Dependence of the number of hydrogen bonds per water molecule on its distance to a hydrophobic surface and a thereupon-based model for hydrophobic attraction

A water molecule in the vicinity of a hydrophobic surface forms fewer hydrogen bonds than a bulk molecule because the 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. Considering the number of hydrogen bonds per bulk water molecule (available experimentally) as the only reference quantity, we propose an improved probabilistic approach to water hydrogen-bonding that allows one to obtain an analytic expression for this dependence. (The original version of this approach [Y. S. Djikaev and E. Ruckenstein, J. Chem. Phys. 130, 124713 (2009)] provides the number of hydrogen bonds per water molecule in the vicinity of a hydrophobic surface as an average over all possible locations and orientations of the molecule.) This function (the number of hydrogen bonds per water molecule versus its distance to a hydrophobic surface) can be used to develop analytic models for the effect of hydrogen-bonding on the hydration of hydrophobic particles and their solvent-mediated interaction. Presenting a model for the latter, we also examine the temperature effect on the solvent-mediated interaction of two parallel hydrophobic plates.