Effect of Water–Water Hydrogen Bonding on the Hydrophobic Hydration of Large-Scale Particles and Its Temperature Dependence

We present a theoretical model for the effect of water hydrogen bonding on the thermodynamics of hydrophobic hydration. The model is based on a combination of the classical density functional theory with the recently developed probabilistic approach to water hydrogen bonding near a hydrophobic surface. This combination allows one to determine the distribution of water molecules in the vicinity of a hydrophobic particle and calculate the thermodynamic quantities of hydrophobic hydration as well as their temperature dependence. The probabilistic approach allows one to implement the effect of the hydrogen bonding ability of water molecules on their interaction with the hydrophobic surface into the formalism of density functional theory. This effect arises because the number and energy of hydrogen bonds that a water molecule forms near a hydrophobic surface differ from their bulk values. Such alteration gives rise to a hydrogen bond contribution to the external potential field whereto a water molecule is subjected in that vicinity. This contribution is shown to play a dominant role in the interaction of a water molecule with the surface. Our approach predicts that in the temperature range from 293 to 333 K: (a) the free energy of hydration of a planar hydrophobic surface in a model liquid water increases with increasing temperature (although its ratio to the temperature decreases); (b) the hydration process is unfavorable both enthalpically and entropically; (c) the entropic contribution to the hydration free energy is much smaller than the enthalpic one and decreases with increasing temperature, potentially becoming negative. The latter is indirectly supported by the experimental observation that under some conditions the hydration of a molecular hydrophobe is entropically favorable as well as by the molecular dynamics simulations predicting positive hydration entropy for sufficiently large hydrophobes.