Hanasaki Itsuo, Nagura Ryo, Kawano Satoyuki
Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University, Machikaneyama-cho 1-3, Toyonaka, Osaka 560-8531, Japan.
J Chem Phys. 2015 Mar 14;142(10):104301. doi: 10.1063/1.4913748.
The Brownian motion of a particle in a fluid is often described by the linear Langevin equation, in which it is assumed that the mass of the particle is sufficiently large compared to the surrounding fluid molecules. This assumption leads to a diffusion coefficient that is independent of the particle mass. The Stokes-Einstein equation indicates that the diffusion coefficient depends solely on the particle size, but the concept of size can be ambiguous when close to the molecular scale. We first examine the Brownian motion of simple model particles based on short-range interactions in water by the molecular dynamics method and show that the diffusion coefficient can vary with mass when this mass is comparable to that of the solvent molecules, and that this effect is evident when the solute particle size is sufficiently small. We then examine the properties of a water molecule considered as a solute in the bulk solvent consisting of the remainder of the water. A comparison with simple solute models is used to clarify the role of force fields. The long-range Coulomb interaction between water molecules is found to lead to a Gaussian force distribution in spite of a mass ratio and nominal size ratio of unity, such that solutes with short-range interactions exhibit non-Gaussian force distribution. Thus, the range of the interaction distance determines the effective size even if it does not represent the volume excluded by the repulsive force field.
流体中粒子的布朗运动通常由线性朗之万方程描述，其中假定粒子的质量与周围流体分子相比足够大。这一假设导致扩散系数与粒子质量无关。斯托克斯 - 爱因斯坦方程表明扩散系数仅取决于粒子大小，但在接近分子尺度时，大小的概念可能含糊不清。我们首先通过分子动力学方法研究基于水中短程相互作用的简单模型粒子的布朗运动，并表明当该质量与溶剂分子质量可比时，扩散系数会随质量变化，且当溶质粒子尺寸足够小时这种效应很明显。然后我们研究了被视为溶质的水分子在由其余水组成的大量溶剂中的性质。通过与简单溶质模型进行比较来阐明力场的作用。尽管质量比和标称尺寸比均为1，但发现水分子之间的长程库仑相互作用会导致高斯力分布，使得具有短程相互作用的溶质表现出非高斯力分布。因此，相互作用距离的范围决定了有效尺寸，即使它并不代表排斥力场排除的体积。
