Dynamic entropy as a measure of caging and persistent particle motion in supercooled liquids

Abstract

The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature T(c). A number of methods exist for estimating the entropy of dynamical systems, and we utilize an approximation based on calculating the mean first-passage time (MFPT) for particle displacement because of its tractability and its accessibility in real and simulation measurements. The MFPT dynamic entropy S(epsilon) is defined as equal to the inverse of the average first-passage time for a particle to exit a sphere of radius epsilon. This measure of the degree of chaotic motion allows us to identify characteristic time and space scales and to quantify the increasingly correlated particle motion and intermittency occurring in supercooled liquids. In particular, we identify a "cage" size defining the scale at which the particles are transiently localized, and we observe persistent particle motion at intermediate length scales beyond the scale where caging occurs. Furthermore, we find that the dynamic entropy at the scale of one interparticle spacing extrapolates to zero as the mode-coupling temperature T(c) is approached.

Local polymer dynamics under strong connectivity constraints: The dendrimer case

“…39 In the case of glass-forming liquids similar mechanisms assuming spatially correlated motion in localized dimensions have also been described. 12,43 As is pointed out in Figs. 3͑a͒-3͑c͒ by arrows, at temperatures above the estimated T g 's and for all the examined models ͗⌬r 2 ͑t * ͒͘ assumes ͑within a small margin indicated by the hatched areas͒ an almost constant value of Ϸ6 Å 2 .…”

Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid

“…Thus the structural relaxation of the liquid appears to be highly cooperative in the spirit of Adam and Gibbs, but where different subvolumes of the liquid are able to relax only after other subvolumes relax. This will be further explored in a separate publication [49].…”

Relationship between dynamical heterogeneities and stretched exponential relaxation

“…This is identical to the first passage time, in the parlance of Allegrini et al [18], but differs formally from the waiting time of Doliwa and Heuer [19] and Denny et al [20] which focuses on hops between energy basins. We say that particle i is trapped as long as its displacement…”

“…While the focus of Ref. [18] is on the inertial regime, which takes place as small distance, on the order of 0.1 atomic radius, we are interested in the atomic displacement leading to a change in the configuration. Figure 4(a) also shows in inset that the trap-time distribution is exponential at the temperature well above the melting point (T m = 0.70 ± 0.05) and its long-time tail well agrees with a stretched exponential fit with β 0 ≈ 0.71 in the supercooled regime.…”

“…Numerically, dynamical heterogeneities have been studied using a wide range of criteria tied various aspects of this feature [5,16,17]. Recently, however, some groups have focused on the renewal or mean first-passage time (MFPT) [18] and the waitingtime distribution (WTD) which provide some link to the structure of the energy landscape [19,20].…”