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Voltage gated inter-cation selective ion channels from graphene nanopores

With the ability to selectively control ionic flux, biological protein ion channels perform a fundamental role in many physiological processes. For practical applications that require the functionality of a biological ion channel, graphene provides a promising solid-state alternative, due to its atomic thinness and mechanical strength. Here, we demonstrate that nanopores introduced into graphene membranes, as large as 50 nm in diameter, exhibit inter-cation selectivity with a ~20x preference for K+ over divalent cations and can be modulated by an applied gate voltage. Liquid atomic force microscopy of the graphene devices reveals surface nanobubbles near the pore to be responsible for the observed selective behavior. Molecular dynamics simulations indicate that translocation of ions across the pore likely occurs via a thin water layer at the edge of the pore and the nanobubble. Our results demonstrate a significant improvement in the inter-cation selectivity displayed by a solid-state nanopore device and by utilizing the pores in a de-wetted state, offers an approach to fabricating selective graphene membranes that does not rely on the fabrication of sub-nm pores.

graphene membrane via a shadow mask. Suspended graphene devices were mounted in a custommade microfluidic cell, allowing for the introduction of electrolyte solution to both sides of the graphene membrane. Measurement of conductance across the graphene membrane was carried out by applying a bias voltage across the device and measuring the resulting current (Fig.1a). The microfluidic cell allowed for electrical contact to the gold electrode, permitting the application of a gate voltage to the graphene while sweeping the transmembrane bias voltage. Additionally, the microfluidic cell was designed to allow atomic force microscopy (AFM) access to the top side of the membrane such that the pore could be imaged while in solution. Devices made from unperforated graphene had a trans-membrane conductance below 150 pS in 0.1 M KCl and 280 pS in 1 M KCl, confirming that graphene is a good barrier to ionic conductance. Graphene devices were perforated via helium ion microscope (HIM) drilling. Scanning transmission electron microscopy (STEM), HIM, and AFM were used to measure the pore diameters and observe the pore structure (Fig. 1b, 1c).
Ionic conductance was first measured in a two-terminal configuration across each device, with the gate terminal floating. For the graphene device in figure 1b, non-linear (activated) I-V characteristics were observed using monovalent electrolyte solutions (Fig. 2a). To account for the differences in bulk conductivity, the normalized conductance was plotted for each cation-chloride where is the measured nanopore conductance in solution i, is the bulk conductivity of solution i and is the bulk conductivity of KCl at a comparable chloride concentration. The normalized conductance reveals the pore(s) to be highly cation selective, with significant preference for K + over other ions measured. For the device shown in figure 1b at Vs = 0 mV, the normalized conductance of KCl was ~4x greater than the other monovalent ions (Na + and Li + ) and ~20x greater than the divalent ion measured (Ca 2+ ) (Fig. 2b). The differences in normalized conductance as well as the absence of conductivity in CaCl2 suggest that the dominant charge carriers are cations; additional experiments using asymmetric ion conditions confirm this result (SI Appendix, Fig. S2).
Next, a gate voltage was applied to the graphene to modulate the ionic current. Before proceeding with voltage-gated measurements, leakage current from source/drain to gate was measured to be less than 300 pA at 500 mV, verifying the device conductance was governed by ion transport and not a result of leakage current. The pore current was then measured under various applied gate voltages. Figure 2c demonstrates the ionic current response to changes in the gate voltage. As a more negative gate voltage is applied, the ionic current increased. As positive gate voltage was applied, there was no significant change in the ionic conductivity. This unipolar behavior is similar to a p-type FET device, likewise suggesting that cations are the majority charge carriers, and is consistent with 2 terminal measurements 27-29 .
To characterize the selectivity of a device, we define the conductance ratio as Si = gi /gKCl. This definition gives a conductance ratio of 1 for a pore that does not distinguish between cation i and K + . The conductance ratio was measured for 10 graphene devices with HIM drilled pores. Six devices had nine approximately 30 nm diameter pores, the same configuration as the device shown in figure 1b, and four had a single 50 nm diameter pore, shown in figure 1c. Five of the six ninepore devices and three of the four single pore devices displayed selective behavior. The mean conductance ratio for these devices is plotted in figure 2d. All samples displayed a similar trend in selectivity, where divalent ions had a lower conductance ratio than the monovalent species measured.
The activated IV behavior and observed selectivity in figure 2 inversely scales with the trend in hydrated radii of the measured cations, K + < Na + < Li + < Ca + < Mg + 1, 23 , where K + has the highest conductance. Additionally, the ability to detect an electrostatic gating response in solution is dependent on the Debye screening length: a measure of a charge carrier's electrostatic range in solution (~1 nm and ~0.3 nm in 0.1 M and 1M KCl, respectively). The pore diameter of a fully wet pore should be within a given solution's Debye length in order to observe direct electrostatic gating effects. However, the discrepancy between imaged pore size and the observed selective gate-responsive behavior suggests that the pores are not fully wet. Similarly, the absolute value of the conductance across the graphene pore is lower than one would expect given a standard model for pore conductance based on the imaged pore diameter 30 ; this also suggests incomplete wetting.
Incomplete wetting of a pore occurs often in nanopore experiments, particularly on hydrophobic surfaces 31 . Nanoscale surface bubbles are known to be present and highly stable on hydrophobic surfaces, such as highly oriented pyrolytic graphite, and occur in at least three types: gaseous nanobubbles, nanobubbles composed of oil 45 , and solid nanoparticles 46 . They are often produced via the exchange of ethanol to aqueous solution, a procedure utilized in the wetting of our graphene devices 32 . STEM imaging of our devices reveals a concentration of hydrocarbons adsorbed onto the surface of the graphene near the pore (SI Appendix, Fig.S3). The presence of these surface adsorbates not only modifies the wettability and the surface charge of the pore, but provide favorable locations (such as step edges or defects) for a nanobubble to pin 33 . AFM imaging of a graphene device in water revealed a nanobubble on the surface of the graphene, occluding the pore Conversely, the device AFM imaged in water that did not possess a nanobubble displayed linear, non-selective I-V characteristics with a conductance consistent with the theoretically expected value for the imaged pore size (SI Appendix, Fig.S7-S8).
To better understand the ion translocation process across a nanobubble at the entrance of a graphene nanopore, we performed molecular dynamics (MD) simulations to explore the free energy profiles (SI Appendix, Fig.S1). Considering the limitation of computational cost, we simulated water-immersed porous graphene membranes containing nanopores with radii in the range of 0.9-2.0 nm, with graphene edges functionalized by carbonyl groups and a gaseous nanobubble partially occluding the pore. As illustrated in Figure 3e, two transport pathways were considered for the ion translocation. In path 1, ions travel through a thin 1 nm thickness water film coating the graphene edges, where the hydration shells (HSs) can be perturbed by the (functionalized) graphene edges. Here the water film thickness is defined as the distance between the water surface and the edge carbon atoms in graphene. In path 2, the HSs must be stripped off, for the ion to translocate across the water/gas interface.
We calculate the potential of mean force (PMF) from the MD simulation, to measure the change of free energy during the ion translocation process ( Figure 4). For path 2, across the water/gas interface, a simple but over-estimation of the free energy barrier is ∆G = (1 -1/ε)q 2 /(4πε0R) = ~10 eV by using the Born model with the assumption that the HSs are fully detached from the ions 41 .
Here ε ≈ 80 is the relative permittivity of water and ε0 is the vacuum permittivity. Our MD simulations show, however, that the HSs are partially retained as the ion translocates across the interface. The free energy barrier is reduced to 51.0 kBT as a result, which is still very significant compared to the thermal fluctuation, indicating that the hydrated ion prefers to stay in the solvent and transport along path 2 is prohibited ( Figure 4a).
Conversely, the free energy barrier along path 1, through the thin water layer of 1 nm coating the graphene edge, is much reduced. Our free energy analysis shows that with the HSs perturbed, or ions captured by the functional groups at the graphene edge 44 , the barriers for the adsorptiondesorption process are on the order of kBT. Specifically, the barrier for Na + with a perturbed 2 nd or 1 st HS is ∆ = 0.8 or 1.9 kBT (Figure 4b), respectively, which is accessible via thermal diffusion and can be enhanced by the applied electrical field.
To explain the contrast between the conductivity of ions, we calculated the hydration radii RH of the ions and conclude with the order K + < Na + < Li + < Ca 2+ < Mg 2+ (Figure 4c), which indicates that ion translocation measured in our experiments is manifested in a size-sieving mechanism. This aligns with the fact that the thickness of water layer is comparable with RH plus the van der Waals distances. These results also suggest that one could further engineer the functional groups of graphene edges to gain control of the selectivity 34 .
The existence of a finite free energy barrier ∆ on the order of kBT indicates a prominent gating effect on the ion translocation process. To explore the gating effect, we carry out non-equilibrium MD simulations by applying an external field Ey = 0.01-1.00 eV/nm, and counting the probability of transmission and rejection events (Figure 4d). The results suggest that the transmission probability of ions through the water film measured in a fixed time interval increases with the field strength, demonstrating less torturous trajectories.

Conclusions
In summary, graphene nanopore devices occluded by a surface nanobubble demonstrated strong inter-cation selectivity, and ionic transport was modulated by an applied gate voltage. By utilizing pores in a de-wetted state, we have demonstrated a cation selective solid-state nanopore device that does not rely on the controlled fabrication of sub-nm pores. MD simulation results indicate that the ion selectivity can be explained by ion transport occurring across thin water films along the edge of the graphene pore, with transmission across the pore highly dependent on an externally applied electric field. Development of a defined process for control of nanobubbles will be necessary for further enhancing selectivity control. This ability to control selective nanopores at low voltages (< 500 mV) and with biologically relevant concentrations (100 mM) is an exciting advancement in sensing and separation technologies, not only providing a solid-state analog to voltage-gated biological ion channels, but having potential for applications in nanofluidic circuitry, water filtration, and energy storage as well.

Conflicts of interest
There are no conflicts to declare.      an SF6-Ar plasma. 20 nm of ALD Al2O3 was deposited, conformally coating the support chip. After a presynthesis anneal of the Cu foil substrate, CVD graphene was grown via low-pressure CVD. Following synthesis, the graphene, while still on the Cu foil substrate, was irradiated with 500 eV Xe + ions for a total fluence of 3.7 x 10 13 Xe + /cm 2 . This process has been shown to not introduce visible >nm hole defects when analyzed by STEM. The Cu foil substrate was then etched away with ammonium persulfate and the CVD graphene was transferred, without a sacrificial carrier layer, over the 5 µm through hole in the silicon nitride window. Once transferred, the graphene was exposed to 180 seconds of UVO to reduce hydrocarbon surface contamination. Through STEM imaging, this was confirmed not to introduce defects into the single-layer graphene itself. The gate electrode was defined via shadow mask lithography to be in contact with the graphene and 5 nm chromium followed by 60 nm gold were deposited via thermal evaporation.

Author
CVD graphene samples were perforated via site specific focused helium ion drilling. For HIM drilling, pores were drilled using a Zeiss ORION NanoFab scanning HIM equipped with a gas field ion source (GFIS) using He + ions at 25 kV. Small pores were drilled with a stationary beam in defined locations with a beam current of 0.5-2.0 pA, and a dwell time of 52 ms per pore. Larger pores were drilled by defining a pattern and dwelling the beam with a 1 nm pixel spacing over that region with a dose on the order of 1 nC/µm 2 (1x10 18 He + /cm 2 ). If a device did not display appreciable conductance upon initial wetting, it was exposed to ethanol  Table S1, which are optimized for a reliable description of the free energy and shell structure of ion solvation, with long-range electrostatic interactions treated by using the particle-mesh-Ewald (PME) method 3
The translocation pathway and PMF of ion transport along paths 1 and 2 (Figure 4a) are determined by umbrella sampling (US) 5 . We use a harmonic-spring biasing to constrain the ionic position at a specific value of d ( Figure S1a). For path 1 in the film and the fully-immersed model models (model 1 and 2 in Figure S1a The hydration radii of ions confined within thin water films are calculated following our previous work 8 , by using a model with a 1-2.5 nm-thick water film on graphene (model 3 in Figure S1).

Control Measurements.
Several control experiments were carried out to verify that the measured current was passing through the graphene pore(s) and not leaking through the graphene/silicon nitride interface or elsewhere. The following control devices were measured: (1) ALD alumina coated silicon nitride membrane with no through-hole, no graphene.
Isolate transport through silicon nitride membrane and through the PDMS sealing the device within microfluidic cell.
Determine limiting conductance for nitride through-hole.
(3) ALD alumina coated silicon nitride membrane with 5 µm through-hole, suspended unperforated CVD graphene. In this configuration, we observed highly rectified behavior, consistent with the conclusion of cations as the majority charge carriers (Fig. S2).
Pore Termination. High magnification aberration-corrected STEM imaging was carried out to reveal the pore geometry, edge structure, and the surface of the graphene (Fig. S3). Carbon was the most prevalent edge termination in the pores imaged, however hydrocarbon contamination, which is prevalent across the surface of the graphene, was also present near the pore edges for several of the devices that were imaged.
Evidence for the presence of a bubble. We found further evidence for the presence of a bubble occluding the pore by varying tip-sample forces during scanning 9 . This was done by reducing the amplitude set point ratio (the ratio between the amplitude set point and the free air amplitude), which increases the forces on the sample from the tip. Figure S4 shows the result of imaging the pore in water with different set points ratios. The lower set point ratio of 30% caused the tip to deform the object over the pore (Fig. S4B) as compared with images using higher set point ratios of 36% (Fig. S4A). This means the object is soft and malleable, and has a similar response to AFM probing as seen in PDMS nanodroplets or gaseous nanobubbles 10 . During the subsequent scan the set point was raised again causing the tip-sample forces to reduce (Fig. S4C), and the bubble topology returned to the same state as before. aqueous solution of the same ionic concentration. (Fig. S6A-C). The bulk conductivity of 0.1M LiCl in ethanol is considerably less than 0.1M LiCl in H20 11,12 . Thus, one would not expect the conductance across the graphene pore to be greater in the ethanol solution unless the transport pathway changed between the two measurements. This change in transport pathway is due to the presence and absence of a nanobubble, witnessed via liquid AFM imaging ( Figure S4).

Conductance measurements in solvents
In situ measurements were also carried out to allow for monitoring of the conductance while switching between ethanol and water solutions ( Figure S6D). Sweeping the bias voltage, the device was first measured in 0.1M LiCl in H2O (blue arrow) and demonstrated little conductance. As 0.1M LiCl in ethanol was introduced and the aqueous solution flushed out, the conductance increased (orange arrow) and stayed at the elevated conductance level while the ethanol solution was present (green arrow). All the while, the voltage was continually swept, down to -500 mV and back to +500 mV. When the water solution was reintroduced and the ethanol solution flushed out, the conductance returned to the lower conductance state (purple arrow) and remained low while water solution was present (yellow arrow). This result was consistent with measurements in figure S6A-C.
AFM and conductivity measurements of a non-occluded pore. We performed conductivity and in-situ AFM measurements of nanopores which were not occluded. Figure S7A shows an AFM image of a HIM drilled nanopore imaged in water. The phase channel was used to plot the image in order to highlight regions of rapid change in the topology of the surface -in this case the edge of the nanopore (Fig. S7C).
Immediately prior to AFM imaging, I-V curves of LiCl, NaCl and CaCl2 solutions all demonstrated linear conductance (Fig. S8). We can estimate the nanopore diameter, d, which should give rise to a conductance Gi for each salt species i by using the theory for ion transport through a cylindrical pore, which yields the formula: where σi is the bulk conductivity, and access resistance is assumed to be the dominant term 13 . Using values for Gi calculated from Fig. S7 and values for σi measured prior conductance measurements, Eq. S1 was used to calculate the predicted pore diameter d for each salt and tabulate the results in Table S2.
The pore conductivities for three different salts give consistent predictions for a pore size of ~75 nm in diameter. Comparing this prediction with the pore size measured with AFM in Fig. S7B, we see there is close agreement between the two. This confirms that when no occlusion is present over the pore, the observed nanopore conductance is consistent with the behavior we would expect for an infinitely thin cylindrical pore of that diameter.

Prevalence and formation of nanobubbles.
To estimate the prevalence of nanobubbles in our experiments, we imaged six devices in water with AFM. We found the presence of nanobubbles in all six devices, four of which are shown in Fig. S10 as an example. Nanobubbles are distributed across the devices and are of various sizes. We found evidence of bubbles occluding the graphene nanopore in four of the six devices measured. The ethanol and water solutions were degassed in a vacuum desiccator for ~1h prior to measurement in three of these devices. In addition, we found that pores frequently had a conductance lower than is predicted analytically, given the imaged diameter of the pore. We interpret this as indirect evidence that the pore was obstructed due to bubble formation. We measured the pore     Fig. S7, and was used with Eq. S1 to estimate the pore size.