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