Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: A systematic analysis of multi-point and multi-time correlations
We report an extensive and systematic investigation of the multi-point and multi-time correlation functions to reveal the spatio-temporal structures of dynamic heterogeneities in glass-forming liquids. Molecular dynamics simulations are carried out for the supercooled states of various prototype models of glass-forming liquids such as binary Kob?Andersen, Wahnstrom, soft-sphere, and network-forming liquids. While the first three models act as fragile liquids exhibiting super- Arrhenius temperature dependence in their relaxation times, the last is a strong glass-former exhibiting Arrhenius behavior. First, we quantify the length scale of the dynamic heterogeneities utilizing the four-point correlation function. The growth of the dynamic length scale with decreasing temperature is characterized by various scaling relations that are analogous to the critical phenomena. We also examine how the growth of the length scale depends upon the model employed. Second, the four-point correlation function is extended to a three-time correlation function to characterize the temporal structures of the dynamic heterogeneities based on our previous studies [K. Kim and S. Saito, Phys. Rev. E 79, 060501(R) (2009); J. Chem. Phys. 133, 044511 (2010)]. We provide comprehensive numerical results obtained from the three-time correlation function for the above models. From these calculations, we examine the time scale of the dynamic heterogeneities and determine the associated lifetime in a consistent and systematic way. Our results indicate that the lifetime of the dynamical heterogeneities becomes much longer than the alpha-relaxation time determined from a two-point correlation function in fragile liquids. The decoupling between the two time scales is remarkable, particularly in supercooled states, and the time scales differ by more than an order of magnitude in a more fragile liquid. In contrast, the lifetime is shorter than the alpha-relaxation time in tetrahedral network-forming strong liquid, even at lower temperatures.

Kim & Saito, J. Chem. Phys. Special Topic on Glass Transition, 138, 12A506 (2013).

Multiple time scales hidden in heterogeneous dynamics of glass-forming liquids

A multitime probing of density fluctuations is introduced to investigate hidden time scales of heterogeneous dynamics in glass-forming liquids. Molecular-dynamics simulations for simple glass-forming liquids are performed and a three-time correlation function is numerically calculated for general time intervals. It is demonstrated that the three-time correlation function is sensitive to the heterogeneous dynamics and that it reveals couplings of correlated motions over a wide range of time scales. Furthermore, the time scale of the heterogeneous dynamics tau_{hetero} is determined by the change in the second time interval in the three-time correlation function. The present results show that the time scale of the heterogeneous dynamics tau_{hetero} becomes larger than the alpha-relaxation time at low temperatures and large wavelengths. We also find a dynamical scaling relation between the time scale tau_{hetero} and the length scale xi of dynamiccal heterogeneity as tau_{hetero} ~ xi^{z} with z=3.

Three-time correlation function of density fluctuation

Temperaturedependence of lifetime of heterogeneous dynamics

Kim & Saito, Phys. Rev. E 79, 060501(R) (4 pages) (2009).

Slow dynamics in random media: Crossover from glass to localization transition

We study slow dynamics of particles moving in a matrix of immobile obstacles using molecular-dynamics simulations. The glass transition point decreases drastically as the obstacle density increases. At higher obstacle densities, the dynamics of mobile particles changes qualitatively from glass-like to a Lorentz-gas-like relaxation. This crossover is studied by density correlation functions, nonergodic parameters, mean square displacement, and nonlinear dynamic susceptibility. Our finding is qualitatively consistent with the results of recent numerical and theoretical studies on various spatially heterogeneous systems. Furthermore, we show that slow dynamics is surprisingly rich and sensitive to obstacle configurations. Especially, the reentrant transition is observed for a particular configuration, although its origin is not directly linked to the similar prediction based on the mode-coupling theory.

Kim, Miyazaki, & Saito, Europhys. Lett. 88, 36002 (5 pages) (2009).