CHAPTER 3: Assembly of Hard Spheres in Liquid Water

The assembly of hard spheres in liquid water can be approached from a model Gibbs free energy for a two-step process in which, first, a large cavity is created in an aqueous phase and, second, the individual hard spheres are successively transferred from that aqueous phase to the cavity. In doing so, one is led to consider the fundamental distinction between the solvation of small molecules and of large objects, the physical basis of which is reviewed. It is shown how volume and surface area scalings of distinct contributions to the free energy constitute a driving force towards assembly as soon as a “hydrophobic transfer” term outweighs the entropic cost associated with bringing together the hard spheres interspersed in the aqueous phase into the cavity. On such a basis, a single cluster composed of a fixed number of hard spheres is found to destabilize at sufficiently high and low temperatures, but also at sufficiently high pressures. Implications of these most basic results for a number of problems of physicochemical and biological interest are outlined. These include micelle formation, liquid–liquid phase separation and microstructure in aqueous solutions of amphiphiles and the thermodynamics of protein folding.