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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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$ 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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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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