The formation of a cavity in water: Changes of water distribution and prediction of the excess chemical potential of a hard-sphere solute under increasing pressure

This work deals with the formation of a spherical cavity in water along the isotherm at 298 K. A striking effect of increasing pressure was found on the radial distribution functions obtained by Monte Carlo simulations, with significantly different behaviors observed when increasing the cavity radius at 8000 atm and 1 atm. At a fixed cavity radius, a pressure increase up to 10,000 atm leads to increased hydration structure. At a constant high pressure, structure is maintained even increasing the cavity radius, while it is lost at atmospheric pressure. Particular focus is on the value at contact, G(r), the central quantity in Scaled Particle Theory that is related to the derivative with respect to the radius of the work required to form the cavity. Within the limit of very small radii, exact conditions were applied to these two quantities. This allowed us to readily determine, at any pressure along the isotherm, the parameters of a simple model used to compute the excess chemical potential associated with the hydration of a hard sphere. This was made possible thanks to heuristic models used to describe how the number density of water changes along the isotherm and how the second moment of water distribution depends on the first moment. Use was also made of additional information on a cavity of molecular size. Apart from the dependence on pressure of hydrophobic solvation, this work also concerns calculation of the so-called cavitation contribution to the free energy of solvation when this is computed within implicit solvent models.