The two-dimensional Lennard-Jones system: Sublimation, vaporization, and melting

Abstract

The solid–vapor equilibrium line and the liquid–vapor equilibrium line near the melting region for classical two-dimensional systems of particles interacting by Lennard-Jones (12,6) pair potentials are determined from Monte Carlo simulations with 224 particles. Structural and thermodynamic properties are evaluated for homogeneous single phases on both sides of the melting transition. The Monte Carlo results show that a cell model approximation to the solid phase has good accuracy for most of the anharmonic 2D solid conditions of this work. Free energies for solid states are constructed starting from the low temperature quasiharmonic solid; for the 2D liquid states the starting point is the virial expansion for the dilute gas. From these free energies the triple-point melting of the periodically extended 224-particle system is found to be first order and the latent heat of melting is determined. Graphic displays are obtained showing the occurrence of dislocation pairs, voids, particle exchange, and mixed phases. The implementation of the simulation is discussed, including problems of superheating and the achievement of equilibrium.

Thermal excitation in a spatially modulated monolayer solid: Incommensurate xenon/graphite

“…We find the melting of Xe/graphite at the triple point likely is a first-order transition, in agreement with Strandburg's review [16]. We note the possibility that calculations on yet larger samples and carried to even longer times might change this, although our results with N = 78 000 and 312 000 and those of Asenjo et al [15] with N = 36 864 give reduced triple-point temperature and latent heat of melting that lie in the range estimated with an early simulation [30] using N = 224.…”

“…Monte Carlo simulations showed [30] that the lattice constant of monolayer Xe on a structureless substrate can be reproduced by near-analytical approximations [quasiharmonic lattice theory (QHT) and cell models] over the temperature range 0-95 K. Now, we compare the temperature-dependent lattice constant L u (T ) of an unconstrained patch, determined from the MD data for the peaks of S(q), to the results of the following calculations: the classical limit ( → 0) of QHT below 40 K; the SCP-MDW approximation over the temperature range 0-80 K; and the classical cell approximation for 50-95 K. In the temperature ranges of their anticipated applicability, these approximations reproduced the MD results to within about 0.01Å. …”

“…They are estimated to contribute 20 K or less to the Xe/graphite differences, using values [30,41] for the triple-point parameters of the 2D Lennard-Jones (LJ) system. Larher [40] estimated the latent heat of melting at the triple point to be h − h s = 96 K, using Eq.…”

Properties of the two-dimensional heterogeneous Lennard-Jones dimers: An integral equation study

“…Low pressure experiments of krypton adsorption on exfoliated graphite and graphitized carbon black indicated a behavior characteristic of 2D fluids. 3,4 In comparison to the research of 3D [5][6][7][8][9] fluids, 1D 10 and 2D fluids have attracted much less attention. Low dimensional systems have in addition to their interest as simple models for real situations, also important to understand the effect of dimensionality on phase transitions.…”

Lane formation in a system of dipolar microswimmers

“…Given the lower boundary ǫ * ≈ 2.5, it is interesting to make a connection to the equilibrium phase diagram of the 2D LJ fluid: This system has a critical point (gas-liquid condensation) at ρ * c = 0.35 and T * c ≈ 0.46, corresponding to a critical coupling strength ǫ * c ≈ 2.17 [27,28]. The triple point (gasliquid-solid) coupling strength is given as ǫ * t ≈ 2.5 (with corresponding liquid density ρ liquid t 0.6 [27]). From this we can conclude that the non-driven LJ system at ρ * = 0.5 and ǫ * = 2.5 is in a strongly correlated state which is, in fact, thermodynamically unstable, i.e., it lies within the coexistence curve of the gas-liquid transition.…”