Confined Monolayer Ice Between CaF2 (111) and Graphene: Structure and Stability

Water monolayer can form in layered confined systems. Here, CaF2 (111) and graphene are chosen as modeling systems to explore the structure and stability of confined monolayer water. First, water molecules tend to intercalate into a confined space between graphene and CaF2, rather than on a bare surface of graphene. Water molecules can move fast in the confined space due to a low diffusion barrier. These water molecules are likely to aggregate together, forming monolayer ice. Four ice phases including ice II, ice III, ice IV, and ice Ih are compared in this confined system. Intriguingly, all the ice phases undergo very small deformation, indicating the 2D monolayer ice can be stable in the CaF2–graphene–confined system. Beyond, projected band structures are also plotted to understand the electronic behavior of these confined ice phases. Nearly all the bands originated from confined ices are flat and locate about 2–3 eV below the Fermi level. Binding energy calculations suggest that the stability sequence in this confined system as follows: Ih-up ≈ Ih-down ≈ II < IV < III. Our results bring new insights into the formation of water monolayer production in such a confined condition.


INTRODUCTION
The behavior of water at surfaces and a nanoconfined space [1] in two, three, or one dimensions is significantly different from that in bulk ice [2][3][4]. Understanding the structural tendencies of nanoconfined water is of great interest in biology [5], material science [6][7][8], nanofluidics [9], tribology, and, most recently, electronics [10,11]. Because of various possible hydrogen bond networks, the structure of water is notoriously perplexed [12], rising as one of the most challenging issues in the 21st century [13]. The subtle interplay between the water-substrate and water-water interactions brings about many new distinctive ice configurations on different substrates [14][15][16][17][18]. In vacuum and on weakly interacting substrates, Xu et al. [14] found a helical ice monolayer with every six water molecules helically arranged along the normal of the basal plane by performing an intensive structural search based on ab initio calculations. On Au(111), a two-dimensional (2D) interlocked ice consisting of two flat hexagonal water layers in which the hexagons in two sheets are in registry is imaged by non-contact atomic force microscopy and identified by density functional calculations [15].
Except for various types of monolayer ice formed on surfaces, 2D monolayer-confined ice also has drawn much attention due to its relevance to a series of processes in nature and industry [19]. Nevertheless, the structures of 2D monolayer ice under distinct confinements are still under debate.
Recently, by performing scanning probe microscopy (SPM), graphene ultrathin coatings are utilized to assist the visualization of interfacial water adlayers. This made remarkable progress on interfacial water. Xu et al. [20] observed water adlayers on mica coated by monolayer graphene at room temperature by using atomic force microscopy. The graphene coating can stably "fix" the water adlayer structures, thus permitting the detection of the structure of the first water adlayers under ambient conditions [21]. Therefore, the presence of ambient water adlayers between graphene [19] and various substrates, including mica [11,[21][22][23][24], SiO 2 [25,26], BaF 2 [27], SiC [28], sapphire [29], Ni [30], Ru, Cu [31], and Si [32], has been widely studied by experimental probing techniques. Taking mica as an example, the structure of the first wetting adlayer confined between graphene and mica is unique, quite different from ice Ih, due to strong mica-water interaction [21]. The structural characteristics of intercalated water adlayers between graphene and mica under a thermal treatment were also investigated by Ochedowski et al [22]. They showed that the intercalated water adlayers are partially removed under mild heating (200°C), and the defect density increases, leading to "nanoblister" formation at a temperature of 600°C, causing a transition from the p-type to n-type for graphene layers [22]. CaF 2 (111)/graphene is an excellent platform to trap water molecules and generate confined ice layers. Recently, the formation of a several monolayer thick hydration layer on a graphene-coated hydrophilic substrate CaF 2 (111) was revealed [33]. The first layer is so stable that it cannot be removed upon heating. After this, hydration layers confined between graphene and the CaF 2 substrate were found to electronically modify graphene as the material's electron density transfers from graphene to the hydration layer [34]. However, the structure and stability of monolayer ice confined between CaF 2 (111) and graphene remain unclear. In an experiment, many factors can influence the hydration layers and properties of graphene [35], such as the types of adhesive tapes [23], other adsorbents [22], and additives. So a theoretical study on structural information and stability of water confined between graphene and CaF 2 at the atomic level is urgently needed.
In this study, the structure and stability of monolayer ice confined between CaF 2 (111) and graphene are investigated systematically based on first-principles calculations. Water molecules tend to aggregate together to form monolayer ice. A water molecule will automatically move to the "edge" of the top surface of the ice layer, promoting monolayer ice growth and prohibiting multilayer nucleation. Beyond, the energy barrier for water diffusion between CaF 2 (111) and graphene is very low. Thus, water molecule can move freely and connect with each other into a monolayer ice between CaF 2 (111) and graphene. Four probable ice phase structures including ice II, ice III, ice IV, and ice Ih are studied in our confined system. All the ice phases are maintained with only small deformations in the CaF 2 -graphene-confined system. Binding energy suggests that the most stable monolayer ice confined between CaF 2 (111) and graphene is phase-III. Confined ice III is thermodynamically stable under a wide temperature and pressure span according to the calculated phase diagram. Furthermore, the band structures of these systems are plotted to explore the electronic properties of confined ice phases. The bands originated from confined ice are flat and locate about 2-3 eV below the Fermi level.

METHODS
All the first-principles calculations are based on the DFT, which is implanted in the Vienna ab initio simulation package code (VASP) [36]. The Perdew-Burke-Ernzerhof version of the generalized gradient approximation (GGA-PBE) was chosen as the exchange-correlation functional [37] along with the dispersion correction introduced by Grimme (PBE + D3) [38]. In this work, all atoms were fully relaxed using DFT with vdW correction to obtain the equilibrium distance. The electron wave functions are solved with plane wave basis set in conjunction with pseudo potentials by the projector augmented wave (PAW) method [39]. The K points in the first Brillouin zone (BZ) are generated in the form of a Monkhorst-Pack 4 × 4 × 1 grid [40]. A 500 eV kinetic cutoff energy was used for the plane wave basis. The structure of water confined between CaF 2 (111) and graphene were optimized using standard local optimization algorithms with convergence criteria of 10 −4 eV for both electronic and ionic relaxation. In our CaF 2 surface slab, there is a net dipole along the Z direction, which will introduce an artificial electric field in calculations with periodic boundary conditions (PBC), and the dipole correction scheme introduced by Neugebauer and Scheffler is applied in all calculations [41,42]. To avoid spurious interactions between neighboring structures in the tetragonal supercell, a vacuum layer of 25 Å was included in all non-periodic directions.
Water molecule diffusion barriers are calculated via the climbing image-nudged elastic band (CI-NEB) [44] method. This technique can efficiently map the minimum energy path and find the saddle points between two given local minima for the system. Six intermediate images are used in CI-NEB calculations. Each image was relaxed until the forces on the atom were less than 0.02 eV/Å.
The binding energies of monolayer ice phases between the CaF 2 and the graphene system are calculated as follows: October 2021 | Volume 9 | Article 740627 where E(Total), E(CaF 2 ), E(Graphene), and E(H 2 O) is total energy of the CaF 2 /H 2 O/graphene system, a clean CaF 2 (111), graphene sheet, and an isolated water molecule, respectively.

Stratification Test and NEB Calculations
CaF 2 (111)-graphene is an excellent platform to trap water [33,34]. These water molecules are likely to aggregate together forming monolayer connecting with each other by hydrogen bonding. We perform stratification test to make certain the confined ice is monolayer or not. As shown in Figure 1A, we put a water molecule on top of the monolayer water structure confined between CaF 2 (111) and graphene. After optimization, the water molecule move to the edge of the existing water structure forming a new monolayer ( Figure 1B). This process is barrierless, during which the binding energy decrease by 0.73 eV/H 2 O. Therefore, the confined ice between CaF 2 (111) and graphene must be monolayer. Furthermore, the water molecule diffusion between CaF 2 (111) and graphene is investigated using the CI-NEB method. As shown in Figure 1C, the water diffusion energy barrier is 0.19 eV from initial adsorption local minima (I.S., Figure 1D) to final adsorption local minima (F.S., Figure 1F). During this process, the water molecule is first locates on the top of Ca atom ( Figure 1D), then moves to the hollow site ( Figure 1E), and finally locates on the top of the neighboring Ca atom ( Figure 1F).
Choosing the total energy of the I.S. system as a reference, the energy of F.S. and T.S. are all listed in the Figures 1E,F (0.19 eV  and −0.06 eV). The speed of water diffusion can be characterized by the water diffusion coefficient D H2O which can be estimated from the diffusion barriers by the following formula: where a is the distance of the hop along the diffusion pathway and ] is the attempt frequency, about 10 13 Hz, which is generally in the range of phonon frequencies [45,46]. ΔE is the diffusion energy barrier [45]. K B is the Boltzmann constant and T represents the temperature. According to the diffusion results, at room temperature (T 300 K), the water diffusion coefficient D H2O is calculated as 8.35 × 10 −6 cm 2 /s. The low diffusion energy barrier and high diffusion speed of water molecule provide strong evidence for monolayer ice formation between CaF 2 (111) and graphene.

Structure and Stability of Confined Ice
Four monolayer ice phases including Ice II [43], III [43], IV [43], and Ih are intercalated between CaF 2 (111) and graphene. All the free-standing structures of the four ice phases are depicted in the Supplementary Figure S1  The monolayer ice II has a planar hexagonal morphology, and it is made up of two kinds of water molecules with different orientations. The plane of every water molecule is perpendicular to the planes of three nearest-neighbor molecules. Besides, the Frontiers in Physics | www.frontiersin.org October 2021 | Volume 9 | Article 740627 monolayer ice II displays considerable net polarization because all the dipole vectors of water molecules are parallel to the longest diagonal of a hexagon. As shown in Figure 2A, under confinement of graphene and CaF 2 (111), the structural motifs of ice II change slightly. The location and orientation of water molecule whose plane is parallel with the CaF 2 (111) is nearly unchanged. Nevertheless, those water molecules whose plane is vertical with CaF 2 (111) rotates slightly to form hydrogen bonds with F atoms. The unit cell is still the six-numbered planar ring, and the hydrogen bond network is the same with ice II which satisfy the ice rule. Different from ice II, monolayer ice III is composed of planar rhombic rings and all the water molecules tilt with respect to the plane of oxygen. When intercalated into CaF 2 (111) and graphene, it distorts slightly. The four-membered unit cell almost remains unchanged, but the orientations of water molecules become disorganized and delamination appears. Unlike ice II-III, oxygen atoms of ice IV are in alternative ridges with different height in the normal direction. Under confinement, the unit cell of ice IV also changes from rhombic to four-and five-membered rings ( Figure 2C).
Ice Ih is also intercalated into the CaF 2 (111) and graphene. Two cases of ice Ih are tried as shown in Figures 2D,E. In the Figure 2D, all the hydrogen atoms are pointing to the graphene coating, while in the Figure 2E, all the hydrogen atoms are pointing to the CaF 2 (111). These two ice configurations are called "Ih-up" and "Ih-down," respectively. In the two cases, the ice structure nearly remains unchanged. The hydrogen atoms tend to point to the CaF 2 (111), so in the structure of "Ih-up," some water molecules rotate to point to the CaF 2 (111).
To further determine the stability of these monolayer ice phases when they are confined between CaF 2 (111) and the graphene system, the binding energies of monolayer ice phases between the CaF 2 and the graphene system are calculated via Eq. 1. The results are shown in Figure 2F. To understand the stability and structural properties through electronic properties, the band structures of the CaF 2 /graphene system and five ice phases confined between CaF 2 (111) and graphene are presented in Figures 3A-F, respectively. Due to the different size of the graphene's supercell, the location of Dirac cone is distinct. The contribution from graphene and CaF 2 (111) is plotted in Figure 3A. Before ice intercalation, the gap of CaF 2 (111) bands is about 6.35 eV; while in the ice confined systems, the gap changes slightly, in the range of (5.5, 6.18) eV. Additionally, in CaF 2 (111)/II/ graphene and CaF 2 (111)/Ih-down/graphene, the CaF 2 (111) bands both move downward probably because most H atoms point to the CaF 2 (111) surface. The contribution to each band from ice phases

Phase Diagram
Binding energy results demonstrate the highly kinetic stability of ice III; nevertheless, under real environment, the water pressure and temperature must be considered. Based on first-principles thermodynamic calculations [47][48][49][50], the free Gibbs energy change ΔG of the CaF 2 (111)/ice III/graphene confined system is defined as: where E Total , E CaF 2 , E Graphene , and E H 2 O is total energy of the CaF 2 /H 2 O/graphene system, clean CaF 2 (111), graphene sheet, and isolated water molecule, respectively. A is the surface area and N H 2 O is the number of the water molecules included in the ice phases. Δμ H 2 O is the chemical potentials of water in gas phase, which can be associated with the DFT results and experimental thermodynamic data, as follows: where P 0 1 bar and the μ g P 0 , T represents the standard chemical potential of gas water, which can be obtained from standard thermodynamic tables [51].
The free Gibbs energy change ΔG of freestanding ice III [III(free)] and the CaF 2 (111)/ice III/graphene [III(confined)] system is depicted in Figure 4A using Eq. 3. When Δμ(H 2 O) is lower than −15.07 eV, ice III is not likely to be confined between CaF 2 (111) and graphene. On the contrary, the confined system will be more favorable. According to Eq. 4 and the phase transition value of Δμ(H 2 O) obtained from Figure 4B, a two-dimensional (T, P) phase diagram is further plotted. Ice III tends to be confined between CaF 2 (111) and graphene under a wide T and P span. For example, at room temperature, confined ice III is more thermodynamically favorable when the water pressure is larger than 10 −10 mTorr. However, the condition for freestanding ice III is harsh, often under ultra-high vacuum. Noted that all our configurations were obtained without compression, applying the compression to reduce the layer distance between graphene and CaF 2 could further tune the structure and stability of water layer, which deserves comprehensive study in the future.

CONCLUSION
In conclusion, we have theoretically studied the structure and stability of monolayer ice phases confined between CaF 2 (111) and graphene. The stratification test and CI-NEB calculations demonstrate the possibility of monolayer ice formation in the CaF 2 (111) and graphene system. Therefore, five systems including monolayer ice II, III, IV, I h -up, and I h -down confined between CaF 2 (111) and graphene are considered. After optimization, all the ice phases undergo very small deformation, indicating that the 2D monolayer ice can be stable in the CaF 2 -graphene-confined system. The electronic properties of these five systems are calculated. Nearly all the bands originated from confined ice are flat and locate about 2-3 eV below the Fermi level. By comparing the binding energy of five systems, the stability sequence is identified as: III > IV > II ≈ Ih-up ≈ Ih-down. Beyond, based on first-principles thermodynamic calculations, a two-dimensional (T, P) phase diagram for III(free) and III(confined) is further plotted. Ice III tends to be confined between CaF 2 (111) and graphene under a wide T and P range.

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.