Evidence for the role of fluctuations in the thermodynamics of nanoscale drops and the implications in computations of the surface tension

TL;DR

This study investigates how fluctuations influence the thermodynamics of nanoscale liquid drops, revealing that traditional mechanical methods are inadequate for small drops and highlighting the significance of energy fluctuations.

Contribution

The paper demonstrates the importance of energy fluctuations in nanoscale drops and challenges the validity of mechanical surface tension calculations for small droplets.

Findings

Energy fluctuations significantly affect nanoscale drop thermodynamics.

Mechanical surface tension calculations are invalid for small drops.

Surface tension approaches the planar limit at larger drop sizes.

Abstract

Test area deformations are used to analyse vapour-liquid interfaces of Lennard-Jones particles by molecular dynamics simulation. For planar vapour-liquid interfaces the change in free energy is captured by the average of the corresponding change in energy, the leading-order contribution. This is consistent with the commonly used mechanical (pressure tensor) route for the surface tension. By contrast for liquid drops one finds a large second-order contribution associated with fluctuations in energy. Both the first- and second-order terms make comparable contributions, invalidating the mechanical relation for the surface tension of small drops. The latter is seen to increase above the planar value for drop radii of ~8 particle diameters, followed by an apparent weak maximum and slow decay to the planar limit, consistent with a small negative Tolman length.