Complete steric exclusion of ions and proton transport through confined monolayer water

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Science  11 Jan 2019:
Vol. 363, Issue 6423, pp. 145-148
DOI: 10.1126/science.aau6771

Only the water may pass

Removing objects by size to keep only the smallest ones is simple in theory, but it requires a sieve, membrane, or filter with holes small enough to allow only the smallest objects to pass. Gopinadhan et al. engineered two-dimensional water channels by removing an atomic plane of atoms from a sandwich made from bulk crystal with a graphene spacer. Water flowed through the channels without resistance, but the channels excluded all ions except for protons because the ion hydration shells could not squeeze through the channels.

Science, this issue p. 145


It has long been an aspirational goal to create artificial structures that allow fast permeation of water but reject even the smallest hydrated ions, replicating the feat achieved by nature in protein channels (e.g., aquaporins). Despite recent progress in creating nanoscale pores and capillaries, these structures 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 angstroms 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 (H+) can diffuse through monolayer water inside the capillaries. These observations improve our understanding of molecular transport at the atomic scale.

Protein channels use a large number of separation mechanisms, including steric (size) exclusion and electrostatic repulsion, to remove salts from water and distinguish between different ions (1). It is believed that angstrom-scale constrictions within these channels (2, 3) play a key role in steric rejection of ions with the smallest hydration diameters DH ≈ 7 Å, typically present in biofluids and seawater (1, 4). Such small constrictions are particularly difficult to replicate artificially because of the lack of fabrication tools capable of operating with such precision and, especially, because the surface roughness of conventional materials is much larger than the required angstrom scale (5). Nonetheless, several artificial systems with nanometer and subnanometer dimensions were recently demonstrated (59), including narrow carbon and boron nitride nanotubes (911), graphene oxide laminates (12, 13), and atomic-scale pores in graphene and MoS2 monolayers (7, 8, 14). The resulting devices exhibited high selectivity with respect to certain groups of ions [for example, they blocked large ions but allowed small ones (13) or rejected anions but allowed cations and vice versa (6, 7, 9)]. Most recently, van der Waals assembly of two-dimensional (2D) crystals (15) was used to make slitlike channels of several angstroms 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 water permeation (16) and blocked large ions, with a complete cutoff for diameters larger than ~10 Å (17). Small ions (for example, those in seawater with typical DH of ~7 Å) still permeated through the channels with little hindrance, indicating that an angstrom-scale confinement comparable to that in aquaporins (2, 3) is essential for steric exclusion of small-diameter ions. In this Report, we describe 2D channels with height h of ~3.4 Å (18), half the size of the smallest hydrated ions (K+ and Cl with DH ≈ 6.6 Å) (1, 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 channel constrictions, a critical factor in their steric selectivity (2, 3).

Our devices were fabricated using the van der Waals assembly described previously (16, 17). In brief, two thin (~50 and 200 nm) atomically flat monocrystals were obtained by cleaving bulk graphite or hexagonal boron nitride (hBN) and placed on top of each other, with stripes of graphene serving as spacers between the two crystals (Fig. 1A). The resulting trilayer assembly can be viewed as a pair of edge dislocations connected by a 2D empty space. This space can accommodate only one atomic layer of water (Fig. 1B). The 2D channels were designed (16, 17) to have a width w ≈ 130 nm and length L of several micrometers. We primarily used many channels in parallel (≥100) to increase measurement sensitivity. The resulting structures were assembled on top of a silicon nitride membrane that separated two isolated containers so that 2D channels provided the only molecular pathway between the containers (Fig. 1A) [for further details, see the supplementary materials (18) and fig. S1]. The principal difference with the capillaries reported earlier (16, 17) is the use of monolayer graphene as spacers. Previously, water permeation could be discerned only for capillaries with thicker spacers (h ≥ 6.7 Å), and molecular dynamics (MD) simulations also suggested that smaller 2D cavities should collapse because of van der Waals attraction between the opposite walls (16). However, further MD analysis (18) has shown that water molecules inside the slits can act as a support and prevent the collapse of even one-atom-high slits with h ≈ 3.4 Å (fig. S2), which agrees with our experimental results (described below) and is corroborated by Raman spectroscopy that shows liquid water inside one-atom-high channels (fig. S3). To detect minute amounts of water that can flow through them, we also needed to introduce the following improvements: (i) a 10-fold increase in the number n of channels probed in parallel, (ii) the use of thicker top crystals to avoid their sagging (16), and (iii) the clipping of channels’ entries (Fig. 1A) by plasma etching to remove their possible blockage by thin edges of the top crystal (18).

Fig. 1 Water flow through one-atom-high capillaries.

(A) Schematic of our fluidic devices. Top and bottom layers were either graphite or hBN crystals, and monolayer graphene was used as the spacers. The trilayer assembly was supported by a free-standing membrane with a rectangular opening. (B) There is space for only one monolayer of water inside such 2D cavities, as indicated by MD simulations (27, 28). (C) Weight loss due to water permeation and its subsequent evaporation (1500 graphite/graphene/graphite channels with L = 2 μm). (Top inset) Evaporation rates for three such channel devices. The indicated rates are per 1 μm channel length. (Bottom inset) Gravimetry setup. The detection limit of our gravimetry (~10−13 g s−1) is comparable to that of helium mass spectrometers and is much lower than that achieved by mass spectrometric analysis of other gases and vapors diffusing through similar devices (16).

The bottom inset of Fig. 1C shows a schematic of the gravimetry setup (16). The device containing 2D channels with graphite walls was sealed in a miniature container filled with water, and the weight loss was recorded as a function of time. For reference, we studied devices made in exactly the same way but without graphene spacers (16, 18). No evaporation could be detected for these reference devices, even after many days of measurements. In contrast, the monolayer channel devices exhibited a weight loss evolving linearly in time (Fig. 1C). The slope of this curve translates directly into a water permeation rate of ~1.5 × 10−12 g/s per micrometer channel length per channel. Three such graphene devices were studied, all showing similar rates (top inset of Fig. 1C). The water permeation rate noted above is ~5% of the rates reported previously for devices with bilayer spacers (h ≈ 6.7 Å) and is below the detection limit achieved in (16). The difference in water evaporation rates through mono- and bilayer capillaries is larger than a factor of 4, which is expected from the h2 dependence for our geometry (16, 18). The additional flow reduction (by another factor of 2) is perhaps not surprising because water becomes increasingly more viscous under strong confinement (18, 20, 21).

Having established that water can flow through our one-atom-high channels, we investigated their permeability with respect to ions. In these experiments, the devices separated two reservoirs filled with chloride solutions (inset of Fig. 2A). The electrical conductance G between the reservoirs was measured using chlorinated Ag/AgCl electrodes or calibrated reference electrodes (17) (fig. S4). First, we tested ion conductance using chloride solutions in 1 M concentrations. Within our detection limit of ~50 pS given by parasitic leakage currents of ~5 pA, no conductance could be detected for any salt (some of which are listed in Fig. 2A). This finding is in contrast to the behavior observed for capillaries with thicker spacers including bilayers (17). The latter (h ≈ 6.7 Å) exhibited G of the order of 10−8 S (1 S = 1 A/V)—that is, three orders of magnitude above our detection limit—in agreement with the conductance expected from the known conductivity σ of the 1 M chloride solutions for the given length L and cross-sectional area n × h × w. The measurements for bilayer devices were reported previously (17) but, for consistency, were repeated in this work. Despite no discernable ion transport through monolayer capillaries (h ≈ 3.4 Å), they unexpectedly showed a substantial conductance if we used HCl rather than salt solutions (Fig. 2A and fig. S4). The measured σ for the acid varied approximately linearly with its concentration C as expected (Fig. 2B), but the absolute values were 3 to 10% of the value for bulk HCl (black curve in Fig. 2B). This is again in contrast to the behavior found for bilayer devices (h ≈ 6.7 Å), which exhibited the conductance that agreed well with that of bulk HCl in the given geometry (Fig. 2B).

Fig. 2 Steric exclusion of salts from one-atom-high capillaries.

(A) Conductance observed for one of our monolayer devices (n = 100; L = 10 μm; hBN/graphene/hBN) using the specified 1 M solutions (symbols). The values of G were extracted from the slopes of I-V curves over a voltage interval of ±30 mV. The error bars show standard deviations (SD) in determining G from the curves. The gray area indicates our typical detection limit given by leakage currents, as found using both reference devices and blank Si nitride membranes. Several other common salts (17) were tested and exhibited no discernable conductance. In total, seven devices with monolayer spacers were found to demonstrate the same behavior. For the case of HCl, G was well above our detection limit, although it varied between different devices from 0.1 to 0.64 nS (fig. S4B), yielding an average G = 0.32 ± 0.2 nS. (Inset) Schematic of our measurement setup. (B) Conductivity σ calculated from the measured G for different HCl concentrations for mono- and bilayer capillaries [red and blue symbols, respectively; red is for the same device as in (A)]. Red line, best linear fit; black curve, literature values for bulk HCl; green symbol, σ for monolayer devices using Nafion (instead of HCl) as proton reservoirs. The horizontal error bar indicates the uncertainty in determining the proton concentration in Nafion films (25).

The fact that no ion currents could be detected for salt solutions indicates steric rejection of all hydrated ions from the one-atom-high channels. It was previously reported (17) that ion permeation remained practically unaffected if DHh but was sharply suppressed (by a factor of 15) if DH exceeded h by 50%. In our case, h ≈ 3.4 Å is half the size of DH of the tested ions, and the extrapolation of the previously observed cutoff (quicker than exponential) (17) suggests that the monolayer capillaries should completely prohibit transport of any hydrated ions. This conclusion does not contradict the finite G observed for HCl because of a high concentration of protons in the latter case. They can diffuse through monolayer water present inside the capillaries, not as ions dressed in large hydration shells (hydronium) but more like subatomic particles jumping between water molecules, according to the Grotthuss mechanism (22, 23).

To corroborate the suggested proton transport scenario, we used the same ion measurement setup but different HCl concentrations in the two reservoirs. The concentration gradient drives both H+ and Cl in the same direction, from the high concentration (Ch) reservoir to the low concentration (Cl) one, and the sign of the electric current I at zero applied voltage V indicates whether most carriers are H+ or Cl (1, 17). Examples of I-V characteristics observed for our monolayer devices are shown in Fig. 3A. One can see that the current at zero V was always positive, which indicates that protons predominantly drive the system toward the equilibrium in an effort to equalize proton concentrations in the two reservoirs. Moreover, for the chosen gradient Δ = Ch/Cl = 3, the I-V curves intersect the current axis at the same V0 = 28 ± 4 mV regardless of the Cl and Ch values. The voltage that compensates the currents caused by concentration gradients is described by the Nernst equation (24) V0 = (tHtCl)(kT/e) ln(Δ)where tH,Cl ∈ [0,1] are the so-called transport numbers for H+ and Cl, k is the Boltzmann constant, T is the temperature (295 ± 3 K in our experiments), and e is the elementary charge. For Δ = 3 and V0 ≈ 28 mV, the formula yields tH – tCl ≈ 1, which can be satisfied only if tH ≈ 1 and tCl ≈ 0. This means that only protons diffuse through our monolayer devices, whereas Cl ions are rejected, in agreement with the conclusions reached from the experiments of Fig. 2.

Fig. 3 Proton transport through monolayer water inside 2D channels.

(A) I-V curves for different concentrations of HCl in the two reservoirs connected by monolayer capillaries. The same concentration gradient Δ was used for all curves. The red symbol denotes voltages at zero I. The vertical bar indicates our maximum leakage currents, whereas the horizontal bar represents the statistical error in determining V0 by using measurements for several monolayer devices. (Inset) Square-like ice is one of the possible states of water inside one-atom-high channels at room temperature, as expected from MD simulations (29, 30). (B) Proton transport using Nafion as proton reservoirs. (Top inset) Schematic of our Nafion devices (hBN/graphene/hBN; n = 100). Blue symbols, resistance as a function of channel length. (Bottom inset) G(n) for several Nafion devices with L = 2 μm. Red and blue lines, best linear fits. Error bars indicate SD, as in Fig. 2.

Proton transport can be probed more directly using Nafion instead of HCl (25). Nafion is a polymer in which protons are the only charge carriers and the counterions (SO3) are fixed within the polymer matrix (26). Using the approach described in (25), we coated our devices with Nafion from both sides and used hydrogenated Pt films as proton-injecting electrodes to convert electric current into a proton flow (top inset of Fig. 3B). For electrical measurements, these devices were placed in a hydrogen atmosphere at 100% relative humidity to ensure high Nafion proton conductivity (25). In comparison with our ion transport measurements, the Nafion devices were much more robust, sustained higher I values (18), exhibited smaller leakage currents (~1 pA), and showed little variations between similar devices. Because polymer molecules are much larger than h, they cannot enter 2D channels; therefore, Nafion served in our experiments only as a reservoir providing protons for the stationary monolayer of water inside the channels. Figure 3B shows examples of the electrical resistance R = 1/G exhibited by our devices. The resistance varied linearly with L and 1/n, as expected. Reference devices with no channels showed negligible conductance (~10−11 S; error bars in Fig. 3B). One can see that R accurately extrapolates to zero in the limit of zero L (blue curve in Fig. 3B), which yields that protons experience little barrier for entry into the capillaries. The experiments yield σ ≈ 2.1 ± 0.2 mS cm−1, whereas the proton concentration in Nafion and, hence, inside the 2D water can be estimated from the conductivity of our Nafion coating. It was found to be ~70 mM but with a relatively large uncertainty, as the proton concentration is sensitive to details of Nafion preparation (25). The resulting σ (green symbol in Fig. 2B) agrees well with that found in the HCl measurements, which further substantiates our conclusion of proton-only transport through one-atom-high channels.

It is instructive to estimate the diffusion constant dp of protons within the monolayer water that fills the capillaries. This quantity is given by dp = σ(kT/eFCp) ≈ 4 × 10−6 cm2 s−1, where Cp is the proton concentration in HCl or Nafion, and F is the Faraday constant (18). This value is an order of magnitude smaller than dp ≈ 9 × 10−5 cm2 s−1 for bulk water (4, 23), which is also apparent from the difference between the red and black curves in Fig. 2B, if one recalls that the conductivity of bulk HCl is ~80% dominated by protons (1). On the other hand, proton transport in 3D water is several times slower than that in 1D water inside subnanometer carbon nanotubes (9, 11), which exhibited dp ≈ 4 × 10−4 cm2 s−1. The anomalously slow proton diffusion in 2D and the nonmonotonic dependence of dp on dimensionality seem puzzling (dp in 2D is much smaller than in both 1D and 3D) but are consistent with different hydrogen bonding for the three cases (18). Indeed, MD simulations suggest (27, 28) that water under 2D confinement should become ordered (icelike) at room temperature (Fig. 3A). The ordered hydrogen bonding in 2D water should suppress rotation of water molecules with respect to 3D water, which is an essential but slowest step for proton transport, according to the Grotthuss mechanism (22, 23). This is in contrast to 1D water that exhibits stringlike hydrogen bonding, which arguably (9, 11) can strongly enhance proton diffusion (fig. S5).

In summary, our one-atom-high cavities allow one monolayer of water inside but exclude all ionic species. This finding is in contrast to the behavior of the twice-as-large slits (h ≈ 6.7 Å), which showed little effect on such small ions as Na+ and Cl (DH ≈ 7 Å). The extreme steric exclusion for h ≈ 3.4 Å is attributed to the fact that it is no longer possible for any ion to squeeze inside the slits by deforming their hydration shells. Protons are different in that they diffuse not as hydrated H+ ions but follow the Grotthuss mechanism. The slow diffusion observed for protons in 2D water suggests that it probably forms a proton-ordered ice at room temperature, in agreement with MD simulations.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S5

References (3155)

References and Notes

  1. See supplementary materials.
Acknowledgments: Funding: This work was supported by the Lloyd’s Register Foundation, Graphene Flagship, European Research Council, and Royal Society. B.R. acknowledges a Royal Society University Research Fellowship; F.C.W. acknowledges the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB22040402). Author contributions: A.K.G. proposed and directed the research with help from K.G. and B.R.; K.G., S.H., and M.L.-H. performed ion and proton transport measurements and their analysis; A.E., A.K., S.H., and B.R. fabricated the devices; A.K., B.R., and Q.Y. did gravimetric measurements and their analysis; A.E. and A.V.T. performed Raman spectroscopy; F.C.W. carried out MD simulations with help of A.K.G.; and K.G., B.R., M.L.-H., and A.K.G. wrote the manuscript. All authors contributed to discussions. Competing interests: We declare no competing interests. Data and materials availability: All data are available in the main text and the supplementary materials. Additional information is available on reasonable request from the authors, according to their contributions.
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