Glass transitions in 1, 2, 3, and 4 dimensional binary Lennard-Jones systems

TL;DR

This study uses simulations to explore how binary Lennard-Jones systems in one to four dimensions undergo glass transitions, revealing dimensional effects on hysteresis, structure, and crystallization difficulty.

Contribution

It provides the first systematic analysis of dimensional dependence of glass transitions in binary Lennard-Jones systems through detailed simulations.

Findings

Glass transitions observed in 2D, 3D, and 4D systems as hysteresis.

Hysteresis area and height follow power-law dependence on scanning rate.

Crystallization becomes harder as dimensionality increases.

Abstract

We investigate the calorimetric liquid-glass transition by performing simulations of a binary Lennard-Jones mixture in one through four dimensions. Starting at a high temperature, the systems are cooled to T=0 and heated back to the ergodic liquid state at constant rates. Glass transitions are observed in two, three and four dimensions as a hysteresis between the cooling and heating curves. This hysteresis appears in the energy and pressure diagrams, and the scanning-rate dependence of the area and height of the hysteresis can be described by power laws. The one dimensional system does not experience a glass transition but its specific heat curve resembles the shape of the $D\geq 2$ results in the supercooled liquid regime above the glass transition. As $D$ increases, the radial distribution functions reflect reduced geometric constraints. Nearest-neighbor distances become smaller with increasing $D$ due to interactions between nearest and next-nearest neighbors. Simulation data for the glasses are compared with crystal and melting data obtained with a Lennard-Jones system with only one type of particle and we find that with increasing $D$ crystallization becomes increasingly more difficult.