Excess densities and equimolar surfaces for spherical cavities in water

For hard spheres with a radius up to 10 A in TIP4P water under ambient conditions, the author studies how the excess number of molecules at the accessible surface depends on the radius of the cavity. Simulation results derived from excess volumes are discussed in terms of radial distribution functions (rdfs), which compare well with extended simple point charge and theoretical rdfs from the literature. The excess number of molecules at the accessible surface inserted in the expression which refers to an arbitrary dividing surface enables one to find the position of the equimolar surface. The surface tension corresponding to this dividing surface was obtained from values of the free energy of cavity formation. For radii in the range of the simulation data, its behavior with curvature is quite different from that usually shown in the literature. A model, which describes how the excess number of molecules at the accessible surface changes with the radius, is discussed in the large length limit by examining consistent rdfs described by a simple analytical form. The inclusion in the model of a logarithmic term has also been considered. Comparison with theoretical results from the literature shows a good agreement for a cavity with a radius of 20 A. For a radius of 100 A and beyond, the model predicts instead sharper density profiles. Such differences have a poor effect on the surface tension at the equimolar surface.