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Electrically Tunable Ion Selectivity of Charged Nanopores Zichuan Ni, Hu Qiu, and Wanlin Guo J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10191 • Publication Date (Web): 07 Dec 2018 Downloaded from http://pubs.acs.org on December 10, 2018

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The Journal of Physical Chemistry

Electrically Tunable Ion Selectivity of Charged Nanopores Zichuan Ni†, Hu Qiu* and Wanlin Guo,

State Key Laboratory of Mechanics and Control of Mechanical Structures and Key Laboratory for Intelligent Nano Materials and Devices of MOE, Institute of Nano Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China.

AUTHOR INFORMATION

*Corresponding Author, Email: [email protected]

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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ABSTRACT

Selective ion transport through nanoscale pores or channels has attracted considerable

attention due to its fundamental role in essential biological activities such as the

propagation of action potentials as well as in diverse applications from nanofiltration

to biosensing. However, a precise and continuous control of ion selectivity over a wide

range remains a challenging task. Here, we show by molecular dynamics simulations

that ion transport through a graphene nanopore can be modulated by electrically biasing

the graphene membrane. The nanopore selectivity between cations and anions can be

continuously and reversibly tuned by varying the sign and magnitude of the electric

charge on graphene. We further show that this tunable selectivity is attributed to the

electrostatic adsorption-induced diffusion of charged ions on oppositely charged

surfaces, which promotes the permeation of these ions. Our work opens a new avenue

for developing nanofluidic devices and mass-selective membranes with finely

controlled selectivity.


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INTRODUCTION Ion transport through biological channels or transporters within cell membranes is fundamental to a wide variety of cell functions, including the maintenance of resting membrane potentials as well as the generation and propagation of action potentials in electrically excitable cells, etc. In typical selective ion channels, only specific species of ions are allowed to rapidly pass through while the passage of other ions are blocked, leading to the known ion selectivity. For instance, a potassium-selective channel can conduct K+ ions at a rate close to the diffusion limit and meanwhile exclude Na+ ions, yielding a K+/Na+ selectivity ratio as high as ~1000,1 although these two monovalent ions are fairly similar, differing just slightly in their atomic radius. Artificial analogues of these biological ion channels, constructed in solid-state systems, have also long been exploited, toward a wide range of applications, including molecular separation, biosensing and water desalination.2-11 In particular, atomically thin nanomaterials such as carbon nanotubes and graphene have emerged as promising synthetic membrane materials.12 For instance, graphene and other two-dimensional materials, the thinnest



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possible membranes, are expected to be the most efficient for molecular separations since the permeance of a membrane scales inversely with its thickness.13-17 Applicable to both biological and synthetic channels, ion selectivity typically arises from either the steric exclusion where only ions smaller than a certain size are allowed to pass through or the charge exclusion where ion transport is governed by electrostatic barriers imposed by charges on channel walls.18 In this context, one could readily modulate ion selectivity by tuning the geometry and chemistry of nanochannels. For instance, Cao et al. found that, based on extensive Poisson and Nernst–Planck (PNP) model calculations, the selectivity of nanopores on a 2 nm-thick membrane can be modulated by adjusting charges on the membrane surface.19 Previous attempts to control ion transport through graphene nanopores has concentrated on changing the pore size and number of graphene layers,20-22 chemical modifications of pore edges2324

or strain engineering of the membrane.25 Sint et al. predicted through molecular

dynamics (MD) simulations that graphene nanopores terminated by positively charged hydrogens (or negatively charged nitrogens and fluorines) favored the passage of anions (or cations).23 Similarly, Zhao et al. found enhanced K+ permeation and


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inhibited Cl- permeation when negative charges were placed at the edge of a graphene nanopore.26 Furthermore, He et al. reported that graphene nanopores functionalized by carbonyl groups or negatively charged carboxylate groups could selectively conduct K+ or Na+, depending on the type of functionalization and the magnitude of driving voltage.24 All these results highlight the feasibility of controlling ion selectivity by customized electrostatic interactions between ions and the charged groups on graphene pore rims; however, a precise modification of functional groups on graphene pore rims is a difficult fabrication challenge. Besides pore functionalization, a uniform surface charge on graphene (not limited to the pore rim) can actually be achieved by adjusting PH-dependent charge state of deprotonatable surface groups on graphene27 or by electrically biasing the membrane.28 In particular, Shankla and Aksimentiev proposed to control ion transport across nanopores on a thick solid-state membrane covered by two charged layers, whereby ion rectification was demonstrated under certain charging status of these two layers and electric fields.28 In this work, we systematically investigate ion transport across nanopores in a monolayer graphene subjected to gradually varying surface charges. It is found that the



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nanopore selectivity depends sensitively on both the sign and magnitude of the graphene charge. A surface diffusion model, namely the electrostatic adsorptioninduced surface diffusion, is proposed to account for the enhanced flow of charged ions through oppositely charged pores. It is further shown that the fraction of the surface diffusion ions in total permeated ions decreases gradually with the pore diameter, leading to reduced yet measureable ion selectivity in large graphene nanopores. This work provides a promising paradigm for achieving continuous and precise tuning of ion transport desirable in nanofluidic applications. METHODS System setup. A single layer of graphene with dimensions of 8 nm × 8 nm was first generated using the Nanotube Builder plugin of VMD.29 The coordinate origin was placed at the geometric center of the graphene sheet, with the z axis perpendicular to the graphene plane. Carbon atoms within a circle of x2 + y2 < (d/2)2 were removed, generating a nanopore with a diameter d. The graphene sheet was then solvated by placing a 4 nm thick water layer on each side of the graphene sheet using the Solvate plugin of VMD. Na+ and Cl- ions were placed in the system by substituting a certain


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number of water molecules to neutralize the system and reach a concentration of 1 M using the Autoionize plugin (Figure 1). In order to modulate ion transport, an adjustable voltage Vg was applied to bias the graphene layer, which, in our MD simulations, was realized by assigning equally distributed partial charges to carbon atoms of the graphene. The resulting surface charge density on graphene varies between -2.4 e/nm2 and 2.4 e/nm2. Note that the numbers of Na+ and Cl- ions may not be identical since a few more Na+ (or Cl-) ions are necessary to neutralize the charge on graphene. Each final system has approximately 49000 atoms. Molecular dynamics simulations. All simulations were performed with the NAMD30 program and visualized with VMD.29 The carbon atoms of graphene were modelled as the CA carbon in the CHARMM27 force field,31 and water was described by the TIP3P model.32 Note that the interaction between cations and the π electron-rich graphene, the so-called cation-π interaction, was not explicitly considered in these classic force fields; the inclusion of such interaction may alter the transport of cations across graphene nanopores. Periodic boundary conditions were used in all the three directions and the particle mesh Ewald (PME) method was used to treat long-distance



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electrostatic interactions.33 The integration time step was 2 fs and atom coordinates were recorded every 5000 steps (i.e., 10 ps). The graphene layer was fixed in all simulations. After minimization, each system was relaxed as the NPT (constant number, pressure and temperature) ensemble for 2 ns where the pressure was maintained at 1 atm using Nosé–Hoover langevin piston control34 and the temperature was maintained at 300 K using Langevin dynamics. Subsequently, the system was further equilibrated as the NVT (constant number, volume and temperature) ensemble for another 4 ns. To model the driving voltage of the transmembrane bias Vs, a uniform electric field E, determined through Vs = Elz, was applied along the –z direction to induce ion flow across the graphene nanopore, where lz is the length of periodic cell along the z axis. The system was simulated under the electrical field for at least 100 ns for data analysis. Alternatively, a hydrostatic pressure of 100 MPa, instead of the electric field, could also be used to induce the flow of water and ions, which was modelled by applying a constant force on water molecules within a 1 nm thick layer far from the graphene surface. Calculation of ionic current. We calculated the instantaneous ionic current I(t) as


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I(t) =

1 𝛥𝑡𝑙𝑧

∑𝑁 𝑖=1 𝑞𝑖 [𝑧𝑖 (𝑡 + 𝛥𝑡) − 𝑧𝑖 (𝑡)]

(1)

where N denotes the number of all target ions in the system, qi is the charge of the ion i, zi is the z coordinate of ion i, Δt = 10 ps is the time interval between two consecutive frames and lz is the length of the periodic cell in the z direction. The final ionic current was obtained by averaging the instantaneous currents over all frames. Calculation of potential of mean force. The umbrella sampling method was adopted to calculate the potential of mean force of Na+ and Cl- ions permeating through the pore. Along the reaction path z, a target ion was placed at (0, 0, zi), where zi ranges from -2 nm to 2 nm with an interval of 0.05 nm, resulting in 80 independent configurations. During the simulation of each configuration, a spring constant of 20 kcal/mol was used to restrain the ion in the z direction around its original position. Each system was simulated for 1 ns, with the last 0.5 ns for data analysis. Finally, the weighted histogram analysis method (WHAM) implemented in the wham program was employed to generate the free energy profiles.35 Calculation of velocity map. The ion movement in a 1.6 nm thick slab, parallel to the x-z cross section of the system and centered at y = 0, was considered. This slab was



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divided into 0.4 nm × 0.4 nm grids in the x-z plane. Local velocity in each grid was calculated by summing up velocity vectors from all frames and then dividing by total number frames. The Streamplot function in matplotlib library of Python was used to generate the final velocity map.36 Identification of ion permeation pathways. For each permeated ion, we tracked its position in a 500 ps period before entering the pore. During this period if a permeated ion never entered the graphene surface region, it was treated as along Path 2, otherwise as Path 1. The graphene surface region is defined as -0.6 nm< z < 0.6 nm and x2+y2 > (0.8 nm)2. This categorizing method is analogue (but not identical) to that used in the numerical simulations of ref. 27. RESULTS AND DISCUSSION Figure 1a shows a typical simulation system considered in the present study for ion transport control. As the graphene membrane is electrically conductive, a gate potential (Vg) can be applied directly to membrane to continuously tune the membrane surface charge. In our simulations, such effect is modelled by assigning equally distributed partial charges to carbon atoms of the graphene, as commonly done in previous


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studies.28,37 It is encouraging to notice recent experiments that successfully demonstrated the use of gate voltage to alter the surface potential of graphene-based nanoporous membranes and to modulate ion diffusion across these membranes.6 Aside from the gate potential Vg, a transmembrane bias Vs (which is 1 V unless otherwise specified) is applied across the graphene layer to induce the transport of ions (Na+ and Cl-) through nanopores. For instance, under a positive voltage Vs which forms a downward electric field, Na+ ions are driven from the cis compartment to the trans compartment, forming a downward Na+ ionic current denoted as INa. Conversely, an upward ionic current is seen for Cl-, labeled as ICl.

Figure 1. Electrically controlled ion transport through a graphene nanopore. (a)

Simulation setup. A graphene layer containing a 1.2 nm diameter pore is embedded in a 1 M

NaCl solution. A transmembrane bias Vs is applied between two compartments of the solution



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(i.e., cis and trans, with the latter being grounded) to induce ion transport across the graphene

nanopore. Meanwhile, another voltage bias Vg is used to electrically bias the graphene relative

to the trans compartment. Na+ and Cl- ions are highlighted as cyan and red spheres, respectively.

(b) Recorded ionic current of Na+ (INa) and Cl- (ICl) ions, together with their summation, Itotal,

as a function of the membrane’s charge density, σ. Inset shows the ion selectivity, defined as

the ratio of the Cl- current to the Na+ current (i.e., ICl/INa, violet line) or its reciprocal (i.e., INa/ICl,

green line). The horizontal axis of the inset is the same as the main plot, and therefore is not

labeled.

Figure 1b shows the dependence of INa and ICl, as well as their summation, Itotal, on the graphene surface charge density, σ. At a first glance, the total ionic current Itotal increases monotonically with the increase of the magnitude of the graphene charge density, regardless of its sign. In contrast, quite complex features are noted in the profiles of INa and ICl. In the baseline state of an electrically neutral graphene (i.e., σ = 0), ICl and INa are 0.58 nA and 0.26 nA, respectively, leading to a selectivity ratio of ICl/INa at 2.2 (Figure 1b inset). Such mild selectivity is not surprising as Na+ and Clions differ in mobility and hydration shell structures. The most striking feature observed 12 ACS Paragon Plus Environment

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here is the completely opposite response of ICl and INa to the change of charge density σ. Specifically, when the graphene carries a positive charge (σ > 0; right half in Figure 1b), the Cl- current ICl increases gradually with increasing σ, while the Na+ current INa decreases. Consequently, the selectivity of Cl- over Na+ rapidly increases with charge density σ. For instance, under a charge density of 2 e/nm2, Cl- current becomes 2.7 times larger than that of the neutral graphene (i.e., σ = 0) and Na+ current becomes 38% of that of the neutral graphene. This asymmetry between Cl- and Na+ ionic currents induces a ICl/INa selectivity ratio as high as 15 (Figure 1b inset). The selectivity here is 4~5 times larger than that achieved through the dehydration-based mechanism.21 These results indicate that one can readily control the selectivity of a nanopore by varying its surface charge densities (or electric bias). On the other hand, when the charging status of the graphene shifts from positive to negative, the Na+ and Cl- current trends become reversal: INa increases while ICl decreases (σ < 0; left half in Figure 1b) with the increasing magnitude of σ, leading to a gradually increasing INa/ICl selectivity (Figure 1b inset). In particular, under the graphene charge at -0.4 e/nm2, the selectivity vanishes, indicated by nearly coincident INa and ICl. This is likely because a balance is established



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for the competition between the negative charge-induced Na+ selectivity and the intrinsic Cl- selectivity of the pore. The salt concentration adopted in above simulations is 1 M, while most of the experimental tests were conducted with relatively low-concentration solutions. To exploit the influence of salt concertation, we performed a test simulation at a lower salt concentration of 0.25 M (under σ = 0.4 e/nm2) and obtained an increased ICl/INa selectivity ratio of 4.7, comparted to that of 3.1 at the 1 M concentration. We expect that, under further decreased salt concentration in experimental situations (which is difficult to simulate due to limited system size), the selectivity could be further enhanced. We also explore the influence of the driving strategy on the ion transport. With the increasing transmembrane bias Vs, both INa and ICl gradually increase, and a high selectivity ratio (> ~10) persists in all considered voltages (Figure S1). Furthermore, instead of applying a transmembrane voltage, the ion transport induced by a hydrostatic pressure was also examined, whereby a similar trend in ion selectivity modulation can be observed (Figure S2).


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Since the selective ion transport is quite sensitive to the graphene surface charge, it is straightforward to correlate the mechanism of such tunable ion selectivity with the electrostatic interaction between ions and the charged graphene. To validate such assumption, we analyze ion distribution and movement around a charged graphene, again with the charge-neutral graphene as a baseline. Figures 2a and 2b present the local density distributions of Na+ and Cl- ions around the neutral graphene on the x-z cross section of the system, respectively. It can be seen that both Na+ and Cl- ions are almost evenly distributed in the system, as no strong interactions exist between ions and the membrane. However, there is a few thin yet visible horizontal ion layers accumulating at the upper graphene surface in the Na+ density map (Figure 2a). This can be attributed to the electric field-induced accumulation of Na+ ions before permeating through the pore. Similarly, the accumulation of Cl- ions is also observed, but around the lower graphene surface as Cl- ions move upward under the electric field (Figure 2b). When the graphene is charged at 2 e/nm2, no significant changes occur in the Na+ density map (Figure 2c), except the observation of relatively weaker ion accumulations on the graphene surface due to electrostatic repulsion. In stark contrast, it is interesting to find



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that, Cl- ions accumulate evidently near the positively charged graphene surface, forming a 0.4 nm thick ion layer on each side (Figure 2d). It is further found that the lower graphene surface seems to attract more ions than the upper surface, likely due to the overall upward movement of Cl- ions. We believe that such Cl- accumulation on the positively charged surface, the result of electrostatic adsorption, should be tightly relevant to the pore capture and permeation of Cl- ions, as will be discussed below.

Figure 2. Ion redistribution induced by graphene surface charge. (a,b) Local density

distribution of Na+ (a) and Cl- (b) on the x-z cross section of the system containing an

electrically neutral graphene. (c,d) Same as a,b but for a graphene membrane with a charge


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density σ of 2 e/nm2. The arrows indicate the direction of the electric field E induced by a

transmembrane voltage.

After knowing the ion distribution features, we further explore how the fast movement of Cl- is achieved in the charged graphene nanopore system. Figure 3 shows the velocity map for Cl- ions across a 2 e/nm2 charged graphene membrane. In general, Cl- ions display a strong trend to move upward, indicated by the large population of upward pointing arrows. Specifically, two ion permeation pathways can be identified: i) ions diffuse through the pore around its central axis, in other words, without close contact with the graphene (highlighted in blue; denoted as Path 1 in Figure 4); ii) ions first adsorb onto the graphene surface and then slide into the pore on the graphene surface, and finally permeate through the pore (highlighted in yellow; denoted as Path 2 in Figure 4).



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Figure 3. Velocity map of the flow of Cl- ions on the x-z cross section of the system

containing a graphene membrane charged at σ = 2 e/nm2. Two distinct ion permeation

pathways are colored in light blue and light yellow, respectively.

Figure 4 presents the comparison of ion permeation along the two identified pathways under various graphene charge densities. It is found that the ion permeation rates along Path 1 of both Na+ and Cl- ions (blue and red dotted lines) fluctuate slightly around 1 ns-1, that is, nearly independent of the graphene charge. This independence suggests that the bulk flow of ions is not affected by the electrostatic interaction between ions and charged surface, which should not be responsible for the observed ion selectivity. On the contrary, in Path 2, ion permeation rates of Na+ and Cl- ions are highly sensitive to the graphene surface charge (blue and red solid lines). At positive charge densities 18 ACS Paragon Plus Environment

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(σ > 0), the Cl- permeation rate along Path 2 (red solid line) increases gradually with increasing σ, while Na+ permeation along Path 2 decreases (blue solid line). The chargedependent ion permeation along Path 2 here is in perfect agreement with that of the recorded ionic current (Figure 1b), indicating that the electrostatic adsorption-induced surface diffusion along Path 2 dominates the electrically controlled ion transport and associated selectivity.

Figure 4. Characterization of ion permeation along different permeation pathways at

various σ. The contribution of two possible pathways to the Na+ and Cl- permeation rate under

various charge densities are measured. In Path 1, ions transport through the pore without close

contact with the pore surface or edge, while in Path 2, ions first adsorb onto the graphene

surface and then diffuse into and permeate through the pore.



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To validate the proposed mechanism, we further examine the ion transport under different pore sizes when the charge densities are fixed to 1.2 e/nm2. The diameterdependent ionic currents are shown in Figure 5a. It is as expected to see that both Na+ and Cl- currents scale with the pore diameter d, but the ICl/INa selectivity ratio (Figure 5a inset) decreases gradually from 18.2 of the smallest pore (~1 nm in diameter) to 5.4 of the largest pore (~2.3 nm in diameter). Here the observation of ion selectivity in pores with diameters much larger than those of hydrated ions is consistent with an experimental report of selective ion transport in very large pores on negatively charged graphene.27 It is rather surprising to note that, despite both exhibiting an increasing trend as d increases, the Cl- permeation rate along Path 1 (red dotted line in Figure 5b) is always comparable to that of Na+ (blue dotted line), which again rules out the contribution of Path 1 permeation to the ion selectivity. In contrast, in the case of Path 2 permeation, the Cl- rate (red solid line) is much higher than that of Na+ (blue solid line), resulting in the observed ion selectivity. Another striking feature is that the proportion of Cl- permeation along Path 2 to total permeation decreases gradually with increasing diameter d (Figure 5b inset). This decrease is in qualitative agreement with


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the decreasing trend of ion selectivity (Figure 5a inset), further validating the key role of surface adsorption induced diffusion (Path 2 permeation) in inducing the ion selectivity. Furthermore, we expect that the pore-size dependence would also be affected by salt concentrations; higher selectivity may be achieved in diluted solutions, as discussed earlier.

Figure 5. Dependence of selective ion transport on pore diameter. (a) Ionic current of Na+

(INa) and Cl- (ICl) ions, together with their summation, Itotal, as a function of the pore diameter,

d. Inset shows the ICl/INa selectivity versus pore diameter. The graphene membranes are all

charged at 1.2 e/nm2. (b) Ion permeation rates along Path 1 and Path 2 versus d. Inset shows

the probability of Path 2 permeation of Cl- ions. The horizontal axis of the insets is the same as

the main plot, and therefore is not labeled.



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Previous reports have suggested a few molecular mechanisms that account for ion selectivity in nanopores. The most well-known one is the ion-specific dehydration effect that dominates the selectivity in nanopores with diameters less than 1 nm, which is caused by the energy penalty difference of dehydration between ions inside the pore.21-22 In our study, the observation of ion selectivity in much larger nanopores implies that dehydration may not be responsible for the selectivity. To validate this assumption, we computed the ion-water oxygen radical distribution (Figure S3) for both Na+ and Cl- ions in charged nanopores with respect to a neutral pore. The results show that partial dehydration of water from the first hydration shell occurs when moving a Cl- ion from the bulk solution to the pore (Figure S3b), while dehydration is hardly seen for Na+ ions (Figure S3a). However, such dehydration effect is nearly unaffected by the charge on graphene, as ions in the neutral and charged graphene pores possess nearly coincident RDF profiles. Besides, the free-energy barriers, encountered while moving an ion from the bulk solution to the pore, also differ slightly between Na+ and Cl- in both charged and uncharged pores (Figure S4; all barriers are in the range of ~1 and ~2 kcal/mol). These observations can rule out the contribution of dehydration to the


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observed charge-dependent ion selectivity in nanopores. As a result, the ion selectivity is mainly attributed to the enhanced flow of oppositely charged ions by means of the electrostatic adsorption-induced surface diffusion on charged membrane surfaces. CONCLUSION In summary, we carried out a series of MD simulations of ion transport through nanopores in charged graphene membranes. With the increase of a positive charge density, the graphene nanopore exhibits enhanced anion flow and suppressed cation flow, leading to electrically tunable anion/cation selectivity. Such selectivity becomes opposite in negative charge densities. No evident dehydration occurs during ion permeation through the charged pore; the ion transport modulation is attributed to the enhanced capture of charged ions, because most of the permeated ions are seen to diffuse into the pore after being adsorbed onto the graphene surface due to the electrostatic attraction. This work presents a new paradigm for modulating ion

selectivity in nanofluidic systems as well as in other membrane-based applications.

ASSOCIATED CONTENT



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Supporting Information Available: I-V curves of a 1.2 nm nanopore (Figure S1), selective ion transport driven by external pressures (Figure S2), radical distribution function profiles (Figure S3), potential of mean force profiles (Figure S4). (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]

Present Addresses

†Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China.

Notes

The authors declare no competing financial interests.

ACKNOWLEDGMENT

This work was supported by National Natural Science Foundation of China (11772152, 51535005, 51472117) and Jiangsu Province (BK20180065), the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (MCMS-0417G03, 24 ACS Paragon Plus Environment

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MCMS-I-0418K01), the Fundamental Research Funds for the Central Universities (NP2017101, NC2018001), and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. The authors acknowledge helpful discussion with Jianxin Zhou.

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