Bulk and interfacial liquid water as a transient network

The special macroscopic properties of liquid water stem from its structure as a complex network of molecules connected by hydrogen bonds. While the dynamics of single molecules within this network has been extensively investigated, only little attention has been paid to the closed loops (meshes) of hydrogen-bonded molecules which determine the network topology. Using molecular dynamics simulations we analyze the size, shape, geometrical arrangement, and dynamical stability of loops containing up to 10 hydrogen bonds. We find that six-membered loops in liquid water even at room temperature retain a striking similarity with the well-known structure of ice. Analyzing the network dynamics we find that rings of more than five hydrogen bonds are stabilized compared to a random collection containing the same number of single bonds. We finally show that in the vicinity of hydrophobic and hydrophilic interfaces loops arrange in a preferred orientation.

Figure 1

(a) Geometric definition of a hydrogen bond. (b) A loop of six hydrogen-bonded water molecules.

Figure 2

Six- and seven-membered loops occur most frequently in bulk water. Inset: A typical six-membered loop has an almost planar shape, which can be approximated by the plane indicated by the gray disk.

Figure 3

Density distribution of the molecules in (a) five-, (b) six-, and (c) seven-membered loops in liquid water projected on the best fitting plane. In ice Ih the six-membered loops show a sharp hexagonal form (d).

Figure 4

The radial distribution functions of six-membered loops in liquid water and ice (spikes) are remarkably similar. Significant differences occur at very small distances only.

Figure 5

Five- and six-membered loops are stabilized compared to random groups while larger loop sizes are less stable than random groups due to short-circuiting (a). Rings, which are destroyed only due to hydrogen bond breaking and not due to short-circuiting, are stabilized compared to random groups for all ring sizes, except four-membered rings (b).

Figure 6

Near real surfaces the water molecules form distinct hydration layers (marked in gray). The coordination number remains almost unchanged except for the outermost molecules. A dummy surface (see text) does not influence the density, but the coordination number starts decreasing at larger distances.

Figure 7

The dashed lines show the occurrence of loops at a dummy surface. At a real diamond interface the occurrence of small loops does not simply drop. The dots mark the minimal distance to the interface at which an average sized loop still fits in arbitrary direction. The positions of the hydration layers are marked in gray (cf. Fig. 6).

Figure 8

While the occurrence of loops in the second hydration layer resembles that of bulk water, very near to the interface the number of loops per molecule drops and the maximum is shifted to five-membered loops.

Figure 9

The interface (normal vector $\vec{e}$) induces a preferred orientation for the loops (normal vector $\vec{n}$). The crosses mark the average maximum COM-molecule distance of each loop size; i.e., the distance below which the loop does not fit in arbitrary orientations and thus an ordering effect is expected.

Figure 10

Loop existence autocorrelation function c(t) in bulk water and in the $0.7\text{nm}$ thick boundary region near hydrophobic model interfaces. Loops in the boundary layer live longer than in the bulk.

Figure 11

The occurrence of loops per OH group of the interface (filled boxes) is shifted to smaller loop sizes compared to loops per water molecule in bulk water (dark border; cf. Fig 2). The results are normalized to the occurrence of six-membered loops.

Figure 12

Loops that contain at least one OH group of the interface are significantly more stable than the pure water loops that are found in the $0.7\text{nm}$ thick boundary region (dashed lines).

Figure 13

The congruency of the correlation functions of random hydrogen bonds and those participating in loops shows that the stabilization of certain loop sizes does not stem from a stabilization of the hydrogen bonds themselves. An exception are hydrogen bonds in four-membered loops that show to be less stable than the average hydrogen bond.

Figure 14

The autocorrelation functions $c\left(t\right)$ (here shown for loops of four to nine hydrogen bonds) are well described by triexponential fits (solid lines), while biexponential fitting is clearly insufficient (dashed lines).

Figure 15

Density and coordination number near the hydrophilic interface and dummy surface (cf. Fig. 6). The outermost molecules manage to maintain the favored number of hydrogen bonds by binding to OH groups (dashed red line). The positions of the hydration layers are marked in gray.

Figure 16

The occurrence of loops at a hydrophilic surface shows a very similar behavior as observed at the hydrophobic interface. Including hydrogen bonds with OH groups increases the number of loops near the interface (dashed lines). The gray areas indicate the position of the density maxima (cf. Fig. 15).

Figure 17

The number of loops decreases the nearer the interface is. The maximum remains at six-membered loops. The number of loops increases by the striped part of the boxes, when OH groups are considered valid members of the hydrogen bond network.

Figure 18

The hydrophilic interface (normal vector $\vec{e}$) induces a preferred orientation for the loops (normal vector $\vec{n}$). The crosses mark the distance below which loops do not fit in arbitrary orientation (cf. Fig. 9).

Figure 19

The life time of loops in the $0.7\text{nm}$ boundary region is significantly longer than in the bulk.