分子大小和形状效应：旋转扩散和托克斯

通过具有两个中心伦纳德·琼斯（2CLJ）势的分子动力学模拟，给出了双原子分子液体的旋转扩散系数和Stokes-Einstein-Debye（SED）关系的公式。剪切粘度η SV和转动扩散系数d - [R表示为分子质量和数量密度的函数ñ / V，或转动惯量，包装分数，温度Ť，相互作用能和分子伸长升*  ≡ 升/ σ，其中ñ是包括在系统体积的分子数V，升在双原子分子的键长，和σ在LJ电位中使用的大小的参数。堆积率和伸长率分别是表示分子大小和形状的变量。这些结果直接产生一个分子基础SED关系为d - [R η SV / Ť  α  v米*三分之一升* -3（Ñ / V），其中，v米*是表示为解析函数只的无量纲分子体积伸长率l / σ。即，该SED方程式不取决于尺寸而是取决于形状。这与基于大小的原始SED关系形成了鲜明对比，后者表明在分子规模上对该关系进行了整体重新考虑。形状项解释了一个悖论，即更多的球形分子（例如N 2）与基于球形粒子的原始SED方程的偏离更大。此外，在没有尺寸的SED关系是与斯托克斯-爱因斯坦关系为表示为的Lennard-Jones和2CLJ液体两者一致Dη SV / Ť  α（Ñ / V）1/3，其中，d是所述平移自扩散系数。

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Formulation of rotational diffusion coefficient and the Stokes-Einstein-Debye (SED) relation is presented for diatomic molecular liquids by molecular dynamics simulation with two-center Lennard-Jones (2CLJ) potentials. Shear viscosity ηsv and rotational diffusion coefficient Dr are expressed as a function of molecular mass and number density N/V, or moment of inertia, packing fraction, temperature T, interaction energy, and molecular elongation l∗ ≡ l/σ, where N is the number of molecules included in the system volume V, l the bond length in the diatomic molecules, and σ the size parameter used in the LJ potentials. The packing fraction and elongation are the variables expressing molecular size and shape, respectively. These results produces directly a molecular-basis SED relation as Drηsv/T ∝ vm∗1/3l∗−3(N/V), where vm∗ is the dimensionless molecular volume expressed as an analytical function only of elongation l/σ. That is, this SED equation depends not on the size but on the shape. This is highly contrasted with the original SED relation based on the size, which suggests overall reconsideration of the relation on a molecular scale. The shape term accounts for a paradox that more spherical molecules such as N2 deviate more strongly from the original SED equation based on a spherical particle. In addition, the SED relation without the size is consistent with the Stokes-Einstein relation for both the Lennard-Jones and 2CLJ liquids expressed as Dηsv/T ∝ (N/V)1/3, where D is the translational self-diffusion coefficient.