A computer simulation study of the temperature dependence of the hydrophobic hydration

Abstract

The test particle method is used to evaluate by molecular dynamics calculations the solubility of rare gases and of methane in water between the freezing point and the critical point. A quantitative agreement is obtained between solubility data and simulation results when the simulated water is modeled by the extended simple point charge model (SPCE). From a thermodynamical point of view, it is shown that the hierarchy of rare gases solubilities in water is governed by the solute–water interaction energy while an entropic term of cavity formation is found to be responsible for the peculiar temperature dependence of the solubility along the coexistence curve, and more precisely, of the solubility minimum exhibited by all the investigated solutes. Near the water critical point, the asymptotic behaviors of the Henry’s constant and of the vapor–liquid partition coefficient, respectively, as deduced from the simulation data follow with a good accuracy the critical laws recently proposed in the literature for these quantities. Moreover, the calculated partial molar volume of the solute shows a steep increase above 473 K and becomes proportional to the isothermal compressibility of the pure solvent in the vicinity of the critical point as it is observed experimentally. From a microscopic point of view, the evaluation of the solute–solvent pair distribution functions permits to establish a relationship between the increase of the solubility with the decrease of the temperature in cold water on the one hand, and the formation of cages of the clathrate-type around the solute on the other hand. Nevertheless, as soon as the boiling point of water is reached the computer simulation shows that the water molecules of the first hydration shell are no longer oriented tangentially to the solute and tend to reorientate towards the bulk. At higher temperatures a deficit of water molecules progressively appears around the solute, a deficit which is directly associated with an increase of the partial molar volume. Although this phenomenon could be related to what is observed in supercritical mixtures it is emphasized that no long range critical fluctuation is present in the simulated sample.

Temperature dependence of the hydrophobic hydration and interaction of simple solutes: An examination of five popular water models

“…When the gas phase has a sufficiently low density, then µ g ex,B ≈ 0, hence L l/g becomes identical to the solubility parameter γ l B = exp −β µ l ex,B . For our study, covering the temperature range between 275 K and 375 K, the excess chemical potential of apolar solutes in the gas phase can be practically considered to be zero (see Table 3 in Ref [46]). The chemical potential of a solute can be obtained from a constant pressure simulation (NPT-Ensemble) of the pure solvent using the Widom particle insertion method [60,61] according to…”

“…F is evaluated using the classical Ewald summation technique with a Ewald convergence factor of 2.98 nm −1 (corresponding to a relative accuracy of the Ewald sum of ≈ 10 −4 ) in combination with a real space cut-off of 9Å and a reciprocal lattice cut-off of | k max | 2 = 25. We have tested our calculations by recalculating the chemical potential for various noble gases and Methane at exactly the same statepoints as reported by Guillot and Guissani [46] while explicitly taking the solute polarisability into account. For higher temperatures (> 473 K) we can quantitatively reproduce their data, whereas for the lower temperatures (the temperature range of our study) and larger particles (Methane, Xenon) differences occur, but which are qualitatively in accordance taking the the estimated error of their relatively short calculations into account.…”

Hydrophobic Effects on a Molecular Scale

“…Spherical volumes v in water were studied extensively using computer simulations. 69,70,71,72,73,74 Similar insertion methods were also used to study polymer solubilities. 75 The simulation studies of Pohorille and Pratt 69,70,71 clarified a number of interesting speculations on hydrophobicity and provided the first discriminating tests of theoretical models for G(λ).…”

Hydration and anomalous solubility of the Bell-Lavis model as solvent

“…The two coexisting phases, I and II, might be either a gas phase II that coexists with a homogeneous liquid phase I [31] or two liquid phases, I and II, of different relative densities, the first poor in solute X and the other rich in X [33].…”

“…They have examined the difference between cavity formation in associating and simple liquids [29,30]. A thorough investigation of noble gas solubility has been undertaken by Guillot and Guissani [31] from the point of view of atomistic models. Our approach is that of a minimal statistical model.…”