Phase behaviors of deeply supercooled bilayer water unseen in bulk water

Significance

Bulk water exhibits rich phase behavior with numerous crystalline and amorphous ice phases. Although a recent femtosecond X-ray scattering experiment provides the first evidence of two forms of liquid water in deeply supercooled droplets, coexistence of the two forms of liquid water is still short-lived due to the known “no-man’s land” issue for bulk water. Here, we demonstrate simulation evidence that, in an isolated nanoslit, two forms of 2D liquid water, namely, the bilayer very low density liquid and bilayer high-density liquid, can arise in deeply supercooled states, but separated by the solid phase of bilayer amorphous ice whose melting line exhibits the isochore end point. A hitherto unreported bilayer very low density amorphous ice, largely in the negative pressure region, is also revealed.

Abstract

Akin to bulk water, water confined to an isolated nanoslit can show a wealth of new 2D phases of ice and amorphous ice, as well as unusual phase behavior. Indeed, 2D water phases, such as bilayer hexagonal ice and monolayer square ice, have been detected in the laboratory, confirming earlier computational predictions. Herein, we report theoretical evidence of a hitherto unreported state, namely, bilayer very low density amorphous ice (BL-VLDA), as well as evidence of a strong first-order transition between BL-VLDA and the BL amorphous ice (BL-A), and a weak first-order transition between BL-VLDA and the BL very low density liquid (BL-VLDL) water. The diffusivity of BL-VLDA is typically in the range of 10⁻⁹ cm²/s to 10⁻¹⁰ cm²/s. Similar to bulk (3D) water, 2D water can exhibit two forms of liquid in the deeply supercooled state. However, unlike supercooled bulk water, for which the two forms of liquid can coexist and merge into one at a critical point, the 2D BL-VLDL and BL high-density liquid (BL-HDL) phases are separated by the highly stable solid phase of BL-A whose melting line exhibits the isochore end point (IEP) near 220 K in the temperature−pressure diagram. Above the IEP temperature, BL-VLDL and BL-HDL are indistinguishable. At negative pressures, the metastable BL-VLDL exhibits a spatially and temporally heterogeneous structure induced by dynamic changes in the nanodomains, a feature much less pronounced in the BL-HDL.

Bulk water is known for its diverse phase behaviors under different thermodynamic conditions (1), including at least 18 crystalline phases (ice I_h, I_c to ice XVII) (2–5) and three amorphous ice phases [i.e., low-density amorphous ice (LDA), high-density amorphous ice (HDA), and very high density amorphous ice (VHDA)] (6–14). Mishima et al. were the first to demonstrate that the HDA phase can be achieved through the pressure-induced amorphization of bulk hexagonal ice I_h at 77 K and 1 GPa (6) or from the LDA phase at 77 K and 0.6 GPa (7). Later, Loerting et al. (11) observed the VHDA phase by the isobaric heating of the HDA phase from 77 K to 165 (177) K at 1.1 (1.9) GPa. They also observed a sequence of polyamorphic transitions (LDA → HDA → VHDA) at 125 K (13). In addition to the rich crystalline and amorphous phases of bulk water, earlier computational simulations uncovered unexpected phase behaviors of model water, most notably, two forms of supercooled liquid water, i.e., low-density liquid (LDL) and high-density liquid (HDL), with their phase boundary terminating at a second critical point (8, 15–22). Although the existence of the LDL−HDL transition and associated second critical point of model water were under debate (23), a recent experimental breakthrough provides the first compelling evidence of two forms of liquid in deeply supercooled water droplets (down to 227 K) (24, 25), as well as the existence of a Widom line emanating from the second critical point at positive pressure (26).

When water is confined to isolated nanopores, such as carbon nanotubes or graphene nanoslits, its phase diagram drastically changes. For example, the comprehensive phase diagram of quasi-1D (Q1D) water confined in an isolated carbon nanotube has been predicted from molecular dynamics (MD) simulations (27–30). In addition, unusual phase behaviors of Q1D water, such as the existence of multiple solid−liquid critical points (30), the existence of two forms of liquid (i.e., LDL and HDL) above 270 K, and the isochore end point (IEP) (27) of Q1D ice in nanotubes, have been predicted.

Similar to Q1D and 3D water, water confined to a hydrophobic nanoslit exhibits not only diverse 2D phases of ice and amorphous ice (31–44) but also unique phase behaviors (45). In a hydrophobic nanoslit with a width in the range of 7 Å to 9 Å, at least six forms of bilayer (BL) ices, three forms of BL amorphous ices (BL-A), and one BL quasi-crystalline ice have been predicted from computational simulations. The BL-A is a highly stable phase due largely to the fact that oxygen atoms in the two layers of BL-A are in registry (named as AA stacking), as in the case of BL hexagonal ice (31, 33). Above ambient pressure and below ambient temperature, BL HDL water can freeze into BL ices with relatively high densities, such as BL-VHDA₁ ice (45), BL-VHDA₂ ice (38), BL-Cairo pentagonal ice (44), BL very high density crystalline ice (BL-VHDI) (38), BL triangular ice with AA stacking (where oxygen atoms in the two layers are in registry) (40), and BL triangular ice with AB stacking (34, 40), depending on the thermodynamic conditions. To date, BL hexagonal ice (or BL ice I) and monolayer square ice have been experimentally detected, confirming earlier computational simulations (46–48).

Herein, we present a comprehensive computational investigation of the rich phase behavior of confined BL water, including the phase behavior in the negative pressure region. We report theoretical evidence for a previously unreported BL-A phase, namely, the BL very low density amorphous ice (BL-VLDA) phase; a strong first-order transition between BL-VLDA and BL-A; a weak first-order (or continuous) transition between BL-VLDA and BL very low density liquid (BL-VLDL) (see BL-VLDA and Its Transition to BL-VLDL or BL-A); the existence of two forms of BL liquid in deeply supercooled water; and the IEP for the BL-A phase. The inherent structures of BL-VLDA and deeply supercooled BL-VLDL are similar, but their diffusive properties are different. BL-VLDL exhibits a spatially and temporally heterogeneous structure induced by dynamic changes in the nanodomains, a feature that is much less pronounced in BL-HDL, whereas BL-VLDA is in the solid phase.

Results and Discussion

BL-HDL, BL-A, and BL-VLDL.

Consistent with previous simulation results (38, 43), when BL liquid is cooled isobarically (at 200 MPa) from 250 K to 200 K in steps, it spontaneously freezes into the BL-A phase (Movie S1). Typical snapshots of the BL-A phase are shown in Fig. 1 A–C, where one can see that, in BL-A, each oxygen atom in the upper layer (colored green) overlaps with the oxygen atom in the lower layer (colored red), and the top view of BL-A exhibits mostly pentagonal, hexagonal, and heptagonal rings. The BL-A phase can be also obtained along the isotherm (200 K) by lowering the lateral pressure from 500 MPa to 300 MPa, as shown in Fig. 2. At 200 K, the area density of BL-A (∼20 nm⁻²) is notably lower than that (>22 nm⁻²) of BL-HDL (Fig. 2A), whereas the diffusivity (mostly in plane) of BL-A (∼5 × 10⁻¹⁰ cm²/s) is about three orders of magnitude lower than that (∼5 × 10⁻⁷ cm²/s) of BL-HDL (Fig. 2C). Clearly, BL-A is a solid phase. The structural differences between BL-A and BL-HDL can also be described by atomic site−site pair correlation functions (PCFs). As shown in Fig. 2 D, 1–4, the PCFs of BL-A exhibit much longer range correlation, while those of BL-HDL display only short-range correlation.

Fig. 1.

Top view (Upper) and side view (Lower) of snapshots of inherent structures of (A) BL-A at 200 K and −50 MPa and (D) BL-VLDA at 180 K and −50 MPa, formed between two hydrophobic walls (with separation h = 7.8 Å). The green spheres are oxygen atoms in the upper layer and the red spheres are oxygen atoms in the lower layer. Top view of the upper layer of (B) BL-A and (E) BL-VLDA and the lower layer of (C) BL-A and (F) BL-VLDA.

Fig. 2.

(A–C) Isotherm (200 K) of BL water confined between two hydrophobic walls (with separation h = 7.8 Å): (A) Area density ρ_area, (B) potential energy per molecule E/N, and (C) diffusion constant D versus pressure P. Each colored symbol corresponds to different initial system configuration: green symbols, BL-VLDL as the initial; red symbols, BL-HDL as the initial; and blue symbols, BL-A as the initial. Different symbols denote different simulation times as summarized in the Inset table in C. The pressure at which BL liquid or BL-A becomes vapor refers to the tensile strength, as illustrated approximately by a black dashed line in B. (D) Projected O−O PCFs to the xy plane in short range (1), projected O−H PCFs to the xy plane in short range (2), projected O−O PCFs to the xy plane in midrange (3), and O−O PCFs in midrange (4) for three states highlighted by circles in A, i.e., BL-HDL (200 K and 400 MPa), BL-LDA (200 K and 200 MPa), and BL-VLDL (200 K and 0 MPa). Two hundred inherent structures are used to compute PCFs.

Interestingly, at negative pressure −50 MPa (isobar), we obtained, by heating the BL-A, a metastable form of BL liquid with notably lower density than BL-A. Hereafter, we name this form of BL liquid that exists largely in the negative pressure region the BL very low density liquid (BL-VLDL). As shown in Fig. 3B, by heating BL-A from 180 K instantly to several higher temperatures at −50 MPa, the BL-A melts into BL-VLDL beyond 230 K, and the area density of BL-VLDL is close to 17 nm⁻², much lower than that (∼20 nm⁻²) of BL-A (Fig. 3A). If the initial state, at −50 MPa, is BL-HDL rather than BL-A, the higher-density liquid still can transform into the BL-VLDL, but at lower temperature of 200, 210, and 220 K (Fig. 3). The BL-VLDL phase can also be obtained from a decompression pathway to the negative pressure region along the 200 K isotherm, e.g., starting from BL-HDL at 0, −50, or −100 MPa (Fig. 2). Again, the area density of BL-VLDL is notably lower than that of BL-A at 200 K (Fig. 2A) and much lower than that of BL-HDL. As shown in Fig. 2C, the more negative the pressure, the higher the diffusivity of BL-VLDL. As the temperature increases from 200 K to 230 K, the diffusivity of BL-VLDL at −50 MPa increases by nearly three orders of magnitude, rising from 9 × 10⁻⁹ cm²/s to 3 × 10⁻⁶ cm²/s (Fig. 3C). Hence, the diffusivity of BL-VLDL is strongly dependent on the degree of supercooling, measured by the difference between the equilibrium freezing point and the temperature of the system. At 200 K and −50 MPa, the diffusivity of BL-VLDL is ∼9 × 10⁻⁹ cm²/s, indicating that the water dynamics are very sluggish. Nevertheless, the diffusivity is still more than one order of magnitude higher than that of BL-A under the same conditions (Fig. 2C). As shown in Fig. 2 D, 1–4, the atomic site−site PCFs of BL-VLDL are nearly the same as those of BL-HDL in the range of 0 Å to 10 Å, but, beyond 15 Å, BL-VLDL still exhibits a certain amount of midrange correlation (blue curve), while BL-HDL does not (red curve).

Fig. 3.

(A–C) Isobar (−50 MPa) of BL water confined between two hydrophobic walls (with separation h = 7.8 Å): (A) Area density ρ_area, (B) potential energy per molecule E/N, and (C) diffusion constant D versus temperature T. Each colored symbol corresponds to different initial system configuration: green symbols, BL-VLDL as the initial; red symbols, BL-HDL as the initial; and blue symbols, BL-A as the initial. Different symbols denote different simulation time as summarized in the Inset table in C. (D) Projected O−O PCFs to the xy plane in short range (1), projected O−H PCFs to the xy plane in short range (2), projected O−O PCFs to the xy plane in midrange (3), and O−O PCFs in midrange (4) for two states highlighted by circles in A, i.e., the BL-VLDA (180 K and −50 MPa) and BL-VLDL (200 K and −50 MPa). Two hundred inherent structures are used to compute PCFs.

One explanation for why the diffusivity of BL-VLDL at negative pressures can span three orders of magnitude, depending on the degree of supercooling, is that BL-VLDL involves intrinsic inhomogeneous structures stemming from dynamical nanodomains (Movie S2). Water molecules in the nanodomains are immobile, but, occasionally, some molecules can relocate from one nanodomain to another (Movie S3). If the diffusivity is measured within a relatively short time interval, some water molecules exhibit higher diffusivity (10⁻⁷ cm²/s to 10⁻⁸ cm²/s) while those clustered in the nanodomains exhibit lower diffusivity (10⁻⁸ cm²/s to 10⁻⁹ cm²/s) (SI Appendix, Fig. S1). Based on simulations with two larger systems (N = 1,440 and 1,920), we find that the system size has little influence on the computed diffusivity (Movie S4). The observed nanodomains are manifestations of the dynamical heterogeneity behavior, similar to that observed in bulk supercooled water (49–51).

The large difference in the area density of BL-HDL and BL-VLDL at 200 K (Fig. 2A) indicates they are two distinct liquid phases at deeply supercooled states. The 200-K isotherm (Fig. 2A) clearly indicates that BL-HDL and BL-VLDL are separated by a solid phase, i.e., BL-A (see Movie S5 for the BL-VLDL to BL-A transition at 250 MPa). Note that the BL-A is isomorphic to the experimentally observed BL hexagonal ice (or BL ice I) because in both bilayer ice structures, the oxygen atoms in the upper and lower layers are exactly in registry (i.e., AA-stacking). Like BL hexagonal ice, BL-A is also a highly stable solid phase. Without the formation of the highly stable BL-A, the BL-HDL and BL-VLDL may merge into a single form of BL liquid, at least in the temperature range of 190 K to 220 K and pressure range of 0 MPa to 300 MPa. Previously, we showed that, for Q1D water confined to an isolated carbon nanotube (27), the Q1D HDL and LDL phases are separated by a highly stable hexagonal ice nanotube solid phase, and the difference between Q1D HDL and LDL disappears above the IEP temperature for the hexagonal ice nanotube. Note, however, that both Q1D HDL and LDL are stable at positive pressures, whereas BL-VLDL is metastable at negative pressures. Like the Q1D system, here the IEP also arises on the melting line of BL-A (see below). As seen from the computed area density and total energy data along the 205-, 210-, and 220-K isotherms (SI Appendix, Figs. S2–S4), the pressure interval for the BL-A phase decreases as the temperature increases and disappears at 220 K, where the BL-HDL and BL-VLDL phases merge into a single BL liquid phase.

To determine the location of the IEP and the melting line of BL-A in the pressure−temperature (P-T) phase diagram, we performed an MD simulation using the direct solid−liquid coexistence method in the constant pressure (P_xx)–length (L_y)–slit-width (h)–enthalpy (H) (NP_xxL_yhH) ensemble (52) (SI Appendix, Fig. S5). As shown in Fig. 4, the BL-A melting line exhibits reentrance melting behavior, i.e., in the temperature range of 200 K to 220 K, BL-VLDL → BL-A → BL-HDL freezing−melting transitions are observed along all isotherms (Fig. 2 and SI Appendix, Figs. S2–S4). The IEP is the highest peak of the melting line, located at ∼100 MPa and ∼220 K. At the IEP, the slope of the melting line, dP/dT|_IEP, is infinity, and the area densities of BL liquid and BL-A are identical. Indeed, as shown in SI Appendix, Figs. S6 and S7, the cooling of BL-HDL along the 200- and 300-MPa isobars leads to BL-A with a notably decreased area density at the transition, while the cooling of BL liquid along the 50-MPa isobar (SI Appendix, Fig. S8) leads to BL-A with a slightly increased area density at the transition. However, the cooling of BL liquid along the 100-MPa isobar (SI Appendix, Fig. S9) leads to little change in the area density at 220 K (where the IEP is located).

Fig. 4.

A P-T phase diagram of BL liquid and amorphous ice confined between two hydrophobic walls (with separation h = 7.8 Å): Transition of BL-VLDL to three other phases (vapor, BL-A, and BL-VLDA) is denoted by green points, while transition of BL-A to other phases is denoted by blue points, and transition of BL-VLDA to BL-A is denoted by purple points. The thick gray line represents the melting line of BL-A. An IEP is located approximately at 220 K and 100 MPa at which dP/dT becomes infinite. Above the IEP, the two forms of supercooled liquids (BL-VLDL and BL-HDL) merge into a single form (BL liquid). The stability limits of various phases to vapor are marked by the long dashed lines, while the stability limit of BL-VLDL and BL-VLDA is represented by a green dotted line.

BL-VLDA and Its Transition to BL-VLDL or BL-A.

As shown in SI Appendix, Figs. S6 and S7, the cooling of BL liquid along the 300- and 200-MPa isobars and the cooling of BL-VLDL along the 50-MPa isobar (SI Appendix, Fig. S8) lead to BL-A. In contrast, the cooling of BL-VLDL below 190 K along the −50- (Fig. 3) and 0-MPa isobars (SI Appendix, Fig. S10) leads to a solid-like phase with notably lower area density (18 nm⁻² to 19 nm⁻²) than that (∼20 nm⁻²) of BL-A (Movie S6). Hence, this previously unreported solid-like phase is named BL-VLDA, as it can be viewed as the glassy state of BL-VLDL. Due to its lower area density than BL-A, BL-VLDA exhibits much larger-sized polygonal rings (Fig. 1 E and F). Additionally, the diffusivity of BL-VLDA (1 × 10⁻⁹ cm²/s to 5 × 10⁻⁹ cm²/s) is one order of magnitude higher than that of BL-A (Fig. 3C and SI Appendix, Fig. S10C). In BL-VLDA, most of the oxygen atoms in the upper layer (colored green) do not overlap with the oxygen atom in the lower layer (colored red) (Fig. 1 D–F). A similarity between BL-A and BL-VLDA, however, is that each oxygen atom has four neighboring hydrogen atoms, thereby satisfying the ice rule (Fig. 1). The 180-K isotherm at various pressures is shown in SI Appendix, Fig. S11. At this deeply supercooled state, the system is either in the BL-A or BL-VLDA solid state, depending on the pressure and initial state of simulation. Clearly, BL-VLDA has a markedly lower area density and higher diffusivity than BL-A.

Both BL-VLDL (at 200 K) and BL-VLDA (at 180 K) show similar PCFs in the short range of 0 Å to 10 Å (Fig. 3 D, 1 and 2). However, in the medium range of 12 Å to 25 Å, the PCFs of BL-VLDA show more pronounced peaks, while those of BL-VLDL show less pronounced peaks (Fig. 3 D, 3 and 4). This is because most water molecules in the solid-like BL-VLDA phase do not diffuse (Movies S7 and S8), while many water molecules in the BL-VLDL phase diffuse outside the dynamical nanodomains (Movies S2 and S3).

In addition to their different diffusivity and structural properties at midrange, BL-VLDL and BL-VLDA also show different dynamical behaviors. We computed the relative standard deviation (RSD) of the time-averaged mean-square displacement over time, which contains information on dynamical changes of the diffusive states (53). If the diffusion of a liquid can be described by Brownian motion, the time-dependent RSD decays as t^−0.5. However, if the scaling exponent α of the time-dependent RSD (i.e., t^−α) is less than 0.5, a slow diffusion process is reflected, deviating from Brownian motion. Such a slow diffusion process results in a power-law trapping-time distribution due to crowding effects (54). As shown in SI Appendix, Fig. S12, the RSD decays as t^−α with α ≈ 0.5 for T ≥ 210 K and P = −100 MPa. However, for T < 210 K, the scaling exponent α gradually goes to zero with decreasing temperature (SI Appendix, Table S1). The decrease in α indicates the gradual slowing of the dynamical process. We introduced a threshold value of α to differentiate BL-VLDL and BL-VLDA, that is, α = 0.21. If α > 0.21, the system behaves like BL-VLDL, whereas, if α < 0.21, the system behaves like BL-VLDA. This α value should be used in conjunction with the diffusivity data (typical diffusivity for BL-VLDA is <5 × 10⁻⁹ cm²/s) to differentiate BL-VLDL and BL-VLDA phases, as the transition between the two phases is weakly first order or may be even continuous based on the metastability computation (see below). In sum, BL-VLDA and BL-VLDL exhibit different dynamic properties, as measured by both the degree of diffusivity and the dynamic changes in the diffusivity, and both properties are closely connected.

P-T Phase Diagram and Metastability Limit Boundaries.

Fig. 4 shows the P-T phase diagram of the system, in which the stability limits (55) for BL-VLDL, BL-LVDA, and BL-A are plotted. The data points in the P-T phase diagram were obtained based on two independent series of MD simulations, one with six isotherms (180, 200, 205, 210, 215, and 220 K) and another with nine isobars (−100, −50, 0, 50, 100, 200, 300, 400, and 450 MPa). Based on the stability limit boundaries, when BL-HDL is decompressed at 200 K, it transforms into BL-A for 50 MPa ≤ P ≤ 450 MPa and into BL-VLDL for P ≤ 0 MPa (Fig. 4). When BL-VLDL is compressed, the BL-VLDL → BL-A transition occurs at the compression limit within 0 MPa ≤ P ≤ 50 MPa (Fig. 4). Discontinuous changes in the area density and potential energy E/N of the BL-VLDL → BL-A transition suggest a strong first-order phase transition. When BL-VLDL is decompressed, it turns into vapor at the tensile limit (Fig. 4). Likewise, when BL-A is decompressed, it does not turn into BL-VLDL within the timespan of MD simulation but rather into the vapor phase at deeply negative pressure beyond the tensile limit (Fig. 4). The tensile limits of BL-A and BL-VLDL at 200 K are −200 and −150 MPa, respectively. When BL-VLDA at 185 K is compressed, it turns into BL-A at the compression limit of 50 MPa, and the transition is strongly first order due to the large change in the area density (Movie S9). In contrast, when BL-VLDA is superheated or when BL-VLDL is supercooled, almost no hysteresis is observed during the BL-VLDL and BL-VLDA transitions (Fig. 4), suggesting that the transitions are either weakly first order or continuous. Overall, the phase diagram includes a vapor phase, two liquid phases, and two amorphous solid phases.

In conclusion, we have shown that deeply supercooled BL water shows rich and unique phase behaviors, including the existence of an IEP at 100 MPa and 220 K, two forms of liquid water separated by a highly stable BL-A phase in the P-T phase diagram, a BL-VLDA, and a direct BL-VLDA-to-BL-A amorphous−amorphous transition at 190 K and 50 MPa. In previous studies (45, 38), direct BL-A-to-BL-VHDA₁ and BL-A-to-BL-VHDA₂ amorphous−amorphous transitions were observed (45, 38) at higher pressure beyond 400 MPa and below the melting point. These phase behaviors of BL water in deeply supercooled states are likely due to the unique interplay among the hydrogen-bonding network of BL water, the non-Brownian slow dynamics at low temperatures, and especially, the 0.78- to 0.80-nm hydrophobic confinement which constrains the motion of BL water. Without such spatial constraints, the deeply supercooled bulk transferable-intermolecular-potentials-4-point-charge (TIP4P) water can exhibit direct transition between HDL and LDL, while, for realistic bulk water, direct transition among LDA, HDA, and VHDA were observed. Can the direct LDL-to-HDL transition be observed in confined water in deeply supercooled state? For 0.76- to 0.85-nm confinement, the answer is that it is unlikely even though, at very low temperature, direct transition among BL-VLDA, BL-A, and BL-VHDA can be observed, as in the case of bulk water. This is because, at higher temperature, either the highly stable BL-A or BL hexagonal ice tends to form, or the BL hexagonal ice with AB stacking (where oxygens in the two layers are out of registry) (33) tends to form in the relatively narrow slit and low pressure range of 0 MPa to 400 MPa. This unique highly stable form of BL-A has no analogy in bulk water. With wider nanoslits, on the other hand, Koga et al. (56) showed that the HDL-to-LDL transition still was not observed for the TIP4P water. Also, Xu and Molinero (57) did not observe HDL-to-LDL transition for confined coarse-grained monatomic water (mW) inside a 1.5-nm cylindrical nanopore. Both simulations imply that, even if the HDL-to-LDL transition could occur in confined water, it would be at much deeper supercooled states compared with a 3D counterpart.

Methods

The simulation system consists of N = 960 water molecules confined between two hydrophobic planar walls, in which the 2D periodic boundary condition (x and y) is imposed. The separation h between the two walls is fixed at 7.8 Å, within which two layers of water can be accommodated. The TIP4P potential (58) is used to describe water−water interactions, and the interaction between a water molecule and the hydrophobic wall is described by the widely used Lennard-Jones 9–3 potential function (38, 44, 45), given by U_wall−O (z) = C₉/z⁹ − C₃/z³, where C₉ = 17,447.5 Å⁹ kJ/mol and C₃ = 76.1496 ų kJ/mol. A cutoff of 12 Å is used for the van der Waals interactions, and the long-range electrostatic interactions are treated by Ewald summation. All simulations are performed in the NP_xxP_yyhT ensemble, where the number of water molecules (N), the lateral pressures in the x and y directions (P_xx and P_yy), the distance (separation) between two walls or the width of the slit pore (h), and the temperature (T) are fixed. See ref. 41. for detailed simulation descriptions, and see SI Appendix for detailed methods for structural and diffusivity analysis.