Thermodynamic properties of low-dimensional (D < 3) Lennard-Jones fluids

Abstract

Molecular dynamics simulations are conducted to explore the thermodynamic properties of one-dimensional (1D) and two-dimensional (2D) Lennard-Jones (LJ) fluids. For this purpose, analytical long-range corrections are derived for the LJ potential up to five spatial dimensions. In 1D, the investigation addresses a hypothetical phase transition, which is theoretically only possible for infinitely long-ranged interactions. Despite employing a large cut-off radius and long-range corrections, no indication of such a transition is observed in terms of pressure, internal energy or chemical potential, which suggests that the dispersive $r^{-6}$ attraction of the LJ potential decays too rapidly. In 2D, thermodynamic properties are sampled over wide temperature and density ranges and used to develop an equation of state that adequately describes the vapor-liquid equilibrium, also near the critical point. Furthermore, the isotropic-hexatic phase transition in 2D is investigated. It is focused on two temperatures, applying finite-size scaling of the Helmholtz energy barrier. At $T=3$, a first-order phase transition is found, but a continuous transition occurs at $T=30$, confirming KTHNY theory. Several thermodynamic properties are studied around the isotropic-hexatic phase transition at those two temperatures.