PROTON CONDUCTING MEMBRANE COMPRISING MONOLITHIC 2D MATERIAL AND IONOMER, A PROCESS FOR PREPARING SAME AND USE OF SAME IN FUEL CELL AND HYDROGEN GAS SENSOR

Abstract

The present invention relates to a graphene-based or other 2-D material membrane which allows the passage of protons and deuterons and to a method of facilitating proton or deuteron permeation through such a membrane. Monocrystalline membranes made from mono- and few-layers of graphene, hBN, molybdenum disulfide (MoS2), and tungsten disulfide (WS2) etc. are disclosed. In effect, the protons or deuterons are charge carriers that pass through the graphene or other 2-D material membrane. This process can be contrasted with the passage of gaseous hydrogen. Hydrogen is an uncharged gaseous species which is diatomic. In other words, the gas is in molecular form when considering the normal barrier properties whereas in the case of the present invention, the species which is being transported through the membrane is a charged ion comprising a single atom. Membranes of the invention find use in a number of applications such as fuel cells.

Claims

1-24. (canceled)

25. A proton conducting membrane comprising: a monolayer or from 2 to 5 layers of a 2D material, wherein the 2D material is monolithic, an ionomer coating provided on at least one side of the 2D material; and optionally a substrate.

26. The membrane as claimed in claim 25, wherein the ionomer is a proton conducting polymer.

27. The membrane as claimed in claim 26, wherein the polymer is a sulfonated polymer, preferably Nafion®.

28. The membrane as claimed in claim 25, wherein the ionomer is provided on one side of the 2D material, or alternatively, is provided on both sides of the 2D material.

29. The membrane as claimed in claim 25, further including a substrate.

30. The membrane as claimed in claim 29, wherein the ionomer and substrate are provided as a single entity.

31. The membrane as claimed in claim 25, wherein the 2-D material is selected from the group consisting of graphene, hBN, Bi.sub.2Te.sub.3, Bi.sub.2Se.sub.3, MoS.sub.2, WS.sub.2, MoSe.sub.2, MoTe.sub.2, TaSe.sub.2, NbSe.sub.2, and NiTe.sub.2.

32. The membrane as claimed in claim 31, wherein the 2-D material is graphene.

33. The membrane as claimed in claim 31, wherein the 2-D material is hBN.

34. The membrane as claimed in claim 25, wherein the 2-D material includes a catalytic metal.

35. The membrane as claimed in claim 34, wherein the metal is one or more selected from the group consisting of Groups 8 to 10 of the periodic table.

36. A method of separating protons from other materials, the method comprising: allowing the protons to pass through the membrane of claim 25.

37. The method of claim 36, wherein a proton concentration gradient exists between different sides of the 2-D material.

38. The method of claim 36, wherein an electrical potential is applied across the membrane.

39. A process for preparing the proton-conducting membrane of claim 25, said process comprising the following steps: providing a monolayer of a 2D material, either coating an ionomer on at least one side of the 2D material so that one side of the ionomer is in contact with the 2-D material and the other side is exposed, or applying a layer of material comprising an ionomer and a nonconductive structural component to one side of the 2-D material; and optionally providing a substrate in contact with an exposed side of the at least one ionomer coating.

Description

FIGURES ILLUSTRATING THE INVENTION

[0091] The 2D proton conducting membranes of the present invention and the associated properties are shown in the following Figures in which:

[0092] FIG. 1 shows: Proton transport through 2D crystals.

[0093] FIG. 1a shows Examples of I-V characteristics for monolayers of hBN, graphite and MoS.sub.2. The upper inset shows experimental schematics. Middle inset: Electron micrograph of a typical graphene membrane before depositing Nafion®. Scale bar: 1 μm. In a scanning electron microscope, 2D crystals give rise to a homogenous dark background and can only be seen if contamination, defects or cracks are present. Small (pA) currents observed for MoS.sub.2 membrane devices (lower inset) are due to parasitic parallel conductance.

[0094] FIG. 1b shows Histograms for 2D crystals exhibiting detectable proton conductivity. Each bar represents a different sample with a 2 μm diameter membrane. Left and right insets: charge density (in electrons per Å2) integrated along the direction perpendicular to graphene and monolayer hBN, respectively. The white areas are minima at the hexagon centers; the maxima correspond to positions of C, B and N atoms.

[0095] FIG. 2 shows: Proton barrier heights and their catalytic suppression.

[0096] FIG. 2a shows T dependences of proton conductivity for 2D crystals. The inset shows log(σ) as a function of inverse T. Symbols are experimental data; solid curves are the best fits to the activation dependence. The T range is limited by freezing of water in Nafion®, and we normally avoided T above 60° C. to prevent accidental damage because of different thermal expansion coefficients.

[0097] FIG. 2b shows Proton conductivity is strongly enhanced if 2D crystals are decorated with catalytic nanoparticles. Each bar is a different device. The shaded area indicates the conductivity range found for bare-hole devices (Nafion®/Pt/Nafion®: no 2D crystal was present in the ensemble but for the sake of a fair comparison the same amount of Pt was evaporated). Inset: Arrhenius-type behavior for graphene with Pt, yielding E=0.24±0.03 eV. Monolayer hBN with Pt exhibits only a weak T dependence which indicates that the barrier becomes comparable to kBT.

[0098] FIG. 3 shows: Current-controlled proton flux. Top inset: Schematics of our experiment. Monolayer graphene decorated with Pt nanoparticles separates a vacuum chamber from the Nafion®/PdHx electrode placed under the same H2/H2O conditions as described above. Protons permeate through the membrane and rapidly recombine on the other side into molecular hydrogen. The hydrogen flux is detected by a mass spectrometer (Inficon UL200). Different symbols refer to different devices, error bars are shown for one of them, and the red line is the theoretically expected flow rate. Bottom inset: Optical image of one of the devices. Graphene contoured by the dashed lines seals a circular aperture of 50 um in diameter. Nafion® is underneath the graphene membrane.

[0099] FIG. 4 shows: Microfabrication process flow. Bottom right: Optical photo of the final device. Scale bar: 1 cm.

[0100] FIG. 5 shows: SEM images of suspended 2D membranes.

[0101] FIG. 5a shows Monolayer graphene with some accidental contamination. One of the particles away from the edge is marked by the white circle.

[0102] FIG. 5b shows Suspended graphene with pillars of hydrocarbon contamination intentionally induced by a focused electron beam. The inset shows a crack in the membrane; scale bar: 100 nm.

[0103] FIG. 6 shows: Bare-hole devices with different apertures. Their conductance exhibits a linear dependence on D as expected for this geometry. The inset illustrates schematics of such devices.

[0104] FIG. 7 shows: Proton conductance through monolayer hBN membranes of different sizes. Conductance scales quadratically with D, that is, linearly with A. Inset shows I-V characteristics for devices with different D.

[0105] FIG. 8 shows: Proton transport limited by Nafion®. Temperature dependences for bare-hole devices, Nafion®/Pt/Nafion® devices and membrane devices with catalytically-activated monolayer hBN. The nominal conductivity is calculated as the measured conductance S divided by the aperture area A.

[0106] FIG. 9 shows: Deflation of micro-balloons to check for atomic scale defects in graphene membranes.

[0107] FIG. 9a shows Height profiles for a typical graphene membrane at different times.

[0108] FIG. 9b shows Maximum height as a function of time. The inset shows a typical AFM image of a pressurized graphene microcavity (color scale: 0 to 130 nm). We measured six graphene membranes with all of them showing the same deflation rates, independently of whether Pt was deposited on top or not. Similar behavior was observed for hBN monolayers.

[0109] FIG. 10 shows: Hydrogen flow detection.

[0110] FIG. 10a shows Schematics of our devices for mass spectroscopy measurements.

[0111] FIG. 10b shows Example of the observed hydrogen flow rates as a function of time and measured current for different negative biases on the graphene membrane, which we applied in steps.

[0112] FIG. 11 shows: Electron clouds of 2D crystals. Integrated charge densities for graphene, monolayer hBN (nitrogen is indicated by blue balls; boron in pink) and monolayer MoS2 (S is in yellow, Mo in brown).

[0113] FIG. 12 shows: CI-NEB simulations. Energy profiles as a function of the proton distance to the center of the hexagonal ring in graphene and hBN (FIG. 12a and FIG. 12b, respectively). Carbon atoms are shown as cyan-colored spheres, nitrogen in blue, boron in pink and protons (H+) in white.

[0114] FIG. 13 shows: AIMD simulations for the proton barrier in graphene with Pt. Carbon atoms are shown in cyan, Pt in ochre, H+ in white.

[0115] FIG. 13a shows Experimental situation is mimicked by placing 4 Pt atoms at a distance of 4 Å from the graphene sheet.

[0116] FIG. 13b shows Figure shows the trajectory of protons with initial kinetic energy E=0.7 eV (the other two Pt atoms cannot be seen due to the perspective). The curved trajectories indicate that the decreased barrier is due to the interaction of protons with Pt.

[0117] FIG. 14 shows: Proton transport through 2D crystals in liquids.

[0118] FIG. 14a shows Examples of I-V characteristics for mono-, bi- and tri-layer hBN covering an aperture of 2 μm in diameter. The inset shows schematics of the liquid cell. In the case of trilayer hBN, the current is within the range given by a parasitic parallel resistance.

[0119] FIG. 14b shows Histograms for the 2D crystals that exhibited clear proton current in the liquid cell setup. Each bar represents a different sample with a 2 um diameter membrane. The shaded area shows the detection limit set by leakage currents.

[0120] As illustrated in the left inset of FIG. 1a, 2D crystals effectively serve as atomically thin barriers between two Nafion® spaces. For electrical measurements, samples were placed in a hydrogen-argon atmosphere at 100% humidity, which ensured high conductivity of Nafion® films. Examples of I-V characteristics measured for devices incorporating monolayers of graphene, hBN and MoS2 are shown in FIG. 1a. This behavior is highly reproducible, as illustrated by statistics in FIG. 1b for a number of different membranes. The measured proton current I is found to vary linearly with bias V, and the conductance S=IIV to be proportional to the membrane area A (see FIGS. 6-8). For devices prepared in the same manner but without a 2D membrane (‘bare hole’), S was about 50 times higher than in the presence of monolayer hBN (FIG. 6). This ensures that the measured areal conductivity σ=SIA is dominated by the 2D crystals and that Nafion® gives rise only to a relatively small series resistance. In the opposite limit of thick barriers (e.g., a few nm thick graphite or thick metal or dielectric films evaporated between the Nafion® spaces), we find a parasitic parallel conductance of about 10 pS, which could be traced back to leakage currents along SiN.sub.x surfaces in high humidity. Within this accuracy, we could not detect any proton current through monolayer MoS.sub.2, bilayer graphene, tetra-layer hBN or thicker 2D crystals.

[0121] The difference in permeation through different 2D crystals can qualitatively be understood if we consider the electron clouds that have to be overcome by passing protons. One can see from the insets of FIG. 1b that monolayer hBN is more ‘porous’ than graphene, reflecting the fact that the boron nitride bond is strongly polarized with valence electrons concentrated around nitrogen atoms. For MoS2, the cloud is much denser because of the larger atoms involved (FIG. 11). The absence of detectable a for bilayer graphene can be attributed to its AB stacking such that ‘pores’ in the electron cloud in one layer are covered by density maxima within the other layer. In contrast, hBN crystals exhibit the AA′ stacking, which leads to an increase in the integrated electron density with increasing number of layers but allows the central pore in the cloud to persist even for multilayer hBN membranes.

[0122] It is instructive to emphasize that there is no correlation between proton and electron transport through 2D crystals. Indeed, hBN exhibits the highest proton conductivity but is a wide gap insulator with the highest tunnel barrier. In contrast, monolayer MoS.sub.2 that shows no discernable proton permeation is a heavily doped semiconductor with electron-type conductivity. Furthermore, numerous studies using transmission and tunneling microscopy and other techniques have so far failed to find even individual pinholes (atomic-scale defects) in graphene and hBN prepared using the same cleavage technique as employed in the present work. In contrast, MoS2 monolayers contain a high density of sulfur vacancies but nonetheless exhibit little proton conductivity. These observations combined with the high reproducibility of our measurements for different devices, the linear scaling with A and the consistent behavior with increasing the number of layers assure that the reported a represent the intrinsic proton properties of the studied membranes.

[0123] To determine the barrier heights E presented by graphene and hBN, we have measured T dependences of their a (FIG. 2a) which are found to exhibit the Arrhenius-type behavior, exp(−ElkBT). Note that conductivity of Nafion® not only contributes little to the overall value of S but also changes only by a factor of about 1.5 for the same T range (FIG. 8). The activation behavior yields E=0.78±0.03, 0.61±0.04 and 0.3±0.02 eV for graphene, bilayer hBN and monolayer hBN, respectively. The proton barrier for graphene is notably lower than the values of 1.2-2.2 eV, which were found using ab initio molecular dynamics simulations and the climbing image nudged elastic band method. We have reproduced those calculations for graphene and extended them onto monolayer hBN as discussed later below. Our results yield E=1.25-1.40 for graphene, and eV for monolayer hBN. The disagreement between the experiment and theory in the absolute value of E is perhaps not surprising given the complex nature of possible pathways and sensitivity of the calculations to pseudopotentials, the exchange-correlation function etc. Alternatively, the difference can arise due to the fact that protons in Nafion®/water move along hydrogen bonds rather than in vacuum as the theory has assumed so far.

[0124] For certain applications, it is desirable to achieve the highest possible proton conductivity. For example, hydrogen fuel cells require membranes with about >1 S per cm.sup.2. This condition is satisfied by monolayers of hBN and graphene above 80 and 110° C., respectively (inset of FIG. 2a). Moreover, graphene remains stable in oxygen and humid atmosphere up to 400° C., and the extrapolation of our results to ‘very safe’ 250° C. yields extremely high σ>10.sup.3 S/cm.sup.2. Furthermore, noticing that platinum group metals have a high affinity for hydrogen, we have investigated their influence on proton transport through 2D crystals. To this end, a discontinuous layer of Pt or Pd (nominally, 1-2 nm thick) was evaporated onto one of the surfaces of 2D crystals. FIG. 2b shows that the added catalytic layer leads to a significant increase in a. For monolayer hBN, the measured S becomes indistinguishable from that of reference ‘bare hole’ devices (FIG. 2b). This shows that our measurements become limited by Nafion®'s series resistance and Pt-activated monolayer hBN is no longer a bottleneck for proton permeation. On the other hand, for graphene and bilayer hBN activated with Pt, the series resistance remains relatively small and the measurements still reflect their intrinsic properties. By studying σ(T), we find that Pt reduces the activation energy E by as much as about 0.5 eV to about 0.24 eV (FIG. 2b). Our simulations of the catalytic effect yield a reduction in E by about 0.65 eV, in qualitative agreement with the experiment. The mechanism behind this barrier reduction can be attributed to attraction of passing protons to Pt (FIG. 10). Note that the measurements in FIG. 2b set only a lower limit of ≈3 S/cm.sup.2 on room-T conductivity of catalytically-activated monolayer hBN and, if the membranes experience qualitatively similar reduction in E as observed for graphene, we expect essentially barrier-less proton transport. It would require membranes with much larger area to determine intrinsic a for catalytically-activated hBN.

[0125] Finally, we demonstrate directly that the observed electric currents are due to proton flux through the 2D membranes. To this end, we have prepared devices such as shown in the insets of FIG. 3. Here, one of the Nafion®/PdH.sub.x electrodes is removed, and the graphene surface decorated with Pt faces a vacuum chamber equipped with a mass spectrometer. If no bias is applied between graphene and the remaining PdH.sub.x electrode, we cannot detect any gas leak (including He) between the hydrogen and vacuum chambers. Similarly, no gas flow could be detected for positive bias on graphene. However, by applying a negative bias we have measured a steady H2 flux into the vacuum chamber. Its value is determined by the number of protons, IIe, passing through the membrane per second. Using the ideal gas law, one can easily derive the relation F=kBT(II2e) where the flow rate F is the value measured by the mass spectrometer tuned to molecular hydrogen. The latter dependence is shown in FIG. 3 by the solid red line, in excellent agreement with the experiment.

[0126] It can be seen from the above that monolayers of graphene, hBN and similar 2D materials can under appropriate conditions represent a new class of proton conductors. This conductivity can be controlled. The 2D proton conductors of the present invention will find use in various hydrogen technologies. For example, 2D crystals can be considered as proton membranes for fuel cells. They are highly conductive to protons and chemically and thermally stable and, at the same time, impermeable to H2, water or methanol. This could be exploited to solve the problem of fuel crossover and poisoning in existing fuel cells. The demonstrated current-controlled source of hydrogen is also appealing at least for its simplicity and, as large-area graphene and hBN films are becoming commercially available, the scheme may be used to harvest hydrogen from gas mixtures or air.

Example 1 Production of a 2D Proton Conductor

[0127] FIG. 4 explains the microfabrication procedures. We start with preparing free-standing silicon nitride (SiN.sub.x) membranes from commercially available Si wafers coated from both sides with 500 nm of SiN.sub.x. An etch mask is made by photolithography. Reactive ion etching (RIE) is employed to remove a 1×1 mm.sup.2 section from one of the SiN.sub.x layers (steps 1&2 in FIG. 4). The Si wafer underneath is etched away by wet chemistry by exposing the wafer to a KOH solution that etches away Si and leaves a free-standing SiN.sub.x membrane of typically 300×300 μm.sup.2 in size (step 3). During step 4, a circular hole is drilled by RIE through the SiN.sub.x membrane using the same procedures as in steps 1&2. Next, a 2D crystal (graphene, hBN or MoS2) is prepared by standard micromechanical exfoliation and transferred on top of the membrane using either the wet or dry technique to cover the aperture in SiN.sub.x (step 5).

[0128] After step 5, the suspended membranes could be examined for their integrity and quality in a scanning electron microscope (SEM). Pristine 2D crystals give little SEM contrast, and it requires some contamination to notice 2D membranes on top of the holes. Contamination can be accidental as in the case of FIG. 5a or induced by the electron beam (FIG. 5b). If cracks or tears are present, they are clearly seen as darker areas (inset of FIG. 5b).

[0129] The fabrication of devices for electrical measurements continues with depositing a proton-conducting polymer layer. A Nafion® 117 solution (5%) is drop-cast or spin-coated on both sides of a suspended 2D membrane (step 6 in FIG. 4). Finally, palladium hydride (PdH.sub.x) electrodes are mechanically attached to the Nafion® layers. To synthesize such electrodes, a 25 μm thick Pd foil is left overnight in a saturated hydrogen-donating solution following the recipe reported in D W Murphy et al, Chem Mater, 5, 767-769, (1993). This leads to atomic hydrogen being absorbed into the crystal lattice of Pd turning it into PdH.sub.x. The resulting devices are placed in a water saturated environment at 130° C. to crosslink the polymer and improve electrical contacts.

[0130] The described experimental design is optimized to take into account the following considerations. First, electric currents in Nafion® are known to be carried exclusively by protons that hop between immobile sulfonate groups and Nafion® is not conductive for electrons. This can be evidenced directly by, for example, inserting a gold film across a Nafion® conductor, which then breaks down the electrical connectivity. Accordingly, protons are the only mobile species that can pass between the transition metal hydride e.g. PdH.sub.x electrodes. PdH.sub.x is used as a proton injecting material that converts an electron flow into a proton one by the following process: PdH.sub.x->Pd+xH.sup.++xe.sup.−. This property, combined with the large area of our electrodes, relative to the membrane area A makes the contact resistance between Nafion® and PdH.sub.x negligible so that the circuit conductance in our experiments is limited by either 2D crystals or, in their absence, by the Nafion® constriction of diameter D.

[0131] For the catalytically-activated measurements, 1-2 nm of Pt were deposited by e-beam evaporation directly onto the suspended membrane to form a discontinuous film prior to the Nafion® coating. Thicker, continuous films were found to block proton currents, which could be witnessed as numerous hydrogen bubbles that appeared under Pt after passing electric current. Typically, our Pt films resulted in about 80% area coverage, which reduced the effective area for proton transport accordingly, as found by depositing such films between Nafion® spaces but without 2D membranes (see below). Pd films were found to be less blocking and continuous films up to 10 nm in thickness did not significantly impede the proton flow. Otherwise, both Pd and Pt films resulted in similar enhancement of proton transport through 2D crystals.

Electrical Measurements of a 2D Proton Conductor

[0132] The devices described above were placed inside a chamber filled with a forming gas (10% H2 in argon) and containing some liquid water to provide 100% relative humidity. I-V curves were recorded by using DC measurements. We varied voltage in a range of typically up to 1 V at sweep rates up to 0.5 V/min. Under these conditions, the curves were non-hysteretic and highly reproducible. The devices were stable for many weeks if not allowed to dry out.

[0133] To characterize our experimental setup, we first measured leakage currents in the absence of a proton conductive path. To this end, two metallic contacts were placed onto the opposite surfaces of a piece of a fresh Si/SiN.sub.x wafer and I-V characteristics were measured under the same humid conditions. Conductance of the order of about 5 pS was normally registered. We also used fully processed devices and then mechanically removed the Nafion® film and electrodes. In the latter case, the parasitic conductance was slightly (by a factor of 2) higher, which is probably due to a residue left of SiN.sub.x surfaces during processing. In principle, it would be possible to reduce the leakage currents by using, for example, separate chambers at the opposite sides of the Si wafer but the observed parasitic conductance was deemed small enough for the purpose of the present work.

[0134] As a reference, we studied conductivity of ‘bare-hole’ devices that were prepared in exactly the same manner as our membrane devices but without depositing a 2D crystal to cover the aperture (step 5 in FIG. 4 is omitted). FIG. 6 shows conductance of such devices as a function of their diameter D. Within the experimental scatter, conductance S increases linearly with D, in agreement with Maxwell's formula: S=σND. The latter is derived by solving Laplace's equation for two semi-spaces that have conductivity σ and are connected by a hole with D much larger than the length d of the opening. In our case, d=500 nm and the condition is comfortably satisfied, except for possibly the smallest membranes in FIG. 6 with D=2 μm.

[0135] From the dependence shown in FIG. 6, we can estimate conductivity of our Nafion® films as 1 mS/cm. As discussed above, Nafion®'s conductivity did not limit our measurements of proton transport through 2D crystals, except for the case of catalytically-activated monolayer hBN. Nonetheless, we note that the found σN is two orders of magnitude smaller than values achievable for highest-quality Nafion®. There are two reasons for this. First, solution-cast Nafion® is known to lose typically one order of magnitude in conductivity. Second, Nafion® is normally pretreated by boiling in H.sub.2O.sub.2 and H.sub.2SO.sub.4 for several hours. If the latter procedure was used, our Nafion® films indeed increased their conductivity by a factor of 10, reaching the standard values for solution-cast Nafion® of about 10 mS/cm. Unfortunately, this harsh treatment could not be applied to our membrane devices that became destroyed with Nafion® films delaminating from SiN.sub.x.

[0136] For consistency, most of the 2D membranes reported in the main text were made 2 μm in diameter. However, we also studied many other membranes with diameters ranging from 1 to 50 μm. We found that their conductance scaled linearly with the aperture area A. FIG. 7 shows this for 10 monolayer hBN devices with D between 1 and 4 μm. Within the typical experimental scatter for devices with the same D, the conductance increases linearly with the area A of 2D membranes, in agreement with general expectations. The same scaling was also observed for graphene membranes.

[0137] As discussed above, the proton conductivity of catalytically-activated monolayer hBN is so high that the series resistance of Nafion® becomes the limiting factor in our measurements. This is further evidenced by comparing T dependences of different devices in which Nafion® was the limiting factor. Those include ‘bare-hole’ devices (Nafion® only), ‘bare-hole’ devices with Pt (Nafion®/Pt/Nafion®) and monolayer hBN membranes activated with Pt.

[0138] FIG. 8 shows a typical behavior of their conductance as a function of T. Consistent with the small activation energy for proton transport in Nafion® (<0.02 eV), we found that temperature effects in all the above devices are small over the entire temperature range (see FIG. 8). The nonmonotonic T dependence for the devices with Pt layers (FIG. 8) remains to be understood but we note that Nafion® often exhibits similar nonmonotonic behavior at higher T, beyond the range of FIG. 8. We speculate that the Pt activation shifts this peak to lower T. Importantly for our experiments, the influence of Pt nanoparticles on local conductivity in the Nafion® constriction is approximately the same independently of whether an hBN membrane is present or not. This further indicates that the proton conductivity of Pt-activated hBN is so high that it becomes unmeasurable in our experimental setup, essentially because of the limited size of currently available hBN crystals.

Absence of Atomic Scale Defects in 2D Proton Conductors

[0139] Visual inspection of membranes in SEM can reliably rule out holes and cracks with sizes down to <10 nm (see FIG. 5b). None of these types of defects were observed in the 2D proton conductors of the invention which were examined using SEM. Occasional cracks such as in FIG. 5b could only be observed if introduced deliberately or a profound mistake was made during handling procedures.

[0140] We verified the integrity of the 2D proton conductors of the invention using Raman spectroscopy because this is known to be extremely sensitive to atomic-scale defects in graphene. The intensity of the D peak provides a good estimate for a concentration of such defects, which could be not only vacancies or larger holes but also adatoms that do not lead to pinholes. We could not discern any D peak in our graphene membranes. This sets an upper limit on the atomic defect density of about 10.sup.8 cm.sup.−2 or one defect per μm.sup.2.

[0141] Furthermore, such a low density of defects in graphene is in stark contrast with a high density (about 10.sup.13 cm.sup.−2) of sulfur vacancies found in mechanically cleaved MoS2. Notwithstanding this fact, no proton current could be detected through our MoS2 membranes. If we assume each vacancy provides a hole of about 1 Å in size, the expected approximately 10.sup.5 vacancies present in our typical MoS2 membranes would provide an effective opening of about 30 nm in diameter. Using the results of FIG. 6, this is expected to lead to a conductance of about 3 nS, that is, >100 times larger than the limit set by our measurements on proton conductance through monolayer MoS2. This shows that individual vacancies in fact provide much smaller proton conductivity than their classical diameter suggests.

[0142] To strengthen the above arguments further, we tried to rule out even individual vacancies from our proton conductive (graphene and hBN) membranes. The most sensitive technique known to detect pinholes is arguably measurements of gas leakage from small pressurized volumes. To this end, a microcavity of typically about 1 μm.sup.3 in size is etched in a Si/SiO2 wafer, sealed with graphene or hBN and then pressurized. If the pressure inside the microcavity is higher than outside, the membrane bulges upwards; if it is lower, downwards. Changes in pressure can be monitored by measuring the height of the bulge as a function of time using atomic force microscopy (AFM). If there are no holes in the membrane, the gas leaks slowly through the oxide layer, and it typically takes many hours until the pressure inside and outside the microcavity equalize. However, the presence of even a single atomicscale hole through which atoms can effuse allows the pressure to equalize in less than one second. We prepared microcavities in a Si/SiO2 wafer and sealed them with monolayer graphene. The microcavities were placed inside a chamber filled with Ar at 200 kPa for typically 4 days to gradually pressurize them. After taking the devices out, the membranes were found to bulge upwards. FIG. 9 shows the deflation of such microballoons with time. The Ar leak rates were found to be about 10.sup.3 atoms per second. If an atomic scale hole is introduced by, for example, ultraviolet chemical etching, the leak rate increases by many orders of magnitude, leading to practically instantaneous deflation. Furthermore, we found no difference in the deflation rates for membranes with and without evaporated Pt. In principle, it could be argued that membranes with pinholes smaller than the kinetic diameter of Ar (0.34 nm) or pinholes blocked with Pt nanoparticles should show no detectable leaks. However, monolayer membranes with sub-nanometer-sized pinholes are known to be rather unstable mechanically due to a tendency of defects to enlarge under strain, which for the applied pressures reached significant values of about 1%. Our micro-balloons remained stable and could be pressurized many times. This behavior confirmed that no individual pinholes were present in graphene and monolayer hBN obtained by mechanical cleavage when preparing the 2D proton conductors of the invention. This confirms that the proton conductance does not proceed via transmission through defects.

Detection of proton flow in the 2D proton conductors by mass spectrometry

[0143] To show directly that the electric current through our 2D proton conductors is carried by protons, we used the apparatus shown in detail in FIG. 10a. Protons transferring through graphene are collected at a catalyst Pt layer where they recombine to form molecular hydrogen: 2H.sup.++2e.sup.−>H.sub.2. The hydrogen flux is then measured with a mass spectrometer. Because the electric current I is defined by the number of protons passing through the graphene membrane, the hydrogen flow F is directly related to the passing current I.

[0144] For this particular experiment, the 2D proton conducting membranes of the invention were made as large as possible (50 μm in diameter) to increase the hydrogen flux to such values that they could be detectable with a mass spectrometer (Inficon UL200). To collect the electric current at the graphene membrane, a metallic contact (100 nm Au/5 nm Cr) was fabricated next to the SiN.sub.x aperture, before transferring graphene on top to cover both aperture and contact. This side of the Si wafer (with graphene on top) was then decorated with 1-2 nm of Pt to increase the proton flux and allow its easier conversion into hydrogen. The opposite face of the graphene membrane was covered with Nafion® and connected to a PdH.sub.x electrode in the same way as previously described.

[0145] The resulting device on the Si wafer was glued with epoxy to a perforated Cu foil that was clamped between two O-rings to separate two chambers: one filled with a gas and the other connected to the mass spectrometer. The setup was checked by filling the gas chamber with helium at the atmospheric pressure. No He leak could be detected above background readings of the spectrometer at about 10.sup.−8 bar cm.sup.3/s. Then, the chamber was filled with our standard gas mixture (10% H2 in argon at 1 bar and at 100% humidity). No hydrogen flux could be detected without applying negative bias to graphene.

[0146] However, by applying such a bias a controllable flow of H2 at a level of about 10.sup.−5 bar cm.sup.3/s was readily detected (see FIG. 10b). This figure shows the hydrogen flow rates F as a function of time for one of our devices using negative biases from 0 to 20 V. When cycling back from 20 to 0 V, the curves retraced themselves, indicating that the membrane was undamaged during the measurements. This is a feature that will be important for applications such as in hydrogen fuel cells.

[0147] Atomic hydrogen is highly unstable with respect to its molecular form, and it is most likely that the conversion into molecular hydrogen takes places at the surface of Pt rather than in the vacuum chamber. Accordingly, the Pt layer has to be discontinuous to let hydrogen escape. For continuous coverage (>5 nm of Pt), we observed formation of small hydrogen bubbles that grew with increasing electric charge passed through the circuit. The largest bubbles eventually erupted.

[0148] It is also instructive to mention the case of continuous Au films evaporated on top of the above devices (already containing a discontinuous Pt layer). We found that a bias applied across such devices again resulted in the formation of bubbles at the interface between graphene and the metal film. The bubbles could burst and sometimes even damage the membrane. This disallowed the use of continuous metal films for the mass spectrometry experiment. The same bubbling effect was observed for hBN membranes covered with a Pt film that provided the continuity of the electrical circuit for insulating hBN.

[0149] These observations serve as yet another indication of proton transfer through graphene and hBN membranes. On the other hand, no bubbles could be observed for thicker 2D crystals that again shows their impermeability to protons.

Theoretical Analysis of Proton Transport Through 2D Crystals

[0150] It is possible to understand our results qualitatively by considering the electron clouds created by different 2D crystals. These clouds impede the passage of protons through 2D membranes. In addition to the plots of the electron density for graphene and hBN monolayers in FIG. 1b, FIG. 11 shows similar plots of these clouds with superimposed positions of C, B and N atoms using the ball-and-stick model of graphene and hBN crystal lattices. In addition, FIG. 11 plots the electron density for monolayer MoS.sub.2. One can immediately see that the latter cloud is much denser than those of monolayer hBN and graphene, which explains the absence of proton transport through MoS2 monolayers.

[0151] For quantitative analysis, we first note that proton permeation through graphene has previously been studied using both ab initio molecular dynamics simulations (AIMD) and the climbing image nudged elastic band method (CI-NEB) (see S. P. Koenig, L. Wang, J. Pellegrino, J. S. Bunch. Selective molecular sieving through porous graphene. Nat. Nanotechnol. 7, 728-732 (2012); W. L. Wang, E. Kaxiras. Graphene hydrate: Theoretical prediction of a new insulating form of graphene. New J. Phys. 12, 125012 (2010); and M. Miao, M. B. Nardelli, Q. Wang, Y. Liu. First principles study of the permeability of graphene to hydrogen atoms. Phys. Chem. Chem. Phys. 15, 16132-16137 (2013). These studies have provided estimates for the proton transport barrier E in graphene ranging from about 1.17 eV to 2.21 eV. We reproduced those results for the case of graphene and extended them onto monolayer hBN.

[0152] All our simulations were performed using the CP2K package with the Pade exchange-correlation functional form based on literature methods (see: L. Tsetserisa, S. T. Pantelides. Graphene: An impermeable or selectively permeable membrane for atomic species? Carbon 67, 58-63 (2014); and J. VandeVondele, M. Krack, F. Mohamed, M. Parrinello, T. Chassaing, J. Hutter. Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Comput. Phys. Commun. 167, 103-128 (2005)). The barrier was estimated as the minimum kinetic energy necessary for proton transfer. The simulations have yielded graphene's E between 1.30 eV and 1.40 eV.

[0153] We calculated the energy for various configurations (usually referred to as ‘images’), which correspond to different distances between a proton and a 2D membrane to provide a series of images for a proton approaching the membrane. The energy was then minimized over obtained images and plotted as a function of distance to 2D crystals. The barrier E was estimated using the differential height of energy profiles. FIG. 12 shows examples of such energy profiles for graphene and monolayer hBN. We have estimated the proton barrier as 1.26 eV and 0.68 eV for graphene and monolayer hBN, respectively.

[0154] We modelled the effect of Pt on proton transport in the same way. The addition of the Pt atoms resulted in a significant reduction of the barrier in graphene to about 0.6 eV; that is, by a factor of 2. The absolute value of the reduction in the barrier height is in good agreement with the experimental observations.

Proton Transport Through 2D Crystals in Liquids

[0155] Although Nafion® was the material of choice in this work due to its stability and convenience of handling, in order to show the generality of our results, we have also investigated proton conductivity of 2D crystals when they were immersed in water solutions. This also shows that the devices of the invention will work in a liquid environment such as that found in some fuel cells and electrochemical cells.

[0156] For these experiments, devices were fabricated in the same way as described previously but instead of covering 2D crystals with Nafion®, they separated two reservoirs containing liquid electrolytes (HCl solutions). A polydimethylsiloxane seal was used to minimize leakage along the 2D crystal/substrate interface (FIG. 14 inset; yellow). Ag/AgCl electrodes were placed in each reservoir to apply a bias across the membranes and measure ionic currents (FIG. 14).

[0157] Typical I-V profiles of single-, bi-, and tri-layers hBN are presented in FIG. 14a. This behavior was highly reproducible as evidenced by the statistics in FIG. 14b. For devices prepared in the same manner but without a 2D crystal, the conductivity S was >10.sup.4 times higher than in the presence of monolayer hBN, which ensured that the 2D crystals limited the proton current. As in the case of Nafion®, we found a parasitic parallel conductance but it was somewhat higher (about 20 pS) for the liquid cell setup. Within this accuracy, we could not detect any proton current through monolayer MoS.sub.2, bilayer graphene, trilayer hBN or any thicker 2D crystals. Most importantly, the measured proton conductivities using electrolytes agree extremely well with the values found using Nafion® as the proton conducting membrane.

[0158] We have shown that 2D proton conducting membranes can be produced from monolayers of graphene and hexagonal boron nitride (hBN) which are unexpectedly permeable to thermal protons. We have also shown that the proton barriers can be further reduced by decorating monolayers of 2D materials, including but not limited to graphene and hBN, with catalytic nanoparticles. Thus other 2D materials can also be rendered proton conducting in accordance with the invention when suitably treated with catalytic metals. The atomically thin proton conductors of the invention are expected to be of interest for many hydrogen-based technologies.