[论文解读] Dynamical Heterogeneity and the interplay between activated and mode coupling dynamics in supercooled liquids

Sarika Maitra Bhattacharyya, Biman Bagchi+1 more|arXiv (Cornell University)|Feb 19, 2007

Material Dynamics and Properties被引用 5

一句话总结

该论文构建了一个自洽的理论框架，统一了模式耦合理论（MCT）与随机一级相变（RFOT）理论，以描述过冷液体中的动力学异质性。通过将连续扩散（通过F₁₂-MCT）与激活跳跃（通过RFOT）耦合，表明跳跃可增强短时MCT动力学，降低非指数性并加速T_c以下的松弛过程，从而避免严格的局域化转变，并解释了实验中观察到的非阿伦尼乌斯行为和非指数性松弛。

ABSTRACT

We present a theoretical analysis of the dynamic structure factor (DSF) of a liquid at and below the mode coupling critical temperature $T_c$, by developing a self-consistent theoretical treatment which includes the contributions both from continuous diffusion, described using general two coupling parameter ($F_{12}$) mode coupling theory (MCT), and from the activated hopping, described using the random first order transition (RFOT) theory, incorporating the effect of dynamical heterogeneity. The theory is valid over the whole temperature plane and shows correct limiting MCT like behavior above $T_{c}$ and goes over to the RFOT theory near the glass transition temperature, $T_{g}$. Between $T_{c}$ and $T_{g}$, the theory predicts that neither the continuous diffusion, described by pure mode coupling theory, nor the hopping motion alone suffices but both contribute to the dynamics while interacting with each other. We show that the interplay between the two contributions conspires to modify the relaxation behavior of the DSF from what would be predicted by a theory with a complete static Gaussian barrier distribution in a manner that may be described as a facilitation effect. Close to $T_c$, coupling between the short time part of MCT dynamics and hopping reduces the stretching given by the F$_{12}$-MCT theory significantly and accelerates structural relaxation. As the temperature is progressively lowered below $T_c$, the equations yield a crossover from MCT dominated regime to the hopping dominated regime. In the combined theory the dynamical heterogeneity is modified because the low barrier components interact with the MCT dynamics to enhance the relaxation rate below $T_c$ and reduces the stretching that would otherwise arise from an input static barrier height distribution.

研究动机与目标

• 解决模式耦合理论（MCT）与RFOT理论在描述过冷液体结构松弛时的矛盾。
• 在单一自洽框架中整合由F₁₂-MCT引起的静态非均匀性与由RFOT引起的能垒高度分布所导致的动力学异质性。
• 理解激活跳跃与连续扩散如何非线性地相互作用，以改变松弛动力学，特别是非指数性参数β。
• 解释为何实验中α松弛呈现非指数性，尽管纯MCT或纯RFOT理论均预测较小的非指数性。

提出的方法

• 在F₁₂-MCT形式中引入两个耦合参数（λ₁, λ₂），以描述具有本征非指数性的连续扩散，从而捕捉静态非均匀性。
• 引入来自RFOT理论的静态能垒高度分布，以模拟激活跳跃动力学，反映构型熵效应。
• 通过将MCT松弛方程与RFOT跳跃速率耦合，推导出自洽解，考虑粘度与结构松弛之间的反馈作用。
• 模型包含非线性反馈效应：跳跃使MCT动力学软化，增强短时扩散并降低有效非指数性。
• 采用解析与数值解法计算总松弛函数φ(t)，通过与Kohlrausch-Williams-Watts函数拟合提取非指数性参数β_total。
• 通过将β_total与MCT贡献（β_MCT）和跳跃贡献（β_static_hop）对比，验证理论，显示非加性、协同效应。

实验结果

研究问题

• RQ1 连续扩散（MCT）与激活跳跃（RFOT）之间的相互作用如何改变过冷液体中的结构松弛动力学？
• RQ2 动力学异质性在多大程度上改变了α松弛的非指数性参数β，使其超出MCT或RFOT单独预测的范围？
• RQ3 跳跃对MCT动力学的反馈如何影响T_c以下的有效粘度与松弛时间尺度？
• RQ4 为何即使MCT动力学本身已呈现非指数性，总松弛仍保持非指数性？这一行为如何受能垒高度分布的影响？

主要发现

• 在T_c以下，总松弛动力学因跳跃促进连续扩散效率而被加速，有效非指数性降低。
• 非指数性参数β_total小于β_MCT与β_static_hop两者，表明MCT与跳跃动力学之间存在非加性、协同效应。
• 当MCT动力学本身已呈现非指数性（β_MCT = 0.5）时，随着跳跃非指数性（β_static_hop）增加，β_total进一步减小，表明跳跃在进一步缩短松弛时间方面效率降低。
• 对于更高的ε值（更低温度），β_total逐渐趋近于β_static_hop，表明在低温下出现向跳跃主导动力学的转变。
• 该理论预测在T_c处不存在严格的局域化转变，与实验观察一致，原因在于跳跃所促进的MCT动力学持续贡献。
• 跳跃对MCT动力学的非线性反馈使有效势垒景观软化，导致能垒高度分布向更低值移动，进一步加速松弛过程。