(Color) Quasipolyhedra, fragments building the hexagonal ice, are shown in (a) and (b). Their volume per fragment is 1.5 and 0.5, respectively. Cubic ice is built of a single kind of fragment shown in (c). Its volume per a fragment is 1. See Appendix B for the definition of volume of a fragment. In (d), a typical configuration of seven fragments surrounding a water molecule (circle) is exemplified, where fragments are drawn by different colors. A snapshot of all the fragments found in the hydrogen bond network at is illustrated in (e), where water molecules and hydrogen bonds are not drawn and fragments are depicted by translucent hulls. The fragments are separated by a small gap in order to show the internal structure. The network is totally tessellated into fragments.
Density, number of network “defects,” and number of rings in the HB network are plotted against temperature with dotted, dashed, and solid lines, respectively, at (a) and (b) . Ring sizes are indicated in the graph. At lower pressure, there is a clear and continuous transition from low- to high-density liquid state between 240 and while these properties are kept constant within the whole range of temperature at . Triangles indicate the number of rings for CRN taken from Ref. 12.
(Color) Total coverage by fragments is plotted against the temperature under (a) and (b) . Coverage by each fragment type is indicated by the bandwidth between the lines. Cryophiles, i.e., fragments which increase by cooling, are plotted with red lines, and thermophiles, i.e., fragments that increase by heating, are plotted with blue lines. Under zero pressure, each fragment increases/decreases monotonically and the cryophiles are supposed to fill the whole network at low temperature limit. Shapes of the major fragments, indicated by capitals, are illustrated in Fig. 4.
Topologies of the major 11 fragments in LDL water are illustrated. Residual distortion (RD) values of individual fragments are indicated. Types C and K are the same as (b) and (c) in Fig. 1.
Volume coverage by fragments is plotted against the fragment size, that is, the number of rings in the fragment. Pressure is (a) and (b) . Temperatures are indicated in the graph. Large fragments which have six or more rings increase below under zero pressure, while the shape of the distribution is almost constant under . Much larger fragments having more than 12 rings are very rare even at low temperature.
Four typical quasi-10-hedral fragments are illustrated. All of them consist of five- to seven-membered rings.
(a) Binding energy of water molecules and (b) decay times of the hydrogen bonds covered by various kinds of fragment are plotted against its residual distortion. Temperature is and pressure is . Averaged binding energy of a water molecule is , indicated by the horizontal line in panel (a), as a reference. In panel (b), horizontal line indicates the average decay time of all the hydrogen bonds . Filled triangles for small fragments (number of rings ) and open circles for large fragments (otherwise). Large fragments are more stable in general. HB of fragments with small RD survives longer. HB in larger fragments survives longer in general. The decay times of hydrogen bonds in four-, five-, six-, seven-, and eight-membered rings are 33, 48, 53, 51, and , respectively.
Compatibilities between major 11 fragments (A-K in Fig. 4) are plotted. Box height indicates the compatibility (see Appendix C for definition). Gray boxes indicate that the corresponding fragments have common rings which are chair-shaped six-membered ring, boat-shaped six-membered ring, boat-shaped seven-membered ring, or flat five-membered ring. Black boxes indicate that both fragments have six-membered rings but their conformation is incompatible (boat vs chair) or the fragments do not have the rings of the same size. Adjacency between other combinations of fragments (indicated in white boxes) is achieved by imposing certain distortion to the fragments.
(Color) Positions of the surface rings of the fragment aggregates are drawn by translucent flakes. Red and blue lines and black dots indicate the created and annihilated hydrogen bonds and network defects observed during , respectively. Temperature is and pressure is . Water molecules are omitted. All ten snapshots during are overlaid in the picture, so the dark area of flakes corresponds to the high probability of finding a surface ring. Top-right region, where no flakes, lines or dots are drawn, indicates that the space is filled by the fragment aggregates without defects and no HB rearrangements happen there.
Two snapshots of the HB network around the rearrangement inside the fragment aggregate. The time interval is . The nodes concerning the rearrangement are pointed by the arrows. Water molecules are omitted and all the fragments adjacent to the two nodes are drawn. The influence area of a single rearrangement contains six fragments, 51 water molecules, and 35 rings. By the rearrangement, two five-membered and three seven-membered rings appear, and six six-membered and two eight-membered rings disappear, while no four-membered rings are included in both structures. Total RD slightly increases from 0.0230 to 0.0237, but still small.
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