The nature of the hydrophobic interaction varies as the solute size increases from methane's to C60's.

The hydrophobic interaction, often combined with the hydrophilic or ionic interactions, makes the behavior of aqueous solutions very rich and plays an important role in biological systems. Theoretical and computer simulation studies have shown that the water-mediated force depends strongly on the size and other chemical properties of the solute, but how it changes with these factors remains unclear. We report here a computer simulation study that illustrates how the hydrophobic pair interaction and the entropic and enthalpic terms change with the solute size when the solute-solvent weak attractive interaction is unchanged with the solute size.

How do water-mediated interactions and osmotic second virial coefficients vary with particle size?

We examine quantitatively the solute-size dependences of the effective interactions between nonpolar solutes in water and in a simple liquid. The potential () of mean force and the osmotic second virial coefficients are calculated with high accuracy from molecular dynamics simulations. As the solute diameter increases from methane's to C's with the solute-solute and solute-solvent attractive interaction parameters fixed to those for the methane-methane and methane-water interactions, the first minimum of () lowers from -1.

Osmotic second virial coefficients for hydrophobic interactions as a function of solute size.

To gain quantitative insight into how the overall strength of the hydrophobic interaction varies with the molecular size, we calculate osmotic second virial coefficients B for hydrophobic spherical molecules of different diameters σ in water based on molecular simulation with corrections to the finite-size and finite-concentration effects. It is shown that B (<0) changes by two orders of magnitude greater as σ increases twofold and its solute-size dependence is best fit by a power law B ∝ σ with the exponent α ≃ 6, which contrasts with the cubic power law that the second virial coefficients of gases obey. It is also found that values of B for the solutes in a nonpolar solvent are positive but they obey the same power law as in water.