Formulas, analogous to the Triezenberg-Zwanzig expression for the surface tension of a planar interface, are presented for the Tolman length, the bending rigidity, and the rigidity constant... Show moreFormulas, analogous to the Triezenberg-Zwanzig expression for the surface tension of a planar interface, are presented for the Tolman length, the bending rigidity, and the rigidity constant associated with Gaussian curvature. These expressions feature the Ornstein-Zernike direct correlation function and are derived from considering the deformation of a liquid drop in the presence of an external field. This approach is in line with the original analysis by Yvon [in Proceedings of the IUPAP Symposium on Thermodynamics, Brussels, 1948]. It is shown that our expressions reduce to previous results from density functional theory when a mean-field approximation is made for the direct correlation function. We stress the importance of the form of the external field used and show how the values of the rigidity constants depend on it Show less
An expression for the difference in pressure between a liquid drop in equilibrium with its vapor Deltap=p([script-l])-p(v) is derived from previous expressions for the components of the Irving... Show moreAn expression for the difference in pressure between a liquid drop in equilibrium with its vapor Deltap=p([script-l])-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 delta from the dependence of Deltap on the equimolar radius. We determine the Tolman length to be delta=-0.10+/-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. Show less
