Role of Attractive Interactions in Structure Ordering and Dynamics of Glass-Forming Liquids

A key question in glass physics is what the origin of slow glassy dynamics is. The liquid structure is a natural candidate; however, an apparently severe counterexample has been known. Two model glass-forming liquids, with the standard Lennard–Jones interaction potential and its Weeks–Chandler–Andersen variation without the attractive tail, exhibit very similar structures at the two-body level but drastically different dynamical behaviors in the supercooled states. Here we look at the liquid structure through a (many-body) structural order parameter $\mathrm{\Theta }$ characterizing the packing capability of local particle arrangements. We show that the structures of these two systems seen by $\mathrm{\Theta }$ are actually very different at a many-body level, but, quite surprisingly, the macroscopic structure ($\mathrm{\Theta }$)-dynamics (${\tau }_{\alpha }$) relationships commonly follow a Vogel–Fulcher–Tammann-like function. Furthermore, the mutual information analysis reveals strong local structure-dynamics correlations. Therefore, we conclude that attractive interactions affect the liquid structure in a nonperturbative manner, but a general structural origin of slow dynamics holds for these systems.

Figure 1

Definition of the structural order parameter. (a) A typical local configuration with a central particle, $o$, and its six neighbors. Two neighbors indicated as $i$ and $j$ have a central angle ${\theta }_{ij}^{(1)}$. (b) The reference configuration with the three indicated particles in perfect relative distances with each other, with a central angle ${\theta }_{ij}^{(2)}$. See text for the expression of order parameter $\mathrm{\Theta }$.

Figure 2

Macroscopic structure and dynamics in LJ and WCA systems. (a) Temperature dependence of ${\tau }_{\alpha }$. High-temperature data, above the onset temperature $T_{\mathrm{on}}$ indicated by arrows, are fitted by the Arrhenius law ${\tau }_{\alpha }\sim \exp (\mathrm{\Delta }E/T)$ (solid lines). (b) Temperature dependence of the structural order, $\mathrm{\Theta }$, which shows clear differences between the two systems. Error bars indicate standard derivations. Solids lines are linear fittings to data below $T_{\mathrm{on}}$: $\mathrm{\Theta }-{\mathrm{\Theta }}_0=\kappa (T-T_0)$. See text for the meaning of parameters. $T_{\mathrm{on}}$ from panel (a) are indicated by arrows. The vertical dashed line indicates $T=0.26$ chosen for calculating the pair correlation function $g(r)$, as shown in (c).

Figure 3

Macroscopic relationship between structural order and dynamics. Structure relaxation time ${\tau }_{\alpha }$ is plotted as a function of $1/(\mathrm{\Theta }-{\mathrm{\Theta }}_0)$. Solid lines are fittings to data below $T_{\mathrm{on}}$ (indicated by arrows) according to the VFT-like relation Eq. (1). Inset: Scaling collapse of ${\tau }_{\alpha }/{\tau }_0$ as a function of rescaled structural order $D_2{\mathrm{\Theta }}_0/(\mathrm{\Theta }-{\mathrm{\Theta }}_0)$ below $T_{\mathrm{on}}$.

Figure 4

Microscopic correlation between structural order and dynamics. (a) Self-intermediate scattering function $F_s(k,t)$ of each particle (background) and the whole system (black circles) for LJ system at $T=0.305$. (b)–(d) Spatial distribution of microscopic ${\tau }_{\alpha }$, bare structural order, $\mathrm{\Theta }$, and its coarse graining with $L=5.5$, ${\mathrm{\Theta }}_{\mathrm{CG}}$, respectively. Note that red color indicates faster dynamics or less ordered structures. (e) Joint probability distribution of microscopic relaxation time ${\log }_{10}({\tau }_{\alpha })$ and bare structural order $\mathrm{\Theta }$ (top), as well as that coarse grained with $L=5.5$, ${\mathrm{\Theta }}_{\mathrm{CG}}$ (bottom). (f),(g) MI between microscopic ${\tau }_{\alpha }$ and $\mathrm{\Theta }$ as a function of coarse graining length $L$ for LJ and WCA systems, respectively. $L=0.5$ means without coarse graining. Temperature decreases from red to blue, corresponding to a range of macroscopic ${\tau }_{\alpha }\sim 3$ to 10 000.

Figure 5

Mutual information between microscopic ${\tau }_{\alpha }$ and local potential energy $E$ as a function of coarse graining length $L$ for (a) LJ and (b) WCA systems. Symbols are the same as Figs. 4 and 4. $\mathrm{MI}(\mathrm{\Theta },{\tau }_{\alpha })$ at temperature of macroscopic ${\tau }_{\alpha }\sim 3000$ is plotted as a comparison.