Quantitative relations between nearest-neighbor persistence and slow heterogeneous dynamics in supercooled liquids

Using molecular dynamics simulations of a binary Lennard-Jones model of glass-forming liquids, we examine how the decay of the normalized neighbor-persistence function CB(t), which decays from unity at short times to zero at long times as particles lose the neighbors that were present in their original first coordination shell, compares with those of other, more conventionally utilized relaxation metrics. In the strongly non-Arrhenius temperature regime below the onset temperature TA, we find that CB(t) can be described using the same generic double-stretched-exponential functional form that is often utilized to fit the self-intermediate scattering function S(q, t) of glass-forming liquids in this regime. The ratio of the bond lifetime τbond associated with CB(t)'s slower decay mode to the α-relaxation time τα varies appreciably and non-monotonically with T, peaking at τbond/τα ≃ 45 at T ≃ Tx, where Tx is a crossover temperature separating the high- and low-temperature regimes of glass-formation. In contrast, τbond remains on the order of the overlap time τov (the time interval over which a typical particle moves by half its diameter), and the peak time τχ for the susceptibility χB(t) associated with the spatial heterogeneity of CB(t) remains on the order of τimm (the characteristic lifetime of immobile-particle clusters), even as each of these quantities varies by roughly 5 orders of magnitude over our studied range of T. Thus, we show that CB(t) and χB(t) provide semi-quantitative spatially-averaged measures of the slow heterogeneous dynamics associated with the persistence of immobile-particle clusters.