Chin. Phys. Lett.  2020, Vol. 37 Issue (10): 104401    DOI: 10.1088/0256-307X/37/10/104401
A Ubiquitous Thermal Conductivity Formula for Liquids, Polymer Glass, and Amorphous Solids
Qing Xi1, Jinxin Zhong1, Jixiong He2, Xiangfan Xu1, Tsuneyoshi Nakayama1,3, Yuanyuan Wang4, Jun Liu2*, Jun Zhou1†*, and Baowen Li5*
1Center for Phononics and Thermal Energy Science, China-EU Joint Lab for Nanophononics, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
2Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA
3Hokkaido University, Sapporo, Hokkaido 060-0826, Japan
4School of Environmental and Materials Engineering, Shanghai Polytechnic University, Shanghai 201209, China
5Paul M Rady Department of Mechanical Engineering, Department of Physics, University of Colorado, Boulder, CO 80305-0427, USA
Cite this article:   
Qing Xi, Jinxin Zhong, Jixiong He et al  2020 Chin. Phys. Lett. 37 104401
Download: PDF(1069KB)   PDF(mobile)(1559KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract The microscopic mechanism of thermal transport in liquids and amorphous solids has been an outstanding problem for a long time. There have been several approaches to explain the thermal conductivities in these systems, for example, Bridgman's formula for simple liquids, the concept of the minimum thermal conductivity for amorphous solids, and the thermal resistance network model for amorphous polymers. Here, we present a ubiquitous formula to calculate the thermal conductivities of liquids and amorphous solids in a unified way, and compare it with previous ones. The calculated thermal conductivities using this formula without fitting parameters are in excellent agreement with the experimental data. Our formula not only provides a detailed microscopic mechanism of heat transfer in these systems, but also resolves the discrepancies between existing formulae and experimental data.
Received: 11 August 2020      Published: 23 September 2020
PACS:  44.10.+i (Heat conduction)  
  66.25.+g (Thermal conduction in nonmetallic liquids)  
  66.70.-f (Nonelectronic thermal conduction and heat-pulse propagation in solids;thermal waves)  
Fund: This work is supported by the National Key R&D Program of China (Grant No. 2017YFB0406004), the National Natural Science Foundation of China (Grant No. 11890703). JH and JL are supported by the National Science Foundation of USA (Award No. CBET-1943813) and the Faculty Research and Professional Development Fund at North Carolina State University.
URL:       OR
E-mail this article
E-mail Alert
Articles by authors
Qing Xi
Jinxin Zhong
Jixiong He
Xiangfan Xu
Tsuneyoshi Nakayama
Yuanyuan Wang
Jun Liu
Jun Zhou
and Baowen Li
[1]Loeb L B 1927 Kinetic Theory of Gases (New York: McGraw-Hill Book Co., Inc.)
[2] Bridgman P W 1923 Proc. Am. Acad. Arts Sci. 59 141
[3] Lin S H, Eyring H and Davis W J 1964 J. Phys. Chem. 68 3017
[4] Powell R E, Roseveare W E and Eyring H 1941 Ind. Eng. Chem. 33 430
[5]Kittel C 2005 Introduction to Solid State Physics 8th edn (New York: John Wiley & Sons)
[6]Debye P J W 1914 Vorträgeüber die Kinetische Theorie der Materie und der Elektrizität (Leipzig: Teubner B G)
[7] Peierls R 1929 Ann. Phys. 395 1055
[8] Kittel C 1949 Phys. Rev. 75 972
[9]Van Krevelen D W and Te Nijenhuis K 2009 Properties of Polymers 4th edn (Amsterdam: Elsevier)
[10] Cahill D G and Pohl R O 1989 Solid State Commun. 70 927
[11] Cahill D G, Watson S K and Pohl R O 1992 Phys. Rev. B 46 6131
[12] Xie X, Yang K, Li D, Tsai T H, Shin J, Braun P V and Cahill D G 2017 Phys. Rev. B 95 035406
[13] Einstein A 1911 Ann. Phys. 340 679
[14]Zallen R 1998 The Physics of Amorphous Solids (New York: John Wiley & Sons) pp 107, 133
[15] Zhou J, Xi Q, He J, Nakayama T, Wang Y Y and Liu J 2020 Phys. Rev. Mater. 4 015601
[16] Simoncelli M, Marzari N and Mauri F 2019 Nat. Phys. 15 809
[17]Stachurski Z H 2015 Fundamentals of Amorphous Solids: Structure, Properties (Beijing: Higher Education Press) pp 23, 116
[18] Liu Z, Wu X, Yang H, Gupte N and Li B 2010 New J. Phys. 12 023016
[19] Xiong K, Liu Z, Zeng C and Li B 2020 Natl. Sci. Rev. 7 270
[20] Nakayama T, Yakubo K and Orbach R L 1994 Rev. Mod. Phys. 66 381
[21]Yaws C L 1995 Handbook of Thermal Conductivity (Houston: Gulf Publishing Company) vol 1–3
[22]Mark J E 2009 Polymer Data Handbook (Oxford: Oxford University Press)
[23] Alexander S 1998 Phys. Rep. 296 65
[24] Trachenko K and Brazhkin V V 2013 Sci. Rep. 3 2188
[25]Frenkel J 1947 Kinetic Theory of Liquids (Oxford: Oxford University Press)
[26] Dyre J C 2006 Rev. Mod. Phys. 78 953
Related articles from Frontiers Journals
[1] Liujun Xu and Jiping Huang. Negative Thermal Transport in Conduction and Advection[J]. Chin. Phys. Lett., 2020, 37(8): 104401
[2] Le-Min Zhang, Bin-Bin Jiao, Shi-Chang Yun, Yan-Mei Kong, Chih-Wei Ku, Da-Peng Chen. A CMOS Compatible MEMS Pirani Vacuum Gauge with Monocrystal Silicon Heaters and Heat Sinks[J]. Chin. Phys. Lett., 2017, 34(2): 104401
[3] Feng Chi, Lian-Liang Sun. Photon-Assisted Heat Generation by Electric Current in a Quantum Dot Attached to Ferromagnetic Leads[J]. Chin. Phys. Lett., 2016, 33(11): 104401
[4] Qiu-Xue Jin, Bo Liu, Yan Liu, Wei-Wei Wang, Heng Wang, Zhen Xu, Dan Gao, Qing Wang, Yang-Yang Xia, Zhi-Tang Song, Song-Lin Feng. Three-Dimensional Simulations of RESET Operation in Phase-Change Random Access Memory with Blade-Type Like Phase Change Layer by Finite Element Modeling[J]. Chin. Phys. Lett., 2016, 33(09): 104401
[5] Mahdi Ezheiyan, Hossein Sadeghi, Mohammad-Hossein Tavakoli. Thermal Analysis Simulation of Germanium Zone Refining Process Assuming a Constant Radio-Frequency Heating Source[J]. Chin. Phys. Lett., 2016, 33(05): 104401
[6] Run Hu, Jin-Yan Hu, Rui-Kang Wu, Bin Xie, Xing-Jian Yu, Xiao-Bing Luo. Examination of the Thermal Cloaking Effectiveness with Layered Engineering Materials[J]. Chin. Phys. Lett., 2016, 33(04): 104401
[7] WANG Zhao-Liang, YUAN Kun-Peng, TANG Da-Wei. Thermal Transport in Methane Hydrate by Molecular Dynamics and Phonon Inelastic Scattering[J]. Chin. Phys. Lett., 2015, 32(10): 104401
[8] DING Xing, MING Yi. Mechanisms Causing Ballistic Thermal Rectification[J]. Chin. Phys. Lett., 2014, 31(04): 104401
[9] LI Hao, WANG Rui, GENG Yong-You, WU Yi-Qun, WEI Jing-Song. Enhancement Effect of Patterning Resolution Induced by an Aluminum Thermal Conduction Layer with AgInSbTe as a Laser Thermal Lithography Film[J]. Chin. Phys. Lett., 2012, 29(7): 104401
[10] LIU Jing,FENG Shi-Wei**,ZHANG Guang-Chen,ZHU Hui,GUO Chun-Sheng,QIAO Yan-Bin,LI Jing-Wan. A Novel Method for Measuring the Temperature in the Active Region of Semiconductor Modules[J]. Chin. Phys. Lett., 2012, 29(4): 104401
[11] XU Wen, CHEN Wei-Zhong**, TAO Feng, . Thermal Rectification in Graded Nonlinear Transmission Lines[J]. Chin. Phys. Lett., 2011, 28(12): 104401
[12] T. Hayat, **, S. Hina, Awatif A. Hendi . Peristaltic Motion of Power-Law Fluid with Heat and Mass Transfer[J]. Chin. Phys. Lett., 2011, 28(8): 104401
[13] CHEN Liang**, ZHANG Wan-Rong, XIE Hong-Yun, JIN Dong-Yue, DING Chun-Bao, FU Qiang, WANG Ren-Qing, XIAO Ying, ZHAO Xin . Restabilizing Mechanisms after the Onset of Thermal Instability in Bipolar Transistors[J]. Chin. Phys. Lett., 2011, 28(7): 104401
[14] LIU Qing-Nian, MENG Song-He, JIANG Chi-Ping, SONG Fan. Critical Biot's number for Determination of the Sensitivity of Spherical Ceramics to Thermal Shock[J]. Chin. Phys. Lett., 2010, 27(8): 104401
[15] GONG Yue-Feng, SONG Zhi-Tang, LING Yun, LIU Yan, LI Yi-Jin, FENG Song-Lin. Three-Dimensional Finite Element Simulations for the Thermal Characteristics of PCRAMs with Different Buffer Layer Materials[J]. Chin. Phys. Lett., 2010, 27(8): 104401
Full text