Physics Department, Wesleyan University, Middletown, Connecticut 06459, USA.
J Chem Phys. 2013 Mar 28;138(12):12A541. doi: 10.1063/1.4790138.
We carefully examine common measures of dynamical heterogeneity for a model polymer melt and test how these scales compare with those hypothesized by the Adam and Gibbs (AG) and random first-order transition (RFOT) theories of relaxation in glass-forming liquids. To this end, we first analyze clusters of highly mobile particles, the string-like collective motion of these mobile particles, and clusters of relative low mobility. We show that the time scale of the high-mobility clusters and strings is associated with a diffusive time scale, while the low-mobility particles' time scale relates to a structural relaxation time. The difference of the characteristic times for the high- and low-mobility particles naturally explains the well-known decoupling of diffusion and structural relaxation time scales. Despite the inherent difference of dynamics between high- and low-mobility particles, we find a high degree of similarity in the geometrical structure of these particle clusters. In particular, we show that the fractal dimensions of these clusters are consistent with those of swollen branched polymers or branched polymers with screened excluded-volume interactions, corresponding to lattice animals and percolation clusters, respectively. In contrast, the fractal dimension of the strings crosses over from that of self-avoiding walks for small strings, to simple random walks for longer, more strongly interacting, strings, corresponding to flexible polymers with screened excluded-volume interactions. We examine the appropriateness of identifying the size scales of either mobile particle clusters or strings with the size of cooperatively rearranging regions (CRR) in the AG and RFOT theories. We find that the string size appears to be the most consistent measure of CRR for both the AG and RFOT models. Identifying strings or clusters with the "mosaic" length of the RFOT model relaxes the conventional assumption that the "entropic droplets" are compact. We also confirm the validity of the entropy formulation of the AG theory, constraining the exponent values of the RFOT theory. This constraint, together with the analysis of size scales, enables us to estimate the characteristic exponents of RFOT.
我们仔细研究了模型聚合物熔体的常见动力学不均匀性度量，并测试了这些标度与玻璃形成液体中 Adam 和 Gibbs (AG) 和随机一级转变 (RFOT) 松弛理论所假设的标度相比如何。为此，我们首先分析了高迁移率粒子的簇、这些高迁移率粒子的串状集体运动以及相对低迁移率的粒子簇。我们表明，高迁移率簇和串的时间标度与扩散时间标度相关，而低迁移率粒子的时间标度与结构弛豫时间相关。高迁移率和低迁移率粒子的特征时间的差异自然解释了众所周知的扩散和结构弛豫时间尺度的解耦。尽管高迁移率和低迁移率粒子之间的动力学存在内在差异，但我们发现这些粒子簇的几何结构具有高度相似性。特别是，我们表明这些簇的分形维数与膨胀支化聚合物或具有屏蔽排斥体积相互作用的支化聚合物一致，分别对应于晶格动物和渗流簇。相比之下，对于小字符串，字符串的分形维数从自回避行走的分形维数过渡到更长、相互作用更强的简单随机行走，对应于具有屏蔽排斥体积相互作用的柔性聚合物。我们研究了将移动粒子簇或字符串的大小与 AG 和 RFOT 理论中的协同重排区域 (CRR) 的大小进行标识的适当性。我们发现，对于 AG 和 RFOT 模型，字符串的大小似乎是 CRR 的最一致度量。将字符串或簇与 RFOT 模型的“镶嵌”长度相关联，放宽了“熵液滴”是紧凑的传统假设。我们还确认了 AG 理论的熵表述的有效性，限制了 RFOT 理论的指数值。这种约束以及大小标度的分析使我们能够估计 RFOT 的特征指数。
