Stability of the First Shell and Hydrogen Bond Network

The axial distribution of water near a methane pair is shown in Fig. 21. Water does not form hydrogen bonds to apolar molecules, so the constrained methane pair creates an excluded volume at the middle where the density of water molecules vanishes. The water distribution peaks at $3.9$ Å and forms a well-defined salvation shell of thickness about $5.5$ Å.

Figure: The axial distribution function of water at the methane-methane separation 4.2 $\AA$..

One can categorize hydrogen bond networks by computing the distribution of non-shorted hydrogen-bonded polygons [21]. In Fig. 22(a), the number of hexagon rings in bulk water dominates the other sizes of polygons. But within the salvation shell, we found that hydrogen-bonded polygon distributions differ significantly between different sizes of methane pairs. At $r=4.8$ Å, there are relatively large numbers of pentagon and heptagon rings, while at nearby similar sizes of methane pair, hexagon rings are still relatively plenty compared with the one shown in Fig. 22(b). It appears that a more stable local water structure is composed of a larger number of pentagon and heptagon rings, which help to stabilize the hydration shell [11]. We note a recent work [9] which studied hydrophobic hydration structure around two small solutes of similar sizes, methane and silane. It is found the number of heptagons increases in the silane hydration shell with respect to the methane case. Also they showed polygon distribution studied by FPMD and three different classical potentials of water are distinctly different.

Figure 22: (a) Hydrogen-bonded polygon distribution in bulk water. We define a hydrogen bond geometrically with a maximum O-O separation of 3.5 Å and a minimum O-H-O angle of 140$^{\circ }$. (b) Hydrogen-bonded polygon distribution of the first hydration shell (two methane molecules are separated by 4.8 Å)..

As the separation increase from $4.4$ Å to $4.8$ Å, the variation of polygon distributions indicates the sensitivities of hydrogen network distribution with solutes.