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 α 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. A thermodynamic identity for B derived earlier [K. Koga, V. Holten, and B. Widom, J. Phys. Chem. B 119, 13391 (2015)] indicates that if B is asymptotically proportional to a power of σ, the exponent α must be equal to or greater than 6.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in (Hidefumi Naito, Ryuichi Okamoto, Tomonari Sumi, Kenichiro Koga; Osmotic second virial coefficients for hydrophobic interactions as a function of solute size. J. Chem. Phys. 14 June 2022; 156 (22): 221104. https://doi.org/10.1063/5.0097547) and may be found at (https://doi.org/10.1063/5.0097547).
This fulltext is available in June 2023.