Tuning Pore Size in Graphene in the Angstrom Regime for Highly Selective Ion–Ion Separation

Zero-dimensional pores spanning only a few angstroms in size in two-dimensional materials such as graphene are some of the most promising systems for designing ion–ion selective membranes. However, the key challenge in the field is that so far a crack-free macroscopic graphene membrane for ion–ion separation has not been realized. Further, methods to tune the pores in the Å-regime to achieve a large ion–ion selectivity from the graphene pore have not been realized. Herein, we report an Å-scale pore size tuning tool for single layer graphene, which incorporates a high density of ion–ion selective pores between 3.5 and 8.5 Å while minimizing the nonselective pores above 10 Å. These pores impose a strong confinement for ions, which results in extremely high selectivity from centimeter-scale porous graphene between monovalent and bivalent ions and near complete blockage of ions with the hydration diameter, DH, greater than 9.0 Å. The ion diffusion study reveals the presence of an energy barrier corresponding to partial dehydration of ions with the barrier increasing with DH. We observe a reversal of K+/Li+ selectivity at elevated temperature and attribute this to the relative size of the dehydrated ions. These results underscore the promise of porous two-dimensional materials for solute–solute separation when Å-scale pores can be incorporated in a precise manner.


Supplementary Note S2
In the H-cell, the ion transport is via diffusion driven by concentration difference of ions across porous graphene in the two well-mixed reservoirs.In the process, the osmotic pressure unavoidably drives water to diffuse from the dilute salt solution to the concentrated salt solution, in a opposite direction to the ion transport 2 .We note that the recorded water permeance of porous graphene resting on the support film was very low (0.0016 L m −2 h −1 bar −1 ) due to the resistance from the Nafion layer in the support film.The ultralow water permeance does not affect our measurements since each single ion test takes about 6 h and the water transport can be ignored.Nafion layer served a dual role, (i) to improve the mechanical robustness of the graphene film, and (ii) to reduce the water crossover from the permeate side to feed side by forward osmosis, given that the feed side had ion solution with concentration of 1 M.The second aspect relates to slow diffusivity of free water through the Nafion layer.
We also note that Nafion support film does not dominate the ion transport through membrane because the ion flux through porous graphene is significantly lower than that from the support film.
We also note that the as-prepared porous graphene has a high pore density of 2.2 × 10 12 cm −2 , with a small distance between each pore in the range of 1-16 nm which should eliminate the perforated screen effect 3 .
We are aware of the presence of thick unstirred layer in the vicinity of porous graphene which could control mass transfer to a certain extent.The presence of an unstirred layer decreases the ion flux as well as ion selectivity.Therefore, porous membrane would demonstrate even higher performance in terms of ion flux and selectivity if the system is optimized to decrease the unstirred layer, e.g., through cross flow condition.

Supplementary Note S3
To understand the presence of charge on graphene pores, we carried out X-ray photoelectron spectroscopy (XPS) to probe O-functional group on the surface.As a control, G ID showed negligible O concentration, consistent with the fact that graphene lattice is composed of sp 2 carbon (Figure S12a).The C1s XPS spectrum from PG 3-4Å shows an obvious shoulder at 286.1 eV corresponding to the presence of O-functional groups.However, the O-functional groups are absent in the graphene sample after subsequent CO 2 -led pore expansion.This is mainly because the O-functional group from O 3 -treatment are generated in the form of Oclusters surrounding the pore 4 which are then gasified during CO 2 expansion.Among the trace functional group, we could identify semiquinone groups (0.39%) which is expected at the pore edge, and ether groups (2.29%), however, their concentrations were similar to that in G ID , indicating their contribution is likely from unavoidable atmospheric contamination (Table S1).

Supplementary Note S4 Simulation Models and Methodology
To compare the hydration shells of ions in the bulk solution and in a confined nanopore, two kinds of models were built.The first model is a cubic simulation box with a size of 30 Å × 30 Å × 30 Å, which contains 900 water molecules and one cation ion (Mg 2+ or K + ), as shown in  The pores were constructed by removing some carbon atoms (12, 24, 36, 42, 54, and 60 carbon missing) from the graphene sheet.After subtracting the carbon atoms, the pore diameter is estimated by fitting the inscribed circle along the center of the edge carbon atom.
Considering the carbon-water interaction, the diameter of the accessible pore is determined by subtracting the distance of the graphitic carbon-water nonbonded interaction length ( 6 2 ).Thus, the pore diameters of pores range from 3.7 Å to 12.0 Å.During the  C -O w = 3.857Å simulations, the graphene sheet was set to be rigid and fixed at its initial position (Z = 0).The cation was restricted at the pore along Z axis it was allowed to move in the other two directions.Interactions in the simulation models were described by the standard 12-6 Lennard-Jones potential together with a Coulombic term.The potential energy was calculated in the form of , (S1) where r is the distance between two atoms, and are the force field parameters characterize   interactions between different atoms, C is the energy constant, is the dielectric constant and  q refers to the atom charge.The simple point charge extended (SPC/E) model 5 was used to describe water molecules.The force field parameters for interactions between atoms of the same type are listed in Table S2. 6Parameters for the graphene-water interactions were taken from previous literature 1 .The Lorentz-Berthelot combination rules were used to obtain parameters for interactions between different species.The short-range interactions were truncated at a cutoff distance of 12 Å, and the long-range Coulomb interactions were computed by utilizing the particle−particle particle−mesh (PPPM) algorithm 7 .Periodic boundary conditions are applied to all three directions.After the initial energy minimization, each system was first equilibrated in the canonical ensemble for 0.1 ns with the timestep of 1 fs.The temperature of the system was maintained at 300 K using a Nose-Hoover thermostat.Then the simulations are performed for another 5 ns to collect the data for further analysis.All the MD simulations were carried out using LAMMPS 8 .The coordination number of ions as a function of pore size is shown in Figure S16.The coordination number gives the number of water molecule in the ion's hydration shell.In Figure S16, the solid lines refer to the bulk values of the coordination number of ions' first hydration shell, and the dashed lines correspond to ions' second hydration shell.We found that no dehydration events occur in the first hydration shell of Mg 2+ when it goes through nanopores whose diameter is larger than 6.1 Å. Evident dehydration happens in the second hydration shell of both ions and first hydration shell of Na + .We estimated the energy penalty associated with water loss, , as following: Δ first and second shell, respectively (Figure 3h).The resulting values of for K + and Mg 2+ Δ are compared in Figure 3j indicating increase in free energy of 0.6 and 1.0 eV, respectively.

Supplementary Note S5
Pore shrinkage in the presence of CH 4 We verified the growth mechanism through the combination of carbon isotope labelling and Raman spectroscopy mapping.For this, first, G ID resting on Cu foil was exposed to CO 2 at 800 ºC to expand intrinsic vacancy defects in micron-sized pores.The motivation behind generation of micron-sized pores is that these large pores can be easily visualized (Figure S17).These pores then become the starting point to study their shrinkage.Figure S17.A CO 2 -expanded micron size pore in graphene.
We then carried out an experiment where micron-sized graphene pore was exposed to 13 C CH 4 at 800 ºC.This was motivated by the fact that Raman spectroscopy can distinguish graphene composed of 12 C versus 13 C, attributing to the red shift of the phonon energy (wavenumber in Raman spectroscopy) 9 due to increased mass of 13 C. Figure S18 illustrates this where a difference of 110 cm -1 in the 2D peak position was observed (2D peak at 2725 cm -1 for 12 C and 2615 cm -1 for 13 C).Similarly, G peak position also goes through a shift.
Therefore, shift in 2D or G peak positions can be used to track the precursor contributing to graphene growth.In the next experiment, G ID was synthesized by 12 C CH 4 , micron-sized pores were created by CO 2 , following which 13 C CH 4 exposed to shrink the pore.The Raman mapping of resulting pore is shown in Figure S19.Mapping and of 2D 12 and 2D 13 peak intensity clearly revealed shrinkage of the pore.The graphene area around the pore yielded 2D peak position from 12 C, representing as-synthesized graphene, while the newly grown graphene domains inside the pore were derived from 13 C.We observed growth in the core of the pore as well as pore shrinkage from the pore edge.Figure S19d shows the acquired spectra from various points (marked by the numbers 1 -6 on Figure S19c) in and around the pore.Y-axis scale for left (containing D and G peaks) and right (containing 2D peak) halves of the figure are different for better readability.Each side of the figure is normalized by the highest observed intensity (belonging to spectrum 6).Spectrum 1 represents the newly added graphene domain by 13 C CH 4 and matched the Raman spectrum of the 13 C-grown graphene in Figure S19.On the contrary, spectrum 6 that was acquired from outside the pore displayed the 12 C-grown SLG characteristics.This study concludes that the carbon precursor solely arrived from 13 C source from the pore healing experiment.This also rules out carbon contamination in the CVD reactor leading to the growth.Next, for pore shrinkage, we also added CO 2 in the presence of 13 C CH 4 .Our hypothesis is that it onsets a competition between CH 4 -aided crystallization of graphene domains starting from the pore edge and CO 2 -aided pore edge expansion, based on a recent kinetic Monte Carlo simulation 10 .For example, while in the absence of CO 2 , we observed growth of new graphene domains in the core of the pore (Figure S19), such domains were not observed in the presence of CO 2 (Figure S29).We only observed pore shrinkage from the edge of graphene.
We attribute this to the etching of any nuclei-forming carbon precursors by CO 2 .
Figure S20.Raman map of 2D peak intensity from porous graphene subjected to pore shrinkage conditions involving exposure to a mixture of 13 C CH 4 and CO 2 .a) 2D peak mapping corresponding to 13 C. b) Corresponding Raman spectra of the points marked by numbers 1 -6.
Another evidence on the competitive roles of CO 2 and CH 4 comes from measuring the shrinkage rate of pores in the presence of varying ratio between CH 4 and CO 2 .Figure S21 clearly shows that the pore shrinkage slows down after introducing CO 2 .Further, at the ratio of 0.5, we did not observe any pore shrinkage.Table S3.Comparison of the ion-ion selectivity data from graphene pores in this study with those from two-dimensional materials in the literature.

Figure S2 .
Figure S2.Formation of undesired large pores by a) pores expansion using O 3 , and b) O 2 plasma (6 s).

Figure
Figure S5.a) AFM image of the reinforced graphene revealing the thickness of the support film.b) Cross-sectional SEM image of the support film.c) Suspended graphene on 1-cmsized annular disk loaded with 7 g weight.The inset shows the top view.d) Top-view SEM image of graphene reinforced with the support film.AFM image of the sample with graphene side in (e) and Nafion side in (f).

Figure S6 .
Figure S6.Picture of the diffusion cell used in this study.

Figure S8 .
Figure S8.Calibration curve for proton using the pH meter.

Figure S9 .
Figure S9.Pore size distribution for the sample PG >10Å .

Figure S10 .
Figure S10.Pore size distribution of PG 3-4Å in terms of number of missing carbon atoms.

Figure S14a .
Figure S14a.In the second model, a monolayer graphene was inserted into the simulation box, which is parallel to the XY plane, as shown in Figure S14b.The size of the second simulation box was adjusted slightly to accommodate the lattice structure of the graphene.

Figure S14 .
Figure S14.MD simulation models.a) Ion and its bulk solution.b) Ion restricted in graphene pore.

Figure S15 .
Figure S15.Radial distribution function g (r) for (a) Mg 2+ and (b) K + in the bulk and around a 6.1 Å pore.

Figure S16 .
Figure S16.Coordination number of water molecules in the first and second hydration shells of Mg 2+ or K + as a function of pore diameter.The solid lines refer to the bulk values of the coordination number of ions' first hydration shell, and the dashed lines correspond to ions' second hydration shell.

Figure S19 .
Figure S19.Raman map of 2D peak intensity from porous graphene subjected to pore shrinkage conditions involving exposed to 13 C CH 4 .2D peak mapping corresponding to 12 C (a) and 13 C (b). Enlarged map of (b) is shown in (c) and the corresponding Raman spectra of the points marked by numbers 1 -6 are shown in (d).

Figure S21 .
Figure S21.The observed pore shrinkage rate at various ratio of CH 4 and CO 2 .

Figure S22 .
Figure S22.ICP curves of Zn 2+ , Al 3+ , and Fe 3+ over time.The measurements were carried out because the hydrolysis effect of these ions is strong releasing a proton.Therefore, ion conductivity doesn't directly reflect ion concentration.

Table S1 .
Summary of the fitting result of XPS spectrum in FigureS14 Figure S13.Comparison of the ion selectivity in single ion and mixed ion test.Here M + refers to either K + , Na + or Li + .