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arXiv 1101.2655cond-mat.softcond-mat.stat-mech
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形成玻璃的二元硬球混合物中增长的动态长度尺度的分析

Analysis of a growing dynamic length scale in a glass-forming binary hard-sphere mixture

Elijah Flenner, Min Zhang, Grzegorz Szamel

摘要:

我们研究了一个长度尺度,它表征了在玻璃形成二元硬球混合物的非均匀动力学的空间范围,直到模式耦合体积分数phi_c。首先,我们描述了系统的动态特性。然后,我们利用一种新的方法[物理学评论Lett。105,217801(2010)],以提取和分析在β和α弛豫时间之间的时间范围内的系综独立动态磁化率chi_4(t)和动态相关长度xi(t)。我们发现,在这个时间范围内,动态关联长度遵循与体积分数无关的曲线xi(t)~ ln(t)。对于更长的时间,xi(t)偏离该曲线,并保持恒定,直到我们可以准确确定长度的最大时间。除了先前建立的α弛豫时间tau_alpha和此时的动态相关长度xi(tau_alpha)之间的相关性tau_alpha ~ exp[xi(tau_alpha)]之外,我们还发现了扩散系数D ~ exp[xi(tau_alpha)^theta]的类似相关性,其中theta约为0.6。我们讨论了这些发现的玻璃化转变的不同理论的相关性。

英文摘要:

We examine a length scale that characterizes the spatial extent of heterogeneous dynamics in a glass-forming binary hard-sphere mixture up to the mode-coupling volume fraction phi_c. First, we characterize the system's dynamics. Then, we utilize a new method [Phys. Rev. Lett. 105, 217801 (2010)] to extract and analyze the ensemble independent dynamic susceptibility chi_4(t) and the dynamic correlation length xi(t) for a range of times between the beta and alpha relaxation times. We find that in this time range the dynamic correlation length follows a volume fraction independent curve xi(t) ~ ln(t). For longer times, xi(t) departs from this curve and remains constant up to the largest time at which we can determine the length accurately. In addition to the previously established correlation tau_alpha ~ exp[xi(tau_alpha)] between the alpha relaxation time, tau_alpha, and the dynamic correlation length at this time, xi(tau_alpha), we also find a similar correlation for the diffusion coefficient D ~ exp[xi(tau_alpha)^theta] with theta approximately 0.6. We discuss the relevance of these findings for different theories of the glass transition.

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