Correlation between 2D Square Ice and 3D Bulk Ice by Critical Crystallization Pressure

TL;DR

This work addresses how nanoscale confinement in graphene nanocapillaries governs the crystallization of water into 2D square ice and links this behavior to 3D bulk ice through the critical crystallization pressure. Using all-atom molecular dynamics with varying capillary widths in all three spatial directions, the authors quantify the interplay between a quasi-macroscopic pressure $P_m$ and an actual pressure $P_a$, revealing an unfreezable threshold when these pressures coincide. They demonstrate that $P_m$ converges toward the bulk crystallization pressure as capillary width increases, while $P_a$ decreases due to stronger squeezing at smaller widths, establishing a direct correlation between 2D square ice and 3D ice via pressure metrics. The findings explain why 2D square ice has a finite number of stable layers and provide fundamental insights for nanoscale phase stability in confined water, with potential implications for nanofluidics and materials design.

Abstract

Low-dimensional ice trapped in nanocapillaries is a fascinating phenomenon and is ubiquitous in our daily lives. As a decisive factor of the confinement effect, the size of nanocapillary significantly affects the critical crystallization pressure and crystalline structure, especially for multi-layered ices. By choosing square ice as a typical two-dimensional (2D) multi-layered ice pattern and using all-atom molecular dynamics simulations, we further unveil the variation mechanism of critical crystallization pressure with the nanocapillary size. The results show a strong dependence of the critical crystallization pressure on the size of the graphene sheet for monolayer, bilayer, and trilayer square ice. The quasi-macroscopic crystallization pressure, the actual pressure of water molecules, and the freezable region between them are all strongly dependent on the nanocapillary width. As the size of the capillary becomes larger in all three directions, the critical crystallization pressure converges to the true macroscopic crystallization pressure, which is very close to the value of the crystallization pressure for bulk ice. A direct correlation is established between 2D square ice and three-dimensional (3D) bulk ice by the critical crystallization pressure. There is an unfreezable threshold for crystallizing spontaneously in practice when the quasi-macroscopic crystallization pressure is equal to the actual pressure, which can explain the limit of nanocapillary width for multi-layered ice.

Figures (6)

• Figure 1: Configuration of the MD simulation system. The red, cyan, and black beads indicate oxygen, hydrogen, and carbon atoms, respectively.
• Figure 2: Results for the bilayer square ice ($h$ = 9.0 Å). (a) Phase transformation of water molecules from liquid to nearly square ice with different pressurization rates (the size of graphene sheets is 26.6 Å $\times$ 21.9 Å). (b) Critical crystallization pressure as a function of graphene size. The black dots represent the characteristic critical crystallization pressure. The black dashed curve is the fitted curve of the characteristic critical crystallization pressure, and the horizontal green and red dashed lines represent the actual pressure and the quasi-macroscopic pressure, respectively. The vertical blue dashed line represents the unfreezable threshold for the graphene size, and the pink shaded area is the unfreezable region. (c) Top views of the simulation snapshots for graphene sheets of different sizes. The red and cyan globules indicate oxygen and hydrogen atoms, respectively, and the blue dashed lines represent hydrogen bonds. The green boxes mark square ice units to guide the eye.
• Figure 3: Results for the monolayer square ice ($h$ = 6.5 Å). (a) Potential energy curves of the confined water with different graphene sizes. (b) Critical crystallization pressure as a function of graphene size. (c) Variations of the potential energy of the confined water for repeated simulations with different initial velocities when the size of graphene sheets is 108.8 Å $\times$ 89.6 Å. (d) Variations of the potential energy of the confined water for repeated simulations with different initial velocities when the size of graphene sheets is 26.6 Å $\times$ 21.9 Å. (e) Top views of the simulation snapshots for graphene sheets of different sizes.
• Figure 4: Results for trilayer square ice ($h$ = 11.5 Å). (a) Potential energy curves of the confined water with different graphene sizes. (b) Critical crystallization pressure as a function of graphene size. (c) Variations of the potential energy of the confined water for repeated simulations with different initial velocities when the size of graphene sheets is 108.8 Å $\times$ 89.6 Å. (d) Variations of the potential energy of the confined water for repeated simulations with different initial velocities when the size of graphene sheets is 26.6 Å $\times$ 21.9 Å. (e) Top views of the simulation snapshots for graphene sheets of different sizes.
• Figure 5: Results for four-layer square ice ($h$ = 14.0 Å). (a) 108.8 Å $\times$ 89.6 Å. (b) 68.0 Å $\times$ 56.0 Å. (c) 42.5 Å $\times$ 35.0 Å. (d) 26.6 Å $\times$ 21.9 Å. The edge colors of the inset snapshots correspond to the curves of the potential energy.