Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Hoża 69, 00-681 Warsaw, Poland.
J Chem Phys. 2012 Feb 21;136(7):071102. doi: 10.1063/1.3689842.
A single Brownian particle of arbitrary shape is considered. The time-dependent translational mean square displacement W(t) of a reference point at this particle is evaluated from the Smoluchowski equation. It is shown that at times larger than the characteristic time scale of the rotational Brownian relaxation, the slope of W(t) becomes independent of the choice of a reference point. Moreover, it is proved that in the long-time limit, the slope of W(t) is determined uniquely by the trace of the translational-translational mobility matrix μ(tt) evaluated with respect to the hydrodynamic center of mobility. The result is applicable to dynamic light scattering measurements, which indeed are performed in the long-time limit.
考虑任意形状的单个布朗粒子。从斯莫卢霍夫斯基方程评估该粒子上参考点的时变平移均方位移 W(t)。结果表明，在比旋转布朗松弛的特征时间尺度大的时间，W(t)的斜率变得与参考点的选择无关。此外，证明在长时间极限下，W(t)的斜率由相对于迁移率的水力中心评估的平移-平移迁移率矩阵 μ(tt)的迹唯一确定。该结果适用于动态光散射测量，实际上是在长时间极限下进行的。
