Multifunctional graphene heterogeneous nanochannel with voltage-tunable ion selectivity | Panda Anku

Fabrication of the GPETNC

The GPETNC consisted of graphene subnanopores and a single conical PETNC, of which the base side was in contact with the graphene (Fig. 1a, b). The GPETNC was designed to take the advantage of both 2D nanopores and rectifying nanochannels, with their primary functional areas (graphene subnanopores and the tip entrance of the conical PETNC) spatially separated for better performances. Such structure was different from the previous structures of nanoporous 2D materials on ordinary supports (which hardly have influences on ion selectivity) with only a single confined functional area (i.e., 2D nanopores)1,2,3,4,5,6,7,8. An asymmetric track-etching technique39,40 was used to fabricate the conical nanochannel in a 12-μm-thick PET membrane. Briefly, a pristine PET membrane was first irradiated by a single swift heavy ion, which could create a nanometer-sized damage track in the membrane, and then asymmetrically etched with one side of the membrane contacting the etchant and the other contacting the stop medium. The fabricated conical PETNC had the base entrance diameter of 840 nm estimated from the etching time and the tip diameter of 140 nm obtained by fitting the size of a theoretical model to experimental data (Supplementary Fig. 1). Monolayer graphene grown by a chemical vapor deposition method41,42 with negligible defects (Supplementary Fig. 2) was transferred on the prepared PET membrane (making graphene on the base side of the PETNC) using a wet transfer procedure with polymethyl methacrylate as the mediator9,43. Ultimately, irradiation of energetic ions9,43 was utilized to introduce subnanopores in the transferred graphene suspended on the PETNC. More details about the fabrication procedures of the GPETNC are presented in “Methods”. Aberration-corrected scanning transmission electron microscope (STEM) was used to characterize the graphene subnanopores created under the ion irradiation, and the pores had the average diameter of 0.5 nm and density of 5.47 × 1011 cm−2 (Supplementary Fig. 3), which are consistent with the results of our recent molecular dynamics simulations44. Figure 1c shows four representative subnanopores with the corresponding atomic structures, and the observed pores (see all of them in Supplementary Fig. 3) had structures in agreement with the theoretical predictions made by Rajan et al.45 when solving the isomer cataloging problem of nanopores in monolayer graphene.

Fig. 1: Structure of graphene-based polyethylene terephthalate nanochannel (GPETNC) and experimental setup.
figure 1

a Three-dimensional structural model of the GPETNC membrane, which consisted of nanoporous monolayer graphene and polyethylene terephthalate membrane with a conically shaped nanochannel. b Cross-sectional schematic illustration of the GPETNC immersed in electrolyte solutions while measuring ion currents under different applied voltages using Ag/AgCl electrodes. The graphene with subnanopores was on the base side of the polyethylene terephthalate nanochannel. c Cs-corrected high-angle annular dark field-scanning transmission electron microscopy (HAADF-STEM) images of representative graphene subnanopores fabricated under ion irradiation. The pores are indicated by blue arrows, and their corresponding atomic structures are illustrated in the right panels. Scale bars are 1 nm.

Tunable ion sieving in the GPETNC

To measure the ion selectivity, the GPETNC was characterized by recording the current-voltage (IV) curves in a custom-designed system with two cells filled with chloride salt solutions using Ag/AgCl electrodes (Fig. 1b). We first considered the cation/anion selectivity of the GPETNC. Graphene nanopores created under ion irradiation have been reported to exhibit extremely high cation/anion selectivity9,43, which means that most anions are impeded when transporting through the pores compared to cations. The cation/anion selectivity arises from the negative charges on graphene nanopores during its transfer or fabrication in experiments, despite the debate of the nature of electric charges on nanoporous graphene surface due to hydroxide adsorption or pore edge due to functional groups in electrolyte solutions22,43,46,47,48,49. Hence, the GPETNC was likewise supposed to have negative charges on the graphene subnanopores and therefore be capable of preventing the transport of anions. We further identified the K+/Cl selectivity of the GPETNC to be 46 using the Goldman–Hodgkin–Katz model50,51 (see details in “Methods”), which does not explicitly depend on the channel size and has been successfully applied in studying the cation/anion selectivity of graphene nanopores9,22,43. The high selectivity ratio confirmed that the transport of Cl through the GPETNC could be neglected compared to that of cations.

Inter-cation selectivity of the GPETNC was obtained by directly comparing the normalized conductance gi of cation i (compared to that of K+), which was the measured ion conductance in 0.1 M cation-chloride solutions (KCl, NaCl, LiCl, MgCl2, and CaCl2) adjusted to consider the differences in electric mobilities and charges of the cations (as shown in “Methods”). The selectivity Si defined using this method is effective to describe the ability of the GPETNC to sieve different ions (a larger Si indicates that cation i can transport more easily) when the ion current caused by Cl is negligible22,43. Figure 2a shows the IV curves of the GPETNC in different chloride salt solutions, which are nonlinear and different from the results of pristine graphene nanopores22,43. Therefore, the normalized conductance gi was calculated at different voltages (Fig. 2b), and the number was found to be voltage-dependent and varied with different ions, which indicates the diverse abilities to transport through the GPETNC.

Fig. 2: Tunable ion selectivity of graphene-based polyethylene terephthalate nanochannel (GPETNC).
figure 2

a IV curves of the GPETNC in different chloride salt solutions with concentrations of 0.1 M. Error bars were the standard deviations from the average of three independent records. b Normalized conductance gi of cation i for the GPETNC at different voltages. c Ion selectivity of the GPETNC at different voltages. d Comparison of ion selectivity of the GPETNC and other nanoporous atomically thin membranes (NATMs) in experiments. The selectivity of different cations was normalized by that of K+. Based on the type of experimental settings, selectivities exhibited here were divided into three groups: conductance (gray), permeation (yellow), and mobility (blue), which indicated that they were obtained by comparing the normalized ion conductance22,43,54, the ion permeation rate12,15,16,55, and the mobility ratio of cation against chloridion56,57, respectively. The light blue region is the range of tunable selectivity of the GPETNC at different voltages in this work (see Supplementary Fig. 5 for the original data). The NATMs in references include graphene16,22,43,54, graphene oxide with various modifications12,15,16,55, molybdenum disulfide (MoS2)56, and composite structures of graphene, MoS2, and hexagonal boron nitride (hBN)57.

The ion selectivity of the GPETNC is presented in Fig. 2c. At negative voltages, ({S}_{{{{{{{{rm{{K}}}}}}}^{+}}}} ; > ;{S}_{{{{{{{{rm{N{a}}}}}}}^{+}}}};approx ;{S}_{{{{{{{{rm{L{i}}}}}}}^{+}}}}; > ;{S}_{{{{{{{{rm{C{a}}}}}}}^{2+}}}};approx ;{S}_{{{{{{{{rm{M{g}}}}}}}^{2+}}}}), which is similar to the order of the ion selectivity of pristine graphene nanopores22,43. In this case, the GPETNC exhibited the ability to sieve the mono- and divalent ions with mono/divalent ion selectivity up to 3.3 (the average selectivity of monovalent ions against that of divalent ones at −1 V). In addition, the ion selectivity was voltage-dependent, especially for monovalent ions (Na+ and Li+), whose selectivity decreased with the increase of applied voltage.

However, at positive voltages, we surprisingly found that the GPETNC exhibited ({S}_{{{{{{{{rm{{K}}}}}}}^{+}}}};gg ;{S}_{{{{{{{{rm{N{a}}}}}}}^{+}}}}; approx ;{S}_{{{{{{{{rm{L{i}}}}}}}^{+}}}}; approx ;{S}_{{{{{{{{rm{C{a}}}}}}}^{2+}}}}; approx ;{S}_{{{{{{{{rm{M{g}}}}}}}^{2+}}}}) with the maximum K+/ions selectivity of about 4.6 at 0.2 V (Fig. 2c), which is different from the results at negative voltages. Under this circumstance, the GPETNC conducted K+ up to ~4.6 times more rapidly than the other ions, which well resembles a biological potassium-selective ion channel, where the ion transport tends to be affected by the transmembrane voltage52,53. Therefore, the results suggest fresh ways to mimic biological ion channels and study the in-channel ion transport mechanism using artificial nanochannels with similar heterogeneous structures. The above findings indicated that the ion selectivity of the GPETNC could be facilely tuned by simply adjusting the applied voltage, and the GPETNC is a promising multifunctional nanochannel as a mono/divalent ion selective device at negative voltages and a biomimetic K+ channel at positive voltages.

We further compared the ion selectivity of the GPETNC with that of some NATMs reported before12,15,16,22,43,54,55,56,57 as shown in Fig. 2d. The light blue region is the range of the tunable ion selectivity of the GPETNC in this work, in contrast with other NATMs with fixed ion selectivity (patches), and the sieving of K+/ Na+(Li+) could be accomplished by the GPETNC while many devices fail in this. The results indicate that the great promise of the GPETNC as a versatile ion selective nanochannel because its ion selectivity can be quickly adjusted by adjusting the applied voltage, with no need in additional modifications to the sample itself. Furthermore, the GPETNC suggests such a heterogeneous nanochannel, in which, for example, nanoporous 2D materials such as MoS2, hBN, GO, and early transition-metal carbides and carbonitrides (MXenes) combined with the conical PETNC, might also exhibit a facilely tunable ion sieving ability.

The ion selectivity of the GPETNC was demonstrated based on the experiments in single electrolyte solutions. We noticed that ion selective nanochannels and membranes are designed and fabricated in order to function in mixed solutions, i.e., to separate a single (or more) ion from a mixture of ions. Therefore, such research is valuable for each emerging ion selective nanochannel. However, for nanochannels with selectivities based on the experiments of ion conductance22,43,54 or mobility56,57, which is characterized by the measured ion current, it is difficult to study their performance in mixed solutions, because all ions contribute to the total current and their portions are hard to be distinguished. Taking K+ and Na+ as an example, we fabricated a GPETNC with ion selectivity shown in Supplementary Fig. 6a, and the IV curve in the mixed solution containing both K+ and Na+ was complicated and indicated the elusive effect of the interaction between K+ and Na+ on the ion transport (Supplementary Fig. 6b). Considering that the experiments in single solutions focusing on the differences in ion conductance/mobility are effective to characterize the ion selectivity of nanochannels and that the selectivity is suggested to be valid in mixed solutions22,43,54,56,57, detailed studies of the interaction between different ions in mixed solutions are beyond the scope of this work, and future research could focus on this.

In addition to the voltage-tunable ion sieving, the GPETNC also exhibited the ability to rectify ion currents as indicated by the nonlinear IV curves of the GPETNC in different chloride salt solutions (Fig. 2a). The extent of the ion rectification is generally characterized by the rectification ratio (i.e., the ratio of the absolute ion currents at opposite voltages according to the IV curves, which was defined as I+1V/I−1V here), and its value also reflects the preferential direction of ion transport in rectifying nanochannels well31,32,58,59. Figure 3a shows the rectification ratios of different ions of the GPETNC. For monovalent ions (K+, Na+, and Li+), their rectification ratios were smaller than 1, which indicated that the transport of these ions in the GPETNC had a preferential direction from the tip side to the base side. However, for divalent ions (Ca2+ and Mg2+), the preferential direction of transport reversed as base-to-tip, as the rectification ratios were found to be larger than 1. Although ion rectification phenomenon exists in a pristine conical PETNC in different chloride salt solutions at the same concentration35,36,37, the rectification ratios are always smaller than 1 for not only monovalent ions but also divalent ones, which indicates that the preferential direction of all of them keeps from the tip to the base entrance. Besides, the preferential direction does not reverse in electrolyte solutions with different concentrations for a pristine conical PETNC35,36,37, and neither did the GPETNC (see Fig. 3b, c). Hence, the opposite rectification of mono- and divalent ion transport was peculiar to the GPETNC, and thus it could serve as a cation-responsive nanofluidic diode.

Fig. 3: Rectification of graphene-based polyethylene terephthalate nanochannel (GPETNC).
figure 3

a Rectification ratio of the GPETNC in different cation-chloride solutions with concentrations of 0.1 M. b IV curves of the GPETNC in KCl solutions with different concentrations. Error bars were the standard deviations from the average of three independent records. c Rectification ratio of the GPETNC in KCl solutions with different concentrations.

Heterogeneous structure of the GPETNC determines its tunable ion selectivity

The performance of a nanochannel can be attributed to its structure60, and the same also applies for the GPETNC with the heterogeneous structure of graphene subnanopores on the base side of a conical PETNC (Fig. 1). The ion selectivity of the GPETNC is attributed to the existence of the graphene subnanopores, because a pristine conical PETNC has entrance diameters much larger than the ion hydrated diameters and therefore it can hardly sieve metal ions35,36,37. However, it is reported that the inter-cation selectivity of pristine graphene nanopores is independent on the applied voltage22,43, even for a cylindrical PETNC support43, which indicates that the voltage-tunable property of the ion selectivity of the GPETNC arises from the use of the conical PETNC (Fig. 1). The main difference between the conical and cylindrical PETNCs is that the former has voltage-dependent ion enrichment/depletion effects inside the channel while the latter does not30,31,32. Hence, the ion sieving of the GPETNC originates from the graphene subnanopores, and it is determined by certain factors (such as the diameter, structure, charge density, and functional groups of the pores)3,4,7,8, which we speculated to be affected by the voltage-dependent enrichment/depletion of ions inside the GPETNC to some extent.

To test the hypothesis, we calculated the distributions of the ion concentration and electric potential in the GPETNC in chloride salt solutions at different applied voltages by numerically solving the Poisson-Nernst-Planck equations (Eqs. (4)–(6) in “Methods”) using COMSOL Multiphysics 5.3a Software (COMSOL, Inc.), and the details of the model and boundary conditions are shown in Supplementary Fig. 7. It is difficult to obtain analytical solutions in nanochannels with complex structures, and thus numerical simulations with the finite element method were used here, which have also been successfully utilized in studying the ion transport in nanofluidics9,10,11,22,27,30,31,32,39,40,61,62,63,64,65,66,67,68, including not only PETNCs39,40,63,64,65,66 but also nanopores in 2D materials9,10,11,22,27,67,68.

Our theoretical calculations indicated that indeed there were the voltage-dependent enrichment and depletion of ions inside the GPETNC, and the distribution of the potassium ion concentration ({c}_{{{{{{{{rm{{K}}}}}}}^{+}}}}) in 0.1 M KCl solution is presented in Fig. 4a as an example. At negative voltages, ({c}_{{{{{{{{rm{{K}}}}}}}^{+}}}}) near the tip of the GPETNC was larger than the bulk value (dashed line), indicating the enrichment of the potassium ions, while they were depleted near the base side. In contrast, at positive voltages, the ion depletion occurred near the tip side of the GPETNC, and the enrichment occurred near the base. The degrees of the ion enrichment/depletion both increased with the increase of the absolute value of the voltage, which is similar to the voltage dependence phenomenon in a pristine conical PETNC39,40,63,64,65,66. ({c}_{{{{{{{{rm{{K}}}}}}}^{+}}}}) at all voltages increased sharply as the location approaches the graphene surface (z = 12 μm), which indicates that a great number of K+ accumulated around there (Fig. 4b) owing to the attraction by the negative charges on the graphene subnanopores. The distribution of Cl also relied on the voltage; it exhibited a similar behavior of enrichment/depletion to that of K+, except for the pronounced depletion nearby the graphene surface (Supplementary Fig. 8a), and for other cation-chloride solutions, similar ion distributions were observed (see Supplementary Fig. 8b–d for the results of 0.1 M CaCl2 solution for example).

Fig. 4: Numerical calculations of distributions of ion concentration and electric potential in graphene-based polyethylene terephthalate nanochannel (GPETNC).
figure 4

a Concentration of potassium ion ({c}_{{{{{{{{rm{{K}}}}}}}^{+}}}}) along the center symmetry axis z of the GPETNC in 0.1 M KCl solution at different voltages. z = 0 and 12 μm represent the tip and base side of the GPETNC, respectively. b Distributions of ({c}_{{{{{{{{rm{{K}}}}}}}^{+}}}}) nearby a graphene subnanopore of the GPETNC in 0.1 M KCl solution at −1 and 1 V. Scale bars are 0.5 nm. c Electric potential ψ at different distances away from the graphene center along a perpendicular path nearby a graphene subnanopore of the GPETNC in 0.1 M KCl solution at −1 and 1 V. The path is 0.75 nm away from the pore center (Supplementary Fig. 8e). The gray dashed lines represent the graphene surfaces in the inner (left) and outer (right) sides of the GPETNC. Δψ indicates the drop between the potential far away from the graphene surface (where ψ hardly changes) and the one on it. d Δψ inner and outer the graphene surface in 0.1 M KCl and CaCl2 solutions at different voltages.

The extreme cation enrichment near the graphene surface could partially screen the negative charges there and reduce the effective surface charge density, which can be reflected by the variation of the electric potential ψ around there27,46. As shown in Fig. 4c, the value of ψ far away from the graphene is close to the applied voltage, and it decreases as the location approaches the graphene surface because of the negative charges. For the same electrolyte solution, the effective charge density of graphene surface ({sigma }_{{{{{{{{rm{gra}}}}}}}}}^{prime}) can be qualitatively reflected by the potential drop Δψ between the value of ψ far away from the graphene surface and the value on the surface; a larger Δψ indicates a higher (|{sigma }_{{{{{{{{rm{gra}}}}}}}}}^{prime}|)27,46. Figure 4d shows that Δψ in the outer side of the graphene surface barely changed at different voltages, because of the nearly unchanged degree of cation enrichment there (see Fig. 4b and Supplementary Fig. 8d). However, Δψ in the inner side decreased with the increment of applied voltage from −1 V to 1 V, especially for monovalent cations, which was caused by the higher degree of the cation accumulation near the graphene surface inner side at a larger voltage (Fig. 4b). The results indicated that the applied voltage affected the cation enrichment near the graphene subnanopores inside the GPETNC, and thus changed the effective surface charge density, making it rely on the voltage (as schematically illustrated in Fig. 5).

Fig. 5: Schematic illustration of the mechanism of ion sieving and rectification in graphene-based polyethylene terephthalate nanochannel (GPETNC).
figure 5

The distribution and transport direction of anions and monovalent cations at negative voltages (a), divalent cations at negative voltages (b), monovalent cations at positive voltages (c), and divalent cations at positive voltages (d). Ion selective graphene subnanopores are on the base side of the conical polyethylene terephthalate nanochannel, where the voltage is applied. For monovalent cations (a, c), the graphene effective charges heavily decrease with the increase of applied voltage (curved arrow) due to the significant voltage-dependent cation enrichment near the graphene (dashed box). However, for divalent cations (b, d), the graphene effective charges slightly decrease with the increase of applied voltage (curved arrow), because the change of the cation enrichment degree is slight (dashed box).

The ion selectivity of the GPETNC arose from its graphene subnanopores as discussed before. It has been reported that the value of charge density of graphene nanopores influences the ion selectivity22,27,29,43,46,69. Our previous molecular dynamics simulations demonstrated that a graphene subnanopore with negative charges had a higher ion selectivity than a pore with no charge43, and things are similar for other subnanometer-sized channels (e.g., a single carbon nanotube with more negative charges has a higher ion selectivity70). Therefore, the inter-cation selectivity of the GPETNC relied on the applied voltage due to the voltage-dependent ({sigma }_{{{{{{{{rm{gra}}}}}}}}}^{prime}) demonstrated in the theoretical calculations. For monovalent cation-chloride solutions, the inner Δψ of the GPETNC at −1 V was much higher than that at 1 V (see Fig. 4d for KCl as an example), indicating a higher (|{sigma }_{{{{{{{{rm{gra}}}}}}}}}^{prime}|), and thus it made the Na+ and Li+ selectivities of the GPETNC at −1 V higher than those at 1 V, as observed in the experiments (Fig. 2c). Nevertheless, for divalent cation-chloride solutions (e.g., CaCl2 in Fig. 4d), the change of Δψ between −1 V and 1 V was much smaller than that in the KCl solution, which indicates a weaker influence of the ion enrichment at different voltages on ({sigma }_{{{{{{{{rm{gra}}}}}}}}}^{prime}) as compared to the situations for monovalent ions (Fig. 5). Hence, the selectivities of Ca2+ and Mg2+ of the GPETNC slightly changed at different voltages. With the increase of applied voltage from −1 to 1 V, the selectivities of Na+ and Li+ decreased, and those of Ca2+ and Mg2+ kept in low values, eventually resulting in the high K+/ions selectivity of the GPETNC at positive voltages as found in the experiments (Fig. 2c). It is worth noting that studies on the influences of graphene nanopore charges on the inter-cation selectivity were rare43,71, and the mechanism of the charges influencing the ion transport was unclear (e.g., affecting the electrostatic repulsion or dehydration degree of ions)3. Such investigations are beyond the scope of this work, and thus future research can, for example, focus on the reasons why the experimentally measured ion selectivity of the GPETNC did not monotonously rely on the voltage, as departed from Δψ in theoretical calculations.

As for the opposite rectification of mono- and divalent ions of the GPETNC, it also arose from its heterogeneous structure. The GPETNC had a high K+/Cl selectivity of 46 as demonstrated before, which indicates that the transport of cations mainly contributes to the ion current. Theoretical calculations indicated the existence of the voltage-dependent cation enrichment/depletion inside the GPETNC (Fig. 4 and Supplementary Fig. 8), and the direction of the cation concentration gradient is the same as that of the applied electric field, i.e., tip-to-base at negative voltages and base-to-tip at positive voltages, enhancing the ion current, as shown in Fig. 5. For monovalent cations, the absolute concentration gradient between the tip and base sides at negative voltages was higher than that at positive voltages (Fig. 4a), thus resulting in a larger diffusion current. In this case, the preferential transport direction of monovalent cations was tip-to-base, as the rectification ratios were characterized to be smaller than 1 (Fig. 2a). However, the situation for the divalent cations was different, i.e., the absolute concentration gradient between the tip and base sides at negative voltages was lower than that at positive voltages (Supplementary Fig. 8b). Thus, divalent cations had the preferential transport in the base-to-tip direction (rectification ratios larger than 1 as shown in Fig. 2a), which was opposite to that of monovalent cations (Fig. 5).

In conclusion, we fabricated a multifunctional heterogeneous GPETNC with facilely voltage-tunable ion sieving ability. The GPETNC exhibited the promise as an efficient mono/divalent ion selective device, an excellent biomimetic ion channel, and a cation-sensitive nanofluidic diode. Its ion selectivity is determined by the graphene subnanopores with negative charges, which are affected by the voltage-dependent enrichment/depletion of ions inside the GPETNC, and the opposite rectification of divalent ions compared to monovalent ones rely on the differences in the diffusion currents caused by the ion concentration gradients. The unique and fascinating performance of the GPETNC results from the interaction between the ion selective graphene subnanopores and the rectifying conical PETNC. Therefore, a device with similar heterogeneous structures (i.e., nanoporous 2D materials supported by rectifying nanochannels), suggested by our work, might also have a voltage-tunable ion selectivity even with a wider range and the cation-sensitive ion rectification with a more excellent rectification ratio. The creation of such composite can be facile and simple, because of the mature fabrication techniques of NATMs72,73,74 and ion rectifying nanochannels30,31,32. For example, a nanochannel with a much stronger rectifying ability, in which the degree of the ion enrichment/depletion is also heavier, could replace the original one of the GPETNC in this work, and thus this new nanochannel might have a much higher ion selectivity and rectification ratio. In addition, GO membranes with fixed interlayer spacing could be transferred onto a cylindrical PETNC with uneven surface charge distribution, which is another rectifying nanochannel75. In this case, one could tune the ion selectivity of this device by simply adjusting the applied voltage, with no need in overcoming the barriers in controlling the interlayer spacing of the pristine GO membranes. The heterogeneous nanochannel devices made by NATMs and traditional rectifying channels to achieve rapidly tunable ion selectivity for diverse applications can be a new and flourishing research avenue.

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