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 R1 and R2. The Helmholtz free energy for such a system is split into three terms: AN+2(R1, R2) = A0 + U12(R1, R2) + AHI(R1, R2). The main problem of the article is formulated in terms of the function AHI(R12). The hydrophobic interaction is defined as the indirect part of the work [AHI(R12 = ∞) − AHI(R12)] associated with the process of bringing the two solute particles from infinity to the distance R12. 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.

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