The excess equimolar radius of liquid drops

TL;DR

This study investigates the curvature dependence of surface tension in liquid drops by analyzing the excess equimolar radius through molecular dynamics simulations, providing insights into its magnitude and methodological considerations.

Contribution

It introduces the excess equimolar radius as a practical measure for curvature effects and critically discusses previous conflicting findings and potential inaccuracies.

Findings

Excess equimolar radius and Tolman length are smaller than sigma/2.

Molecular dynamics simulations cover radii from 4 to 33 sigma.

Methodological critique of previous approaches.

Abstract

The curvature dependence of the surface tension is related to the excess equimolar radius of liquid drops, i.e., the deviation of the equimolar radius from that defined with the macroscopic capillarity approximation. Based on the Tolman [J. Chem. Phys. 17, 333 (1949)] approach and its interpretation by Nijmeijer et al. [J. Chem. Phys. 96, 565 (1991)], the surface tension of spherical interfaces is analysed in terms of the pressure difference due to curvature. In the present study, the excess equimolar radius, which can be obtained directly from the density profile, is used instead of the Tolman length. Liquid drops of the truncated-shifted Lennard-Jones fluid are investigated by molecular dynamics simulation in the canonical ensemble, with equimolar radii ranging from 4 to 33 times the Lennard-Jones size parameter sigma. In these simulations, the magnitudes of the excess equimolar radius and the Tolman length are shown to be smaller than sigma/2. Other methodical approaches, from which mutually contradicting findings have been reported, are critically discussed, outlining possible sources of inaccuracy.