Pressure tensor of a spherical interface

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.