Saltzman Erica J, Schweizer Kenneth S
Department of Materials Science and Seitz Materials Research Laboratory, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 May;77(5 Pt 1):051504. doi: 10.1103/PhysRevE.77.051504. Epub 2008 May 23.
Our microscopic stochastic nonlinear Langevin equation theory of activated dynamics has been employed to study the real-space van Hove function of dense hard sphere fluids and suspensions. At very short times, the van Hove function is a narrow Gaussian. At sufficiently high volume fractions, such that the entropic barrier to relaxation is greater than the thermal energy, its functional form evolves with time to include a rapidly decaying component at small displacements and a long-range exponential tail. The "jump" or decay length scale associated with the tail increases with time (or particle root-mean-square displacement) at fixed volume fraction, and with volume fraction at the mean alpha relaxation time. The jump length at the alpha relaxation time is predicted to be proportional to a measure of the decoupling of self-diffusion and structural relaxation. At long times corresponding to mean displacements of order a particle diameter, the volume fraction dependence of the decay length disappears. A good superposition of the exponential tail feature based on the jump length as a scaling variable is predicted at high volume fractions. Overall, the theoretical results are in good accord with recent simulations and experiments. The basic aspects of the theory are also compared with a classic jump model and a dynamically facilitated continuous time random-walk model. Decoupling of the time scales of different parts of the relaxation process predicted by the theory is qualitatively similar to facilitated dynamics models based on the concept of persistence and exchange times if the elementary event is assumed to be associated with transport on a length scale significantly smaller than the particle size.
我们运用活化动力学的微观随机非线性朗之万方程理论，研究了致密硬球流体和悬浮液的实空间范霍夫函数。在极短时间内，范霍夫函数是一个窄高斯函数。在足够高的体积分数下，使得弛豫的熵垒大于热能时，其函数形式会随时间演化，在小位移处包含一个快速衰减的分量和一个长程指数尾部。与尾部相关的“跳跃”或衰减长度尺度在固定体积分数下随时间（或粒子均方根位移）增加，在平均α弛豫时间下随体积分数增加。预计在α弛豫时间的跳跃长度与自扩散和结构弛豫解耦的一种度量成正比。在对应于粒子直径量级平均位移的长时间下，衰减长度的体积分数依赖性消失。预计在高体积分数下，基于跳跃长度作为标度变量的指数尾部特征能很好地叠加。总体而言，理论结果与最近的模拟和实验结果吻合良好。该理论的基本方面也与一个经典跳跃模型和一个动态促进连续时间随机游走模型进行了比较。如果假设基本事件与在远小于粒子尺寸的长度尺度上的输运相关，那么该理论预测的弛豫过程不同部分时间尺度的解耦在定性上类似于基于持久性和交换时间概念的促进动力学模型。
