Temperature effect on the small-to-large crossover lengthscale of hydrophobic hydration

The thermodynamics of hydration is expected to change gradually from entropic for small solutes to enthalpic for large ones. The small-to-large crossover lengthscale of hydrophobic hydration depends on the thermodynamic conditions of the solvent such as temperature, pressure, presence of additives, etc. We attempt to shed some light on the temperature dependence of the crossover lengthscale by using a probabilistic approach to water hydrogen bonding that allows one to obtain an analytic expression for the number of bonds per water molecule as a function of both its distance to a solute and solute radius. Incorporating that approach into the density functional theory, one can examine the solute size effects on its hydration over the entire small-to-large lengthscale range at a series of different temperatures. Knowing the dependence of the hydration free energy on the temperature and solute size, one can also obtain its enthalpic and entropic contributions as functions of both temperature and solute size. These functions can provide some interesting insight into the temperature dependence of the crossover lengthscale of hydrophobic hydration. The model was applied to the hydration of spherical particles of various radii in water in the temperature range from T = 293.15 K to T = 333.15 K. The model predictions for the temperature dependence of the hydration free energy of small hydrophobes are consistent with the experimental and simulational data on the hydration of simple molecular solutes. Three alternative definitions for the small-to-large crossover length-scale of hydrophobic hydration are proposed, and their temperature dependence is obtained. Depending on the definition and temperature, the small-to-large crossover in the hydration mechanism is predicted to occur for hydrophobes of radii from one to several nanometers. Independent of its definition, the crossover length-scale is predicted to decrease with increasing temperature.