Johari-Goldstein ß relaxation in glassy dynamics originates from two-scale energy landscape.

Supercooled liquids undergo complicated structural relaxation processes, which have been a long-standing problem in both experimental and theoretical aspects of condensed matter physics. In particular, past experiments widely observed for many types of molecular liquids that relaxation dynamics separated into two distinct processes at low temperatures. One of the possible interpretations is that this separation originates from the two-scale hierarchical topography of the potential energy landscape; however, it has never been verified. Molecular dynamics simulations are a promising approach to tackle this issue, but we must overcome laborious difficulties. First, we must handle a model of molecular liquids that is computationally demanding compared to simple spherical models, which have been intensively studied but show only a slower process: α relaxation. Second, we must reach a sufficiently low-temperature regime where the two processes become well-separated. Here, we handle an asymmetric dimer system that exhibits a faster process: Johari-Goldstein ß relaxation. Then, we employ the parallel tempering method to access the low-temperature regime. These laborious efforts enable us to investigate the potential energy landscape in detail and unveil the first direct evidence of the topographic hierarchy that induces the ß relaxation. We also successfully characterize the microscopic motions of particles during each relaxation process. Finally, we study the correlation between low-frequency modes and two relaxation processes. Our results establish a fundamental and comprehensive understanding of experimentally observed relaxation dynamics in supercooled liquids.

Instantaneous normal modes of glass-forming liquids during the athermal relaxation process of the steepest descent algorithm.

Understanding glass formation by quenching remains a challenge in soft condensed matter physics. Recent numerical studies on steepest descent dynamics, which is one of the simplest models of quenching, revealed that quenched liquids undergo slow relaxation with a power law towards mechanical equilibrium and that the late stage of this process is governed by local rearrangements of particles. These advances motivate the detailed study of instantaneous normal modes during the relaxation process because the glassy dynamics is considered to be governed by stationary points of the potential energy landscape. Here, we performed a normal mode analysis of configurations during the steepest descent dynamics and found that the dynamics is driven by almost flat directions of the potential energy landscape at long times. These directions correspond to localized modes and we characterized them in terms of their statistics and structure using methods developed in the study of local minima of the potential energy landscape.

Non-phononic density of states of two-dimensional glasses revealed by random pinning.

The vibrational density of states of glasses is considerably different from that of crystals. In particular, there exist spatially localized vibrational modes in glasses. The density of states of these non-phononic modes has been observed to follow g(ω) ∝ ω4, where ω is the frequency. However, in two-dimensional systems, the abundance of phonons makes it difficult to accurately determine this non-phononic density of states because they are strongly coupled to non-phononic modes and yield strong system-size and preparation-protocol dependencies. In this article, we utilize the random pinning method to suppress phonons and disentangle their coupling with non-phononic modes and successfully calculate their density of states as g(ω) ∝ ω4. We also study their localization properties and confirm that low-frequency non-phononic modes in pinned systems are truly localized without far-field contributions. We finally discuss the excess density of states over the Debye value that results from the hybridization of phonons and non-phononic modes.

Low-frequency vibrational states in ideal glasses with random pinning.

Glasses exhibit spatially localized vibrations in the low-frequency regime. These localized modes emerge below the boson peak frequency ω_{BP}, and their vibrational densities of state follow g(ω)∝ω^{4} (ω is frequency). Here, we attempt to address how the localized vibrations behave through the ideal glass transition. To do this, we employ a random pinning method, which enables us to study the thermodynamic glass transition. We find that the localized vibrations survive even in equilibrium glass states. Remarkably, the localized vibrations still maintain the properties of appearance below ω_{BP} and g(ω)∝ω^{4}. Our results provide important insight into the material properties of ideal glasses.

Vibrational properties of two-dimensional dimer packings near the jamming transition.

Jammed particulate systems composed of various shapes of particles undergo the jamming transition as they are compressed or decompressed. To date, sphere packings have been extensively studied in many previous works, where isostaticity at the transition and scaling laws with the pressure of various quantities, including the contact number and the vibrational density of states, have been established. Additionally, much attention has been paid to nonspherical packings, and particularly recent work has made progress in understanding ellipsoidal packings. In this work, we study the dimer packings in two dimensions, which have been much less understood than systems of spheres and ellipsoids. We first study the contact number of dimers near the jamming transition. It turns out that packings of dimers have "rotational rattlers," each of which still has a free rotational motion. After correcting this effect, we show that dimers become isostatic at the jamming, and the excess contact number obeys the same critical law and finite-size scaling law as those of spheres. We next study the vibrational properties of dimers near the transition. We find that the vibrational density of states of dimers exhibits two characteristic plateaus that are separated by a peak. The high-frequency plateau is dominated by the translational degree of freedom, while the low-frequency plateau is dominated by the rotational degree of freedom. We establish the critical scaling laws of the characteristic frequencies of the plateaus and the peak near the transition. In addition, we present detailed characterizations of the real space displacement fields of vibrational modes in the translational and rotational plateaus.