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Square ice in graphene nanocapillaries


Bulk water exists in many forms, including liquid, vapour and numerous crystalline and amorphous phases of ice, with hexagonal ice being responsible for the fascinating variety of snowflakes1,2. Much less noticeable but equally ubiquitous is water adsorbed at interfaces and confined in microscopic pores. Such low-dimensional water determines aspects of various phenomena in materials science, geology, biology, tribology and nanotechnology3,4,5,6,7,8. Theory suggests many possible phases for adsorbed and confined water9,10,11,12,13,14,15,16,17, but it has proved challenging to assess its crystal structure experimentally17,18,19,20,21,22,23. Here we report high-resolution electron microscopy imaging of water locked between two graphene sheets, an archetypal example of hydrophobic confinement. The observations show that the nanoconfined water at room temperature forms ‘square ice’—a phase having symmetry qualitatively different from the conventional tetrahedral geometry of hydrogen bonding between water molecules. Square ice has a high packing density with a lattice constant of 2.83 Å and can assemble in bilayer and trilayer crystallites. Molecular dynamics simulations indicate that square ice should be present inside hydrophobic nanochannels independently of their exact atomic nature.

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Figure 1: Square ice.
Figure 2: Few-layer ice and its stacking order.

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This work was supported by the DFG (Germany), the European Research Council, the EU Graphene Flagship, the National Natural Science Foundation of China, the Ministry of Science, Research and Arts of Baden-Wuerttemberg (Germany), the Office of Naval Research, the Air Force Office of Scientific Research, the Anhui Provincial Natural Science Foundation (China), the Finnish Cultural Foundation and the Fundamental Research Funds for the Central Universities of China. MD simulations were carried out at Supercomputing Center of the University of Science and Technology of China.

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Authors and Affiliations



U.K., I.V.G and A.K.G. proposed and directed the project. G.A.-S. and O.L. designed the experiments and samples, performed TEM measurements and analysed them. H.A.W. and F.C.W. carried out MD simulations (with feedback from A.K.G.). I.V.G. and A.K.G. wrote the manuscript with help from all the authors.

Corresponding authors

Correspondence to U. Kaiser, H. A. Wu or I. V. Grigorieva.

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Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 2D water captured between graphene monolayers.

a, Confined water at low magnification. The lateral size of such water pockets was typically 100 nm. The chequered pattern reveals a collection of ice crystallites. b, Another example of a high-magnification image of 2D ice. The inset shows selected area electron diffraction from a region approximately 120 nm in diameter. The four diffraction spots connected for clarity by the red lines yield a = 2.83 ± 0.03 Å, the same as the value obtained using the fast Fourier transform in Fig. 1.

Extended Data Figure 2 Large water droplets and their EELS.

a, Low-magnification TEM image of a reference sample in which water was trapped in large bubbles (diameter of 100 nm). b, Spectrum near the oxygen K-edge from the droplets shown in a. The four marked peaks at 532 eV, 537 eV, 545 eV and 550 eV are in agreement with the previously studied spectra for mixtures of water vapour and liquid water39,40.

Extended Data Figure 3 Dynamics of 2D ice crystallites and formation of defects.

af, High-resolution snapshots from the Supplementary Video illustrate continuous reorganization of ice crystallites. Red lines highlight some of the changes: the bilayer crystal in a thins down to a monolayer in b, then splits into two crystals separated by a grain boundary in c, and a trilayer is formed in the same area in d. In e, a new crystallite, outlined in blue, appears in the top right corner, growing and propagating towards the centre in f. Other crystallites also change from panel to panel. gj, Examples of an edge dislocation (g) and tilt grain boundaries (i) in 2D ice. h and j are the same images as g and i, respectively, but with reduced contrast; atomic rows are overlaid with red and blue lines to highlight the defects. Red lines mark existing atomic rows; blue lines mark extra rows originating from dislocations; green shapes outline defects without discernible atomic structures. k, l, Monolayer ice found in MD simulations also shows dislocations, indicating that they are intrinsic to the formation of 2D ice at room temperature.

Extended Data Figure 4 Quantifying the contrast to determine the number of layers in 2D ice.

a, An example of the original TEM images used in our analysis (same image as in Fig. 2a). b, The filter calculates the local variance that is displayed as a greyscale value. c, The lattice pattern that remains visible in the variance image (b) is suppressed by applying the Gaussian blur. d, The final root-mean-square contrast map (that is, the standard deviation map) is obtained by calculating the square root of each pixel value of the variance image (c).

Extended Data Figure 5 MD simulations setup.

a, Initial configuration. b, Top view of the empty graphene channel, also showing how the external pressure P is applied to mimic the van der Waals pressure.

Extended Data Figure 6 MD simulations of a monolayer of water in a 6.5-Å-high graphene capillary.

Only one layer of water molecules can fit in. Red and grey circles represent oxygen and hydrogen atoms, respectively. Square ice is formed in this case, independently of whether the confinement is provided by rigid (a) or flexible (b) graphene sheets.

Extended Data Figure 7 MD simulations for a 9-Å-high graphene capillary.

a, b, Top (a) and side (b) views of a bilayer of water formed at P = 0.5 GPa. Different colours in a correspond to different vertical positions of water molecules in different layers: dark blue and red mark the bottom and top positions, respectively and lighter colours correspond to intermediate positions. Although the water molecules are clearly arranged in two layers, no intralayer ordering is present and hydrogen bonds preserve their tetrahedral coordination as in bulk water. c, d, As in a and b but at 1.0 GPa. Ordered bilayer ice is formed, with identical square lattices in the two layers, as illustrated by snapshots of the top and bottom layers in e. The ordering is accompanied by switching hydrogen bonds to in-plane coordination. f, g, Schematic illustration of AB and AA stacking. The stacking found in c and d is AB.

Extended Data Figure 8 Van der Waals pressure acting on water trapped between graphene sheets.

a, Schematic illustration of water confined by graphene. Owing to adhesion between the graphene layers, water is squeezed into a 2D puddle. Parameters d and δ are used in our estimation of van der Waals pressure (see Methods). b, c, MD simulations of van der Waals pressure exerted on a gas bubble (1,000 He atoms) trapped between two freely moving graphene sheets, showing side (b) and top (c) views of the He nanoballoon. In b, the graphene layers are not shown for clarity, and in c they are in light grey. df, Simulations of 2D ice formed by a water nanodroplet (100 molecules) confined between two freely moving flexible graphene sheets. Oxygen atoms are shown in red, hydrogen in light grey and graphene in dark grey: side (d) and top (e, f) view at equilibrium Simulations in d and e were performed using the SPC/E model and, in f, using TIP4P/2005. For clarity, graphene is not shown in e and f. The lattice parameter in e and f is about 2.8 Å within the modelling accuracy.

Extended Data Figure 9 MD simulations of the order–disorder transition in trilayer ice.

Top (a) and side (b) views of trilayer ice formed at P ≈ 1.4 GPa in the graphene capillary with h = 11.5 Å. Different colours correspond to water molecules in different layers (same colour coding as in Extended Data Fig. 7). No clear stacking sequence can be determined for this structure. c, d, Potential energy per atom in 2D ice as a function of applied pressure for the bilayer (c) and trilayer (d) ice.

Extended Data Figure 10 Square ice in nanocapillaries with different hydrophobicity.

ad, Water droplets on surfaces with ε = 0.01 kcal mol−1, 0.05 kcal mol−1, 0.1 kcal mol−1 and 0.2 kcal mol−1, respectively. The changes in the relative strength of water–water and water–surface interactions result in different contact angles. For comparison, ε for the graphene–water interaction is 0.07 kcal mol−1. eh, Monolayer ice confined between surfaces with ε corresponding to ad, respectively. In this case, the modelled walls are generic and do not have a discrete atomic structure, that is, their potential is uniform. h = 6.5 Å, the same as for the modelling of monolayer ice in the graphene nanocapillary in Extended Data Fig. 6.

Related audio

Supplementary information

Dynamics of square ice

An accelerated time sequence of 101 frames recorded over approximately 4 minutes, showing dynamics of the 2D ice. The sequence was recorded with an exposure time of 1 second per frame and acquisition rate of 1 frame per 2 seconds. The dose rate in the sequence was maintained at 1.7∙107 e s-1 nm-2. To compose the sequence, raw images have been aligned and corrected for slightly non-uniform illumination. (MOV 12933 kb)

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Algara-Siller, G., Lehtinen, O., Wang, F. et al. Square ice in graphene nanocapillaries. Nature 519, 443–445 (2015).

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