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arXiv 0704.1508cond-mat.mtrl-sci
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非均匀玻璃形成液体中的反常扩散和拉伸指数:低温行为

Anomalous diffusion and stretched exponentials in heterogeneous glass-forming liquids: Low-temperature behavior

J. S. Langer, S. Mukhopadhyay

摘要:

本文提出了一个非均匀玻璃形成液体模型,并计算了在其中运动的标记分子的低温行为,该模型表现出与波数相关的自中间散射函数在长时间极限下的拉伸指数衰减。在接近玻璃化转变的温度下,非均匀性在程度上比分子间距大得多,散射函数的时间依赖性从具有大波数的指数$b=1/2$的拉伸指数衰减跨越到具有小波数的$b = 1$的正常扩散行为。早期破笼性$β$松弛和晚期$α$松弛之间存在明显的分离。的散射函数的空间表示表现出一个非常宽的指数(非高斯)尾巴足够大的值的分子位移在所有有限的时间。

英文摘要:

We propose a model of a heterogeneous glass forming liquid and compute the low-temperature behavior of a tagged molecule moving within it. This model exhibits stretched-exponential decay of the wavenumber-dependent, self intermediate scattering function in the limit of long times. At temperatures close to the glass transition, where the heterogeneities are much larger in extent than the molecular spacing, the time dependence of the scattering function crosses over from stretched-exponential decay with an index $b=1/2$ at large wave numbers to normal, diffusive behavior with $b = 1$ at small wavenumbers. There is a clear separation between early-stage, cage-breaking $β$ relaxation and late-stage $α$ relaxation. The spatial representation of the scattering function exhibits an anomalously broad exponential (non-Gaussian) tail for sufficiently large values of the molecular displacement at all finite times.

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