World Premier International Research Center, Advanced Institute for Materials Research and Institute of Fluid Science, Tohoku University, Sendai 980-8577, Japan.
J Phys Chem B. 2011 Dec 8;115(48):14030-45. doi: 10.1021/jp203583u. Epub 2011 Aug 11.
The long-time self-diffusion coefficients D(S)(L) in distinctly different glass-forming liquids are analyzed from a unified point of view recently proposed by the present author. It is shown that as long as the systems are in equilibrium, they are all described by the following two types of master curves, depending on whether the control parameter is intensive or extensive: D(S)(L)(x) = d(0)x(-1)(1 - x)(2+η) exp[cx(3+η)(1 - x)(2+η)] for a reduced intensive control parameter x, such as a reduced inverse temperature, and D(S)(L)(x) = d(0)x(-1)(1 - x)(2) for a reduced extensive control parameter x, such as a reduced volume fraction, where d(0) and c are constant. Here, the exponent η (≠0) results from many-body correlations in a supercooled liquid state. The constants η and c depend on the systems and are given by (η,c) = (4/3,62) for fragile liquids, (5/3, 62) for strong liquids, and (0,0) for other glass-forming systems in which the peak heights of their non-Gaussian parameters are always much less than 1.0. It is also shown that all of the data for the diffusion coefficient start to deviate from the master curves at lower temperatures (or higher volume fraction), where the systems become out of equilibrium, leading to a glass state.
最近，作者从一个统一的观点分析了具有明显不同玻璃形成能力的液体中的长时间自扩散系数 D(S)(L)。结果表明，只要系统处于平衡状态，它们都可以用以下两种类型的主曲线来描述，这取决于控制参数是强度参数还是扩展参数：对于减少的强度控制参数 x，例如降低的逆温度，D(S)(L)(x) = d(0)x(-1)(1 - x)(2+η) exp[cx(3+η)(1 - x)(2+η)]；对于减少的扩展控制参数 x，例如降低的体积分数，D(S)(L)(x) = d(0)x(-1)(1 - x)(2)，其中 d(0) 和 c 是常数。这里，指数 η(≠0)是由过冷液体状态中的多体相关产生的。常数 η 和 c 取决于系统，对于脆弱液体，它们的值为 (η,c) = (4/3,62)；对于强液体，它们的值为 (5/3, 62)；对于其他玻璃形成系统，它们的值为 (0,0)，因为这些系统的非高斯参数的峰值高度总是远小于 1.0。结果还表明，所有扩散系数的数据在较低温度（或较高体积分数）下开始偏离主曲线，此时系统变得不平衡，导致玻璃态。
