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The Tolman length delta [TolmanJ. Chem. Phys. 17, 333 (1949)] measures the extent by which the surface tension of a small liquid drop deviates from its planar value. Despite increasing theoretical attention, debate continues on even the sign of Tolman's length for simple liquids. Recent thermodynamic treatments have proposed a relation between the Tolman length and the isothermal compressibility of the liquid at two-phase coexistence, delta approximately -kappa([script-l])sigma. Here, we review the derivation of this relation and show how it is related to earlier thermodynamic expressions. Its applicability is discussed in the context of the squared-gradient model for the liquid-vapor interface. It is found that the relation is semiquantitatively correct for this model unless one is too close to the critical point.

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.

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In this paper we show how the use of the Irving-Kirkwood expression for the pressure tensor leads to expressions for the pressure difference, the surface tension of the flat interface, and the Tolman length which agree with the expressions found using microscopic sum rules. The use of the Schofield-Henderson expression for the pressure tensor for a particular contour different from the contour that leads to the Irving-Kirkwood expression is found to give incorrect results for the pressure difference and, in particular, also for the Tolman length. The distance between the so-called mechanical surface of tension and the Gibbs dividing surface is found not to be given by Tolman's length. Using an approximate expression for the pair density it is possible to find values for the location of the mechanical surface of tension and for Tolman's length which are in reasonably good agreement with values found by Nijmeijer et al. in molecular dynamics simulations.