Thermodynamics of cavity formation in water and n-hexane using the Widom particle insertion method

Abstract

The Widom particle insertion (WPI) method is used to compute the free energy, enthalpy, and entropy associated with the creation of empty cavities of different sizes in water and n-hexane. These thermodynamic parameters are computed from the likelihood of encountering such cavities in thermally equilibrated configurations from 4 ns (1 ns=10−9 s) molecular dynamics trajectories of the neat liquids. The obtained free energy values are in excellent agreement with those computed previously, using the same or other methods. We find that the entropy term is large and unfavorable in both liquids, but more so in water than in hexane. The change in internal energy is, on the other hand, virtually zero in hexane and slightly favorable in water. Comparison with scaled particle theory (SPT) predictions shows good agreement for the free energy values for small cavities, but the theory systematically underestimates these values for large cavities. In contrast, the free energy components obtained by the two methods show several significant differences. With WPI, the entropy of cavity formation is unfavorable in both liquids for all cavity sizes. SPT yields an unfavorable entropy only for water. In hexane, however, the predicted entropy is negative for small cavities, but changes sign for cavity radii >1.1 Å. In addition, SPT yields an unfavorable enthalpy of cavity formation in water, whereas with WPI this term is small but favorable. Taking n-hexane as a model for organic solvents, our calculations thus suggest that the process of cavity formation is similar in water and these solvents, a conclusion which seems to make good physical sense. SPT reaches an opposite conclusion, which seems harder to rationalize, and probably arises from the highly simplified solvent model used by this theory.