Viscous Fluids弛豫的协同激活势垒跳跃理论I.硬球流体的一般公式及其应用
Elastically Cooperative Activated Barrier Hopping Theory of Relaxation in Viscous Fluids. I. General Formulation and Application to Hard Sphere Fluids
摘要：
我们推广了单粒子跳跃的力级非线性朗之万方程理论，使之包括与液体长程弹性形变有关的集体效应。激活的α弛豫事件是一个混合的空间字符，涉及两个不同的，但相互关联的，本地和集体的障碍。在低于堵塞的体积分数或高于零开尔文的温度下没有分歧。首先开发和实施的硬球流体的背景下，分析和数值的想法。在一个中间的体积分数的交叉制度，当地的笼过程是占主导地位的方式与一个明显的Arabius行为一致。超Arrhenius集体障碍是更强烈地依赖于体积分数，占主导地位的高粘性制度，并很好地描述了一个非奇异的法律低于干扰。集体势垒的增加取决于热密度波动的幅度、剪切模量或瞬态局部化长度以及不断增长的微观跳跃长度。α弛豫时间的计算与最近的实验和模拟致密流体和悬浮液的硬球。与弹性模型和熵危机的思想理论的比较进行了探讨。本文的工作为建立一个准普适的、无拟合参数的热分子液体弛豫理论奠定了基础。
英文摘要：
We generalize the force-level Nonlinear Langevin Equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time.
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