On the use of multiple interpolation functions in scaled particle theory to improve the predictions of the properties of the hard-sphere fluid.

We present a modification to a previously proposed method of adapting scaled particle theory (SPT) to an arbitrary hard-sphere equation of state that satisfies a large number of exact SPT conditions, including thermodynamic consistency. By introducing a set of functions to interpolate the density of hard-spheres centers at the cavity surface, a broad range of hard-sphere properties, in particular the planar surface tension and related properties, are predicted with high accuracy as compared to simulation data. Similarly accurate results are obtained when this modified interpolation scheme is incorporated into a self-consistent version of SPT, i.e., an equation of state is a predicted output of the method. Hence, SPT is now able to closely match the surface thermodynamic properties of the hard-sphere fluid either without using any adjustable parameters or by simply setting the pressure and chemical potential via a reliable equation of state. We also consider other interpolation schemes, some of which better represent certain exact relations that can be derived within SPT. The limited success of these more rigorous approaches provides insights into the various trade-offs between the simplicity and rigor of the chosen interpolation method, as well as the accuracy of the results, that arise in any (inexact) version of SPT.