We report a computer-simulation study of homogeneous gas–liquid nucleation in a Lennard-Jones system. Using umbrella sampling, we compute the free energy of a cluster as a function of its size. A thermodynamic integration scheme is employed to determine the height of the nucleation barrier as a function of supersaturation. Our simulations illustrate that the mechanical and the thermodynamical surfaces of tension and surface tension differ significantly. In particular, we show that the mechanical definition of the surface tension cannot be used to compute this barrier height. We find that the relations recently proposed by McGraw and Laaksonen [J. Chem. Phys. 106, 5284 (1997)] for the height of the barrier and for the size of the critical nucleus are obeyed.

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Computer simulation study of gas–liquid nucleation in a Lennard-Jones system

Canonical molecular dynamics (MD) and Monte Carlo (MC) simulations for liquid/vapor equilibrium in truncated Lennard-Jones fluid have been carried out. Different results for coexistence properties (orthobaric densities, normal and tangential pressure profiles, and surface tension) have been reported in each method. These differences are attributed in literature to different set up conditions, e.g., size of simulation cell, number of particles, cut-off radius, time of simulations, etc., applied by different authors. In the present study we show that observed disagreement between simulation results is due to the fact that different authors inadvertently simulated different model fluids. The origin of the problem lies in details of truncation procedure used in simulation studies. Care has to be exercised in doing the comparison between both methods because in MC calculations one deals with the truncated potential, while in MD calculations one uses the truncated forces, i.e., derivative of the potential. The truncated force does not uniquely define the primordial potential. It results in MD and MC simulations being performed for different potential models. No differences in the coexistence properties obtained from MD and MC simulations are found when the same potential model is used. An additional force due to the discontinuity of the truncated potential at cut-off distance becomes crucial for inhomogeneous fluids and has to be included into the virial calculations in MC and MD, and into the computation of trajectories in MD simulations. The normal pressure profile for the truncated potential is constant through the interface and both vapor and liquid regions only when this contribution is taken into account, and ignoring it results in incorrect value of surface tension.

https://web.mst.edu/~hale/argonMC/References/JCP.1999.Trokhymchuk.LJ.liq.sim.Tc.pots..pdf

Computer simulations of liquid/vapor interface in Lennard-Jones fluids: Some questions and answers

Size dependent interface energy and its applications

We have calculated the free energy of solvation for hard sphere solutes, as large as 20 A in diameter, in two simple-point-charge models of water. These results were obtained using umbrella sampling of ensembles with fixed, ambient temperature and pressure. For the same water models, we have also calculated the surface tension of a liquid−vapor interface at room temperature. Analogous calculations were carried out for three thermodynamic states of the Lennard-Jones (LJ) fluid near liquid−vapor coexistence. For both water and the LJ fluid at the conditions we have simulated, extrapolation of our results suggests that the planar interface between coexisting liquid and vapor phases has the same surface tension as the planar limit of hard sphere solvation. We expect this correspondence to be a general result for fluids at thermodynamic states close to phase coexistence, as measured by the difference in chemical potential between bulk liquid and vapor phases, and far from the critical point. The solvation free...

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Scaling of Hydrophobic Solvation Free Energies

Vapour–liquid equilibria of the Lennard–Jones potential, truncated and shifted at 2.5σ, are studied using molecular dynamics simulations, an attractive option for studying inhomogeneous systems. Comprehensive simulation data are reported for three cases: no interface, a planar interface, and a spherical interface between the coexisting phases, covering a wide range of temperatures. Spherical droplets are also studied for a range of radii between 5 and 16σ. The size dependence of the surface tension, based on the Irving–Kirkwood pressure tensor, and other properties is quantified for spherical interfaces. All simulation results are correlated with a consistent set of empirical equations. A comparison with the results of other authors as well as with experimental data for noble gases and methane is also presented.

https://web.mst.edu/~hale/argonMC/References/Mol.Phys.2005.Vrabek.coexist.LJ.argon.pdf

Comprehensive study of the vapour–liquid coexistence of the truncated and shifted Lennard–Jones fluid including planar and spherical interface properties

The first order curvature correction to the surface tension of a drop is given by Tolman’s length. Up until now, no accurate estimates of this length existed for realistic fluids. Recently Blokhuis and Bedeaux proposed a new relation that expresses Tolman’s length as an integral over the pair distribution function of a planar liquid–vapor interface. We have used this relation to obtain estimates of Tolman’s length from molecular dynamics simulations of a Lennard‐Jones liquid–vapor interface. We found it to be positive and small for a range of temperatures running from the triple‐point temperature to the critical temperature.

C. Bruin

Papers

Molecular dynamics study of the curvature correction to the surface tension