Order and correlation contributions to the entropy of hydrophobic solvation

Abstract

The entropy of hydrophobic solvation has been explained as the result of ordered solvation structures, of hydrogen bonds, of the small size of the water molecule, of dispersion forces, and of solvent density fluctuations. We report a new approach to the calculation of the entropy of hydrophobic solvation, along with tests of and comparisons to several other methods. The methods are assessed in the light of the available thermodynamic and spectroscopic information on the effects of temperature on hydrophobic solvation. Five model hydrophobes in SPC/E water give benchmark solvation entropies via Widom's test-particle insertion method, and other methods and models are tested against these particle-insertion results. Entropies associated with distributions of tetrahedral order, of electric field, and of solvent dipole orientations are examined. We find these contributions are small compared to the benchmark particle-insertion entropy. Competitive with or better than other theories in accuracy, but with no free parameters, is the new estimate of the entropy contributed by correlations between dipole moments. Dipole correlations account for most of the hydrophobic solvation entropy for all models studied and capture the distinctive temperature dependence seen in thermodynamic and spectroscopic experiments. Entropies based on pair and many-body correlations in number density approach the correct magnitudes but fail to describe temperature and size dependences, respectively. Hydrogen-bond definitions and free energies that best reproduce entropies from simulations are reported, but it is difficult to choose one hydrogen bond model that fits a variety of experiments. The use of information theory, scaled-particle theory, and related methods is discussed briefly. Our results provide a test of the Frank-Evans hypothesis that the negative solvation entropy is due to structured water near the solute, complement the spectroscopic detection of that solvation structure by identifying the structural feature responsible for the entropy change, and point to a possible explanation for the observed dependence on length scale. Our key results are that the hydrophobic effect, i.e. the signature, temperature-dependent, solvation entropy of nonpolar molecules in water, is largely due to a dispersion force arising from correlations between rotating permanent dipole

Pair correlations that link the hydrophobic and Hofmeister effects

“…This stabilisation may be quantified by pair correlation functions that contribute to the potential of mean force between each water and the ion, and to the free energy. Recently, we 23 reported derivations for water-water and water-solute pair correlation functions, and found that these correlations can explain the entropy of hydrophobic solvation of small non-polar species in water. This was similar to results obtained by Lazaridis and Paulaitus, 58 who found that the entropy and heat capacities of hydrophobic hydration are well accounted for by solute-water correlations alone.…”

“…We recently used this method to account for the entropy of hydrophobic solvation. 23 The aim here is to explore the contribution of pair correlations to the solvation free energy of ions in water, and whether a Hofmeister series can be found in these correlations.…”

“…(O) = 78.2 K, and q(H) = 0.4238 e. The SPC/E water model is chosen so as to compare results from these simulations to those reported by us 23 for the entropy of hydrophobic solvation in SPC/E water. All ten ions were represented by a point charge with a Lennard-Jones (LJ).…”

The coalescence of polystyrene in correlated binary solvents

“…We approximate the solute cavity as a sphere and assume that the distribution of solvent molecules outside the cavity to be uniform. This first approximation is supported by simulation studies 22 and does not change the dependence of free energy on size. 26 The amount of lost correlation is then a two-body integral, expressed as …”

“…22 The angular-dependent radial distribution function, g ij , between two dipole moments, l 1 of molecular species i and l 2 of molecular species j separated by r, may be given in terms of the angular dependent PMF as…”