Theory of the hydrophobic effect
Authors: Pratt Lawrence R. , Chandler David 
Published: February 2003

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.