  Hydrophobic hydration plays a crucial role in self-assembly processes over
multiple length-scales, but the extrapolation of molecular-scale models to
larger length-scale hydration phenomena is sometimes not warranted.
Scaled-particle theories are based upon an interpolative view of that issue. We
revisit the scaled-particle theory proposed thirty years ago by Stillinger,
adopt a practical generalization, and consider the implications for hydrophobic
hydration in light of our current understanding. The generalization is based
upon identifying a molecular length, implicit in previous applications of
scaled-particle models, that provides an effective radius for joining
microscopic and macroscopic descriptions. We demonstrate that the generalized
theory correctly reproduces many of the anomalous thermodynamic properties of
hydrophobic hydration for molecularly sized solutes, including solubility
minima and entropy convergence, successfully interpolates between the
microscopic and macroscopic extremes, and provides new insights into the
underlying molecular mechanisms. The results are discussed in terms of
length-scales associated with component phenomena; in particular we first
discuss the micro-macroscopic joining radius identified by the theory, then we
discuss in turn the Tolman length that leads to an analogous length describing
curvature corrections of a surface area model of hydrophobic hydration free
energies, and the length-scales on which entropy convergence of hydration free
energies are expected.
