Tunable Anion-Selective Transport through Monolayer Graphene and Hexagonal Boron Nitride

Membranes that selectively filter for both anions and cations are central to technological applications from clean energy generation to desalination devices. 2D materials have immense potential as these ion-selective membranes due to their thinness, mechanical strength, and tunable surface chemistry; however, currently, only cation-selective membranes have been reported. Here we demonstrate the controllable cation and anion selectivity of both monolayer graphene and hexagonal boron nitride. In particular, we measure the ionic current through membranes grown by chemical vapor deposition containing well-known defects inherent to scalably produced and wet-transferred 2D materials. We observe a striking change from cation selectivity with monovalent ions to anion selectivity by controlling the concentration of multivalent ions and inducing charge inversion on the 2D membrane. Furthermore, we find good agreement between our experimental data and theoretical predictions from the Goldman–Hodgkin–Katz equation and use this model to extract selectivity ratios. These tunable selective membranes conduct up to 500 anions for each cation and thus show potential for osmotic power generation.

For a typical example of the data analysis, Figure S1 presents data for a graphene membrane with 10mM HfCl 4 in the cis reservoir and 100mM, 10mM and 1mM of HfCl 4 in the trans reservoir respectively. To assess the degree of selectivity in this case, we extract the current (circles) and voltage (diamonds) intercepts from IV curves in Figure S1b corresponds to a positive selective current (from the definition of conventional current), and thus indicates anion selectivity. The opposite behavior would be expected for cation selective membranes. The direction of these gradients can therefore establish toward which ions the membrane is selective with the magnitude of the gradient indicative of the magnitude of selectivity. A greater variety of concentrations are used within full analysis, omitted here for simplicity. For reference, here the GHK fit shows that the selectivity toward anions is ∼248 greater than toward cations. Figure S1: Establishing Anion Selectivity using HfCl 4 . (a) Experimental IV curves shown with a GHK fit, circles indicating current offsets and diamonds the reversal potentials. Cis concentration is fixed, trans salt concentration varying according to legend. (b) Extracted voltage and current offset data from (a) is shown against trans concentration. The gradient of the linear fit is a measure of selectivity. (c) GHK modelled fit to the reversal potential data allowing extraction of a selectivity ratio, another measure of selectivity. Dashed line shows the GHK output for a cation selective membrane.

S2: Further examples with Zirconium Tetrachloride (ZrCl 4 )
Extending our work beyond HfCl 4 , experiments with graphene are repeated using zirconium tetrachloride, ZrCl 4 . Figure S2 shows the current and voltage selectivity for this system.
For all cis concentrations, the membrane remains anion selective showing 63% selectivity (S=0.63) with 10mM in the cis reservoir and ∼73% for both 100mM and 1M in the cis reservoir. As expected, due to the high conductivity of 1M, the current selectivity is greater in magnitude for 1M than 100mM and 10mM. In all cases, the positive direction once again indicates anion selectivity. Within Figure S3, experimental data presented from Figure S2 is fit to the expanded GHK equation. It can be seen that the data is fit reasonably well to the GHK equation, providing selectivity ratios indicative of anion selection. These ratios range from ∼57 for S4 10mM to ∼1080 for 1M. These are broadly similar to those of HfCl 4 , which is expected given their similar valency. Figure S3: Selectivity ratio according to the GHK equation. GHK fit shown with the selectivity ratio as fitting parameter. Experimental error is shown. Legends indicate the salt in cis -(a) 10mM ZrCl 4 is shown to be ∼57 more selective to anions over cations. (b) 100mM ZrCl 4 is shown to be ∼1835 and (c) 1M ZrCl 4 ∼1080 more selective to anions over cations.

S3: Selectivity with hexagonal Boron Nitride (hBN)
In order to demonstrate that the ion selectivity we see is not limited to graphene we have shown transport across hexagonal Boron Nitride (hBN). In Figure S4 we repeat key experiments with hBN in systems with reservoirs containing solution of only KCl, only HfCl 4 and mixed environments. In Figure S4a we show selectivity with KCl, indicating cation selectivity. Figure S4b shows anion selectivity with HfCl 4 . Note here that data for voltage and current is shown together. Finally, we see the crossing over from cation to non-selective to anion selectivity in Figurec S4c with addition of increasing concentrations of a constant HfCl 4 background.

S4: Solution pH
As discussed, substrate conditions around a 2D material affect its surface charge. With a floating membrane, the salt solution acts as its substrate. The pH of a solution could thus have an effect on the effective surface charge on the membrane. It has been shown previously S1 that by altering the pH of 100mM KCl, graphene and hBN can be made nonselective when acidic, with cation selectivity restored from neutral through to a basic regime.
In this paper, we study the transport of ions and the effect of multivalent ionic charge on the surface therefore solutions are unbuffered with unaltered pH levels -these are shown in Table S1. In looking at the effect of pH we first repeat measurements using 100mM KCl with adjusted pH levels from 0 to 14. Selectivity measured for both graphene and hBN using these solutions are presented in Figure S5. It is shown here that with a monovalent salt, an acidic pH renders the membrane non-selective and above a neutral pH, cation selectivity is restored, consistent with previous observations. S1 To further probe the effect of pH, we attempt to detangle the effects of solution concentration, ionic charge and pH.
Adjusting the pH of the two multivalent solutions used in this paper, HfCl 4 and ZrCl 4 , resulted in precipitation. However, trivalent solutions lanthanum chloride (LaCl 3 ) and cerium chloride (CeCl 3 ) also exhibit tunable ionic selectivity and their pH can be more readily altered. Figure S6   At the other end of the pH scale, potassium phosphate (K 3 PO 4 ) has a basic pH ranging S8 from 11 to 13 for 10mM to 1M. In Figure S7 the selectivity is shown for K 3 PO 4 , KCl and KCl made basic to match K 3 PO 4 (B-KCl). We can see that both K 3 PO 4 and KCl exhibit cation selectivity for all cis concentrations tested. B-KCl shows the expected cation selective behavior. The pH changes here have, once again, not altered the direction of selective behaviour. In both the acidic and basic regimes, the altered magnitude of selectivity could be due to changes in conductivity as a result of altering pH levels. Figure S7: Selectivity is shown for a potassium phosphate (K 3 PO 4 ), potassium chloride (KCl) and KCl acidified to match K 3 PO 4 (B-KCl). Data point labels indicate the pH of the solution. Selectivity is shown as a percentage against respective cis reservoir concentrations.

S5: Selectivity with trivalent and divalent ions
The effect of charge inversion studied in this paper using tetravalent ions can also be achieved with use of trivalent ions. Figure S8 and S9 present data for selectivity experiments on graphene using cerium chloride (CeCl 3 ) and lanthanum chloride (LaCl 3 ). In both, the membrane is weakly anion selective at 100mM and higher cis concentrations. At 10mM we see a transitional point from anion to cation selective behaviour, consistent with theoretical observations. S2 In Figure S8, three distinct regimes are seen with 10mM in the cis reservoir, sometimes the membrane is cation or anion selective and sometimes non-selective. If the critical concentration is close to 10mM, this would provide an explanation for this behavior.
In Figure S9, LaCl 3 shows a similar behavior. In both cases, the membrane is cation selective at 1mM cis concentration. The implication here is that trivalent ions require a higher concentration of between 1mM -10mM to invert the charge on the membrane surface, compared to tetravalent ions which exhibit only anion selective behavior.
As with tetravalent salts, in Figure S10 selectivity is measured for a KCl gradient with a constant addition of LaCl 3 . In this system we find that cation selectivity with 100mM KCl remains despite an addition of 10mM LaCl 3 . Upon increasing this addition to 100mM, the system becomes less cation selective, ultimately inverting to anion selective behavior at 1M LaCl 3 addition.
Given the ability for multivalent ions to alter the system selectivity it remains to probe the behavior of a divalent ion. Figure S11 presents selectivity data for magnesium chloride (MgCl 2 ). Given the transition point from cation to anion was around 10mM-100mM for trivalent salts, the expected value would be higher than 100mM for a divalent species. For cis concentrations ranging from 10mM to 1M we see only cation selective behaviour. This observation is consistent with literature. S2,S3 Figure S8: Selectivity on graphene for cerium chloride (CeCl 3 ). Anion selective behaviour seen for cis concentrations above 10mM and cation behavior below 10mM. At a cis concentration of 10mM, the membrane exhibits some anion/cation/non-selective behavior. Figure S9: Selectivity on graphene for lanthanum chloride (LaCl 3 ). Anion selective behaviour seen for cis concentrations above 10mM and cation behavior below 10mM. At a cis concentration of 10mM, the membrane exhibits some anion/cation/non-selective behavior. Figure S10: Tunable ionic selectivity on graphene using a trivalent salt -lanthanum chloride (LaCl 3 . Voltage offsets for 100mM KCl with a background concentration of LaCl 3 showing a change in the selectivity from cation to anion with increasing concentration of LaCl 3 . Figure S11: Ionic selectivity on graphene with a divalent salt -magnesium chloride (MgCl 2 ). The gradient of the linear fit is shown and is a measure of selectivity. Positive gradients indicate cation selective behavior which is observed for all cis concentrations. S13

S6: Goldman-Hodgkin-Katz
For an ion species, x, the current flux through a pore according to Goldman-Hodgkin-Katz (GHK) is as follows, S4 where P x is the permeability of x, c trans , c cis ion concentrations and z x the ionic valency.
Taking the simple monovalent case of KCl: Giving: Which simplifies further to: Finally rearranging to give:

S14
The form of GHK presented in equation 2 means the experimentally measured reversal (or Nernst) potential and known concentrations can be used to determine ionic permeability.
Experimental data is fit to this equation using the R nonlinear package nlsLM. This uses a Levenberg-Marquardt algorithim with standard experimental error on the value of V rev used as weighting parameters. Standard error is extracted from the fitting and used as bounds on the fitting parameter, P .
A similar derivation is followed for divalent ions, giving the following relation: And for tri-valent ions, where, For tetravalent ions, the analytical derivation into a form useful for direct fitting is difficult. Using the following form, The graphene was transferred by using a PMMA scaffold to support the graphene whilst the Cu foil beneath is etched with ammonium persulphate. It was transferred onto 280 nm SiO 2 on Si. Graphene characterization is carried out using Raman spectroscopy maps over 150 x150 µm 2 area. The well understood response of graphene from Raman spectra S6 allows for extraction of a breadth of information. Figure S12 presents Raman maps for graphene transferred onto SiO 2 . Figure S12a.i is a Raman map of the 2D/G peak ratios, with values shown in the legend. A histogram of the 2D/G peak ratio is shown in Figure S12a.ii, with a nominal ratio of ∼2.7 indicative of mono-layer graphene. In FigureS12b.i a map of the S17 full width at half maximum (FWHM) of the 2D width is presented with the histogram in b.ii -the narrow width indicates a sharp 2D peak, characteristic of high quality mono-layer graphene. In characterising hBN growth quality, SEM and Raman spectroscopy techniques are used. Finally, the samples were dried and PC was dissolved in chloroform. Following this transfer, Figure S14 shows optical and SEM images of the material. Visibly, there are regions of multilayer growth alongside surrounding regions of monolayer hBN. The SEM image in Figure   S14b shows some wrinkles and steps in the hBN film from the iron catalyst used in growth.

S8: Processing of TEM images
In an effort to image beyond the diffraction limit and closer to the information limit, a technique referred to as 'exit wave reconstruction' can be used. Due to lens aberrations and aperture limitations, recorded images from a transmission electron microscope (TEM) will be a degraded version of the true image. These factors can be described by the contrast transfer function (CTF), S9 formulating of which requires microscope aberrations to be wellknown. With knowledge of the phase and amplitude of the electron wave, the wave function can be obtained iteratively. S10 In order to obtain the phase information, a through focal series is used. The CTF is focal plane sensitive and thus an image series taken through the focal plane will contain both amplitude and phase data. In the images presented in Figure 4, a focal series of 51 images, taken at 1nm steps is used. Using the QSTEM system, S11 the python library PyQSTEM is used to provide the transfer function generation using the microscope parameters in Table S2.
Following this, the inverse of the assumed CTF is used to decouple the aberration degradation and obtain the 'true' electron exit wave. With this, the final 'true' phase image is generated.

S9: Membrane Conductance
Quartz nanocapillaries are an integral part of our system and so careful characterisation is important. Capillaries are 'pulled' using calibrated recipes the resultant capillary sizes of which are confirmed using both conductance measurements and SEM images. Figure S15a shows a typical micrograph of a pulled capillary indicating a diameter of around 150nm (accounting for gold coating), which is around the expected value. From conductance measurements, statistics can be gathered on the distribution of nanocapillary sizes, Figure S15b.
Variability here could indicate larger/smaller than expected pore or one with a distorted shape amongst other possibilities such as blockages, therefore this check allows for discarding unsuitable capillaries. Figure S15: a. Micrograph of a quartz nanocapillary coated in gold. Diameter of the pore opening is around 150nm after accounting for the gold coating. b. Distribution of nanocapillary diameter based on conductance measurements. c. Micrograph of nanocapillary images on the side, contrast enhanced image shows inner wall with the taper angle denoted.
In addition to measuring the conductance of the nanocapillary with no adhered material (bare), conductance with material sealed onto the tip (sealed) is recorded as an indication of the quality of seal achieved. This sealed conductance contains information about the membrane as well as the bare capillary and therefore to use the conductance as characterisation S21 of the membrane it is necessary to subtract the effect of the capillary. Figure S16 shows this analysis process. With known parameters of the capillary such as taper angle and solution conductance, the bare conductance is used to calculate the capillary diameter and extract the cone resistance. S12,S13 This cone resistance is subtracted from the sealed conductance leaving the membrane resistance. Using an empirical formula from Garaj et al., S14 we are able to use this membrane resistance to estimate the combined equivalent pore size that would account for this resistance. Figure S16: Flow chart showing the steps taken in collecting current-voltage/conductance data from quartz nanocapillaries with no adhered material (bare) and with material (sealed). Input and output are indicated with a red arrow and the formulas used for any calculations are shown.
S22 Table S3 provides a selection of capillary details for a variety of solutions. The worked example shows a range of pore sizes and capillary diameters across a wide cross section of solution conductances and capillary resistances. The taper angle is calculated from a variety of SEM images as demonstrated in Figure S15c and is thus a known value for a batch of capillaries following the same pulling protocol.

S10: Effective Screening Lengths in our System
Debye screening lengths are readily calculated from the Debye-Hückel approximation for a symmetric monovalent electrolyte, where " r and " 0 are dielectric constant and permittivity of free space respectively, C 0 is the concentration of electrolyte (M), T is temperature (K) and R and F are gas and Faraday constants respectively. However, at increasing concentrations and for asymmetric ions, the linear approximation is not valid and analytical solutions to the relationship are needed. Using empirical and modelled curves from McBridge et al., S15 we can estimate Debye screening lengths for concentrations and ionic valences relevant to our system.  Table S4 presents the Debye lengths for electrolytes ranging from asymmetric tetravalent (4:1) to monovalent (1:1). Of primary importance for our system and findings is the case for tetravalent electrolytes, such as HfCl 4 and ZrCl 4 . In these cases, for cis concentrations where we see selectivity, the Debye screening length is at most ∼3nm. Moreover, in Figure S17, a comparison of selectivity across a range of ions are presented. The hydrated radii for the ions participating in selective transport is estimated S16 and shown against their selectivity.
There is no clear trend with selectivity and ionic radii, further implying that steric effects are not chiefly responsible for selectivity but instead electrostatics is playing a large role. Figure S17: Selectivity is shown against estimated hydrated ionic radii for the respective ion participating in selective transport. Anion/cation transport is denoted by symbol color. No clear trend is seen between ionic radii and selectivity.

S25
Finally, in Figure S18 the mangitude of selectivity is shown as the estimate combined pore size -a measure of the membrane conductance. Here we see that though there exists variability, a clear trend relating the selectivity achieved with the membrane conductance is absent. This holds for a monovalent, divalent, trivalent and tetravalent salts across cis concentrations ranging from 10mM to 1M. Figure S18: Magnitude of selectivity is shown against estimated combined pore size which is a measure of membrane conductance. No clear trend is seen between membrane conductance and selectivity.

S11: Raman Shifts
Graphene and indeed most materials, possess a surface charge in solution. This has been previously estimated that as -0.6 C/m 2 for graphene S17 and -0.16 C/m 2 for hBN. S18 Moreover, given the nature of Raman spectroscopy, the peak positions of the Raman signature of graphene will be affected by such parameters as surface charge. S19 In Figure S19 we show the peak positions from in situ Raman for graphene on various salt solutions. The data here is from several accumulations and repeats with a Lorentzian curve fit used to extract peak positions. In all cases of graphene on KCl we see an increase in peak position relative to the position measured with MilliQ water (MQ). Conversely, in all cases of HfCl 4 we see a decrease in peak position. The inset provides full example spectra of three different cases. Figure S19: In situ Raman spectra of graphene on salt solution as labelled in the legend. Several accumulations are averaged and a Lorentzian curve is fit to extract peak positions.
Our in situ Raman spectra method means we do not have a sufficiently high SNR to delve into the specific details of the spectral properties. Therefore, we cannot, with confidence, use this data to extract specific surface charging values. More important here is to see that there is clearly an affect on the surface charge due to the extrinsic salt solution environment.

S12: GHK Fits
For data presented in Figure 5 within the Main text, Figure S20 presents the respective GHK fits, showing good agreement.