Glass Transition in Supercooled Liquids with Medium-Range Crystalline Order

The origin of the rapid dynamical slowdown in glass forming liquids in the growth of static length scales, possibly associated with identifiable structural ordering, is a much debated issue. Growth of medium range crystalline order (MRCO) has been observed in various model systems to be associated with glassy behavior. Such observations raise the question of whether molecular mechanisms for the glass transition in liquids with and without MRCO are the same. In this study we perform extensive molecular dynamics simulations of a number of glass forming liquids and show that the static and dynamic properties of glasses with MRCO are different from those of other glass forming liquids with no predominant local order. We also resolve an important issue regarding the so-called point-to-set method for determining static length scales, and demonstrate it to be a robust method for determining static correlation lengths in glass formers.

Figure 1

Dynamic heterogeneity and MRCO for the 2dKA system. A snapshot of the system with $N=2000$ at $T=0.930$ and $\rho =1.20$ with particles colored according to their local hexatic order parameter $|{\psi }_6^i|$, as indicated in the right side color bar of the figure. The arrows are the displacements of particles calculated over ${\tau }_{\alpha }$ relaxation time starting from this initial configuration.

Figure 2

Top panel: Growth of dynamic and static length scales. (a) Correlation lengths as functions of temperature $T$ for the 2dKA system. Symbols for different quantities are as follows: Green circles for the dynamic length scale ${\xi }_d$ obtained from $S_4(q,{\tau }_{\alpha })$; orange triangles for ${\xi }_d$ obtained from $S_4(q,{\tau }_b)$ [48] (details in the Supplemental Material [15]); Red squares for ${\xi }_d$ calculated from Binder cumulant FSS; blue right triangles for the PTS length scale ${\xi }_{\mathrm{pts}}$; purple lower triangles for the static length scale obtained from FSS of ${\tau }_{\alpha }$; pink diamonds for the static length scale obtained from FSS of the smallest eigenvalue of the Hessian matrix; brown diamonds for the hexatic correlation length ${\xi }_6$. Same colors and symbols are used in (b) and (c). Length scales obtained from FSS, which are known up to a multiplicative constant, have been scaled to match the values obtained from other methods. (b) Correlation lengths as functions of density $\rho$ for the 2dIPL system. (c) Correlation lengths as functions of temperature $T$ for the 2dR10 system. Bottom panel: The $\alpha$-relaxation time (scaled by its value in the infinite size limit) is plotted against the Binder cumulant for different temperatures (densities in the 2dIPL model) and system sizes for 2dKA, 2dIPL, and 2dR10 models (from left to right).

Figure 3

Top left panel: Probability distribution of polydispersity for cavities of different radii. The black vertical line denotes the mean polydispersity of 11%. Inset shows the number of samples required to get the average polydispersity within 2% of the bulk value. Top right panel: Probability distribution of packing fraction. The black vertical line denotes the bulk packing fraction 0.76. Labels for different data sets are the radii of the cavities. Bottom left panel: Comparison of different length scales for the 2dPoly system showing that the corrected PTS length agrees with other static and dynamical length scales computed. Bottom right panel: The $\alpha$-relaxation time (scaled by its value in the infinite size limit) is plotted against the Binder cumulant for different temperatures and system sizes for the 2dPoly model.