The variation of the number of hydrogen bonds per water molecule in the vicinity of a hydrophobic surface and its effect on hydrophobic interactions

A water molecule in the vicinity of a hydrophobic surface forms fewer and energetically altered hydrogen bonds compared to a bulk molecule because the hydrophobic surface restricts the space available for other water molecules necessary for its hydrogen bonding. In this vicinity, the number of hydrogen bonds per water molecule depends on its distance to the surface and its orientation. We review recent advances in analytic models of water hydrogen bonding and of its role in hydrophobic hydration and hydrophobic interactions with the emphasis on the models providing the number of hydrogen bonds per liquid water molecule as a function of its distance to a hydrophobic surface. The first such model [Luzar A, Svetina S, Zeks B. J Chem Phys. 1985;82:5146-54] was based on two reference quantities: energy of a hydrogen bond and ratio of number of broken and formed bonds, both in the vicinity of the surface. In the recent, probabilistic hydrogen bond model [Djikaev YS, Ruckenstein E. J Chem Phys. 2010; 133: doi:10.1063/1.3499318.] the number of hydrogen bonds per bulk water molecule serves as a single reference to obtain an analytic expression for this dependence (the number of hydrogen bonds per water molecule vs its distance to a hydrophobic surface). This function can be used to develop analytic models for the role of hydrogen bonding in the hydration of hydrophobic particles and their solvent-mediated interaction and to examine the temperature effects on these phenomena.