Ohtori Norikazu, Ishii Yoshiki
Department of Chemistry, 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.
J Chem Phys. 2015 Oct 28;143(16):164514. doi: 10.1063/1.4934627.
Explicit expressions of the self-diffusion coefficient, D(i), and shear viscosity, η(sv), are presented for Lennard-Jones (LJ) binary mixtures in the liquid states along the saturated vapor line. The variables necessary for the expressions were derived from dimensional analysis of the properties: atomic mass, number density, packing fraction, temperature, and the size and energy parameters used in the LJ potential. The unknown dependence of the properties on each variable was determined by molecular dynamics (MD) calculations for an equimolar mixture of Ar and Kr at the temperature of 140 K and density of 1676 kg m(-3). The scaling equations obtained by multiplying all the single-variable dependences can well express D(i) and η(sv) evaluated by the MD simulation for a whole range of compositions and temperatures without any significant coupling between the variables. The equation for Di can also explain the dual atomic-mass dependence, i.e., the average-mass and the individual-mass dependence; the latter accounts for the "isotope effect" on Di. The Stokes-Einstein (SE) relation obtained from these equations is fully consistent with the SE relation for pure LJ liquids and that for infinitely dilute solutions. The main differences from the original SE relation are the presence of dependence on the individual mass and on the individual energy parameter. In addition, the packing-fraction dependence turned out to bridge another gap between the present and original SE relations as well as unifying the SE relation between pure liquids and infinitely dilute solutions.
给出了沿饱和蒸气压线处于液态的 Lennard-Jones（LJ）二元混合物的自扩散系数 D(i) 和剪切粘度 η(sv) 的显式表达式。这些表达式所需的变量是通过对以下性质进行量纲分析得出的：原子质量、数密度、堆积分数、温度以及 LJ 势中使用的尺寸和能量参数。通过对 140 K 温度和 1676 kg m⁻³ 密度下的 Ar 和 Kr 等摩尔混合物进行分子动力学（MD）计算，确定了各性质对每个变量的未知依赖性。将所有单变量依赖性相乘得到的标度方程能够很好地表达在整个组成和温度范围内通过 MD 模拟评估得到的 D(i) 和 η(sv)，且变量之间不存在任何显著的耦合。Di 的方程还可以解释双原子质量依赖性，即平均质量依赖性和单个质量依赖性；后者解释了 Di 上的“同位素效应”。从这些方程得到的斯托克斯 - 爱因斯坦（SE）关系与纯 LJ 液体的 SE 关系以及无限稀释溶液的 SE 关系完全一致。与原始 SE 关系的主要区别在于存在对单个质量和单个能量参数的依赖性。此外，堆积分数依赖性结果弥合了当前和原始 SE 关系之间的另一个差距，同时也统一了纯液体和无限稀释溶液之间的 SE 关系。
