Probing Dynamic Heterogeneity and Amorphous Order Using Rotational Dynamics of Rodlike Particles in Supercooled Liquids

Probing dynamic and static correlations in glass-forming supercooled liquids has been a challenge for decades despite extensive research. Dynamic correlation, which manifests itself as dynamic heterogeneity, is ubiquitous in various systems starting from molecular glass-forming liquids, dense colloidal systems to collections of cells. On the other hand, the mere concept of growing many-body static correlations in these dense disordered systems in the supercooled regime remains somewhat elusive. Its existence is still actively debated. We propose a method to extract dynamic and static correlations using rodlike particles as a probe. This method can be implemented in experiments to study the growth of static and dynamic correlations in molecular glass-forming liquids and other soft-matter systems, including biological systems that show glassy dynamics. Finally, we analytically derive the exact form of the distribution of rotational decorrelation time of the probe rod molecules and rationalize the observed log-normal-like distribution reported in previous experimental studies on the dynamics of elongated probe molecules in supercooled glycerol.

Figure 1

(a) Schematic representation of rod particles in the supercooled liquid medium. (b) Evolution of non-normal parameter [${\alpha }_{3D}(t,T)$] for different rod lengths in the 3DKA model at temperature $T=0.50$. Inset of (c): evolution of ${\alpha }_{3D}(t)$ for rods of length $L_{\mathrm{rod}}=2.5$ in the same supercooled liquid model at different temperatures. (c) Variation in peak value of ${\alpha }_{3D}^P$ with rod length in the 3DKA system at different supercooling temperatures. Bottom panels: collapse of ${\alpha }_{2D}^P$ or ${\alpha }_{3D}^P$ obtained by scaling the rod length with appropriate correlation length scale ${\xi }_{\mathrm{rod}}$ for all three systems [3DKA, 3DHP, and 2DMKA from (d) to (f)]. In these plots’ insets, the scaling length scale is compared with ${\xi }_D$ of the parent liquid obtained by FSS of ${\chi }_4^P$ [24]. Both the length scales are found to be in good agreement with each other.

Figure 2

(a) Distribution of FPT for rods of various lengths scaled by the moment of inertia [$I(L_{\mathrm{rod}})$] in the 2DMKA system at temperature $T=1.5$ (high temperature) with one absorbing boundary at ${\varphi }_c=\pi /8$. Note that we use unbounded coordinates for this calculation, i.e., $\varphi \in [-\mathrm{\infty },+\mathrm{\infty }]$. (b) The same distribution with two absorbing boundaries at $\varphi =\pm {\varphi }_c$. The bold line is fit to Eq. (8).

Figure 3

(a) Distribution of unscaled and (b) scaled FPT (scaled with moment of inertia) for rods of various lengths in 3DKA system at temperature $T=2.0$ (high temperature) with absorbing boundary at ${\theta }_c=\pi /8$. Similar scaled distributions at temperature $T=1.0$ and $T=0.5$ (low temperatures) with the same boundary conditions are shown in (c),(d). Solid lines are fit to Eq. (8).

Figure 4

(a) Variation in negative of skewness (${\chi }_{\mathrm{FPT}}$) of distribution, $P[\ln (t)]$ with rod length, where $t$ is the FPT of rod immersed in the 3DKA model liquid at various supercooling temperatures. An increase in skewness with decreasing rod length and increasing supercooling can be clearly seen. (b) The scaling collapse of ${\chi }_{\mathrm{FPT}}$ obtained by scaling rod length with appropriate length scale ${\xi }_{\mathrm{rod}}^S(T)$ to obtain a master curve. (d),(f) The similarly obtained collapses for 3DHP and 2DMKA models, respectively. The obtained length scale is plotted and compared with the ${\xi }_S$ obtained with traditional methods like PTS (3DKA and 2DMKA) and finite-size scaling (FSS) of ${\tau }_{\alpha }$ using block analysis (3DHP) in (c) (3DKA), (e) (3DHP), and in the inset of (f) (2DMKA).

Figure 5

(a) Distribution of Dye molecules’ correlation time in supercooled glycerol for four different temperatures. Data is taken from Ref. [39]. The distribution is rescaled by the mean correlation time. Note the clear signature of a short time shoulder in the distribution at lower temperatures. Inset shows the skewness of the distributions. (b) FPT distribution for a rod of length $2.8$ embedded in the 3DKA model for various temperatures. The dashed line through the data points is the best fit to Ref. [(8)]. The inset shows the skewness of the distribution. The similarity between experimental data and simulation results are very striking.