刚性棒悬浮液模型中旋转弛豫的修正定标原理。

Modified scaling principle for rotational relaxation in a model for suspensions of rigid rods.

机构信息

Department of Chemistry, Stanford University, Stanford, California 94305, USA.

出版信息

J Chem Phys. 2013 Jul 28;139(4):044905. doi: 10.1063/1.4816001.

PMID:23902017

Abstract

We have performed simulations of the model of infinitely thin rigid rods undergoing rotational and translational diffusion, subject to the restriction that no two rods can cross one another, for various concentrations well into the semidilute regime. We used a modification of the algorithm of Doi et al. [J. Phys. Soc. Jpn. 53, 3000 (1984)] that simulates diffusive dynamics using a Monte Carlo method and a nonzero time step. In the limit of zero time step, this algorithm is an exact description of diffusive dynamics subject to the noncrossing restriction. For a wide range of concentrations in the semidilute regime, we report values of the long time rotational diffusion constant of the rods, extrapolated to the limit of zero time step, for various sets of values of the infinite dilution (bare) diffusion constants. These results are compared with the results of a previous simulation of the model by Doi et al. and of previous simulations of rods with finite aspect ratio by Fixman and by Cobb and Butler that had been extrapolated to the limit of infinitely thin rods. The predictions of the Doi-Edwards (DE) scaling law do not hold for this model for the concentrations studied. The simulation data for the model display two deviations from the predictions of the DE theory that have been observed in experimental systems in the semidilute regime, namely, the very slow approach toward DE scaling behavior as the concentration is increased and the large value of the prefactor in the DE scaling law. We present a modified scaling principle for this model that is consistent with the simulation results for a broad range of concentrations in the semidilute regime. The modified scaling principle takes into account two physical effects, which we call "leakage" and "drift," that were found to be important for the transport properties of a simpler model of nonrotating rods on a lattice [Y.-L. S. Tse and H. C. Andersen, J. Chem. Phys. 136, 024904 (2012)].

摘要

我们对无限细刚性棒在旋转和平动扩散过程中的模型进行了模拟，该模型受到的约束是没有两根棒可以相互交叉，各种浓度都远高于半稀相区。我们使用了一种改进的多伊等人的算法[J. Phys. Soc. Jpn. 53, 3000（1984）]，该算法使用蒙特卡罗方法和非零时间步长模拟扩散动力学。在时间步长为零时的极限下，该算法是受非交叉限制的扩散动力学的精确描述。在半稀相区的广泛浓度范围内，我们报告了在各种无限稀释（裸）扩散常数的情况下，棒的长时间旋转扩散常数的极限值，该极限值是在时间步长为零时外推得到的。这些结果与多伊等人之前对该模型的模拟结果以及之前对有限纵横比棒的模拟结果进行了比较，这些模拟结果已经被外推到无限细棒的极限。对于这个模型，多伊-爱德华兹（DE）标度定律的预测在研究的浓度范围内并不成立。该模型的模拟数据显示了两种偏离 DE 理论预测的情况，这在半稀相区的实验系统中已经观察到，即随着浓度的增加，DE 标度行为的缓慢接近以及 DE 标度律中的大的前因子。我们提出了一种适用于该模型的改进的标度原理，该原理与半稀相区广泛浓度范围内的模拟结果一致。改进的标度原理考虑了两种物理效应，我们称之为“泄漏”和“漂移”，这两种效应对晶格上非旋转棒的更简单模型的输运性质非常重要[Y.-L. S. Tse 和 H. C. Andersen，J. Chem. Phys. 136, 024904（2012）]。