Assessing the role of static length scales behind glassy dynamics in polydisperse hard disks

Abstract

The possible role of growing static order in the dynamical slowing down toward the glass transition has recently attracted considerable attention. On the basis of random first-order transition theory, a new method to measure the static correlation length of amorphous order, called "point-to-set" (PTS) length, has been proposed and used to show that the dynamic length grows much faster than the static length. Here, we study the nature of the PTS length, using a polydisperse hard-disk system, which is a model that is known to exhibit a growing hexatic order upon densification. We show that the PTS correlation length is decoupled from the steeper increase of the correlation length of hexatic order and dynamic heterogeneity, while closely mirroring the decay length of two-body density correlations. Our results thus provide a clear example that other forms of order can play an important role in the slowing down of the dynamics, casting a serious doubt on the order-agnostic nature of the PTS length and its relevance to slow dynamics, provided that a polydisperse hard-disk system is a typical glass former.glass transition | structural length scales | pinning | hexatic order | slow dynamics W hen we supercool a liquid while avoiding crystallization, dynamics becomes heterogeneous (1, 2) and slows down significantly toward the glass transition, below which a system becomes a nonergodic state. Now there is a consensus that this slowing down accompanies the growth of dynamical correlation length (3). Several different physical scenarios have been proposed, yet the origin is still a matter of serious debate: although some scenarios describe the glass transition as a purely kinetic phenomenon (4), others posit a growing static order (5) or a loss of configurational entropy (6) behind dynamical slowing down. Among this last category, we will focus here on two distinct approaches. The first one is random first-order transition (RFOT) theory (7-9), which is based on a finite dimensional extension of mean-field models with an exponentially large number of metastable states. The second approach, recently proposed by some of us (10, 11), ascribes the growth of the dynamical correlation length with the corresponding growth of the static correlation length. Here, we focus on these two scenarios based on static order and consider which is more relevant to the origin of glassy slow dynamics, using a simple model glass former, 2D polydisperse hard disks (12, 13).In RFOT, metastable states are thought to have amorphous order, whose correlation length diverges toward the ideal glass transition point. It was recently suggested that the so-called point-to-set (PTS) length, which is the correlation length of amorphous order, can be extracted by pinning a finite fraction of particles and studying the dependence of the overlap function on the pinning particle concentration. According to the RFOT theory, amorphous order develops in any glass-forming liquids and this method is thought to be able to pick up the static correlation length whatever...

Deconstructing the glass transition through critical experiments on colloids

“…Moreover, ξ 6 grows much faster compared to other static lengths, such as the point-to-set length for various pinning geometries and the two-point for a simulated 2D hard sphere liquid with polydispersity of 11%. Adapted from [301].…”

“…The method is simple enough to apply to experimental systems, particularly since it only requires time-averaged snapshots of particle configurations, which can easily be obtained from video microscopy experiments. It would be most interesting to compute this length for a slightly polydisperse hard sphere system, for which Tanaka and coworkers have shown that ξ 6 grows much faster than ξ P T S [301].…”

Nonclassical pathways of crystallization in colloidal systems

“…However, on approaching the glass transition, the icosahedral order does not grow in size, whereas bond-orientational order grows [5,60]. A link between slow dynamics and regions of extended bond-orientational order has been found both in polydisperse hard spheres [5,12,60,68], hard disks [67,92,93], and colloidal ellipsoids [94].…”

Understanding the dynamics of glass-forming liquids with random pinning within the random first order transition theory

“…There is a recent controversy about the usefulness of the PTS length scale for two-dimensional glass forming system with short-range bond-orientational order [31]. It is claimed that the PTS correlation length is insensitive to the growth of structural order in system with pronounced short-range bond-orientational order and hence the length scale associated with structural order, which governs the relaxation time, is not the same as the PTS length scale.…”