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温稠密和热稠密端条件下的物质粘性在诸多场景有着重要应用, 例如: 惯性约束聚变靶丸设计, 天体结构演化研究, 极端条件下界面不稳定性和混合发展规律研究等. 由于粘性实验技术能够达到的温压范围非常有限, 因而, 极端条件下物质粘性数据的获取方式主要是通过理论计算. 本文阐述了计算温稠密和热稠密极端条件下物质粘性的多种理论方法, 包括以量子分子动力学模拟(QMD)为代表的数值模拟方法和以随机游走屏蔽势粘性模型(RWSP-VM)为代表的解析公式. 通过评估从低原子序数到高原子序数的多种单质(H, C, Al, Fe, Ge, W, U)的粘性数据, 讨论了各种方法的适用条件, 评估了各种解析公式的可靠性和适用范围. 可以看到, 数值模拟方法获得的数据量以及覆盖范围仍然有限, 不同的数值模拟方法之间还存在一定分歧, 解析公式仍然是快速获取大量粘性数据的可靠方式. 基于物理建模和模拟数据的拟合公式, 例如单质等离子体模型(OCP), 集成的Yukawa粘性模型(IYVM)等, 兼顾了模拟数据的精度和解析计算的效率. 基于物理建模的RWSP-VM模型, 不依赖于模拟数据, 却在较宽温压范围内具有与模拟数据相当的精度, 是获取温稠密和热稠密物质的粘性数据的高效方法. 本文数据集可在
https://doi.org/10.57760/sciencedb.j00213.00180 访问获取.The viscosities of matters under extreme conditions, i.e. warm dense matter (WDM) and hot dense matter (HDM), have significant applications in various fields, such as the design of inertial confinement fusion targets, the astrophysical structure evolution, and the interfacial instability and mixing development under extreme conditions. Since the temperature and pressure ranges accessible by experimental techniques for viscosity measurement are very limited, the acquisition of viscosity data under extreme conditions mainly relies on theoretical calculations. This work introduces a variety of molecular dynamics (MD) methods and models for calculating the viscosities of WDM and HDM, they being quantum MD (QMD), orbital-free MD (OFMD), average atom model combined with hypernetted chain (AAHNC), effective potential theory combined with average atom model (EPT+AA), hybrid kinetics MD (KMD), integrated Yukawa viscosity model (IYVM), Stanton-Murillo transport model (SMT), pseudo-ion in jellium (PIJ), one-component plasma model (OCP), and random-walk shielding-potential viscosity model (RWSP-VM). Simultaneously, the viscosities of various elements obtained by these methods are shown, ranging from low to high atomic number (Z), i.e., H, C, Al, Fe, Ge, W, and U. The accuracy and the applicability of each method are analyzed in detail by comparison. RWSP-VM, which is based on physical modeling and independent of MD data, has comparable accuracy to simulation data over a wide range of temperature and pressure, and is an efficient method of obtaining viscosity data of WDM and HDM. This work will pave the way for calculating the shear viscosities under extreme conditions, and may play an important role in promoting the relevant applications. The data calculated from RWSP-VM in this work are openly available athttps://doi.org/10.57760/sciencedb.j00213.00180 .-
Keywords:
- shear viscosity /
- molecular dynamics /
- ab initio calculations /
- kinetic theory
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图 1 H的粘性. (a)—(d) 密度分别为0.1, 1, 10, 100 g/cm3. 黑色实线, 红色虚线, 蓝色点线和, 绿色虚点线和青色点点线分别为模型RWSP-VM, SMT, OCP, IYVM和PIJ的由公式计算的结果. 黑色十字, 红色星号, 蓝色方块和绿色圆圈分别为AAHNC, KMD, EPT+AA和OFMD的计算结果, 数据来源文献[54]
Fig. 1. Shear viscosity of H. (a)–(d) stand for the densities of 0.1, 1, 10, 100 g/cm3, respectively. Black solid, red dashed, blue dotted, and green dash-dot curves stand for the results of RWSP-VM, SMT, OCP, IYVM, and PIJ respectively. Black crosses, red stars, blue squares, and green diamonds stand for the results of AAHNC, KMD, EPT+AA, and OFMD, respectively, which are from Ref.[54].
图 3 Al的粘性. (a)—(d) 密度分别为0.27, 2.7, 8.1, 27 g/cm3. 黑色实线, 红色虚线, 蓝色点线, 绿色虚点线和青色虚点点线分别为模型RWSP-VM, SMT, OCP, IYVM和PIJ的由公式计算的结果. 黑色十字为AAHNC (CMD)的计算结果, 数据来源文献[47]
Fig. 3. Shear viscosity of Al. (a)–(d) stand for the densities of 0.27, 2.7, 8.1, and 27 g/cm3, respectively. Black solid, red dashed, blue dotted, green dash-dot, and cyan dash-dot-dot curves stand for the results of RWSP-VM, SMT, OCP, IYVM, and PIJ, respectively. Black crosses stand for the results of AAHNC (CMD), which are from Ref.[47].
图 4 Fe的粘性. (a)—(f) 密度分别为1.6, 4.0, 7.9, 16, 32, 40 g/cm3. 曲线图例与图 3的一致, 除了橙色实线代表EPT+AA[27]. 红色圆圈, 蓝色方块和黑色十字分别为OFMD1[55], OFMD2[27]和AAHNC (CMD)[39]的计算结果
Fig. 4. Shear viscosity of Fe. (a)–(f) stand for the densities of 1.6, 4.0, 7.9, 16, 32, and 40 g/cm3, respectively. The legends of the curves are the same as Fig. 3. Red circles, blue squares, and black crosses stand for the results of OFMD1[55], OFMD2[27], and AAHNC (CMD)[39], respectively.
图 7 U的粘性. (a)—(i) 密度分别为$ \rho_0 $的0.1, 1, 2, 3, 4, 5, 6, 8, 10倍, 其中$ \rho_0 = 18.93\ {\rm{g}}/{\rm{cm}}^3 $. 曲线的图例与图 3一致. 黑色圆圈, 红色十字和蓝色叉分别为OFMD[57], AAHNC (CMD)和AAHNC (LMD)[48]的计算结果. (j), (k), (l)分别为(a), (b), (f)的放大图
Fig. 7. Shear viscosity of U. (a)–(i) stand for the densities of (0.1, 1, 2, 3, 4, 5, 6, 8, and 10)$ \rho_0 $, where $ \rho_0 = 18.93\ {\rm{g}}/{\rm{cm}}^3 $. The legends of the curves are the same as Fig. 3. Black circles, red crosses (+), and blue crosses (×) stand for the results of OFMD[57], AAHNC (CMD), and AAHNC (LMD)[48], respectively. (j), (k), (l) represent the zoom of (a), (b), (f), respectively.
表 1 约化的碰撞积分(28)—(29)式在(2, 2)阶的拟合系数[36]
Table 1. Coefficients for Eqs. (28)–(29) of the reduced collision integrals at index pair of (2, 2)[36]
$ a_1 $ $ a_2 $ $ a_3 $ $ a_4 $ $ a_5 $ 0.85401 –0.22898 –0.60059 0.80591 –0.30555 $ b_0 $ $ b_1 $ $ b_2 $ $ b_3 $ $ b_4 $ 0.43475 –0.21147 0.11116 0.19665 0.15195 
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$ a_0 $ $ a_1 $ $ a_2 $ $ a_3 $ 0.794811 0.0425698 0.00205782 7.03658×10–5 $ b_0 $ $ b_1 $ $ b_2 $ $ b_3 $ $ b_4 $ 0.862151 0.0429942 –0.000270798 3.25441×10–6 –1.15019×10–8
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表 B1 本文使用的基本物理常量以及物质的一些基本物理量
Table B1. Fundamental physical constants and some basic physical quantities of the materials used in this work.
符号 物理量 表达式 e 元电荷 $ k_{\rm{B}} $ 玻尔兹曼常量 $ \hbar $ 约化普朗克常量 $ m_e $ 电子质量 $ \varepsilon_0 $ 真空电导率 $ a_{\rm{ws}} $ Wigner-Seitz半径 $ (4\pi n/3)^{-1/3} $ $ E_{\rm{F}} $ 费米能量 $ \hbar^2(3 \pi^2 n_e)^{2/3}/(2 m_e) $ m 离子质量 n 离子数密度 $ n_{\mathrm{e}} $ 电离的电子数密度 $ \overline{Z}n $ $ q^2 $ 电荷平方 $ (\overline{Z}e)^2/(4 \pi \varepsilon_0) $ T 温度 Z 原子序数 $ \overline{Z} $ 平均电离度 $ \overline{Z^2} $ 电离度方均值 Γ 耦合参数 $ q^2/(a_{\rm{ws}} k_{\rm{B}} T) $ θ 电子简并参数 $ k_{\rm{B}} T/E_F $ κ 屏蔽参数 $ a_{\rm{ws}}/\lambda $ λ 屏蔽距离 根据模型需要取值 $ \omega_{\rm{p}} $ 等离子体频率 $ \sqrt{4\pi q^2 n/m} $
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[1] Dornheim T, Groth S, Bonitz M 2018 Phys. Rep. 744 1
Google Scholar
[2] Karasiev V V, Sjostrom T, Chakraborty D, Dufty J W, Runge K, Harris F E, Trickey S B 2014 In Graziani F, Desjarlais M P, Redmer R, Trickey S B, editors, Frontiers and Challenges in Warm Dense Matter (Cham: Springer International Publishing), pp 61–85
[3] Graziani F R, Bauer J D, Murillo M S 2014 Phys. Rev. E 90 033104
Google Scholar
[4] Regan S, Goncharov V, Sangster T, Campbell E, Betti R, Bates J, Bauer K, Bernat T, Bhandarkar S, Boehly T, Bonino M, Bose A, Cao D, Carlson L, Chapman R, Chapman T, Collins G, Collins T, Craxton R, Delettrez J, Edgell D, Epstein R, Farrell M, Forrest C, Follett R, Frenje J, Froula D, Johnson M G, Gibson C, Gonzalez L, Goyon C, Glebov V, Gopalaswamy V, Greenwood A, Harding D, Hohenberger M, Hu S, Huang H, Hund J, Igumenshchev I, Jacobs-Perkins D, Janezic R, Karasik M, Kelly J, Kessler T, Knauer J, Kosc T, Luo R, Loucks S, Marozas J, Marshall F, Mauldin M, McCrory R, Mckenty P, Michel D, Michel P, Moody J, Myatt J, Nikroo A, Nilson P, Obenschain S, Palastro J, Peebles J, Petrasso R, Petta N, Radha P, Ralph J, Rosenberg M, Sampat S, Schmitt A, Schmitt M, Schoff M, Seka W, Shah R, Rygg J, Shaw J, Short R, Shmayda W, Shoup M, Shvydky A, Solodov A, Sorce C, Stadermann M, Stoeckl C, Sweet W, Taylor C, Taylor R, Theobald W, Turnbull D, Ulreich J, Wittman M, Woo K, Youngblood K, Zuegel J 2018 Nucl. Fusion 59 032007
[5] Bruno D, Catalfamo C, Capitelli M, Colonna G, De Pascale O, Diomede P, Gorse C, Laricchiuta A, Longo S, Giordano D, Pirani F 2010 Phys. Plasmas 17 112315
Google Scholar
[6] 殷建伟, 潘昊, 吴子辉, 郝鹏程, 段卓平, 胡晓棉 2017 66 204701
Google Scholar
Yin J W, Pan H, Wu Z H, Hao P C, Duan Z P, Hu X M 2017 Acta Phys. Sin. 66 204701
Google Scholar
[7] Allen M P, Tildesley D J 1989 Computer Simulation of Liquids (Oxford: Clarendon Press
[8] Alfè D, Gillan M J 1998 Phys. Rev. Lett. 81 5161
Google Scholar
[9] Wang S, Liu H 2017 In Gervasi O, Murgante B, Misra S, Borruso G, Torre C M, Rocha A M A, Taniar D, Apduhan B O, Stankova E, Cuzzocrea A, editors, Computational Science and Its Applications - ICCSA 2017 (Cham: Springer International Publishing), pp 787–795
[10] Wang S, Zhang G, Sun B, Song H, Tian M, Fang J, Liu H 2019 Chin. J. Comput. Phys. 36 253
[11] Wang C, Long Y, Tian M F, He X T, Zhang P 2013 Phys. Rev. E 87 043105
Google Scholar
[12] Wang C, Wang Z B, Chen Q F, Zhang P 2014 Phys. Rev. E 89 023101
Google Scholar
[13] Li D, Wang C, Kang W, Yan J, Zhang P 2015 Phys. Rev. E 92 043108
Google Scholar
[14] Li Z G, Zhang W, Fu Z J, Dai J Y, Chen Q F, Chen X R 2017 Phys. Plasmas 24 052903
Google Scholar
[15] Wang Z Q, Tang J, Hou Y, Chen Q F, Chen X R, Dai J Y, Meng X J, Gu Y J, Liu L, Li G J, Lan Y S, Li Z G 2020 Phys. Rev. E 101 023302
Google Scholar
[16] Cheng Y, Wang H, Wang S, Gao X, Li Q, Fang J, Song H, Chu W, Zhang G, Song H, Liu H 2021 AIP Adv. 11 015043
Google Scholar
[17] Hou Y, Bredow R, Yuan J, Redmer R 2015 Phys. Rev. E 91 033114
Google Scholar
[18] Hou Y, Jin F, Yuan J 2006 Phys. Plasmas 13 093301
Google Scholar
[19] Hou Y, Jin F, Yuan J 2007 J. Phys.: Condens. Matter 19 425204
Google Scholar
[20] van Leeuwen J, Groeneveld J, de Boer J 1959 Physica (Amsterdam) 25 792
Google Scholar
[21] De Boer J, Van Leeuwen J, Groeneveld J 1964 Physica (Amsterdam) 30 2265
Google Scholar
[22] Wünsch K, Hilse P, Schlanges M, Gericke D O 2008 Phys. Rev. E 77 056404
Google Scholar
[23] Lambert F, Clérouin J, Zérah G 2006 Phys. Rev. E 73 016403
Google Scholar
[24] Blanchet A, Torrent M, Clérouin J 2020 Phys. Plasmas 27 122706
Google Scholar
[25] Lambert F, Clérouin J, Mazevet S, Gilles D 2007 Contrib. Plasma Phys. 47 272
Google Scholar
[26] Brack M, Bhaduri R K 2003 Semiclassical Physics (Boulder: Westview Press
[27] Daligault J, Baalrud S D, Starrett C E, Saumon D, Sjostrom T 2016 Phys. Rev. Lett. 116 075002
Google Scholar
[28] Starrett C E, Saumon D 2013 Phys. Rev. E 87 013104
Google Scholar
[29] Starrett C E, Saumon D, Daligault J, Hamel S 2014 Phys. Rev. E 90 033110
Google Scholar
[30] Baalrud S D, Daligault J 2013 Phys. Rev. Lett. 110 235001
Google Scholar
[31] Baalrud S D, Daligault J 2015 Phys. Rev. E 91 063107
Google Scholar
[32] Haxhimali T, Rudd R E, Cabot W H, Graziani F R 2015 Phys. Rev. E 92 053110
Google Scholar
[33] Chapman S, Cowling T G 1970 The Mathematical Theory of Non-Uniform Gases (Cambridge, England: Cambridge University Press
[34] Murillo M S 2008 High Energy Density Phys. 4 49
Google Scholar
[35] Johnson Z A, Silvestri L G, Petrov G M, Stanton L G, Murillo M S 2024 Phys. Plasmas 31 082701
Google Scholar
[36] Stanton L G, Murillo M S 2016 Phys. Rev. E 93 043203
Google Scholar
[37] Arnault P 2013 High Energy Density Phys. 9 711
Google Scholar
[38] Daligault J, Rasmussen K O, Baalrud S D 2014 Phys. Rev. E 90 033105
Google Scholar
[39] Cheng Y, Liu H, Hou Y, Meng X, Li Q, Liu Y, Gao X, Yuan J, Song H, Wang J 2022 Phys. Rev. E 106 014142
Google Scholar
[40] Cheng Y, Gao X, Li Q, Liu Y, Song H, Liu H 2023 arXiv e-prints arXiv: 2305.16551
[41] Thomas L H 1927 Math. Proc. Cambridge Philos. Soc. 23 542
Google Scholar
[42] More R M 1985 Adv. At. Mol. Phys. 21 305
[43] Vanderbilt D 1990 Phys. Rev. B 41 7892
Google Scholar
[44] Danel J F, Kazandjian L, Zérah G 2012 Phys. Rev. E 85 066701
Google Scholar
[45] Gordon R G, Kim Y S 1972 J. Chem. Phys. 56 3122
Google Scholar
[46] Kim Y S, Gordon R G 1974 Phys. Rev. B 9 3548
Google Scholar
[47] Hou Y, Fu Y, Bredow R, Kang D, Redmer R, Yuan J 2017 High Energy Density Phys. 22 21
Google Scholar
[48] Hou Y, Jin Y, Zhang P, Kang D, Gao C, Redmer R, Yuan J 2021 Matter Radiat. Extrem. 6 026901
Google Scholar
[49] Ornstein L, Zernike F 1914 Proc. K. Ned. Akad. Wet. 17 793
[50] Rosenfeld Y 1986 J. Stat. Phys. 42 437
Google Scholar
[51] Decoster A, Raviart P A, Markowich P A, Perthame B 1998 Modeling of Collisions (Paris: Gauthier-Villars
[52] Bastea S 2005 Phys. Rev. E 71 056405
Google Scholar
[53] Baus M, Hansen J P 1980 Phys. Rep. 59 1
Google Scholar
[54] Grabowski P, Hansen S, Murillo M, Stanton L, Graziani F, Zylstra A, Baalrud S, Arnault P, Baczewski A, Benedict L, Blancard C, ÄffertÃk O, Clérouin J, Collins L, Copeland S, Correa A, Dai J, Daligault J, Desjarlais M, Dharma-wardana M, Faussurier G, Haack J, Haxhimali T, Hayes-Sterbenz A, Hou Y, Hu S, Jensen D, Jungman G, Kagan G, Kang D, Kress J, Ma Q, Marciante M, Meyer E, Rudd R, Saumon D, Shulenburger L, Singleton R, Sjostrom T, Stanek L, Starrett C, Ticknor C, Valaitis S, Venzke J, White A 2020 High Energy Density Phys. 37 100905
Google Scholar
[55] Sun H, Kang D, Hou Y, Dai J 2017 Matter Radiat. Extrem. 2 287
Google Scholar
[56] Clérouin J, Arnault P, Ticknor C, Kress J D, Collins L A 2016 Phys. Rev. Lett. 116 115003
Google Scholar
[57] Kress J, Cohen J S, Kilcrease D, Horner D, Collins L 2011 High Energy Density Phys. 7 155
Google Scholar
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