Faculty of Science, Niigata University, 8050 Ikarashi 2-no cho, Nishi-ku, Niigata 950-2181, Japan.
Graduate School of Science and Technology, Niigata University, 8050 Ikarashi 2-no cho, Nishi-ku, Niigata 950-2181, Japan.
Phys Rev E. 2017 May;95(5-1):052122. doi: 10.1103/PhysRevE.95.052122. Epub 2017 May 12.
We have examined the conditions under which the breakdown of the Stokes-Einstein (SE) relation occurs in pure Lennard-Jones (LJ) fluids over a wide range of temperatures and packing fractions beyond the critical point. To this end, the temperature and packing-fraction dependence of the self-diffusion coefficient, D, and the shear viscosity, η_{sv}, were evaluated for Xe using molecular dynamics calculations with the Green-Kubo formula. The results showed good agreement with the experimental values. The breakdown was determined in light of the SE equation which we have recently derived for pure LJ liquids: Dη_{sv}=(k_{B}T/2π)(N/V)^{1/3}, where k_{B} is the Boltzmann constant, T is the temperature, and N is the particle number included in the system volume V. We have found that the breakdown occurs in the lower range of the packing fraction, η<0.2, and derived the SE relation in its broken form as Dη_{sv}=0.007(1-η)^{-5}η^{-4/3}(k_{B}T/ε)^{n}k_{B}T(N/V)^{1/3}, where n increases from 0 up to 1 with the decreasing η. The equation clearly shows that the breakdown mainly occurs because the packing-fraction dependence does not cancel out between D and η_{sv} in this region, which is attributed to the gaseous behavior in the packing-fraction dependence of the shear viscosity under a constant number density. In addition, the gaseous behavior in the temperature dependence of the shear viscosity also partially causes the breakdown.
我们研究了在超过临界点的广泛温度和填充分数范围内，纯 Lennard-Jones（LJ）流体中斯托克斯-爱因斯坦（SE）关系破裂的条件。为此，使用分子动力学计算和格林-库伯公式评估了 Xe 的自扩散系数 D 和剪切粘度 η_{sv} 对温度和填充分数的依赖性。结果与实验值吻合良好。根据我们最近为纯 LJ 液体推导的 SE 方程确定了破裂：Dη_{sv}=(k_{B}T/2π)(N/V)^{1/3}，其中 k_{B} 是玻尔兹曼常数，T 是温度，N 是系统体积 V 中包含的粒子数。我们发现破裂发生在填充分数较低的范围内 η<0.2，并得出了破裂形式的 SE 关系，即 Dη_{sv}=0.007(1-η)^{-5}η^{-4/3}(k_{B}T/ε)^{n}k_{B}T(N/V)^{1/3}，其中 n 随着 η 的减小从 0 增加到 1。该方程清楚地表明，在该区域内，D 和 η_{sv} 之间的填充分数依赖性没有相互抵消，这主要是由于在恒定数密度下剪切粘度的填充分数依赖性中的气态行为所致。此外，剪切粘度的温度依赖性中的气态行为也部分导致了破裂。
