Percolation and three-dimensional structure of supercritical water

It is well established that at ambient and supercooled conditions water can be described as a percolating network of H bonds. This work is aimed at identifying, by neutron diffraction experiments combined with computer simulations, a percolation line in supercritical water, where the extension of the H-bond network is in question. It is found that in real supercritical water liquidlike states are observed at or above the percolation threshold, while below this threshold gaslike water forms small, sheetlike configurations. Inspection of the three-dimensional arrangement of water molecules suggests that crossing of this percolation line is accompanied by a change of symmetry in the first neighboring shell of molecules from trigonal below the line to tetrahedral above.

Figure 1

Density and pressure values of the experimental points investigated are reported as solid circles; the empty circle represents the critical point of water. The critical isotherm ($T=647.096\text{K}$, solid line) is also reported along with the isotherms at $T=673$ (dashed line) and $753\text{K}$ (dotted line). All experimental temperatures and pressures exceed the critical values; the state at density lower than the critical one is in the so-called gaslike phase, all the others are in the liquidlike one.

Figure 2

Top: Experimental IDCSs (circles) along with their EPSR fit (solid line) for the three samples measured at state point $B^{\text{expt}}$. The fit residuals are reported with their error bars to show the substantial absence of residual structures. Data for HDO and ${\text{D}}_2\text{O}$ have been arbitrarily shifted for clarity. Bottom: Total neutron weighted radial distribution function for ${\text{H}}_2\text{O}$, HDO, and ${\text{D}}_2\text{O}$ (thick solid line), compared with the Fourier transform of the data-fit residuals (thin line). Data have been arbitrarily shifted for clarity.

Figure 3

(Color online) Comparison between the $g_{\text{OO}}\left(r\right)$ function obtained at state point $A^{\text{expt}}$ by the EPSR routine after refinement of the empirical potential (black solid line) and by running with the SPC/E reference potential alone (red line with circles). The green line with triangles is the difference of the two curves. The first neighbor peak is reported in the inset on a larger scale, in order to evidence the shift of the peak.

Figure 4

(Color online) EPSR fits of the experimental data for the three isotopic compositions at all state point considered. Data for HDO and ${\text{D}}_2\text{O}$ have been arbitrarily shifted for clarity. Data in the gaslike region are reported in black; in red with circles the data from Ref. [13]; present data in the liquidlike region are reported in green (dashed line) $\left(T=673\text{K}\right)$ and blue with squares $\left(T=753\text{K}\right)$. Changes of all functions for $Q$ values below $5{\text{Å}}^{-1}$ are evident, along with the increase of density fluctuations when the critical density is approached. These are visible in the ${\text{D}}_2\text{O}$ data and not in the ${\text{H}}_2\text{O}$, due to near cancellation between $b_{\text{H}}$ and $b_{\text{O}}$ [${\left({\overline{b}}_{{\text{D}}_2\text{O}}\right)}^2=0.407\text{b}$; ${\left({\overline{b}}_{{\text{H}}_2\text{O}}\right)}^2=0.028$].

Figure 5

(Color online) OO radial distribution functions at all investigated state points. Same symbols as for Fig. 4. Notice the gaslike behavior at state point $A^{\text{expt}}$ (see also Figs. 6, 7).

Figure 6

(Color online) OH radial distribution functions at all investigated state points. Same symbols as in Fig. 4.

Figure 7

(Color online) HH radial distribution functions at all investigated state points. Same symbols as in Fig. 4.

Figure 8

(Color online) Distribution function of the angle $\theta$ formed between two oxygen atoms lying within a distance of 3.5 Å from the oxygen in the origin of the reference frame. Same symbols as in Fig. 4 for supercritical water; the black dashed line refers to ambient water [36] and shows the peak characteristic of the tetrahedral coordination (at 104°), absent in supercitical states.

Figure 9

(Color online) Distribution function of the H-bond angle $\gamma$. Same symbols as in Fig. 8. Note the significant weakening of the H-bond linearity in supercritical water.

Figure 10

(Color online) Spatial density functions for water molecules, however oriented, around a central molecule, giving a 3D rendering of the relative positions of neighboring molecules. The first row refers to state point $A^{\text{expt}}$, the second to state point $B^{\ast \text{expt}}$, the third to state point $B^{\text{expt}}$, and the fourth to state point $D^{\text{expt}}$. The first column shows the first neighboring shell with a contrast equal to 0.2, while in the second the same $r$ range is reported with a contrast equal to 0.5. The third column shows an $r$ range including both first and second neighboring shells, with a contrast equal to 0.4. Notice the triangular symmetry of the SDFs at state point $A^{\text{expt}}$ in contrast with the characteristic tetrahedral one at the other state points for both first and second shells (first and last columns).

Figure 11

Distribution function of clusters in the four investigated states. The theoretical distribution for a system at the percolation threshold [see Eq. (1)] is reported as the solid line, in order to highlight differences between percolating ($B^{\ast \text{expt}}$, $B^{\text{expt}}$, and $D^{\text{expt}}$) and nonpercolating $\left(A^{\text{expt}}\right)$ states.

Figure 12

In order to demonstrate that our conclusions about the presence of percolating water clusters in supercritical water are independent of the chosen maximum length of the H bond, we report here the distribution function of clusters at state points $A^{\text{expt}}$ and $B^{\text{expt}}$, calculated for different values of this length, namely, 2.3 (open circles), 2.4 (solid squares), and 2.5 Å (open triangles). The theoretical distribution for a system at the percolation threshold [see Eq. (1)] is reported as solid line.

Figure 13

Fraction of water molecules with $i$ H bonds in the four states investigated. This distribution is almost symmetric and centered above the threshold value of 1.55 H bonds per molecule at all liquidlike state points; at the gaslike state it is instead asymmetric and gives an average value of 0.8 H bonds per molecule.

Figure 14

Distribution function of chains of water molecules at state point $A^{\text{expt}}$ showing monotonic decrease with increasing chain length and a second maximum in liquidlike states.