Statistical Mechanical Study of Hydrophobic Interaction. I. Interaction between Two Identical Nonpolar Solute Particles

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Abstract
The tendency of two nonpolar particles to adhere to each other in aqueous environment is examined within the framework of classical statistical mechanics. The system under investigation consists of N solvent molecules and two simple solute particles at fixed positions R 1 and R 2. The Helmholtz free energy for such a system is split into three terms: A N+2 ( R 1 , R 2 ) = A 0 + U 12 ( R 1 , R 2 ) + A HI ( R 1 , R 2 ) . The main problem of the article is formulated in terms of the function A HI (R 12 ) . The hydrophobic interaction is defined as the indirect part of the work [A HI (R 12 = ∞) − A HI (R 12 )] associated with the process of bringing the two solute particles from infinity to the distance R 12 . Three different estimates of the strength of the hydrophobic interaction for various solute–solute distances are discussed. A quantity, based on available experimental data, is suggested to serve as a simple and practical index for comparing the hydrophobic interaction in various media. Using this quantity, the unique behavior of liquid water with regard to hydrophobic interaction is established.