Long-wavelength fluctuations and the glass transition in two dimensions and three dimensions

Abstract

Phase transitions significantly differ between 2D and 3D systems, but the influence of dimensionality on the glass transition is unresolved. We use microscopy to study colloidal systems as they approach their glass transitions at high concentrations and find differences between two dimensions and three dimensions. We find that, in two dimensions, particles can undergo large displacements without changing their position relative to their neighbors, in contrast with three dimensions. This is related to Mermin-Wagner long-wavelength fluctuations that influence phase transitions in two dimensions. However, when measuring particle motion only relative to their neighbors, two dimensions and three dimensions have similar behavior as the glass transition is approached, showing that the long-wavelength fluctuations do not cause a fundamental distinction between 2D and 3D glass transitions.colloidal glass transition | dimensionality | long-wavelength fluctuations | phase transition | two-dimensional physics I f a liquid can be cooled rapidly to avoid crystallization, it can form into a glass: an amorphous solid. The underlying cause of the glass transition is far from clear, although there are a variety of theories (1-3). One recent method of understanding the glass transition has been to simulate the glass transition in a variety of dimensions (including four dimensions or higher) (4-8). Indeed, the glass transition is often thought to be similar in two and three dimensions (9, 10), and in simple simulation cases such as hard particles, one might expect that dimensionality plays no role. As a counterargument, 2D and 3D fluid mechanics are qualitatively quite different (11). Likewise, melting is also known to be qualitatively different in two and three dimensions (12-15).Recent simulations give evidence that the glass transition is also quite different in two and three dimensions (4, 5). In particular, Flenner and Szamel (4) simulated several different glassforming systems in two and three dimensions and found that the dynamics of these systems were fundamentally different in two and three dimensions. They examined translational particle motion (motion relative to a particle's initial position) and bond-orientational motion (topological changes of neighboring particles). They found that, in two dimensions, these two types of motion became decoupled near the glass transition. In these cases, particles could move appreciable distances but did so with their neighbors, so that their local structure changed slowly. In three dimensions, this was not the case; translational and bondorientational motions were coupled. They additionally observed that the transient localization of particles well known in three dimensions was absent in the 2D data. To quote Flenner and Szamel, "these results strongly suggest that the glass transition in two dimensions is different from in three dimensions."In this work, we use colloidal experiments to test dimensiondependent dynamics approaching the glass transition. Colloidal samples at high concen...

Mermin–Wagner fluctuations in 2D amorphous solids

“…On a local scale, Mermin-Wagner fluctuations do not change the cage-escape process, and thus the microscopic mechanism of 2D and 3D glass transitions are not necessarily different. Recent work by Vivek et al using cage-relative intermediate scattering functions support this idea (31), and computer simulations by Shiba et al independently found similar results (32). Fig.…”

Glass transitions may be similar in two and three dimensions, after all

“…New theoretical tools and predictions do emerge, new phenomena are unveiled, and clever experiments are nonetheless carried out. In this vein, the two recent experimental papers in PNAS by Vivek et al (1) and Illing et al (2) convincingly address an issue at the junction of two fundamental questions in glass physics: the role of the dimensionality of space on the glass transition and the possible existence of long-wavelength fluctuations in 2D amorphous solids.…”

“…They are also stimulating as they raise new questions and open avenues for further experimental and numerical investigations. Among the fundamental issues triggered by the studies in Vivek et al and Illing et al (1,2) are the theoretical foundations of these Mermin-Wagner fluctuations in 2D glassformers and the possible interference with other types of fluctuations. As stressed above, the observed glass transition is not a bona fide phase transition and notions such as rigidity and solidity for glasses still require some more robust theoretical underpinning.…”

“…The strength of the soft-matter systems studied in Vivek et al and Illing et al (1,2), with big and slow colloidal particles that one can track in space and time at an individual level, comes with a down side for what concerns glass formation. The slowing down of dynamics with decreasing temperature or increasing concentration cannot be probed over more than four to five orders-of-magnitude in relaxation time (much like computer simulation studies of liquid models).…”

Unveiling Dimensionality Dependence of Glassy Dynamics: 2D Infinite Fluctuation Eclipses Inherent Structural Relaxation

“…For the glass transition from supercooled liquids to amorphous solids, the dimensionality dependence of the fluctuation has become an issue only recently. Gigantic fluctuation in 2D supercooled liquids has been observed that is far stronger than that in their 3D counterparts [10][11][12]. The aim of this Letter is to elucidate the similarity of this fluctuation to that in crystals [13], and also to investigate the heterogeneous dynamics in both 2D and 3D systems.…”