The dielectric constant ε of interfacial water has been predicted to be smaller than that of bulk water (ε ≈ 80) because the rotational freedom of water dipoles is expected to decrease near surfaces, yet experimental evidence is lacking. We report local capacitance measurements for water confined between two atomically flat walls separated by various distances down to 1 nanometer. Our experiments reveal the presence of an interfacial layer with vanishingly small polarization such that its out-of-plane ε is only ~2. The electrically dead layer is found to be two to three molecules thick. These results provide much-needed feedback for theories describing water-mediated surface interactions and the behavior of interfacial water, and show a way to investigate the dielectric properties of other fluids and solids under extreme confinement.

In the field of nanofluidics, it has been an ultimate but seemingly distant goal to controllably fabricate capillaries with dimensions approaching the size of small ions and water molecules. We report ion transport through ultimately narrow slits that are fabricated by effectively removing a single atomic plane from a bulk crystal. The atomically flat angstrom-scale slits exhibit little surface charge, allowing elucidation of the role of steric effects. We find that ions with hydrated diameters larger than the slit size can still permeate through, albeit with reduced mobility. The confinement also leads to a notable asymmetry between anions and cations of the same diameter. Our results provide a platform for studying the effects of angstrom-scale confinement, which is important for the development of nanofluidics, molecular separation, and other nanoscale technologies.

Graphene oxide (GO) membranes continue to attract intense interest due to their unique molecular sieving properties combined with fast permeation rates 1-9 . However, the membranes' use has been limited mostly to aqueous solutions because GO membranes appear to be impermeable to organic solvents 1 , a phenomenon not fully understood yet. Here, we report efficient and fast filtration of organic solutions through GO laminates containing smooth two-dimensional (

Biological membranes allow permeation of water molecules but can reject even smallest ions. Behind these exquisite separation properties are protein channels with angstrom-scale constrictions (e.g., aquaporins). Despite recent progress in creating nanoscale pores and capillaries, they still remain distinctly larger than protein channels. We report capillaries made by effectively extracting one atomic plane from bulk crystals, which leaves a two-dimensional slit of a few Å in height. Water moves through these capillaries with little resistance whereas no permeation could be detected even for such small ions as Na + and Cl -. Only protons can diffuse through monolayer water inside the capillaries. The observations improve our understanding of molecular transport at the atomic scale and suggest further ways to replicate the impressive machinery of living cells.It has long been an aspirational goal to create artificial structures and devices with separation properties similar to those of biological membranes 1-5 . The latter utilize a number of separation mechanisms but it is believed that angstrom-scale constrictions within protein channels 6,7 play a key role in steric (size) exclusion of ions with the smallest hydration diameters D H  7 Å, typically present in biofluids and seawater 8,9 . Such constrictions are particularly difficult to replicate artificially because of the lack of fabrication tools capable to operate with such precision and, also, because the surface roughness of materials is typically much larger than the required angstrom scale 1 . Nonetheless, several artificial systems with nanometer and sub-nanometer dimensions were recently demonstrated, including narrow carbon and boron-nitride nanotubes 5,10,11 , graphene oxide laminates 12,13 and atomic-scale pores in graphene and MoS 2 monolayers 3,4,14 . The resulting devices exhibited high selectivity with respect to certain groups of ions (for example, they blocked large ions but allowed small ones 12,13 or rejected anions but allowed cations and vice versa 2,3,5 ). Most recently, van der Waals assembly of two-dimensional (2D) crystals 15 was used to make slit-like channels of several Å in height 16,17 . They were atomically smooth and chemically inert and exhibited little ( 10 -4 C cm -2 ) surface charge 17 . The channels allowed fast water permeation 16 and blocked large ions with a complete cutoff for diameters larger than 10 Å (ref. 17 ). Small ions (for example, those in seawater with D H of 7 Å) still permeated through those channels with little hindrance, showing that an angstrom-scale confinement comparable to that in aquaporins 6,7 is essential for steric exclusion of small-diameter ions. In this report, we describe 2D channels with the height h of about 3.4 Å (ref. 18), which are twice smaller than any hydrated ion (smallest ions are K + and Clwith D H  6.6 Å) 8,19 but sufficiently large to allow water inside (effective size of water molecules is 2.8 Å). The achieved confinement matches the size of protein constrictions in biological ...

Despite being only one-atom thick, defect-free graphene is considered to be completely impermeable to all gases and liquids [1][2][3][4][5][6][7][8][9][10] . This conclusion is based on theory 3-8 and supported by experiments 1,9,10 that could not detect gas permeation through micrometre-size membranes within a detection limit of 10 5 to 10 6 atoms per second. Here, using small monocrystalline containers tightly sealed with graphene, we show that defect-free graphene is impermeable with an accuracy of eight to nine orders of magnitude higher than in the previous experiments. We could discern permeation of just a few helium atoms per hour, and this detection limit is also valid for all other tested gases (neon, nitrogen, oxygen, argon, krypton and xenon), except for hydrogen. Hydrogen shows noticeable permeation, even though its molecule is larger than helium and should experience a higher energy barrier. The puzzling observation is attributed to a two-stage process that involves dissociation of molecular hydrogen at catalytically active graphene ripples, followed by adsorbed atoms flipping to the other side of the graphene sheet with a relatively low activation energy of about 1.0 electronvolt, a value close to that previously reported for proton transport 11,12 . Our work provides a key reference for the impermeability of two-dimensional materials and is important from a fundamental perspective and for their potential applications.From a theory standpoint, monolayer graphene imposes a very high energy barrier for penetration of atoms and molecules. Density-functional-theory calculations predict that the barrier E is at least several eV 2-6 , which should prohibit any gas permeation under ambient conditions. Indeed, one can estimate that at room temperature T it would take longer than the lifetime of the universe to find an atom energetic enough to pierce a defect-free membrane of any realistic size. These expectations agree with experiments that reported no detectable gas permeation through mechanically-exfoliated graphene. The highest sensitivity was achieved using micrometersize wells etched in oxidized silicon wafers, which were sealed with graphene 1,9,10 . In those measurements, a pressurized gas (e.g., helium) could permeate along the SiO 2 layer and gradually fill the microcontainers making so-called 'nanoballoons'. Their consecutive deflation in air could be monitored using atomic force microscopy (AFM), and it was shown that the leakage occurred only along the SiO 2 surface, within several minutes but independently of the number of graphene layers used for the sealing 1 . These studies allowed a conclusion that graphene membranes were impermeable to all gases, at least with the achieved accuracy of 10 5 -10 6 atoms s -1 . This was further corroborated by creating individual atomic-scale defects in graphene nanoballoons, which resulted in their relatively fast deflation/inflation and confirmed the high sensitivity of the method 9,10 .

No abstract

Capillary condensation of water is ubiquitous in nature and technology. It routinely occurs in granular and porous media, can strongly alter such properties as adhesion, lubrication, friction and corrosion, and is important in many processes employed by microelectronics, pharmaceutical, food and other industries [1][2][3][4] . The century-old Kelvin equation 5 is commonly used to describe condensation phenomena and shown to hold well for liquid menisci with diameters as small as several nm [1][2][3][4][6][7][8][9][10][11][12][13][14] . For even smaller capillaries that are involved in condensation under ambient humidity and so of particular practical interest, the Kelvin equation is expected to break down because the required confinement becomes comparable to the size of water molecules . Here we take advantage of van der Waals assembly of two-dimensional crystals to create atomic-scale capillaries and study condensation inside. Our smallest capillaries are less than 4 Å in height and can accommodate just a monolayer of water. Surprisingly, even at this scale, the macroscopic Kelvin equation using the characteristics of bulk water is found to describe accurately the condensation transition in strongly hydrophilic (mica) capillaries and remains qualitatively valid for weakly hydrophilic (graphite) ones. We show that this agreement is somewhat fortuitous and can be attributed to elastic deformation of capillary walls [23][24][25] , which suppresses giant oscillatory behavior expected due to commensurability between atomic-scale confinement and water molecules 20,21 . Our work provides a much-needed basis for understanding of capillary effects at the smallest possible scale important in many realistic situations.The Kelvin equation predicts that capillaries become spontaneously filled with water at the relative humidity RHK = exp (-2σ/kBTdρN)where σ ≈ 73 mJ m -2 is the surface tension of water at room temperature T, ρN ≈ 3.3×10 28 m -3 is the number density of water, kB is the Boltzmann constant, and d is the diameter of the meniscus curvature. For a two-dimensional (2D) confinement created by parallel walls separated by a distance h, d = h/cos(θ) where θ is the contact angle of water on the walls' material. For capillary condensation to occur at relative humidity (RH) considerably below 100%, equation 1 dictates that d must be comparable to 2σ/kBTρN ≈ 1.1 nm. For example, under typical ambient RH of 40-50%, water is expected to condense in slits with h < 1.5 nm and cylindrical pores with diameters < 3 nm, if θ is close to zero. Even stronger confinement is required for capillaries involving less hydrophilic materials. So far, a broad consensus has been reached that the Kelvin equation remains accurate for menisci with d ≥ 8 nm [1][2][3][4][6][7][8][9][10][11] and can also describe condensation phenomena in hydrophilic pores as small as 4 nm in diameter 12-14 . To achieve agreement with the experiments at this scale, the Kelvin equation is usually modified to account for so-called wetting films that are adsorbed on...

Most techniques for image analysis consider the image labels fixed and without uncertainty. In this paper, we address the problem of ordinal/rank label prediction based on training samples with uncertain labels. First, the core ranking model is designed as the bilinear fusing of multiple candidate kernels. Then, the parameters for feature selection and kernel selection are learned by maximum a posteriori for given samples and uncertain labels. The convergency provable Expectation-Maximization (EM) method is used for inferring these parameters. The effectiveness of the proposed algorithm is finally validated by the extensive experiments on age ranking task. The FG-NET and Yamaha aging database are used for the experiments, and our algorithm significantly outperforms those state-of-the-art algorithms ever reported in literature.