Beyond the Van Der Waals loop: What can be learned from simulating Lennard-Jones fluids inside the region of phase coexistence

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Abstract
As a rule, mean-field theories applied to a fluid that can undergo a transition from saturated vapor at density ρυ to a liquid at density ρℓ yield a van der Waals loop. For example, isotherms of the chemical potential μ(T,ρ) as a function of the density ρ at a fixed temperature T less than the critical temperature Tc exhibit a maximum and a minimum. Metastable and unstable parts of the van der Waals loop can be eliminated by the Maxwell construction. Van der Waals loops and the corresponding double minimum potentials are mean-field artifacts. Simulations at fixed μ=μcoex for ρυ<ρ<ρℓ yield a loop, but for sufficiently large systems this loop does not resemble the van der Waals loop and reflects interfacial effects on phase coexistence due to finite size effects. In contrast to the van der Waals loop, all parts of the loop found in simulations are thermodynamically stable. The successive umbrella sampling algorithm is described as a convenient tool for seeing these effects. It is shown that the maximum of the loop is not the stability limit of a metastable vapor but signifies the droplet evaporation-condensation transition. The descending part of the loop contains information on Tolman-like corrections to the surface tension, rather than describing unstable states.

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