A microscopic theory is developed which can describe many of the structural and thermodynamic properties of infinitely dilute solutions of apolar solutes in liquid water. The theory is based on an integral equation for the pair correlation functions associated with spherical apolar species dissolved in water. It requires as input the experimentally determined oxygen–oxygen correlation function for pure liquid water. The theory is tested by computing thermodynamic properties for aqueous solutions of apolar solute species. The predictions of both the Henry’s Law constant and the entropy of solution are in good agreement with experiment. The calculation of the latter quantity is essentially independent of any adjustable parameters. It is shown how the correlation functions we have calculated can be used to predict the solubility of more complicated, aspherical, and nonrigid solutes in liquid water. For the more complex molecules it is convenient to study the difference between the excess chemical potential of the molecule and the chemical potentials of its separated components (Ben‐Naim’s measure of the hydrophobic interaction strength δA^(HI)_M). A generalized formula for δA^(HI)_M is presented which reduces to Ben‐Naim’s result in the special case of a rigid solute. The calculations of δA^(HI)_M for normal alkanes through n‐decane are independent of unknown and adjustable mean field parameters. For ethane, the theoretical results for δA^(HI)_M are in good agreement with experimental data. To treat longer alkanes multipoint correlation functions are required. It is shown that the standard superposition approximation for the multipoint correlation functions predicts qualitatively incorrect results. A correction to the superposition approximation is developed. Its use yields theoretical values for δA^(HI)_M which agree well with experiment. We also calculate free energies of transfer of n‐alkane solutes from a hydrocarbon solvent to liquid water. Here, too, our results are in good agreement with experiment. After testing the theory against experiment, several experimentally inaccessible aspects of the hydrophobic effect are discussed. Analysis of pair correlation functions between spherical apolar species indicates that the hydrophobic interaction becomes more attractive as the solute size is increased at constant temperature, or as the temperature is decreased. The solute–solute correlations in liquid water are compared with those in a nonassociated (hard‐spherelike) solvent. Plots are presented which indicate that the insertion of an apolar species increases the intermolecular structure of water in the vicinity of the apolar solute. The effects of solvent environments on the conformations of small chain molecules are discussed. It is shown that hydrocarbon solvents as well as water tend to reduce the spatial extension of the chain molecules from what is found in the gas phase. However, calculations which take cognizance of the detailed structure of the solvent liquids reveal that the average conformational structure of some n‐alkanes may be more compact in some nonassociated solvents than in water.

A molecular model of poorly understood hydrophobic effects is heuristically developed using the methods of information theory. Because primitive hydrophobic effects can be tied to the probability of observing a molecular-sized cavity in the solvent, the probability distribution of the number of solvent centers in a cavity volume is modeled on the basis of the two moments available from the density and radial distribution of oxygen atoms in liquid water. The modeled distribution then yields the probability that no solvent centers are found in the cavity volume. This model is shown to account quantitatively for the central hydrophobic phenomena of cavity formation and association of inert gas solutes. The connection of information theory to statistical thermodynamics provides a basis for clarification of hydrophobic effects. The simplicity and flexibility of the approach suggest that it should permit applications to conformational equilibria of nonpolar solutes and hydrophobic residues in biopolymers.

Proteins can be denatured by pressures of a few hundred MPa. This finding apparently contradicts the most widely used model of protein stability, where the formation of a hydrophobic core drives protein folding. The pressure denaturation puzzle is resolved by focusing on the pressure-dependent transfer of water into the protein interior, in contrast to the transfer of nonpolar residues into water, the approach commonly taken in models of protein unfolding. Pressure denaturation of proteins can then be explained by the pressure destabilization of hydrophobic aggregates by using an information theory model of hydrophobic interactions. Pressure-denatured proteins, unlike heat-denatured proteins, retain a compact structure with water molecules penetrating their core. Activation volumes for hydrophobic contributions to protein folding and unfolding kinetics are positive. Clathrate hydrates are predicted to form by virtually the same mechanism that drives pressure denaturation of proteins.

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 $\text{microscopic}\leftrightarrow \text{macroscopic}$ 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.