Temperature dependence of local solubility of hydrophobic molecules in the liquid-vapor interface of water

One important aspect of the hydrophobic effect is that solubility of small, nonpolar molecules in liquid water decreases with increasing temperature. We investigate here how the characteristic temperature dependence in liquid water persists or changes in the vicinity of the liquid-vapor interface. From the molecular dynamics simulation and the test-particle insertion method, the local solubility Σ of methane in the liquid-vapor interface of water as well as Σ of nonpolar solutes in the interface of simple liquids are calculated as a function of the distance z from the interface. We then examine the temperature dependence of Σ under two conditions: variation of Σ at fixed position z and that at fixed local solvent density around the solute molecule. It is found that the temperature dependence of Σ at fixed z depends on the position z and the system, whereas Σ at fixed local density decreases with increasing temperature for all the model solutions at any fixed density between vapor and liquid phases. The monotonic decrease of Σ under the fixed-density condition in the liquid-vapor interface is in accord with what we know for the solubility of nonpolar molecules in bulk liquid water under the fixed-volume condition but it is much robust since the solvent density to be fixed can be anything between the coexisting vapor and liquid phases. A unique feature found in the water interface is that there is a minimum in the local solubility profile Σ(z) on the liquid side of the interface. We find that with decreasing temperature the minimum of Σ grows and at the same time the first peak in the oscillatory density profile of water develops. It is likely that the minimum of Σ is due to the layering structure of the free interface of water.