An expression for the difference in pressure between a liquid drop in equilibrium with its vapor ⌬p = p ᐉ − p v is derived from previous expressions for the components of the Irving-Kirkwood pressure tensor. This expression, as well as the bulk values of the pressure tensor, is then evaluated via molecular dynamics simulations of particles interacting through a truncated Lennard-Jones potential. We determine the Tolman length ␦ from the dependence of ⌬p on the equimolar radius. We determine the Tolman length to be ␦ = −0.10Ϯ 0.02 in units of the particle diameter. This is the first determination of the Tolman length for liquid droplets via the pressure tensor route through computer simulation that is negative, in contrast to all previous results from simulation, but in agreement with results from density functional theory. In addition, we study the planar liquid-vapor interface and observe a dependence of the physical properties of the system on the system size, as measured by the surface area.

The interfacial tension of the planar interface and rigidity constants are determined for a simple liquid-vapor interface by means of a lattice-gas model. They are compared with results from the van der Waals model and from an analytical expansion around the critical point. The three approaches are in agreement in the regions where these theories apply.

We use molecular dynamics simulations of particles interacting through a truncated Lennard-Jones potential to study the surface properties of the curved liquid-vapor interface. We determine the Tolman length ␦, investigate its critical behavior, and provide first results for the rigidity constants of bending, k, and of Gaussian curvature, k . The rigidity constant of bending, determined at three different temperatures, is found to be positive and of the order of one-half k B T. The rigidity constant of Gaussian curvature, determined at a single temperature, is of the same order of magnitude.

It is argued that to arrive at a quantitative description of the surface tension of a liquid drop as a function of its inverse radius, it is necessary to include the bending rigidity k and Gaussian rigidityk in its description. New formulas for k andk in the context of density functional theory with a non-local, integral expression for the interaction between molecules are presented. These expressions are used to investigate the influence of the choice of Gibbs dividing surface and it is shown that for a onecomponent system, the equimolar surface has a special status in the sense that both k andk are then the least sensitive to a change in the location of the dividing surface.Furthermore, the equimolar value for k corresponds to its maximum value and the equimolar value fork corresponds to its minimum value. An explicit evaluation using a short-ranged interaction potential between molecules, shows that k is negative with a value around minus 0.5-1.0 k B T and thatk is positive with a value which is a bit more than half the magnitude of k. Finally, for dispersion forces between molecules, we show that a term proportional to log(R)/R 2 replaces the rigidity constants and we determine the (universal) proportionality constants.

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