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The thermodynamics of hydration changes gradually from entropic for smallsolutes to enthalpic for large ones. The small-to-large crossover lengthscaleof hydrophobic hydration depends on the thermodynamic conditions of the solventsuch as temperature, pressure, presence of additives, etc... We attempt to shedsome light on the temperature dependence of the crossover lengthscale by usinga probabilistic approach to water hydrogen bonding that allows one to obtain ananalytic expression for the number of bonds per water molecule as a function ofboth its distance to a solute and solute radius. Incorporating that approachinto the density functional theory, one can examine the solute size effects onits hydration over the entire small-to-large lengthscale range at differenttemperatures. Knowing the dependence of the hydration free energy ontemperature and solute size, one can obtain its enthalpic and entropiccontributions as functions of temperature and solute size. These function canprovide interesting insight into the temperature dependence of the crossoverlengthscale of hydrophobic hydration. The model was applied to the hydration ofspherical particles of various radii in water in the temperature range fromT=293.15 K to T=333.15 K. The model predictions for the temperature dependenceof the hydration free energy of small hydrophobes are consistent with theexperimental and simulational data. Three alternative definitions for thesmall-to-large crossover length-scale of hydrophobic hydration are proposed,and their temperature dependence is obtained. Depending on the definition andtemperature, the small-to-large crossover in the hydration mechanism ispredicted to occur for hydrophobes of radii from one to several nanometers.Independent of its definition, the crossover length-scale is predicted todecrease with increasing temperature.

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