Thermodynamically Consistent Adaptation of Scaled Particle Theory to an Arbitrary Hard-Sphere Equation of State

Abstract

Scaled particle theory (SPT) is adapted to an arbitrary hard-sphere equation of state (EOS) while utilizing an SPT interpolation function that satisfies all the exact conditions of SPT and, as such, is thermodynamically consistent. The new modification of SPT is tailored to predict with high accuracy the reversible work of forming a cavity in a hard-sphere fluid, but it also estimates the surface tension and excess surface adsorption. The application of additional SPT conditions also provides estimates of the first two derivatives of the hard-sphere radial distribution function (RDF) at contact. When various accurate equations of state are used, in particular, the Carnahan−Starling EOS, the resulting work of cavity formation is nearly identical to accurate Monte Carlo simulation data and the predictions of the recent SPT6 [Heying and Corti, J. Phys. Chem. B 2004, 108, 19756]. The estimates of the surface tension and surface adsorption at moderate to high packing fractions deviate somewhat from both previous theoretical techniques and the simulation. Meanwhile, EOS-based predictions of the initial slope of the RDF are very close to simulation estimates. Predictions of the initial curvature, like those of SPT6, deviate from simulation, but not drastically so. The overall accuracy of our version of SPT demonstrates that a thermodynamically consistent modification of SPT provides correct predictions of the work of cavity formation and is, therefore, suitable for use as the ideally repulsive reference state in various solvation theories of liquids.