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 w(r) of mean force and the osmotic second virial coefficients B are calculated with high accuracy from molecular dynamics simulations. As the solute diameter increases from methane's to C₆₀'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 w(r) lowers from -1.1 to -4.7 in units of the thermal energy kT. Correspondingly, the magnitude of B (<0) increases proportional to σ with some power close to 6 or 7, which reinforces the solute-size dependence of B found earlier for a smaller range of σ [H. Naito, R. Okamoto, T. Sumi and K. Koga, J. Chem. Phys., 2022, 156, 221104]. We also demonstrate that the strength of the attractive interactions between solute and solvent molecules can qualitatively change the characteristics of the effective pair interaction between solute particles, both in water and in a simple liquid. If the solute-solvent attractive force is set to be weaker (stronger) than a threshold, the effective interaction becomes increasingly attractive (repulsive) with increasing solute size.