size selective ion sieving with ultrahigh water permeance through laminar graphene membranes

Journal Pre-proof Tunable charge/size selective ion sieving with ultrahigh water permeance through laminar graphene membranes Wisit Hirunpinyopas, Pawin Iamprasertkun, Mark A. Bissett, Robert A.W. Dryfe PII:

S0008-6223(19)30935-2

DOI:

https://doi.org/10.1016/j.carbon.2019.09.030

Reference:

CARBON 14600

To appear in:

Carbon

Received Date: 30 July 2019 Revised Date:

4 September 2019

Accepted Date: 9 September 2019

Please cite this article as: W. Hirunpinyopas, P. Iamprasertkun, M.A. Bissett, R.A.W. Dryfe, Tunable charge/size selective ion sieving with ultrahigh water permeance through laminar graphene membranes, Carbon (2019), doi: https://doi.org/10.1016/j.carbon.2019.09.030. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Graphical Abstract

Tunable Charge/Size Selective Ion Sieving with Ultrahigh Water Permeance through Laminar Graphene Membranes Wisit Hirunpinyopas a, b, Pawin Iamprasertkun a, b, Mark A. Bissett a, c, *, Robert A. W. Dryfe a, b, * a

National Graphene Institute, University of Manchester, Oxford Road, Manchester,

M13 9PL, United Kingdom b

School of Chemistry, University of Manchester, Oxford Road, Manchester, M13 9PL,

United Kingdom c

School of Materials, University of Manchester, Oxford Road, Manchester, M13 9PL,

United Kingdom

*Corresponding authors E-mail address: [email protected] or [email protected]

Keywords: graphene, membrane, ion transport, electrochemistry, filtration

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Abstract Graphene oxide (GO) and reduced graphene oxide (rGO) membranes have attracted significant attention as a potential technology for energy storage, gas separation, and water purification technologies. However, these membranes have a significant drawback as they became swollen, hence unstable, after exposure to aqueous solutions. Here, we describe membranes produced from graphene prepared by liquid phase exfoliation, possessing a low oxygen content, unlike the GO/rGO systems, and demonstrate their applicability in ion sieving in aqueous solutions. These low oxygen graphene membranes formed from flakes of varying size are used to determine the effect of flake morphology on ion transport. Interestingly decreasing flake length and thickness leads to an increase in the number and tortuosity of nanochannels between the layers, resulting in a significant reduction of ion transport. The smaller flakes show an increased surface charge, due to the level of defects, which impedes chloride mobility allowing for both physical sieving and charge repulsion. Moreover, the graphene membranes reported here exhibit excellent Na+ rejection properties (~97%) with water permeance ~10 times higher than those reported for GO membranes, while demonstrating high stability in aqueous solutions with no observed swelling. These materials are therefore extremely promising for future applications in water purification.

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1. Introduction The extraordinary electrical, mechanical and thermal properties of graphene are welldocumented.[1, 2] This two-dimensional material has potential uses in a wide range of technologies such as energy storage,[3] composites/coatings,[4] biomedical,[5] and membrane[6, 7] applications. Among those applications, graphene-based membranes have provoked considerable interest for use as filtration technologies, especially for water treatment, which is relevant to the increasing proportion of the world suffering from fresh water scarcity. Graphene oxide (GO)-based membranes, consisting of stacks of laminar GO sheets, have been widely researched for the treatment of water via methods including desalination, ion-exchange, and electro-dialysis. GO-based membranes were shown to generate fresh water from seawater through the nanochannels formed between the individual layers of re-stacked material.[6, 8] However, GO-based membranes are unstable when exposed to aqueous solution as the expansion of interlayer spacing (an increase from 0.8 nm to 6-7 nm)[9] results in poor ionic rejection. A number of strategies have been demonstrated to counter this swelling, including the use of chemical cross-linking (diamine monomers/cationic metals),[10, 11] physical confinement (polymer encapsulant),[8] and partial chemical reduction (HI vapour) to minimize oxygen-containing functional groups.[12] Each of these methods has its limitations for practical widespread implementation in water purification technologies. Pristine graphene-based membranes have received little attention for use in water treatment because of the very narrow interlayer spacing (~0.34 nm), which tend to form impermeable layers as previously reported for reduced graphene oxide (rGO) membranes.[12, 13] However, small ionic solutes and water molecules are more likely to transport through

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the spacing between the restacked, exfoliated material if there is a high degree of disordered restacking within the membrane. This has been reported in our previous work using MoS2based membranes for desalination and nanofiltration, demonstrated by cross-sectional scanning transmission electron microscope (STEM) images showing individual laminar stacking of MoS2 nanosheets.[14] Moreover, in terms of surface morphology, the pristine graphene nanochannel has been predicted to give higher water permeation than GO and MoS2 nanochannels, an effect attributed to lower hydraulic friction from the absence of oxygenated functional groups, and alignment of water molecules in rhombus-shaped networks as calculated by MD simulations[15] and observed experimentally.[16] Furthermore, one of the essential factors that has not been comprehensively and quantitatively demonstrated is the performance of flake-containing membranes as a function of the flake aspect ratio (i.e. length and thickness). Size-dependence plays a crucial role in many applications (e.g. phonon dynamics and gas evolution).[17, 18] For example, Gholamvand et al.[17] studied the effect of WS2 nanosheet length and thickness for electrochemical applications (e.g., hydrogen evolution and double layer capacitance), indicating that the current density and capacitance are inversely proportional to the mean flake length and thickness, respectively. However for ion transport studies, the effect of flake dimensions is still unclear. Large or thick flakes are expected to provide a smoother pathway with perfect laminar stacking while small or thin flakes would produce more tortuous capillary channels with randomly stacked materials. In this work, we describe the preparation of graphene-based membranes, with a low concentration of oxygen-containing functional groups, and study the dependence of ion transport on flake dimensions. We utilize size-selected centrifugation to generate the different flake dimensions denoted as ‘large’, ‘medium’, and ‘small’ graphene flakes. Membranes of comparable thickness (~3 µm thick) were prepared to investigate the potential-dependent ion 4

transport and water permeance through their laminar structure. We find that ion mobility reduced with decreasing lateral flake length and thickness. This is attributed to the increasing surface area of the small flake sizes, as well as a greater number of exposed edges, leading to a large number of complex nanochannels which form highly tortuous pathways inside the membranes. Furthermore, these membranes were subsequently tested at high osmotic pressure to determine the salt rejection and water permeation rate.

2. Experimental 2.1. Materials Agarose powder (bio-reagent grade) and graphite flakes (99% carbon, ~150 µm > 80%) were purchased from Sigma-Aldrich. N-Methyl-2-pyrrolidone (NMP, 99% purity) was purchased from Alfa Aesar. Omnipore membrane filters (polyvinylidene fluoride, PVDF, hydrophilic, 0.1 µm pore size, and 13 mm diameter) were purchased from Merck Millipore Limited. All aqueous solutions were prepared from ultrapure deionized water (Milli Q water purification system, 18.2 MΩ cm resistivity at room temperature). 2.2. Producing Graphene Dispersion and Graphene-Based Membranes The graphene dispersion was prepared using ultrasound-assisted liquid-phase exfoliation (LPE).[19, 20] Briefly, graphite powder (1 g) in 100 mL of N-Methyl-2pyrrolidone (NMP) was sonicated via bath sonication with a frequency of 37 KHz and power of 328 W for 12 h at 15 °C as shown in Figure 1a. The black dispersion thereby obtained was centrifuged twice at 1500 rpm (196 g) for 30 min to remove any non-exfoliated materials. The supernatant, containing a variety of graphene flake dimensions, was separated from sediment by removing the top 80% of the graphene dispersion. As the average lateral flake

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size and thickness decreased with increasing centrifugation rates, it is possible to control the centrifugation speeds to form size-selected dispersions, providing a range of lateral flake lengths and thicknesses.[21] The dispersion after removing non-exfoliated materials was centrifuged again at 5500 rpm (2637 g) twice for 30 min. The supernatant was gently removed and the sediment was re-dispersed in 10 mL isopropanol followed by mild sonication. This dispersion from sediment was denoted as large/thick flakes (1500 rpm ˂ lGP ˂ 5500 rpm). The latter supernatant was then centrifuged at 13000 rpm (14737 g) twice which provided the medium (5500 rpm ˂ mGP ˂ 13000 rpm) and small/thin (sGP ˃ 13000 rpm) flakes from sediment and supernatant, respectively, as shown in Figure 1b. Graphene-based membranes were fabricated using a programmable syringe pump with an applied volumetric flow rate of 10 mL h−1. The graphene dispersion was diluted in isopropanol by a factor of 1:20 followed by filtering through a pre-weighed PVDF membrane. The membranes were then dried at 60 °C in an oven overnight and re-weighed to get the actual mass loading. Figure 1c shows a photograph of a graphene membrane with a PVDF support, demonstrating high flexibility without damage (determined by optical microscopy). Membranes were prepared in three different mass loadings to control their thickness. They were then cross-sectioned and measured by scanning electron microscopy (SEM). The thickness calibrations are shown in Figure S1. Graphene membranes were prepared using the different sets of dispersions (denoted as lGP, mGP, and sGP) with comparable thickness (~3 µm thick) for all measurements. In addition, the mass loading and density were calculated as shown in Table S1. The graphene density clearly decreases with decreasing dimensions (lateral flake length and thickness). This is because of both the low number of layers (mostly mono- and bilayers) and high defect level on basal planes with a large amount of exposed edge for small/thin graphene (sGP) flakes, which results in a high

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proportion of randomly stacked graphene laminates relating to the inability to form a perfect Bernal restacking.[22]

Figure 1. Exfoliation and size separation process: a) Schematic showing the synthesis of graphene dispersion via a bath sonication process. b) Schematic showing the separation process of the graphene dispersions. c) Photographs of graphene-based membranes with PVDF support showing high flexibility without visible damage.

2.3. Characterizations of Graphene Dispersion and Graphene-Based Membranes 2.3.1. Graphene Dispersion Zeta (ζ) potential measurements were obtained using a Malvern Nanosizer Z (NIBS) with Zetasizer software. The Smoluchowski equation was used to determine the ζpotential.[23] A Malvern Zetasizer Nano ZS, using a 633 nm HeNe laser was used to measure graphene flake size. Samples were measured in quartz cuvettes (10 mm path length), with operation in backscatter mode at an angle of 173°. 7

2.3.2. Graphene-Based Membranes Atomic force microscopy (AFM) was carried out with NanoWizard® 4 NanoScience AFM (JPK instruments) with quantitative imaging (QI™) mode in air under ambient conditions using the Au-coated side of the cantilever (PPP-NCHAuD). AFM images were obtained directly on the graphene membranes with PVDF support. The membranes were attached on a glass slide during the scanning. The image sizes ranged around 25 µm2, 9 µm2, and 1 µm2 for the lGP, mGP, and sGP membranes, respectively, with the peak force setpoint of 30-70 nN. The images were scanned at speeds of 130, 75, and 31 µm/s for the lGP, mGP, and sGP membranes, respectively, with 512 lines per image. The lateral flake lengths of each graphene membrane were counted from ca. 300 flakes using ImageJ software. Scanning electron microscopy (SEM) images were obtained using a FEI Quanta 650 FEG ESEM. All SEM images were obtained with an accelerating voltage of 15 kV, under high vacuum conditions utilizing secondary electron detection. Powder X-ray Diffraction (PXRD) patterns of the starting materials (graphite flakes) and the graphene membranes were obtained using a PANalytical X’pert X-ray diffractometer. The patterns were recorded while spinning in the range 2θ = 5-70°, with a step size of 0.017° with a scan step time of 66 s, which used a CuKα radiation source (0.154 nm wavelength) operating at 40 kV and 30 mA. The (002) peak positions of graphene were corrected using the PVDF peak at 2θ of 20.17° as a reference peak.[14] Raman spectra were measured using a Renishaw inVia microscope with a 532 nm (2.33 eV) excitation laser, incident perpendicular to the graphene membranes. The laser power was 1 mW with a 50× objective lens, and a grating of 1800 l/mm. Spectra were obtained between 1250-2800 cm−1 and averaged over 3 accumulations.

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2.4. Measurement of Ion Transport The as-prepared graphene membranes were assembled between two polyethylene terephthalate (PET) sheets as support with an exposed area of 0.264 cm2. This was inserted in a custom-made H-beaker cell consisting of two liquid reservoirs (50 mL) contacted with Pt electrodes and Ag/AgCl reference electrodes (REs) using a four-electrode configuration (see Supporting Information).[24] The Ag/AgCl REs were connected to the main solution via 3 M KCl agarose salt bridges inside Luggin capillaries to eliminate the liquid-junction potentials arising from salt concentration gradient. The solutions between the two reservoirs were stirred to minimize the concentration polarization. The transmembrane potential was cycled using a triangular potential waveform from −200 mV to 200 mV at a rate of 1 mV s–1, with a reversed cycle to verify that there was no hysteresis in the I-V response.

3. Results and Discussion 3.1. Determination of Size-selected Graphene Flakes Figure 2a shows photographs of graphene dispersions as size-selected dispersions. They were diluted by isopropanol to the same concentration (C = ~10 µg mL−1) to highlight the differing opacity. Noticeably, on dilution in isopropanol, the solutions centrifuged at higher centrifugation speeds appear darker due to contributions from both absorption and scattering, as shown in Figure 2b. To obtain accurate extinction coefficient values (α), the scattering exponents (n) were extracted using a power law scattering background (α λ–n) at the wavelength region of 700-800 nm.[25, 26] This indicates that the scattering exponent (n) increased with decreasing graphene flake size as shown in Figure 2b, which agrees well with previous literature.[25] This allows us to measure the actual extinction coefficient from the

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Beer-Lambert law (A/l = αC) using absorbance per cell length (A/l) at 660 nm, divided by concentration. The actual coefficient values of large (αL ), medium (αM ), and small (αS ) flake sizes are 3995, 4231, and 5278 mL mg–1 m–1, respectively. Interestingly, the extinction coefficient increased with decreasing graphene lateral flake size, mirroring the trend of higher optical absorbance for thinner flakes reported by Backes et. al.[27] Dynamic light scattering (DLS), a fast and simple analytical method, was used to measure the mean graphene flake sizes produced from centrifugation-based size selection as shown in Figure 2c. The dispersions were diluted with isopropanol to a concentration of ~5 µg mL–1 to minimize flake aggregation. The size distribution was reported as Z-average diameter (an averaged particle size), for which the mean of Z-averaged values were 1043 ± 90 nm, 355 ± 11 nm, and 99 ± 3 nm for large, medium, and small flake lengths, respectively. This method, used to estimate the two-dimensional (2D) lateral flake sizes, was reported by Lotya et al.,[28] and shown to yield a reliable empirical relationship between size distribution from DLS and the lateral flake size as measured by transmission electron microscopy (TEM). DLS, generally suited for spherical objects, is still however not highly accurate for measuring flake length directly of dispersed 2D-materials. We also determined graphene lateral sizes using statistical analysis of atomic force microscopy (AFM) data for comparison. Figure 2d-f plots the distribution of measured graphene flakes for membranes prepared by the three different sets of centrifugation speeds. We measured ca. 300 flakes on individual graphene membranes. This allows us to compare size distribution from DLS data and measured flake sizes from the AFM images. The mean lateral flake sizes determined by AFM analysis correspond to 913 ± 16 nm, 305 ± 6 nm, and 115 ± 3 nm for large, medium, and small flake lengths, respectively. The correlation between DLS data and statistical AFM is presented in Figure S2, illustrating good agreement with an empirical relationship. The relative errors of

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the mean flake sizes measured from both techniques are less than 15%, which is a welldefined correlation.

Figure 2. Size-selected graphene flakes. a) Photographs of the graphene dispersions consisting of solutions denoted as large (1500 rpm ˂ lGP ˂ 500 rpm), medium (5500 rpm ˂ mGP ˂ 13000 rpm), and small (sGP > 13000 rpm) flake sizes for a given concentration (~10 11

µg mL–1). The solutions were diluted by isopropanol to emphasize the difference in opacity. b) UV-visible absorption spectra for a set of graphene dispersions showing different extinction coefficients with decreasing graphene flake size. Note that all spectra are superimposed on a scattering background.[25, 26] c) Hydrodynamic size plot obtained by dynamic light scattering (DLS) of the graphene different sizes. The dispersions were prepared at a constant concentration of 5 µg mL–1. These data correspond to the mean averaged particle size of lGP (1043 ± 90 nm), mGP (355 ± 11 nm), and sGP (99 ± 3 nm). Histograms of graphene flake lengths, as measured by statistical AFM, for the graphene membranes prepared by three different ranges of centrifuge speeds denoted as d) large, e) medium, and f) small lateral lengths, respectively. The lateral flake lengths were counted from ca. 300 flakes for each individual membrane. The mean lateral flake size for large, medium, and small are 913 ± 16 nm, 305 ± 6 nm, and 115 ± 3 nm, respectively. The histograms were fitted using the Lorentzian function as shown in the black lines. The insets show AFM images of the graphene membranes using quantitative imaging (QI™) mode during scanning (see Supporting Information).

3.2. Morphologies and Defects of Size-Selected Graphene Flakes To further investigate the graphene membranes, SEM was performed to examine the graphene morphologies. Figure 3a-c show plan view and cross-sectional SEM images for graphene membranes prepared from the set of size-selected dispersions. These membranes consist of disordered arrays of flakes forming stacked laminar graphene sheets. These are similar to the AFM images shown in Figure 2d-f (inset). In addition, cross-sectional SEM images (Figure 3a-c: bottom) show the laminar structure of the individual graphene sheets, also illustrating the closely packed and mostly horizontal orientation of the restacked flakes.

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The PXRD patterns comparing the (002) peak of the graphene membranes (~3 µm thick) are shown in Figure 3d. It is clearly seen that the (002) peak of graphene with decreasing flake sizes is notably broader compared to the larger flakes and graphite flakes. This is because of the decreasing number of layers (mostly single layer) and the lateral flake size, which result in the increasing FWHM of the (002) peak. In addition, membranes prepared with sizeselected graphene were also measured in a wet condition to test their stability (e.g. swelling) after immersion for 48 h in ultra-pure deionized water. The (002) peaks of the graphene membranes in wet conditions are identical to the dry condition peak, indicating a consistent d-spacing of the hydrated graphene membranes of ~0.34 nm.[9] The full range of PXRD patterns show the expected PVDF peaks and only the (002) peak of graphene as shown in Figure S3, indicating no diffraction pattern of (001) characteristic of graphene oxide (GO) at 2θ ≈ 10°. This is due to the small amount of oxygenated functional groups (< 2%) on the carbon plane, as determined by X-ray photoelectron spectroscopy (XPS) analysis (see Figure S4). This observation suggests the graphene membranes with low residual oxygen content can be used in a wide range of aqueous applications, especially water purification, unlike the case of GO/rGO membranes which tend to swell in water.[6, 9] To estimate the defect formation after exfoliation and centrifugation-based size selection, Raman analysis was performed directly on as-prepared graphene membranes. Figure 3e shows the Raman spectra of the graphene membranes produced from three sets of flake dimensions, compared to the starting material. Three bands are observed, namely the Dband (~1350 cm−1), G-band (~1580 cm−1), and 2D-band (~2700 cm−1). The D-band is generally used to indicate the presence of defects on the basal plane and edges.[29] It is clearly seen that by decreasing flake size the D-band intensity dramatically increased, as would be expected due to the increasing density of edges. We also quantified the graphene defects using the D to G band intensity ratio (ID/IG) as shown in Figure 3f. The ID/IG ratio 13

significantly increased with decreasing graphene flake size, especially for the sGP membrane (ID/IG = ~1.3). This confirmed that the smaller flakes display abundant defects due to the increasing density of graphene edge sites.[30, 31] Moreover, the shape of 2D-band can also be used to identify the number of layers (flake thickness) as shown in Figure 3e. These approximately indicated that the lGP, mGP, and sGP membranes consisted mostly of 5, 2, and 1 layer thick flakes, respectively, which is in agreement with previous studies by Ferrari et al.[32] The thickness of the graphene flakes after formation of the membranes can also be measured by analyzing the line profiles across step edges on the AFM images, as shown in Figure S5.

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Figure 3. SEM images of graphene membranes: a) lGP (large), b) mGP (medium), and c) sGP (small) membranes. The top and bottom images are top-down and cross-sectional SEM images. All scale bars are 500 nm. d) The PXRD pattern of the (002) peak position of the graphene membranes (produced from different graphene flake sizes) at comparable thickness (~3 µm), and the bulk starting materials. The dried membranes (red solid lines) were compared after exposure in deionized water for 48 h (blue dot line). All the PXRD patterns were calibrated using the PVDF peak (2θ = 20.17°) as a reference.[14] e) Raman spectra of graphene membranes with size-dependent material showing high disorder in sp2 carbon hybridization with decreasing graphene lateral sizes. f) Comparison between the D to G intensity ratio (ID/IG) averaged from 25 Raman spectra for each membrane.

3.3. Ion Transport through Laminar Graphene Membranes 3.3.1. Potential Dependent Ionic Sieving In terms of surface morphology, the graphene membranes prepared by liquid-phase exfoliation provides a low oxygen content (< 2%) compared to that reported for GO (> 40%) and rGO (> 10%) membranes.[33] This lends high stability without any swelling in aqueous solutions unlike those membranes, which in turn permits study of ion transport in aqueous media. To investigate ion transport through the graphene membranes, the apparatus schematically shown in Figure 4a was assembled. Two liquid reservoirs were separated by a membrane and the current measured using a four-electrode system (see Figure S6). The I-V characteristics of the three graphene membranes of comparable thickness (~3 µm) was measured using a KCl solution (0.1 M) between two liquid reservoirs as shown in Figure 4b. Figure 4c shows the ionic conductance of these membranes determined by fitting the slopes of the ionic current as a function of the applied voltage, after subtracting the conductance 15

measured for the same electrolyte with bare PVDF. This indicated that decreasing the graphene flake size can reduce ion transport through the laminar stacked graphene membranes (reduction of the gradient of the I-V responses). The high ionic resistances of the small flake membrane may result from the more probable nanocapillary channels nanocapillary channels, formed as a result of the disordered laminar stacking, as well as the abundance of defects compared to the other membranes with larger flakes. To further investigate the effect of flake size-dependent surface charge, the conductance for each membrane was measured with a variety of KCl concentrations. Figure 4d shows the I-V characteristics of symmetric KCl solutions (10−1 to 10−3 M) for the sGP membrane. By decreasing the KCl concentration, conductances for the three membranes initially fell linearly on dilution from CKCl = 0.1 M, indicating that conductance corresponded to the bulk solution value. However, the conductances were observed to deviate from the bulk values, leading to a saturation at low CKCl, as shown in Figure 4e. This observation is consistent with the concept of a “charged confining surface”, which has been invoked in previous works using nanochannel slits,[34-36] carbon/boron nitride nanotubes,[37, 38] single-layer MoS2/graphene nanopores,[39, 40] and GO membranes.[41] This results from the compression of the electrical double layers (EDLs) in the nanochannels,[41] an effect which was more significant in the sGP membrane because the deviation in conductance was found to occur at higher ionic strength.

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Figure 4. Ion transport through laminar graphene membranes with flake size dependent. a) Schematic showing the experimental setup using a four-electrode system. b) I-V characteristics of the graphene-based membranes prepared from the set of size-selected dispersions with comparable thickness (3 µm) using 0.1 M KCl reservoir concentrations (see inset). c) Corresponding ionic conductance (G = ∆I/∆V) of the graphene membranes after subtraction of the conductance of a bare PVDF membrane (see Supporting Information). d) I-

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V characteristics of the sGP membrane. KCl concentrations were varied from 10−3 M to 10−1 M. e) Conductance (G) for the three graphene membranes over the full range of KCl concentrations (10−1 M to 10−8 M). The dashed lines represent the conductance expected in each membrane from the conductivity of the bulk solution. Error bars indicate the standard deviation of at least three independent measurements using different membrane samples.

Such charge effects manifest themselves in differences in cation and anion mobility: the cation to anion mobility ratio was evaluated through drift-diffusion experiments performed under a combined concentration and voltage difference.[40, 41] The GoldmanHodgkin-Katz (GHK) equation, which assumes independent ion movements across the membrane, was used to calculate the mobility ratio (µ +/µ −), see Eq. 1.[35, 41, 42]

z2‒ µ+ = ‒ µ‒ z2+

FE C‒ f ‒ C‒ p exp(z‒ RTm ) FE C+ f ‒ C+ p exp(z+ m ) RT

FE 1 ‒ exp(z+ RTm ) FE 1 ‒ exp(z‒ m ) RT

(1)

where Em is the membrane potential (i.e. zero-current potential), [C−]f and [C+]p are the concentration of anions and cations in the feed and permeate reservoirs, respectively, z+ and z− are the valences of cations and anions, respectively, and other symbols have their usual meanings. To understand the effect of charge selectivity through the graphene nanochannels, K+ and Cl− were used for studying ion transport through membranes as their hydrated ion radii are reported to be similar (K+ = 3.31 Å and Cl− = 3.32 Å).[35, 43] Figure 5a shows the IV characteristics of KCl, measured at a concentration gradient (10 mM/100 mM). It is clearly seen that the zero-current potential shifts to a more positive value with decreasing graphene 18

flake sizes. The corresponding K+ and Cl− mobility ratio (µK+ /µ - ) of these graphene Cl

membranes was plotted as a function of graphene flake sizes as shown in Figure 5b. This indicates that the mobility ratio significantly increased with decreasing graphene flake sizes, especially for the sGP membrane. The corresponding increase in absolute flake charge, inferred from the decrease in ζ-potential (see Figure 5c) from ca. −20 mV to −50 mV for large and small flakes, respectively, presumably results from the increase in oxygen content and defect density, which is consistent with the XPS and Raman analysis, respectively. Moreover, the individual mobilities of K+ and Cl− can be also evaluated. For this we used conductivity values measured at relatively high concentration (CKCl = 0.1 M) for which there is a negligible surface charge contribution (see Figure 4e).[39-41] The conductivity can be expressed as σ ≈ F(CKCl µK+ + CKCl µ - ),[35] (see Table S2: electrolyte conductivity of each Cl

membrane). The mobility ratio can be combined with the latter equation to obtain the individual mobilities as shown in Figure 5d. The black and cyan columns represent the K+ and Cl− mobilities, respectively. The ionic mobility within the sGP membrane decreased by over one order of magnitude compared to the other membranes. The increase in negative charge on the sGP membrane’s surface, suppresses the Cl− mobility to a greater extent. Figure 5e schematically illustrates the charge and size selective ion sieving mechanism operative with smaller graphene flakes.

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Figure 5. K+ and Cl− mobility through laminar graphene membranes. a) I-V characteristics of KCl for the graphene membranes with comparable thickness (3 µm), measured under the KCl concentration ratio (10 mM/100 mM). b) K+ and Cl− mobility ratio (µK+ /µ - ), calculated by Cl

the GHK equation (Eq. 1) using zero-current potential from a). Note the dashed line represents equivalent K+ and Cl− mobility (µK+ = µ - ). c) ζ-potential of the graphene Cl

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dispersions (lGP, mGP, and sGP). The solutions were diluted by isopropanol and adjusted to the same concentration (5 µg mL−1). d) Corresponding individual mobility (black and cyan columns are K+ and Cl− mobility, respectively), demonstrating µ

Cl-

decreased with increasing

negative surface charge of the graphene membranes. e) Schematic showing the mechanism of selective ion transport due to decreasing lateral flake length and thickness.

Additionally, the ionic permeability of the membranes was investigated with various chloride solutions using a constant concentration ratio between the permeate (10 mM) and the feed (100 mM) reservoirs. The I-V characteristics of the different chloride solutions (KCl, BaCl2, and AlCl3) for the sGP membrane are shown in Figure 6a. Due to the different hydrated ion radii and diffusion rates of the cations and anions a net current flows at zero applied voltage, resulting in the I-V curves being shifted along the voltage axis. The zerocurrent potential decreased to a more negative potential with increasing hydrated cation radius, indicating that transport of larger cations can be suppressed. Figure 6b shows the mobility ratio (µ +/µ −) of a variety of chloride solutions from mono-, bi-, and trivalent ions as a function of hydrated cation radii (RH). It is clearly seen that with increasing hydrated cation radius (K+ to Al3+) the mobility ratio changes by one order of magnitude which agrees well with previous works studying size effect in ion transport through angstrom-scale slits[35] and laminar MoS2 membranes.[44] To distinguish between cation and chloride counter ion mobility, the analysis of mobility ratio and ionic conductivity was repeated to extract individual mobility as shown in Figure 6c. The cation mobility decreased by over one order of magnitude for the sGP membrane, whereas the change was slightly less for the lGP membranes. From these results, the sGP membrane with high negative surface charge and defect density enables the suppression of the ion transport due to the complex formation of

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nanochannels with high charge selectivity. In general, the trend expected for water purification is one of increased ion rejection being coupled to decreased water permeation.[14, 45] To understand the membrane wettability, water contact angle (WCA) measurements were also performed on the graphene membranes as shown in Figure S7 (see Supporting Information). The WCA on the sGP membrane is significantly lower than the other membranes, as described by the hemi-wicking model[46, 47] (see Figure S8). This increased hydrophilicity is attributed to a larger number of edges exposed, causing the spreading and ingress of water through the laminar stacked membrane.

Ionic current (µA)

a 150

AlCl3

sGP membrane

100

BaCl2

Zero-current potential

50

KCl 0 Feed 100 mM

-50

Graphene PVDF

A

Permeate 10 mM

-100 -200

-100

0

100

200

Applied voltage (mV)

b

c

10

Na+

K+

Li+

Ba2+

Mg2+ Ce3+ Cr3+ Al3+

Bulk

K+

Na+

1

Mobility (10-8 m2 V-1 s-1)

Mobility ratio (Cations/Cl-)

10

Li+ 2+

Ba

Mg2+ Ce3+ 3+ Cr

0.1

Al3+

lGP sGP

1

GO

0.1

3.6

3.9

4.2

4.5

4.8

Nafion XL PFSA

Cations mobility Cl- mobility Literature cations mobility

0.01 3.3

Hydrated radii, RH, (Å)

lGP

Nafion-117 AR103-AEM

MoS2/SY

0.01 3.3

CR61-CEM

Ti3C2Tx

3.6

3.9

4.2

sGP

4.5

4.8

Hydrated radii, RH, (Å)

Figure 6. Ion mobility through laminar graphene membranes. a) I-V characteristics of the sGP membrane at 3 µm thick, showing cations of three different charges measured under the

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concentration ratio (10 mM/100 mM). The inset shows a schematic of the drift-diffusion experiment for a variety of chloride solutions. b) Mobility ratio (µ +/µ −) as a function of hydrated cation radii (RH) for the lGP (■ symbols) and sGP (● symbols) membranes with comparable thickness (~3 µm). c) Ion mobility of cations (■● symbols) with their chloride

counter ions (□○ symbols) of the graphene membranes as a function of RH (see Supporting

Information). Diamond (♦◊ symbols) represent literature values for cations and anions in

bulk solutions,[48] while triangles represent cation mobility reported for other laminar 2D material membranes (yellow-coloured highlight); the GO membranes (▲ symbol)[41] and the Ti3C2Tx (MXene) membranes (▼ symbol),[49] and the commercial porous polymeric membranes (blue-coloured highlight); CR61-CEM and AR103-AEM (► symbol) as the cation and anion exchange membranes, respectively,[50] and Nafion membranes (◄ symbol).[51, 52] Star (★ symbol) represents K+ mobility in dye-functionalized MoS2 membranes (MoS2/SY).[44] The ionic mobility (µ i) reported in cation/anion exchange membranes (CEM/AEM) and Nafion membranes were estimated from ion diffusion coefficients (Di) using the Nernst-Einstein relation (Di = µ iRT/F). Trend lines in b) and c) are added as guides to the eye. Error bars in b) and c) are not visible on the scale used. Note the semilogarithmic scale.

3.3.2. Na+ Rejection and Water Permeance To determine the salt permeability through the graphene membranes, permeate resistivity and in-situ potentiometric measurements were performed by measuring the zerocurrent potential difference between two Ag/AgCl REs placed in the permeate (1mM NaCl) and the feed (1M NaCl) reservoirs over 3 h (Figure S9).[39] It was shown that all graphene membranes (lGP, mGP, and sGP) can efficiently reject NaCl. The relative resistivity of these 23

membranes dropped by less than 10% compared to a bare PVDF membrane, which is a similar performance to our previous work using dye functionalized MoS2 membranes.[14] To understand the salt rejection and water permeance, we also performed a forward osmosis (FO) experiment by filling equal volumes (10 mL) of ~3 M sucrose and 0.1 M NaCl in the permeate and feed reservoirs, respectively, separated by the graphene membrane for 30 h (see Supporting Information). The osmotic pressure gradient obtained is ~75 bar which draws water molecules from the NaCl reservoir to the sucrose reservoir. This technique has been previously applied to measure water permeation and salt rejection in GO and MoS2 membranes.[6, 8, 14] The Na+ rejection was estimated as 1 − Cp/Cf, where Cp and Cf are Na+ concentration in the permeate and feed reservoirs, respectively, measured ex situ by inductively coupled plasma optical emission spectroscopy (ICP-OES). The rejection efficiency obtained was nearly 97%, coupled with a high water permeance of 0.063 L m−2 h−1 bar−1 (see Table 1) which is higher than those reported for the GO and MoS2 membranes by factors of 10 and 2, respectively. This finding is consistent with the aforementioned MD simulations, which predicted that water permeance through graphene nanochannels would be faster than through the GO and MoS2 analogues due to the lower hydraulic friction of the smoother, non-oxidized surface.[15] For Na+ rejection, there are two dominant mechanisms. First, size exclusion is due to distortions of the ionic hydration shell (DH = 7.16 Å for hydrated Na+ diameter) in nanocapillary channels (channel height = 3.4 Å).[35, 41] Secondly, charge selectivity is due to negative surface charge on graphene membranes depending on the degree of defect and edge density on graphene nanosheets (Figure 5e and 6c).

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Table 1. Comparison of literature values of laminar stacked membranes for desalination performance using forward osmosis (FO) experiment. Membranes

Membrane thickness

Water permeance (L m−2 h−1 bar−1)

Rejection (%) (0.1 M NaCl: feed)

Ref.

GO membranes Pristine GO

5 µm

0.008

60

[8]

GO-Graphene

5 µm

0.007

97

[8]

MoS2 membranes MoS2/SY

5 µm

0.033

~99

[14]

MoS2

N/A

0.0022

N/A

[53]

Graphene membranes lGP

3 µm

0.063

~96.9

This work

mGP

3 µm

0.025

~98.1

This work

sGP

3 µm

0.018

~99.5

This work

4. Conclusions We have used centrifugation-based size selection to investigate ion transport through laminar graphene membranes under an applied electric field and concentration difference. The membrane formed from the smallest graphene flakes (sGP) can reduce ion mobility by a factor of ten compared to membranes with medium and larger flakes (lGP and mGP), previously reported laminar membranes (GO and Ti3C2Tx membranes), and commercial ion exchange membranes. These graphene membranes provided high stability (no detectable swelling) in aqueous solution, in contrast to the widely reported GO/rGO membranes. Ion transport through the graphene membranes is controlled by size exclusion and charge selectivity, due to defect and edge density with a highly disordered laminar stacking

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generating tortuous nanocapillaries. Salt rejection and the water permeance through the graphene membranes are significantly higher than those previously reported for GO and MoS2 membranes. Furthermore, the high durability, lack of swelling and scalability of graphene membranes can be further utilized for applications in water purification as ionexchange and electro-dialysis membranes.

Supporting Information Graphene-based membranes with thickness calibrations; the correlation between DLS data and statistical AFM; ion transport measurements; further characterizations including XRD, XPS, water contact angle (WCA) experiment; electrolyte conductivity measurements; ion permeation and water permeance experiment; (PDF)

Acknowledgments W.H. wished to acknowledge the Development and Promotion of Science and Technology Talents Project (DPST), Royal Government of Thailand scholarship. We also thank funding from Engineering and Physical Sciences Research Council, UK (EP/R023034/1, EP/N032888/1, EP/P00119X/1, EP/S019367/1, and EP/P025021/1).

Conflict of Interest The authors declare no conflict of interest.

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