Article pubs.acs.org/JPCC
Polymorphism of Water in Two Dimensions Tanglaw Roman* and Axel Groß Institute of Theoretical Chemistry, Ulm University, 89069 Ulm, Germany ABSTRACT: The structure of interfacial water is governed by a delicate interplay between water−substrate and water−water interactions. In order to identify the structure-determining factors of ordered two-dimensional water, first calculations of free-standing water layers have been performed. We demonstrate that square bilayers, rhombic bilayers, truncated-square bilayers, and secondary-prism bilayers are energetically more favorable than the traditionally considered hexagonal bilayer. These two-dimensional water structures are stabilized by a combination of high coordination and optimum tetrahedral bonding geometry. The identified structuredetermining factors responsible for the polymorphism of water in two dimensions will be operative in any confined water structure. Graphene influence on the stability of water sheets is for the first time explicitly treated using first-principles electronic structure calculations, and changes in some ordered water structures due to non-negligible graphene−water interaction are described.
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INTRODUCTION Interfaces with water play important roles in many fields of natural sciences such as biology, (electro-)chemistry, materials science, and earth science.1,2 While these solid−liquid interfaces are all around us, we still have not yet understood how interfacial water really behaves. What is clear is that the structure of water layers directly at the solid−liquid interface is governed by an interplay between the water−water and water− substrate interactions.3,4 A basic understanding of the factors influencing the structure of the water layers is crucial for comprehending the function of water at interfaces, as interfacial water often exhibits properties that are distinctively different from those of bulk water.5−7 Finding the most stable lowdimensional water polymorphs is an important step toward this fundamental understanding, since these systems provide benchmarks in which water−water interaction solely determines the structure and properties of interfacial water. It has long been assumed that water at flat surfaces tends to form hexagonal ice-like layers,8 and only through the corrugation of the underlying substrate some other geometry might be imposed on the water layer.4,9,10 Hence, the recent high-resolution electron microscopy observation of square ice confined between two graphene sheets11 was rather surprising, as the water−graphene interaction possesses only a weak dependence on the position and orientation of the water molecule.12,13 There is an ongoing discussion about whether or not the transmission electron microscopy images11 should be attributed to a film of square water or to accumulated salt sandwiched between graphene sheets.14,15 Still, this experimental study has raised interest in the fundamental question of whether under ambient conditions two-dimensional water layers can realize geometries that are not feasible for bulk ice.16 © 2016 American Chemical Society
All experimentally observed two-dimensional water structures are subject to water−substrate interactions that influence their shape. On the other hand, theoretical studies allow one to address two-dimensional water structures which are only subject to the water−water interactions. This allows one to disentangle the influence of the water−water interaction from the water−substrate interaction.17−20 Therefore, we have performed a systematic study of the stability of free-standing water structures using first-principles electronic structure calculations based on density functional theory (DFT). In the DFT calculations, we have employed the RPBE functional21 together with dispersion corrections22 which is known to give a reliable description of water properties23,24 and the water− surface interaction.25 This allows us to rank the stabilities of two-dimensional water structures to a high level of accuracy. An unbiased search for lowest-energy configurations based on seven different structural motifs has been performed. Sweeping across area densities, we can establish connections between different two-dimensional water structures, and gain insight into transitions to multilayer water. Additionally, water sheets with hexagonal, square, and truncated-square motifs confined within graphene sheets have been studied in order to simulate realistic environments needed for the comparison with the experiment.
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COMPUTATIONAL METHODS Periodic DFT calculations were done using the Vienna ab initio simulation package (VASP)26 and the revised PBE (RPBE) functional27 with the D3 scheme for computing dispersion effects using the form of the damping function proposed by Becke and Johnson.28 This flavor of DFT was chosen because Received: May 30, 2016 Published: June 6, 2016 13649
DOI: 10.1021/acs.jpcc.6b05435 J. Phys. Chem. C 2016, 120, 13649−13655
Article
The Journal of Physical Chemistry C this has previously been shown to be good at describing the interaction between water molecules,23,24 and is now also being used extensively in the construction of neural network potentials for accurate descriptions of water near interfaces,29 whereas PBE is known to overstructure water.23,30 It is furthermore well-suited for modeling interactions with graphene because of its good prediction of the graphene lattice constant, and also because of the inclusion of van der Waals interactions. The calculated graphene lattice constant of 2.472 Å was used. This value is 0.5% larger than the graphite basal plane lattice constant of 2.4589 Å derived from X-ray spectrometry.31 For comparison, the lattice constant that PBE32 predicts is 2.467 Å, while RPBE-D3 using zerodamping22 yields 2.480 Å. An energy cutoff of 450 eV is chosen; furthermore, the convergence of the result with respect to the k-point sampling was carefully checked. Water sheets are separated by at least 30 Å in the periodic supercell scheme. Structure relaxation calculations were terminated once the forces on all atoms became less than 0.01 eV/Å. Selected calculations repeated with the PBE functional and RPBE-D3 with zero-damping yielded the same trends. Two water molecules in a periodic cell were used to model the water layer of regular hexagons. Four water molecules were used for the layers comprised of squares, rhombuses (i.e., rhombuses with acute interior angles), and triangles, while eight water molecules were used for truncated-square bilayers and secondary-prism bilayers. Two types of periodic supercells were used in the calculations: rhombuses (for rhombus, regular hexagonal, and triangular motifs) and squares (square, rhombus, truncatedsquare, and secondary-prism motifs). By monitoring how the predicted minimum-energy structure evolves as a function of the number of random initial configurations, we estimate that, for a system with four water molecules in the supercell, 200 initial configurations should be enough to obtain the global minimum structure to within an error bar of 1 meV. A system with eight water molecules requires about 1000 initial configurations to reach this level of accuracy. Water sheet formation energies are expressed per molecule, and plotted with respect to the energy of a free water molecule, i.e., E = 0 when the water molecules are very far apart Eform = [Esheet − NEmol]/N
E(graphene−water) = [Etot − 2Eg − E H2O ‐ sheet]/A
(2)
E(water−water) = [E H2O ‐ sheet − NE H2O ‐ mol]/A
(3)
where Etot is the energy of the full system in which water is confined within graphene, EH2O‑mol is the energy of a free water molecule, Eg is the energy of the graphene sheet, EH2O‑sheet is the energy of a given water layer, and A is the area of the supercell. Finally, some conventions used in this paper: a sheet of water can be comprised of one to a few (in this work restricted to a maximum of two) layers consisting of irreducible, ordered twodimensional networks of water molecules. Layers that comprise a sheet are similar in structure, and are most stable when stacked directly upon each other. A single water layer can have a bilayer structure. Some papers use the term bilayer to denote a two-layer-thick sheet of water. For clarity, we use the term bilayer to designate a layer that is a superposition of two distinct parallel planes containing water molecules.
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RESULTS AND DISCUSSION First, we concentrate on free-standing two-dimensional water structures. The particular geometries were selected on the basis of the simplest planar motifsspace-filling tilings of triangles, squares, rhombuses, rectangles, hexagons, and octagons. The optimum area density of a given water layer was first estimated on the basis of typical water−water distances and a probable structure that maximizes the ice rules.33 Water molecules on these lattices were given random orientations, and then relaxed using conjugate gradient optimization. Up to 2048 initial configurations were used per motif in order to determine the arrangement of water molecules that minimizes energy. All molecules were allowed to relax freely along the directions parallel to the water layer except for the triangular structure, in which the oxygen atoms had to be partially constrained in order to retain the triangular arrangement. Each water sheet shown in Figure 1, with the exception of the rhombus structure rh(I), possesses bilayer structure; i.e., not all atoms of one water layer are at the same height. Testing our minimum-structure search method with isolated clusters, the cyclic form of a water tetramer shown in Figure 1a was found to be the most stable structure, in agreement with the current consensus in scientific literature.34−37 Each water molecule is both a donor and an acceptor of a hydrogen bond in this structural isomer. In contrast, in the bilateral-symmetric (H2O)4 isomer (Figure 1b), a water molecule is either donating or accepting two hydrogen bonds. There are two types of water molecules in this structure, based on their orientation: molecules which are flat-lying with respect to the tetramer plane and molecules whose planes are normal to the tetramer plane. Two-dimensional water structures based on hexagons (hex), rhombuses (rh), squares (sq), and triangles (tri) are illustrated in Figure 1c−j. Figure 1h shows a bilayer water structure that projects onto a motif of irregular hexagons, resembling the (1120̅ )/secondary-prism face of ice Ih. We hence name this two-dimensional water structure the secondary-prism (sp) water bilayer. In a competitive-growth method where the more stable ice face edges out the less stable, it was found that the secondary-prism face dominates at the ice−water interface.38 Recent classical molecular dynamics simulations of water confined using Lennard-Jones water−hydrophobic wall interactions39−41 yielded four planar water sheets (4·82 monolayer
(1)
where Emol is the energy of a free water molecule, Esheet is the energy of the given water sheet, and N is the number of water molecules comprising the water sheet. The graphene and water layers are structurally incommensurate; i.e., their different symmetries and lattice constants present a considerable mismatch. In order to use commensurate supercells of a computationally acceptable size, we adjusted the water layer densities to a certain extent: 12.28 molecules/nm2 for the square water sheet on graphene, 12.25 molecules/nm2 for hexagonal water, and 12.40 molecules/nm2 for truncatedsquare water. These values differ within 1.3% of each other. These surface densities were chosen in order to be as close as possible to the high packing density (12.49 molecules/nm2) reported in ref 11 while minimizing system size, and hence computational cost. Square water was modeled using rectangles with an aspect ratio of 1.00074. Graphene sheets were stacked in an AB manner. Water−graphene and water−water energy contributions were calculated using the following 13650
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Figure 2. Comparison of bilayer and planar two-dimensional water structures. Corrugated water sheets are always more stable.
planar hexagonal bilayer (hex), respectively. The figure demonstrates that the bilayer forms of water sheets are lower in energy compared with their completely planar counterparts, regardless of the motif. A comprehensive survey of the stabilities of unconstrained, free-standing water sheets is given in Figure 3, spanning all motifs in Figure 1. In contrast to Figure 2, both one- and twolayer sheets are included in order to compare their stability. Their energies are plotted over a wide range of area densities in order to illustrate how these ordered water structures change as
Figure 1. Illustration of the motifs employed in the search for stable two-dimensional water structures. Water tetramers [tet]: (a) cyclic (up−down−up−down), (b) bilateral symmetric. Water sheets, where water molecules are ordered in an array of (c) regular hexagons, otherwise known as a hexagonal bilayer [hex], (d) rhombus, planar (with interior angles of 104.5°) [rh(I)], (e) squares [sq], (f) rhombic bilayer [rh(II)], (g) triangles [tri], (h) Ih secondary-prism bilayer [sp], (i) truncated-square bilayers [tsq], (j) two-layer square [sq 2L], (k) herringbone [hb], (l) squares (side view), and (m) truncated-square bilayers (side view). Blue/red coloring of oxygen atoms is used as an aid for visualizing corrugation (c−i) and distinguishing the two water layers (j, k). The sheets are shown at their optimum area densities, except for the truncated-square bilayer (tsq) and the secondary-prism bilayer (sp) sheets, which are shown here at densities close to 12.3 molecules/nm2. Since multilayer versions of sp and tsq are stably formed by straightforward stacking, panels h and i also show sp 2L and tsq 2L, respectively (as well as the (112̅0) face of ice Ih and the (001) face of the hypothetical three-dimensional ice tsq). Unit cells are delineated in green.
ice, planar hexagonal, high-density flat rhombic, and irregular pentagons) and two bilayer water sheets (puckered rhombic, with and without net polarization). Note that, in contrast to other studies, we did not use any confining planar potentials in our geometry optimizations of water layers. We thus found structures which sometimes have resemblances to those previously suggested but are still distinctly different. In Figure 2, we contrast the stabilities of planar (partially constrained, where all oxygen atoms are kept coplanar) from bilayer (buckled/corrugated and unconstrained) water for selected structural motifs. It is useful to point out that partially constraining the water sheet relaxation can reproduce the 4·82 monolayer ice and planar hexagonal structures, which in Figure 2 correspond to planar truncated-square bilayer (tsq) and
Figure 3. Relative stabilities of one- (1L) and two-layer (2L) sheets of water. The plots are labeled according to the water structure exhibited at their respective energy minima. Motifs of the lowest-energy water structures at a given region of area density are shown. The formation energy of 3D ice tsq is plotted against the density of water molecules of a single truncated-square bilayer from the (001) face of this 3D crystal. Analogously, the area density used for Ih is that of the basal plane of the optimized solid. 13651
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̈ one may naively designate as stable because of its network of linear O−H···O linkages and perfect nearest-neighbor number of 4. However, the absence of some degree of intermolecular tetrahedral geometry makes this sheet an unfavored structure. This issue is resolved in the rhombic bilayer rh(II), which is more stable than a hexagonal bilayer. The most stable singlelayer water structures at densities between 11.2 and 15.4 molecules/nm2, the truncated-square bilayers and secondaryprism bilayers, are hydrogen-bonded to only three neighboring molecules, but they are arranged in a near-tetrahedral bonding geometry. For a two-layer structure of water, the coordination can be increased through interlayer bonding. This now renders the two-layer hexagonal structure to be the most stable. Lastly, we mention that the water sheet sq 2L shown in Figure 1j is only a metastable structure at 23.2 molecules/nm2. Maximizing intra- and interlayer hydrogen bonding and tetrahedral coordination does not lead to the formation of a perfect twolayer square lattice. These results contribute to understanding water layers in contact with solid surfaces as they clarify the role of the water− water interaction in the structure formation. Note that, on metal surfaces, a compensation effect between water−water and water−metal interaction has been found:3 the stronger the water−metal interaction, the weaker the water−water interaction within the first layer and vice versa. This explains the stability of water layers at steps which are pinned at the metal step edge atoms but only weakly interacting with the metal atoms above the terraces so that a strong hydrogen-bonded network can form.9 We are now turning to water sheets that are confined to two dimensions by some external layers. Recently, a square structure of water sandwiched between two graphene layers has been identified using high-resolution electron microscopy imaging.11 There is some ongoing discussion about the nature of the square structure that has been imaged.14,15 Still, it is instructive to look at possible water structures in such an arrangement from a theoretical point of view. Molecular dynamics simulations based on an empirical force field11 proposed that square water arises from a bonding network best described by, but not identical to, the rh(II) layer in the current study, which we find to considerably deviate from a square motif both at its optimum area density and at 12.3 molecules/ nm2 (Figure 1f). The latter value corresponds to the density of water molecules per layer derived from the experiment. A recent DFT study46 considered four motifs of one-layer water: hexagonal, pentagonal, rhombic, and square tilings of water confined through Morse potentials. From this set of water structures, the authors predict that hexagonal and pentagonal structures will prevail at ambient pressure, while higher pressures favor the formation of high-density rhombic and square phases. DFT calculations of water sheets using Lennard-Jones confining potentials for the oxygen atoms47 found flat square, rippled square, and honeycomb structures of one-layer water (which correspond to the sq planar, rh(II) bilayer, and hex bilayer we report here), suggesting agreement with experimentally observed square water.11 Moving to thicker water sheets however presented a very different picture, as molecular dynamics for two-layer sheets of water suggested the presence of a triangular phase of water but not a lattice comprised solely of squares.48 However, these studies did not consider the tsq and sp structures we discuss in our Article, which are lowest in energy, lower than hexagonal and square water. We can be sure that the reported water sheet comprised
water is compressed laterally. In order to see this more clearly, we have defined area density as the total number of water molecules per unit area, regardless of how many layers of water comprise the sheet, or how corrugated a given water layer is. Motifs of most stable structures are illustrated at the bottom of the figure. Up to a density of 15.4 molecules/nm2, one-layer (1L) structures are most stable, whereas for higher densities two-layer (2L) structures become most stable. At area densities below 6.6 molecules/nm2, water sheets comprised of interacting water tetramers were found to be most stable. This low-density region can be assigned to interacting clusters of water in general, which may not have a clear periodic structure. From 6.6 molecules/nm2 onward, water forms an ordered lattice, beginning with a truncated-square (tsq) structure, which possesses a 4-fold-symmetric arrangement of oxygen atoms. This is replaced by the Ih secondary-prism (sp) structure, which has 2-fold symmetry, between 11.2 and 15.4 molecules/nm2. A truly hexagonal water structure only becomes stable as a stacked two-layer system in the region of area density from 15.4 up to 23.0 molecules/nm2. This is in fact the most stable water sheet in energy per molecule among the one- and two-layer structures covered in this work, explaining its reported hydrophobicity,42 and the room-temperature order in interfacial water found using ab initio molecular dynamics.43 Finally, at area densities greater than 23.0 molecules/nm2, stacked truncated-square bilayers dominate among the water sheets that are only up to two layers thick. Figure 3 illustrates that the free-standing single hexagonal bilayer is not the structure of lowest total energy. At their respective optimum area densities, single-layer sq and rh(II) are more stable layers compared with the hex structure. Freestanding truncated-square (tsq) bilayers and secondary-prism (sp) bilayers of water do not have optimum area densities, as compression readily leads to the formation of two-layer water sheets. These two water structures are, however, also lower in energy than the hexagonal bilayer. At the same time, we point out that an infinite stacking of truncated-square bilayers is a metastable 3D water structure (Figure 3) which can reconstruct into the more stable bulk Ih, consistent with what we expect from nature. The regular hexagon lattice was for decades the default structure assigned to water adsorbed on solid surfaces, most especially on hexagonal closed-packed metal surfaces.8 Our results show that in fact a sufficiently strong coupling to a surface with hexagonal symmetry is required to form a single hexagonal water layer, which obviously does not seem to be the case for water on Pt(111).44,45 In order to understand the trends in the stability among the considered structures, it is crucial to analyze the factors determining the energetics. We find that what makes a particular water layer more stable cannot be attributed to a single factor. The number of O−H···O linkages formed, their corresponding bond lengths, how linear these linkages are, the symmetry with respect to neighboring molecules, and even the relative orientations of planes of individual water molecules all play an important role, but it is also essential to realize that these factors are not independent of each other. Stable 3D ice is formed when each water molecule donates two hydrogen bonds and accepts two hydrogen bonds, and when the four O− H···O linkages are spatially separated in a tetrahedral geometry. Ice Ihthe most common form of ice we have on our planet accomplishes this. As a case study in the two-dimensional domain, the rh(I) water layer is a completely planar sheet that 13652
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Figure 4. Water adsorbed on and confined within graphene sheets: (a) stability of one-layer water, (b) stability of two-layer water, (c) separation between graphene sheets confining water, (d) side view of confined hex 2L water, (e) side view of confined tsq 2L water.
of nonisogonal pentagons41,46 is not more stable than tsq and sp because of its planar structure. In order to check whether confinement of water between graphene sheets influences the stability of the water structures, we have performed calculations for water layers adsorbed explicitly on graphene and additionally for water trapped between two graphene layers. Note that the modeling of crystalline water layers between graphene sheets in a periodic setup requires finding an appropriate commensurate lattice for both subsystems. As the lattices of the considered water layers and graphene differ both in symmetry and size of their periodicities, we had to use unit cells containing up to 3096 atoms leading to a significant computational effort simulating these systems. Figure 4a shows the relative stabilities of one-layer water with three different structures trapped between graphene sheets; Figure 4b shows the analogue when another layer is added. At the experimentally derived water density per layer, we always find the truncated-square bilayers to be most stable, more stable than the hexagonal layers. Our water calculations do not predict any pure square structures of water to be the most stable, as proposed in ref 11. Square-bilayer water on graphene and within two graphene sheets broke down into a disordered water layer, and is therefore not included in the stability data presented in Figure 4a. Although the relative stability of the three motifs considered in Figure 4 is unchanged upon confinement, we find that the additional stabilization through the graphene−water interaction depends on the particular geometry of the water layers. In order to understand formation energies better, it is useful to decompose the computed energies of the water layers into separate contributions from the water−graphene and water− water interactions. The breakdown is listed in Table 1. The
Table 1. Breakdown of the Energy of Confined Water Sheetsa system
graphene−water
water−water
ratio
hex, bilayer sq, planar tsq, bilayer hex 2L sq 2L tsq 2L
−2.072 −1.686 −1.451 −2.000 −1.880 −1.460
−5.146 −4.696 −5.802 −12.282 −12.628 −13.685
0.403 0.359 0.250 0.163 0.149 0.107
a
All values are expressed in eV/nm2. The ratio of the graphene−water contribution to the water−water contribution is also given.
interaction of a water layer with graphene is not negligible, considering the significant magnitudes of graphene−water interaction we report here, although it is weaker13,18 than bonding at water−metal interfaces. As one may expect, the role of graphene−water interaction in stabilizing confined ordered structures of water becomes less important with increasing water sheet thickness. Even if free-standing square water is not predicted to be most stable, it is interesting to test whether it is kinetically stabilized, i.e., whether its transformation is hindered by sufficiently large barriers. Square bilayer (sq) and rh(II) water readily broke down into disordered structures on graphene and within two graphene sheets; planar sq on the other hand retained its order within graphene confinement. At a density of 24.5 molecules/ nm2, hexagonal sheets reconstructed in order to minimize energy as the water sheet comprised of two hexagonal bilayers are markedly strained, by 73 meV/molecule. Graphene−water interaction destroys the double-bilayer network, forming an open, nonplanar structure (Figure 4d). A more ordered structure that is similar in energy is the two-layer herringbone 13653
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Siller et al.11 that confined two-dimensional water can crystallize in a phase that has a symmetry that is qualitatively different from the conventional hexagonal geometry of hydrogen bonding between water molecules. Our findings should aid future first-principles modeling of water at interfaces of arbitrary symmetries and interaction strengths, and we hope this work could encourage investigators to explore beyond hexagonal water at interfaces. Experimental verification of the existence of truncated-square, secondary prism, and herringbone water structures is still being awaited.
(hb) water sheet (Figure 1k), which also resulted from hex 2L reconstruction, but yielded a smaller separation between graphene sheets. The herringbone structure was found to be stable only within graphene confinement. On the other hand, we found that the two-layer sheet of square water confined in graphene is metastablethe order was not destroyed upon structure optimization even with 312 water molecules in the calculation. The number of layers of water that comprise a confined ordered sheet of water is obviously connected to the size of the constricting framework. Molecular dynamics simulations using a 5−7 Å separation between graphene sheets produced ordered water sheets that are one layer thick, while a 7−9 Å separation yielded two-layer water sheets.39,41 Our DFT calculations show that separation of graphene sheets is in addition strongly linked to the motif of the water sheet they enclose (Figure 4c). Calculations predict that confined truncated-square bilayers are most stable at a graphene interlayer separation of 8.4 Å, while squares and hexagons prefer graphene separations less than 7.5 Å. One could argue that the separation of the two graphene sheets enclosing water is a factor that can be used to control the motif of water that is formed: square water is more favored when water is more constricted by the graphene sheets.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Useful discussions with O. Lehtinen, T. Lehnert, and U. Kaiser are gratefully acknowledged. This research has been supported by the German Science Foundation (DFG) through the research unit FOR 1376 (DFG contract GR 1503/21-2) and by the Baden-Württemberg Foundation within the Network of Competence “Functional Nanostructures”. Computational time at the bwForCluster for computational and theoretical chemistry JUSTUS of the bwHPC project of the Federal State of Baden-Württemberg and at the Leibniz-Rechenzentrum (LRZ) of the Bavarian Academy of Sciences is gratefully acknowledged.
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CONCLUSIONS We have compared the stability of free-standing sheets of water, using unconfined two-dimensional sheets, i.e., without the need for hydrophobic walls of arbitrary separations. This procedure has allowed us to explore bilayer structures more, and hence discover lower-energy water layers that have never been reported before. A search for the most stable two-dimensional ordered structures of water was done, mapping the stabilities of seven one-layer water sheets and four two-layer water sheets over a wide range of area densities, offering a new perspective on growth toward multilayer water. Both the quantity and quality of hydrogen bonds that hold the water sheet together were found important in determining the layers in which water molecules are most strongly bound to each other. Intermolecular bonding at near-tetrahedral angles achieves this. Our calculations could not confirm the experimentally proposed pure square structure11 of two-dimensional water to be most stable. At the same time, we also did not find that hexagonal water layers are necessarily the most stable. Freestanding single water sheets with square, rhombus, truncatedsquare, and secondary-prism motifs were found to be lower in energy compared with the standard sheet in which water molecules are arranged in regular hexagons. This is the first time the tsq and sp water sheets have been reported, sheets which are lower in energy than any of the two-dimensional structures of water reported up until now. As the sp structure corresponds to the (112̅0) termination of ice Ih, it might be interesting to study ice growth along this direction instead of focusing on the more weakly bound water sheets based on Ih(0001). Water sheets at similar surface area densities/surface coverages that are bounded by two graphene sheets were also compared. Graphene−water interaction is strong enough to restructure some confined water sheets. At the experimentally proposed density per water layer, we find one- and two-layer structures consisting of truncated-square motifs to be most stable, independent of the fact of whether the water layers are free-standing, adsorbed on graphene, or sandwiched between two graphene sheets. Thus, we confirm the assertion of Algara-
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DOI: 10.1021/acs.jpcc.6b05435 J. Phys. Chem. C 2016, 120, 13649−13655
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DOI: 10.1021/acs.jpcc.6b05435 J. Phys. Chem. C 2016, 120, 13649−13655
