  The structural and interfacial properties of a nanoscopic liquid drops are
assessed by means of mechanical, thermodynamical, and statistical mechanical
approaches that are discussed in detail, including original developments at
both the macroscopic level and the microscopic level of density functional
theory (DFT). We emphasize that any approach, such as classical nucleation
theory, which is based on a purely macroscopic viewpoint does not lead to a
reliable representation when the radius of the drop becomes microscopic. The
so-called mechanical route which corresponds to a molecular-level extension of
the macroscopic theory of elasticity, and is particularly popular in molecular
dynamics simulation, also appears to be unreliable due to the inherent
ambiguity in the definition of the microscopic pressure tensor, an observation
which has been known for decades but is frequently ignored. In this vein, we
propose a non-local mean-field DFT for Lennard-Jones (LJ) fluids to examine
drops of varying size. A comparison of the predictions of our DFT with the
recent simulation data based on a second-order fluctuation analysis [J. G.
Sampayo et al., JCP 132, 141101 (2010)] reveals the consistency of the two
treatments. This observation points out the significance of fluctuation effects
in small drops, in contrast to what one observes in the case of planar
interfaces which are governed by the laws of mechanical equilibrium. A small
negative Tolman length and a non-monotonic behaviour of the surface tension
with the drop radius are predicted for the LJ fluid. Finally, the limits of a
validity of the Tolman approach, the effect of the range of the intermolecular
potential, and the behaviour of bubbles are briefly discussed.
