The binomial cell model of hydrophobic solvation

On the basis of the cell model of dense fluids, we derive the binomial distribution law for a number of solvent particles occupying a given void of excluded volume (a cavity) which arises in a bulk solvent as a fluctuation. It is inserted as a default distribution in the information theory approach (Hummer, G.; Garde, S.; Garcia, A. E.; Paulaitis, M. E.; Pratt, L. R. J. Phys. Chem. B 1998,102, 10469) for treating the thermodynamics of cavitation; the imaginary process is considered as a component of the total solvation process. Computations of cavitation free energies, entropies, and enthalpies for 11 hydrocarbons in water solvent are compared with results of the computer simulation of these properties reported by E. Gallicchio et al. (Gallicchio, E.; Kubo, M. M.; Levy, R. J. Phys. Chem. B 2000, 104, 6271). A similar analysis of cavitation for model spherical solutes in water in a wide range of cavity radii is also provided. Linear correlation between the cavitation free energy and the cavity volume is observed and justified. The present binomial approach for treating cavitation effects efficiently covers a large range of cavity volumes upsilon's (10(2) Angstrom(3) < upsilon < 10(3) Angstrom(3)).