Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
J Chem Phys. 2013 Mar 28;138(12):12A526. doi: 10.1063/1.4775741.
We investigate numerically the temperature and density dependence of the Stokes-Einstein ratio, Dη∕T, and of two commonly-used variants thereof, Dτ and Dτ∕T, where D is a diffusivity, η the shear viscosity, and τ a structural relaxation time. We consider a family of atomic binary mixtures with systematically-softened repulsive interactions, and the Lewis-Wahnström model of ortho-terphenyl (OTP). The three quantities grow significantly as the temperature decreases in the supercooled regime, a well-known phenomenon. At higher temperatures, Dτ exhibits negative violations of Stokes-Einstein behavior, i.e., decrease upon cooling, for the atomic systems, though not for OTP. We consider two choices for the relaxation time, one based on the decay of the self-intermediate scattering function, and the other on the integral of the stress autocorrelation function. The instantaneous shear modulus exhibits appreciable temperature dependence for the two classes of systems investigated here. Our results suggest that commonly-invoked assumptions, such as τ ∼ η and τ ∼ η∕T, should be critically evaluated across a wide spectrum of systems and thermodynamic conditions. We find the Stokes-Einstein ratio, Dη∕T, to be constant across a broad range of temperatures and densities for the two classes of systems investigated here.
我们通过数值方法研究了斯特克斯-爱因斯坦比 Dη∕T 及其两种常用变体 Dτ 和 Dτ∕T 的温度和密度依赖性，其中 D 是扩散系数，η 是剪切黏度，τ 是结构弛豫时间。我们考虑了一类具有系统软化排斥相互作用的原子二元混合物和路易斯-瓦恩斯特朗模型的邻位三联苯（OTP）。这三个量在过冷区随着温度的降低显著增加，这是一个众所周知的现象。在较高温度下，对于原子系统，Dτ 表现出对斯特克斯-爱因斯坦行为的负偏离，即随着冷却而减小，尽管对于 OTP 则没有。我们考虑了两种弛豫时间的选择，一种基于自中间散射函数的衰减，另一种基于应力自相关函数的积分。瞬时剪切模量对于所研究的两类系统都表现出相当大的温度依赖性。我们的结果表明，应该在广泛的系统和热力学条件下，对诸如 τ ∼ η 和 τ ∼ η∕T 等常用假设进行严格评估。我们发现，在所研究的两类系统中，Dη∕T 在很宽的温度和密度范围内保持恒定。
