Everybody knows that the formation of cavity in a fluid requires work W = p*V ~ R^3 (pressure times cavity volume). If it is a small cavity, the work involves also a surface term, sigma*A ~ R^2 (surface tension times cavity area) as a correction of the main term. The smallest may require also surface moment terms ~R^1, R^0 etc.; but these should be really small.
Atomistic simulations of liquid pentane-heptane [J. Comp. Chem. 35 (2014) 776] yield peculiar cavity distribution and W = const*R^1. And this is for the large cavities (R = 3-6 A). Small cavities, in fact, seem OK (they follow the Poisson distribution and W ~ R^3).
The more I think, the more I don’t see a good reason. A first hypothesis: there is a problem with the simulation. Any other suggestions? Any ideas for experimental data to confirm/reject W = const*R^1 (e.g., hydrophobic effects/solubility data/...)? Any physical explanations/physical reasons to reject it?
Not to give the answer but rather to suggest for the possible discussion: usually, solvation thermodynamic functions for a series of related compounds (but not only) in a given solvent are linear to the electronic polarizability/molecular volume ~r3 of a solute. It might be useful to look at the solvation free energies of isomers characterized by similar molecular volumes (and polarizabilities) but strongly differing in the shape, e.g., neopentane and n-pentane, hexamethylbenzene vs. hexylbenzene, or pyrene vs. tetracene (and I would vote for playing with :rigid: molecules such as pyrene and tetracene, rather than with flexible alkanes) - the differences in simulating the thermodynamic contributions to the solvation functions as well as the experimental solvation thermodynamic functions might become elucidative.
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