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We report an extensive and systematic investigation of the multi-point andmulti-time correlation functions to reveal the spatio-temporal structures ofdynamic heterogeneities in glass-forming liquids. Molecular dynamicssimulations are carried out for the supercooled states of various prototypemodels of glass-forming liquids such as binary Kob-Andersen, Wahnstrom,soft-sphere, and network-forming liquids. First, we quantify the length scaleof the dynamic heterogeneities utilizing the four-point correlation function.The growth of the dynamic length scale with decreasing temperature ischaracterized by various scaling relations that are analogous to the criticalphenomena. We also examine how the growth of the length scale depends upon themodel employed. Second, the four-point correlation function is extended to athree-time correlation function to characterize the temporal structures of thedynamic heterogeneities based on our previous studies. We provide comprehensivenumerical results obtained from the three-time correlation function for theabove models. From these calculations, we examine the time scale of the dynamicheterogeneities and determine the associated lifetime in a consistent andsystematic way. Our results indicate that the lifetime of the dynamicalheterogeneities becomes much longer than the alpha relaxation time determinedfrom a two-point correlation function in fragile liquids. The decouplingbetween 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 fragileliquid. In contrast, the lifetime is shorter than the alpha-relaxation time intetrahedral network-forming strong liquid, even at lower temperatures.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

Multiple length and time scales of dynamic heterogeneities in model  glass-forming liquids: A systematic analysis of multi-point and multi-time  correlations