Chiral Ordering in Supercooled Liquid Water and Amorphous Ice

The emergence of homochiral domains in supercooled liquid water is presented using molecular dynamics simulations. An individual water molecule possesses neither a chiral center nor a twisted conformation that can cause spontaneous chiral resolution. However, an aggregation of water molecules will naturally give rise to a collective chirality. Such homochiral domains possess obvious topological and geometrical orders and are energetically more stable than the average. However, homochiral domains cannot grow into macroscopic homogeneous structures due to geometrical frustrations arising from their icosahedral local order. Homochiral domains are the major constituent of supercooled liquid water and the origin of heterogeneity in that substance, and are expected to be enhanced in low-density amorphous ice at lower temperatures.

Figure 1

Distributions of bond twists, ${\chi }_b$, for supercooled liquid water and ice. The melting temperature of the employed model is approximately 250 K.

Figure 2

Distribution of ring twists. (a) Overall distribution of the ring twists, ${\chi }_r$, at 200 K (black) and 240 K (green). (b) Contributions of five- to seven-membered rings to the distribution at 200 K are shown with a stacked chart. The probability is defined on a per-ring basis. See Supplemental Method [29] for detail. (c) Overall distribution of the vitrite twist at 200 K (black) and 240 K (green). (d) Lower part of panel (c) at 200 K is expanded and the contributions from major types of vitrites are shown.

Figure 3

Vitrites in ice and in supercooled water. (a) Various stable and metastable ice structures can be decomposed into vitrites (crystallites). Major vitrite types $B$, $D$, and $H$ are labeled. (b) An icosahedron comprises 20 almost-regular tetrahedra. Polytope ‘240’ structure is made from an icosahdron by regularly inserting vertices at the centers of one fifth of the tetrahedra and can also be decomposed into several type B vitrites. XPolytope is an aggregate of vitrites $A$ and $B$. (c) A snapshot of the entire system of the supercooled liquid water at 200 K is decomposed into vitrites. Vitrite types $A$, $B$, $D$, $H$, and $Z$ are shown with filled polyhedra and other types are shown with outlines. Label $D$ points the largest ice Ic nucleus that appears in the trajectory. Abundance of each vitrite type is listed in Table S1. (d) Vitrite types $A$ and $B$ (xPolytope) are gradated from blue to red according to their twists, ${\chi }_v$, in the same snapshot used in panel c. Only the vitrites with $|{\chi }_v|>0.25$ are shown with filled polyhedral and others are shown with outlines.

Figure 4

The mole fraction of water molecules belonging to any xPolytope is plotted against temperature.

Figure 5

Correlation between structure, dynamics, and chirality. (a) Solid and dashed lines show the averaged rotation angles in 2 ns and the averaged binding energies of two water molecules constituting a hydrogen bond, respectively, as functions of multiplicities $M(D)$ (blue lines, ice Ic) and $M(B)$ (black lines, polytope ‘240’). (b) Size of the largest cluster at 200 K plotted against time. Red and blue lines are for xPolytopes with ${\chi }_v>0.25$ and ${\chi }_v<-0.25$, respectively. Light blue is for the nucleus of ice Ic (vitrite $D$). Inserted are the shapes of the largest clusters at 1,114 ns (indicated by a dashed line), which is the same instant shown in Figs. 3 and 3. A large ice nucleus appears at $1\mu \mathrm{s}$ and persists for 300 ns. (c) Cluster size distributions at 240 K (red) and 200 K (black). Dots and solid lines indicate ice Ic and xPolytope, respectively.