Colloquium: Scaled particle theory and the length scales of hydrophobicity

Hydrophobic hydration plays a crucial role in self-assembly processes over multiple length scales, from the microscopic origins of inert gas solubility in water, to the mesoscopic organization of proteins and surfactant structures, to macroscopic phase separation. Many theoretical studies focus on the molecularly detailed interactions between oil and water, 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 microscopic <-> macroscopic issue. This Colloquium revisits the scaled particle theory proposed 30 years ago by Stillinger [J. Solution Chem. 2, 141 (1973)], adopts a practical generalization, and considers 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, which provides an effective radius for joining microscopic and macroscopic descriptions. It will be demonstrated 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 model considered here serves as a reference for theories that bridge microscopic and macroscopic hydrophobic effects. The results are discussed in terms of length scales associated with component phenomena. In particular, first there is a discussion of the microscopic-macroscopic joining radius identified by the theory; then follows a discussion of the Tolman length that describes curvature corrections to a surface area model of hydrophobic hydration free energies and the length scales on which entropy convergence of hydration free energies are expected.