Structure-Dynamics Correlation and Its Link to Fragility and Dynamic Heterogeneity

TL;DR

The study investigates whether fragility universally governs structure–dynamics coupling in glass-formers by analyzing LJ, WCA, and softened LJ $(q,p)$ models across densities. It uses a mean-field based structural order parameter (SOP), macroscopic and microscopic activation barriers, and isoconfigurational ensembles to dissect structure–dynamics correlations. The results show that macroscopic barrier slopes correlate with fragility in LJ/WCA, but microscopic barrier slopes more closely track structure–dynamics coupling, which itself correlates with mobility-contrast rather than spatial correlation length; two systems with maximal coupling (LJ at $\rho=1.1$ and $(8,5)$) differ in fragility yet share broad mobility distributions and high non-Gaussianity, underscoring a decoupling from $\chi_4$. Dynamics near the spinodal and enthalpy-dominated regimes emerge as key drivers of heterogeneity, challenging the view that fragility alone dictates structure–dynamics coupling. Overall, the work highlights multiple facets of dynamic heterogeneity and cautions against assuming a universal link between fragility, $\chi_4$, and structure–dynamics correlations.

Abstract

Understanding the connection between structure, dynamics, and fragility, the rate at which the relaxation time grows with decreasing temperature, is central to unravelling the glass transition. Fragility is often associated with dynamic heterogeneity, implying that if structure influences dynamics, more fragile systems should exhibit stronger structure dynamics correlations. In this study, we test the generality of this assumption using: Lennard Jones (LJ) and Weeks Chandler Andersen (WCA) systems, where fragility is tuned via density, and a modified LJ (q,p) system, where fragility is varied by changing the potential softness. We define a structural order parameter based on a mean field caging potential and analyse energy barriers at both macroscopic and microscopic levels. While the macroscopic free energy barrier slope correlates with fragility, the microscopic free energy barrier does not show a consistent trend. Instead, it exhibits a strong correlation with a structure dynamics correlation measure obtained from isoconfigurational ensemble simulations. Interestingly, the two systems showing the highest structure dynamics correlation, LJ at rho = 1.1 and the (8,5) model, are respectively the least and most fragile within their classes. These systems exhibit broad mobility distributions, large non Gaussian parameters, yet low four point susceptibilities, suggesting a decoupling between spatial correlation length and mobility contrast. Both systems lie in the enthalpy dominated regime and are close to the spinodal, pointing to mechanical instability as a source of heterogeneity. Our results reveal that structure dynamics correlation is more closely linked to the contrast in individual particle mobility than to the spatial extent of dynamic correlations that typically scale with fragility.

Figures (16)

• Figure 1: Left Panels: Macroscopic free energy barrier, $\Delta E^{\text{ma}}$, plotted against the inverse macroscopic structural order parameter, $\beta\Phi$, for three sets of systems: (a)LJ and (c)WCA, each examined at four different densities, and (e) modified LJ $(q,p)$ system. Right Panels: The inverse activation energy $1/\Delta E^{ma}$ plotted against $1/\Delta((\beta\phi)^{-1})$ for the same systems. The slope of the linear fits yields the $B'/A'$ values used in the fragility analysis(see Fig.\ref{['Fig_fragility']}). The colour coding in the right panels matches that of the left panels.
• Figure 2: Left Panels:Microscopic free energy barrier, $\Delta E$, versus the inverse microscopic structural order parameter, $\beta\phi$, for three sets of systems: (b)LJ and (d)WCA, each examined at four different densities, and (f) modified LJ $(q,p)$ system. Right Panels:Temperature dependence of both the macroscopic structural order parameter, $(\beta\Phi)^{-1}$, (closed symbols) and the average microscopic structural order parameter $\langle(\beta\phi)^{-1}\rangle$,(open symbols) for the same systems. Dotted lines represent linear fits used to extract slope parameters for further analysis. The colour coding in the left panels matches that of the right panels.
• Figure 3: Master plot of the VFT equation w.r.t SOP, (Eq.\ref{['vft_sop']}) for all the systems—LJ and WCA at four different densities, and modified LJ $(q,p)$ system. The inset displays the corresponding master of the VFT equation with respect to temperature T (Eq.\ref{['vft_T']}). The collapse of the data confirms the validity of the equations and the consistency of the extracted VFT parameters, as listed in Table I.
• Figure 4: The main panel displays $\gamma T_{\mathrm{VFT}}$ plotted against $K_{\mathrm{VFT}}$ for three sets of systems: LJ, WCA, and modified LJ $(q,p)$ system. Each set exhibits a clear linear relationship, indicating a consistent correlation between the parameters. Inset: The scaled slope of the macroscopic free energy barrier plot, $B'/A'$, derived from the $1/\Delta E^{\mathrm{ma}}$ versus $1/\Delta((\beta\Phi)^{-1})$ plot in the right panels of Fig.\ref{['Fig_macro']}, is plotted against $\gamma T_{\mathrm{VFT}}$. All data points lie on the $y = x$ line, demonstrating that the two quantities are numerically identical, validating our analysis.
• Figure 5: Left panels: Microscopic free energy barrier, $\Delta E$, plotted as a function of inverse microscopic structural order parameter, $1/\Delta((\beta\phi)^{-1})$, for three sets of systems: (a)LJ and (c)WCA, each examined at four different densities, and (e) modified LJ $(q,p)$ system. Right panels: Scaled microscopic free energy barrier, $\Delta E/A$, plotted against $1/\Delta((\beta\phi)^{-1})$ for the same systems shown in the left panels. The colour coding in the right panels matches that of the left panels.