Gas-liquid nucleation in a two dimensional system

We study the nucleation of liquid phase from a supersaturated vapor in two dimensions, where the particles interact through Lennard-Jones (LJ) pairwise potential. Using different Monte Carlo simulation methods, we calculate the free energy barrier for nucleation, the line tension, and bulk densities of equilibrium liquid and vapor phases, and also investigate the size and shape of the critical nucleus. The study is carried out at an intermediate level of supersaturation (away from the spinodal limit). In two dimensions, a surprisingly large cutoff (rc ≥ 7.0σ, σ is the diameter of LJ particles) in the truncation of the LJ potential is required to obtain converged results. A lower cutoff [typically 2.5σ which is generally sufficient in three dimensional (3D) studies] leads to a substantial error in the values of the line tension, nucleation barrier, and characteristics of the critical cluster. It is found that in two dimensions, the classical nucleation theory (CNT) fails to provide a reliable estimate of the free energy barrier. It underestimates the barrier by as much as 50% at the saturation ratio S = 1.1 (defined as S = P/PC, where PC is the coexistence pressure) and at the reduced temperature T* = 0.427 (defined as T* = kBT/ε, where ε is the depth of the potential well). Interestingly, CNT has been found to overestimate the nucleation free energy barrier in 3D systems near the triple point. In fact, the agreement of the calculated nucleation rate with CNT is much worse in two dimensions than in three dimensions. The reason for the inadequacy of the CNT can be attributed to the noncircular nature of the critical clusters. Although the shape becomes increasingly circular and the clusters become more compact with increase in cutoff radius, an appreciable noncircular nature remains even without any cutoff to make the simple CNT inaccurate