Correlation of Local Order with Particle Mobility in Supercooled Liquids Is Highly System Dependent

We investigate the connection between local structure and dynamical heterogeneity in supercooled liquids. Through the study of four different models, we show that the correlation between a particle’s mobility and the degree of local order in nearby regions is highly system dependent. Our results suggest that the correlation between local structure and dynamics is weak or absent in systems that conform well to the mean-field picture of glassy dynamics and strong in those that deviate from this paradigm. Finally, we investigate the role of order-agnostic point-to-set correlations and reveal that they provide similar information content to local structure measures, at least in the system where local order is most pronounced.

Figure 1

Interpolated histograms of particle mobility. Numbers at the top right indicate Spearman rank correlation coefficients $K$ [45]. The first column shows the correlation between mobility and $n_{\mathrm{LPS}}$ with the LPS defined in the text. The second column shows correlation with $E_i$, the sum of a particle and its neighbors’ pair energies. White dotted lines show the average value of the quantity on the horizontal and vertical axes.

Figure 2

Time dependence of predictability metrics and correlation coefficients as a function of time for four models. Closed symbols correspond to data comparing mobility with $n_{\mathrm{LPS}}$ as in the left-hand column of Fig. 1 and open symbol comparing local energy $E_i$ (defined in text) to mobility, as in the right-hand column of that figure. $K$ is the Spearman rank correlation coefficient [45]. Precision is defined as the percentage of particles in the top (bottom) 2% of $n_{\mathrm{LPS}}$ ($E_i$), which are in the bottom 10% of ${\mu }_i$. Horizontal dashed lines show the result for the precision metrics that would result from random classification of particles as slow.

Figure 3

(a) Cavity overlaps and PSA overlaps (with the value for a bulk system $q_b$ subtracted) indicating ergodic sampling at this cavity size and temperature. The dashed line shows the overlap probability distribution $P(q-q_b)$. (b) On average, cavities containing a large number of LPS centers have high overlap. “Inner” points count only LPSs which are within $R=2.5$ of the center of the cavity. The dashed line shows the average overlap and arrows show the average number of LPS. (c) and (d) show the full data distribution and Spearman rank correlation coefficients [45]. The data in (b) are obtained from (c) and (d) by averaging over vertical slabs of width 3.