages," The Journal of Physical Chemistry C, vol. 119, no. 4, pp. 1748-1752, 2015.
[37] G. L. Harris, Properties of silicon carbide (no. 13). Iet, 1995.
[38] S. Chen et al., "Thermal conductivity of isotopically modified graphene," Nature materials, vol. 11, no. 3, pp. 203-207, 2012.
[39] M. H. Gass, U. Bangert, A. L. Bleloch, P. Wang, R. R. Nair, and A. Geim, "Free-standing graphene at atomic resolution," Nature nanotechnology, vol. 3, no. 11, pp. 676-681, 2008.
[40] T. Yamamoto and K. Watanabe, "Nonequilibrium Green’s function approach to phonon transport in defective carbon nanotubes," Phys. Rev. Lett., vol. 96, no. 25, p. 255503, 2006.
[41] C. Ren, Z. Xu, W. Zhang, Y. Li, Z. Zhu, and P. Huai, "Theoretical study of heat conduction in carbon nanotube hetero-junctions," Phys. Lett. A, vol. 374, no. 17-18, pp. 1860-1865, 2010.
[42] H. Zhang, G. Lee, and K. Cho, "Thermal transport in graphene and effects of vacancy defects," Physical Review B, vol. 84, no. 11, p. 115460, 09/27/ 2011, doi: 10.1103/PhysRevB.84.115460.
[43] D. Morelli, J. Heremans, and G. Slack, "Estimation of the isotope effect on the lattice thermal conductivity of group IV and group III-V semiconductors," Physical Review B, vol. 66, no. 19, p. 195304, 2002.
[44] C. Chang et al., "Isotope effect on the thermal conductivity of boron nitride nanotubes," Phys. Rev. Lett., vol. 97, no. 8, p. 085901, 2006.
[45] N. Mingo, K. Esfarjani, D. Broido, and D. Stewart, "Cluster scattering effects on phonon conduction in graphene," Physical Review B, vol. 81, no. 4, p. 045408, 2010.
[46] B. J. Alder and T. E. Wainwright, "Studies in molecular dynamics. I. General method," The Journal of Chemical Physics, vol. 31, no. 2, pp. 459-466, 1959.
[47] J. M. Haile, Molecular dynamics simulation: elementary methods. John Wiley & Sons, Inc., 1992.
[48] A. R. Leach, Molecular modelling: principles and applications. Pearson education, 2001.
[49] J.-P. Hansen and I. R. McDonald, Theory of simple liquids: with applications to soft matter. Academic press, 2013.
[50] P. K. Schelling, S. R. Phillpot, and P. Keblinski, "Comparison of atomic-level simulation methods for computing thermal conductivity," Physical Review B, vol. 65, no. 14, p. 144306, 2002.
[51] F. Müller-Plathe, "A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity," The Journal of chemical physics, vol. 106, no. 14, pp. 6082-6085, 1997.
[52] J. B. J. Baron Fourier, The analytical theory of heat. Courier Corporation, 2003.
[53] A. K. Rappé, C. J. Casewit, K. Colwell, W. A. Goddard III, and W. M. Skiff, "UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations," Journal of the American chemical society, vol. 114, no. 25, pp. 10024-10035, 1992.
[54] J. E. Lennard-Jones, "Cohesion," Proceedings of the Physical Society, vol. 43, no. 5, p. 461, 1931.
[55] P. M. Morse, "Diatomic molecules according to the wave mechanics. II. Vibrational levels," Phys. Rev., vol. 34, no. 1, p. 57, 1929.
[56] M. S. Daw and M. I. Baskes, "Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals," Physical Review B, vol. 29, no. 12, p. 6443, 1984.
[57] M. I. Baskes, "Modified embedded-atom potentials for cubic materials and impurities," Physical review B, vol. 46, no. 5, p. 2727, 1992.
[58] J. Tersoff, "Empirical interatomic potential for silicon with improved elastic properties," Physical Review B, vol. 38, no. 14, p. 9902, 1988.
[59] J. F. Justo, M. Z. Bazant, E. Kaxiras, V. V. Bulatov, and S. Yip, "Interatomic potential for silicon defects and disordered phases," Physical review B, vol. 58, no. 5, p. 2539, 1998.
[60] J. Tersoff, "Structural properties of ${mathit{sp}}^{3}$-bonded hydrogenated amorphous carbon," Physical Review B, vol. 44, no. 21, pp. 12039-12042, 12/01/ 1991, doi: 10.1103/PhysRevB.44.12039.
[61] J. Tersoff, "New empirical approach for the structure and energy of covalent systems," Physical review B, vol. 37, no. 12, p. 6991, 1988.
[62] Y.-K. Kwon and P. Kim, "Unusually high thermal conductivity in carbon nanotubes," High Thermal Conductivity Materials, pp. 227-265, 2006.
[63] W. G. Hoover, "Canonical dynamics: Equilibrium phase-space distributions," Phys. Rev. A, vol. 31, no. 3, p. 1695, 1985.
[64] J. W. Gibbs, "On the equilibrium of heterogeneous substances," Transactions of Connecticut Academy of Arts and Sciences, pp. 108-248, 1876.
[65] S. Nosé, "A molecular dynamics method for simulations in the canonical ensemble," Mol. Phys., vol. 52, no. 2, pp. 255-268, 1984.
[66] G. Bussi, D. Donadio, and M. Parrinello, "Canonical sampling through velocity rescaling," The Journal of Chemical Physics, vol. 126, no. 1, 2007, doi: 10.1063/1.2408420.
[67] H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak, "Molecular dynamics with coupling to an external bath," The Journal of Chemical Physics, vol. 81, no. 8, pp. 3684-3690, 1984, doi: 10.1063/1.448118.
[68] W. G. Hoover, Computational statistical mechanics. Elsevier, 2012.
[69] S. Adelman and J. Doll, "Generalized Langevin equation approach for atom/solid‐surface scattering: General formulation for classical scattering off harmonic solids," The Journal of chemical physics, vol. 64, no. 6, pp. 2375-2388, 1976.
[70] D. J. Evans and B. L. Holian, "The nose–hoover thermostat," The Journal of chemical physics, vol. 83, no. 8, pp. 4069-4074, 1985.
[71] H. J. Berendsen, J. v. Postma, W. F. Van Gunsteren, A. DiNola, and J. R. Haak, "Molecular dynamics with coupling to an external bath," The Journal of chemical physics, vol. 81, no. 8, pp. 3684-3690, 1984.
[72] M. Parrinello and A. Rahman, "Polymorphic transitions in single crystals: A new molecular dynamics method," J. Appl. Phys., vol. 52, no. 12, pp. 7182-7190, 1981.
[73] S. Nosé, "A unified formulation of the constant temperature molecular dynamics methods," The Journal of chemical physics, vol. 81, no. 1, pp. 511-519, 1984.
[74] M. Tuckerman, Statistical mechanics: theory and molecular simulation. Oxford university press, 2010.
[75] R. K. Pathria, Statistical mechanics. Elsevier, 2016.
[76] T. Ikeshoji and B. Hafskjold, "Non-equilibrium molecular dynamics calculation of heat conduction in liquid and through liquid-gas interface," Mol. Phys., vol. 81, no. 2, pp. 251-261, 1994.
[77] R. J. LeVeque, Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. SIAM, 2007.
[78] L. Verlet, "Computer" experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules," Phys. Rev., vol. 159, no. 1, p. 98, 1967.
[79] W. C. Swope, H. C. Andersen, P. H. Berens, and K. R. Wilson, "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters," The Journal of chemical physics, vol. 76, no. 1, pp. 637-649, 1982.
[80] C. W. Gear, "The automatic integration of ordinary differential equations," Communications of the ACM, vol. 14, no. 3, pp. 176-179, 1971.
[81] M. Griebel, S. Knapek, and G. Zumbusch, "Numerical simulation in molecular dynamics, vol. 5 of Texts in Computational Science and Engineering," ed: Springer, Berlin, 2007.
[82] A. Stukowski, "Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool," Modell. Simul. Mater. Sci. Eng., vol. 18, no. 1, p. 015012, 2009.
[83] A. A. Balandin, "Thermal properties of graphene and nanostructured carbon materials," Nature materials, vol. 10, no. 8, pp. 569-581, 2011.
[84] X. Xu et al., "Length-dependent thermal conductivity in suspended single-layer graphene," Nature communications, vol. 5, no. 1, p. 3689, 2014.
[85] A. Cao, "Molecular dynamics simulation study on heat transport in monolayer graphene sheet with various geometries," J. Appl. Phys., vol. 111, no. 8, p. 083528, 2012.
[86] A. Bagri, S.-P. Kim, R. S. Ruoff, and V. B. Shenoy, "Thermal transport across twin grain boundaries in polycrystalline graphene from nonequilibrium molecular dynamics simulations," Nano Lett., vol. 11, no. 9, pp. 3917-3921, 2011.
[87] H. Li et al., "Thermal conductivity of twisted bilayer graphene," Nanoscale, vol. 6, no. 22, pp. 13402-13408, 2014.
校內:2028-08-08公開