Free energy of critical droplets—from the binodal to the spinodal

Abstract

Arguably, the main challenge of nucleation theory is to accurately evaluate the work of formation of a critical embryo of the new phase, which governs the nucleation rate. In Classical Nucleation Theory (CNT) this work of formation is estimated using the capillarity approximation, which relies on the value of the planar surface tension. This approximation has been blamed for the large discrepancies between predictions from CNT and experiments. In this work, we present a study of the free energy of formation of critical clusters of the Lennard-Jones fluid truncated and shifted at $2.5\sigma$ using Monte Carlo simulations, density gradient theory, and density functional theory. We find that density gradient theory and density functional theory accurately reproduce molecular simulation results of critical droplet sizes and their free energies. The capillarity approximation grossly overestimates the free energy of small droplets. The incorporation of curvature corrections up to second order with the Helfrich expansion greatly remedies this and performs very well for most of the experimentally accessible region. However, it is imprecise for the smallest droplets and largest metastabilities, since it does not account for a vanishing nucleation barrier at the spinodal. To remedy this, we propose a scaling function that uses all relevant ingredients without adding fitting parameters. The scaling function reproduces accurately the free energy of formation of critical droplets for the entire metastability range and all temperatures examined, and deviates from density gradient theory by less than one $\kT$

Does Maxwell's hypothesis of air saturation near the surface of evaporating liquid hold at all spatial scales?

“…The asymptotic structure of the solution of the two models should be similar, and the results obtained in the present paper should make the analysis of the Enskog-Vlasov equation much easier. (vii) Note that, strictly speaking, the surface tension depends on the drop's curvature (Tolman's effect), which can have a profound influence on, say, cavitation (Menzl et al 2016;Magaletti, Gallo & Casciola 2021;Aasen et al 2023;Lamas et al 2023).…”

Special Topic Preface: Nucleation—Current understanding approaching 150 years after Gibbs

“…Aasen et al 43 find good agreement between free energies of droplet formation in the Lennard-Jones fluid obtained from Monte Carlo simulations, gradient theory, and density functional theory. The capillarity approximation significantly overestimates small droplet free energies, but incorporation of curvature corrections up to second order remedies the discrepancy for experimentally accessible situations.…”