Supporting Information Scalable Graphene‐Based Membrane for Ionic Sieving with Ultrahigh Charge Selectivity Seunghyun Hong1, Charlotte Constans1,2,, Marcos Vinicius Surmani Martins1,3, Yong Chin Seow1, Juan Alfredo Guevara Carrió1,4, and Slaven Garaj1,2,5,6 * 1
Centre for Advanced 2D Materials, National University of Singapore, Singapore 117542 Department of Physics, National University of Singapore, Singapore 117551 3 Department of Materials Science and Engineering, National University of Singapore, Singapore 117575 4 Engineering School, Presbyterian University Mackenzie, São Paulo, 01302‐907, Brazil 5 NUS Nanoscience & Nanotechnology Institute, National University of Singapore, Singapore 117581 6 Department of Biomedical Engineering, National University of Singapore, Singapore 117583 *Correspondence to:
[email protected] 2
Table of Contents: 1. Physiochemical characterizations of graphene oxide nanosheets 2. Interplanar spacing expansion of graphene oxide membranes in water 3. Quantitative analysis of ion selectivity across the membranes 4. Calculation of ionic conductance and surface charge density 5. pH‐dependent ionic conductances and surface charge densities 6. Effects of excess hydronium or hydroxide ions 7. pH‐dependent drift‐diffusion measurements 8. Mean field model for ion transport in the nanochannels 9. Validation of the analytical continuum models 10. Ion strength‐dependent ionic conductance and cation permselectivity 11. Voltage drop across bare SiNx scaffold S1
1. Physiochemical characterizations of graphene oxide nanosheets
Figure S1 Characterizations of GO nanosheets (a) AFM map and the height profile for monolayer GO nanosheet, investigated by atomic force microscopy. (Dimension Fastscan, Bruker) Two‐dimensional GO nanosheets at ambient conditions are ~1 nm thick with mean planar width of 1 μm. (b) Fourier Transform Infrared spectrum (FTIR) of air‐dried GO laminates, displaying diverse functionalities such as (C‐O) Epoxy at 1260 cm‐1, (O‐H) or C‐O Carboxy at 1390 cm‐1, (C=O) Carbonyl and Carboxyl at 1718 cm‐1, and O‐H Hydroxyl at 3431 cm‐1 1
2. Interplanar spacing expansion of graphene oxide membranes in water
Figure S2 Interplanar spacing expansion of GO membranes in water (a) X‐ray diffraction (XRD) spectra comparison of dried and wet GO films. The inter‐plane distance of GO reflection (100), was determined from a Rietveld refinement using conventional XRD data and program GSAS. Using the space group P6/mmm, a Rietveld refinement was performed with program GSAS (General Structure Analysis System) until discordance factors R wp = 7.00 %, R p = 5.46 %, R Bragg = 6.33 % and χ2 = 1.138 2. The obtained cell parameters are a = b = 10.517(3) Å and c = 1.9(1) Å. The investigated interlayer spacing of dried and wet GO by XRD is around 8.5754 Å and 12.1615 Å, respectively. (b) Respective height profile of dried and wet GO films, measured by in‐situ liquid AFM shows similar increase in interlayer spacing after wetting.
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3. Quantitative analysis of ion selectivity across the membranes To describe ionic transport across the membrane, driven by voltage and concentration gradients, we assume that ions move across the membrane independently and that the electric potential drops linearly across the membrane. Using Boltzmann‐Planck framework, we derived so called Goldman‐Hodgkin‐Katz equations3, connecting the current density J and membrane potential Vm to the concentration and voltage gradient across the membrane:
∆
∆ ∆
(1)
(2)
total
ln
(3)
where is ionic current density for cations ( ), and anions ( ), and total is the total current is membrane permeability ( ∙ ) and is the valence for each density across the membrane. ionic species. and are ionic concentrations in the feed and permeate chambers, respectively. ΔV is the applied voltage, Vm is the membrane potential, R is the universal gas constant ), 9.6485 10 C ∙ mol is Faraday’s constant, T is the temperature. The (8.314 J ∙ ⁄ intrinsic ionic diffusivity within the membrane could be deduced when ion’s partition coefficient is known; is membrane thickness. The current density is calculated from ionic current, where effective area of the membrane is calculated as the geometric mean of the top and the bottom aperture areas of the GO membrane. We could directly deduce the permeability ratio of the ions (and ion selectivity) from the membrane potential . We first measure the zero current potential , the potential for which the total current through the membrane is zero 4‐6. We could now calculate the membrane potential by subtracting from the redox potential redox : redox (4) The redox potential arises from the unequal chloride concentration at the two Ag/AgCl electrodes, and it given the following relation: redox
ln
(5)
where / and / are the activity coefficient and concentration of the chloride ion on the high concentration side (H) and the low concentration side (L) of the membrane. To compare our results with previous experiments, we calculated molar flux density or permeation rate, p (mol‐cm‐2‐h‐1), which is determined by the classical solubility‐diffusion model 3 as: (6)
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4. Calculation of ionic conductance and surface charge density The ionic conductance (G0) of the membrane is deduced from the slope of I‐V curves, measured in the Ohmic regime at voltages between ‐10 to +10 mV, for equal salt concentrations on both sides of the membrane. We put forward the simplest model that could predict variation of the membrane’s conductivity with the surface charge on the GO flakes, without taking any assumption of the chemistry of GO flakes nor fluidic properties. We assume that the surface charge on the nanochannel walls increases the conductivity of nanochannels by increasing the local concentration of the counterions, to preserve the charge neutrality within the channel. The total conductivity of the channel is now given by: K
Cl‐
⁄
2
K
⁄
(7)
where the first part of the equation corresponds to the Ohmic conductance due to the bulk concentration of ions, and the second part is the contribution from the excess counterions; q is the elementary charge; K and Cl‐ are the ionic mobilities of cations and anions, respectively; NA is Avogadro’s number; cB is the electrolyte’s bulk concentration; σS is the surface charge density; w and l are the width and length of channel, respectively. Here the left term is the surface‐charge governed conductance, which dominates at low salt concentration, and the right term is the bulk conductance dominant at high concentration. The approximated length of the single nanochannel across the membrane is derived from the thickness of the membrane. 7, 8 The width of the single channels is approximated to be the lateral sizes of the graphene oxide nanosheets. The G0 can be calculated by dividing the calculated Ohmic conductances by the number of channels. To obtain the number of channels, we assume that measured conductance at high 1M where the surface charges are mostly screened is determined by bulk concentration regime i.e. behaviors.
5. pH‐dependent ionic conductances and surface charge densities Figure S4b illustrates the surface charge densities of graphene oxide nanochannels, which were calculated using the ionic conductances obtained at different pH values and molarities. (Figure S4a) The vanishing COO‐ surface group due to the protonation at low pH leads to a reduction in the surface charge. Dissociation of other groups present on the GO sheets also contributes to the pH‐regulated surface charge variation.
Figure S3 (a) Ionic conductances across the single nanochannel of graphene oxide membranes, measured at three different KCl concentrations in the pH ranges of 2 to 12 (b) Surface charge densities as functions of salt concentration and pH in KCl. The charge densities were expressed in terms of the amount of charged carriers per area (e/μm2).
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6. Effects of excess hydronium or hydroxide ions The ionic currents associated with the excess hydronium (H3O+) or hydroxide (OH‐) ions are subtracted from all drift‐diffusion and conductance measurements since those excess species can significantly contribute to the ionic conductance as shown in Figure S4a. In addition, we observe the increase of the interlayer spacing at pH 11.7 by around 0.3 nm compared to those below pH 10, as previously reported. (Figure S4b) 9
Figure S4 (a) pH‐dependent current‐voltage transport of electrolytes exclusive of solute KCl. Highly deprotonated nanochannel by hydroxide ions (OH‐) in KOH aqueous solution is exhibiting highly rectifying current profile compared to that of HCl. Inset is the surface charge density of GO channels evaluated at pH 2.77 and 11.26, respectively. (b) pH‐dependent variation of the interstitial spacing, obtained from membranes immersed in different pH solutions using in‐situ AFM analysis.
7. pH‐dependent drift‐diffusion measurements
Figure S5 (a and b) Current‐voltage transport behaviors under asymmetric conditions (10‐1 M KCl and varying pH on the feed chamber, and 10‐2 M and constant pH of ~ 6 on the permeate chamber). The ionic currents associated with the excess hydronium (H3O+) or hydroxide (OH‐) ions are subtracted at each different pH.
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8. Mean field model for ion transport in the nanochannels
Figure S6 Schematic of the graphene oxide nanochannel presumed as a rectangular channel with dimensions of effective height, hG, channel length, Lchannel, and channel width, 2R (or wG). When the charged surface is immersed in an electrolyte, the electrostatic surface potential created by surface charges attracts counter‐ions and repels co‐ions. The region referred as the diffuse region of the electrical double layer has a higher density of counterions and a lower density of co‐ions than the bulk. In this regime, the electrical potential decays exponentially with distance given by Debye length (λD=κ‐1) 10 /
∑
(8)
) is the dielectric constant or where is the number density of ions of the type i in the bulk, ε (= permittivity, and kB is the Boltzmann constant. In a thin region between the surface and the diffuse layer, there is a layer of bound or tightly associated counterions, generally defined as the Stern layer. This region is of the order of one or two solvated ions thick and also referred as the bound part of the double layer. In this region, it is assumed that the potential falls linearly from the surface to the interface between the diffuse layer and the Stern layer. A graphene oxide nanocapillary is modeled as a rectangular channel formed by two separated sheets of graphene oxide separated by the distance h. The channel is delimited by the pristine graphene on top and bottom, and by oxidized regions of graphene on the sides. The Stern layer takes into account the finite size of the charged‐surface functional groups. An electric field is applied along z‐axis. The following equations are solved along the x‐axis. We consider there is no friction between the water and top/bottom layers of pristine graphene. The surface potential ( on the charged walls in the electrolytes satisfies Poisson‐Boltzmann equation as below ∑ (9) (10)
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By combining above two equations, sinh
ɸ
ɸ
) (11)
Stern layer where showing linearly varying potential can be obtained as below with regard to boundary . 0 0 and conditions (12) In order to determine the surface charge density on the walls and the potential (ΦD), chemical reactions occurred on the oxidized surface regime, corresponding to the protonation of carboxyl or hydroxyl groups as below, were took into account 11. GO + H+ ↔ GOH GOH + H+ ↔ GOH The equilibrium equations of the above reactions are defined by 10
10
and
where the hydrogen activity at the surfaces is [H+] 0 = [H+] bulk
ɸR
and Ni is the density of surface
sites. By taking into account the total surface density of active sites and surface charge density, the Behriens‐ Grier equation could be obtained 12 10
exp
2
exp
0 (13)
10
∑ . Here, pK and pL where the total surface density of activity sites (Г) is ∑ don’t correspond to bulk values for protonation of carboxyl and hydroxyl groups, they are effective equilibrium constants chosen as to match the experimental results. And the Grahame equation was applied to calculate the surface charge density associated with the double layer potential. 13 sinh (14) σ , it gives the surface
By solving equations (12) and (13) self‐consistently with regard to
charge density and the surface density of each species Ni as a function of pH, electrolyte concentration, and the four chemical parameters, Г, δ, pK and pL. In order to model the conductances across the membranes, the ion distribution and velocity field in the nanochannels was calculated with the Navier‐Stokes equation and Boltzmann distribution, assuming that inertial and pressure terms are negligible and a no‐slip condition at x=R. 14 and ∙
(15) (16)
S7
wherein inertial and pressure terms are negligible compared to viscosity and electrostatic force, and is given. Therefore: 0 (17) with regard to the boundary conditions (no‐slip boundary condition), 0 0 and R 0 We obtain the solution as (18) The current is produced by the drifting of ions under the electric field and by the flow of water carrying the ions 2 (19) 2 Finally, we could obtain the conductance as
(20) with
.
9. Validation of the analytical continuum models In order to validate the model as shown in Figure S6, the analysis was also carried out with a rectangular channel possessing charge polarity on planar surfaces and a cylindrical pore, respectively. Figure S7 is demonstrating the nanochannel with charge‐polarized planar sheets. The highly concentrated counter‐ ions between two polarized nanosheets resulted in overestimated ionic conductance under electric field gradients compared to experimental values at different pH and molarities. Deviation in the ionic conductance indicates that dominant conducting pathways of ions in the graphene oxide membranes should consist of but two dimensional, pristine graphene nanocapillaries with partially charged regions, not fully functionalized channels. In addition, the investigation was carried out for a quasi‐one dimensional cylindrical nanochannel with surface charges on circumference of cylindrical channel. (Figure S8) These models are totally inconsistent with experimental observations.
Figure S7 (a) Analytical model with a rectangular pore possessing the surface charges on the top and bottom‐sheets. (b and c) Calculated molarity and pH‐dependent ionic conductances, respectively, by applying the parameters: 0.6 nm‐2, R = 25 nm, hG = 0.9 nm, δ = 1.3 nm, pK = 0, pL = 6, L channel = 0.3 mm, ‐7 2 = 3.1 x 10 m /V‐s, = 5.5 x 10‐8 m2 /V‐s. Solid lines show the calculated results from the analytical model, and the filled markers in Figure S8b and c are corresponding to experimentally obtained data shown in Figure S3a and Figure 3d, respectively
S8
Figure S8 (a) Analytical model of a cylindrical nanochannel with surface charges on circumference of cylindrical channel. (b and c) Calculated molarity and pH‐dependent ionic conductance, respectively, by applying the parameters: 0.6 nm‐2, R pore = 0.45 nm, δ = 0.1 nm, pK = 0, pL = 6, L pore = 0.05 mm, = ‐7 2 3.1 x 10 m / V‐s, = 5.5 x 10‐8 m2 / V‐s. Solid lines show the calculated results from the analytical model, and the filled markers in Figure S9b and c are corresponding to experimentally obtained data shown in Figure S3a and Figure 3d, respectively.
10. Ion strength‐dependent ionic conductance and cation permselectivity
Figure S9 (a) Current‐voltage curves measured at different salt concentrations at around pH 5.5. Inset shows the rectification factor RF as a function of molarity, describing the relative ratio of the measured currents at scan voltages of ± 80 mV. (b) Current‐voltage curves obtained from different feed concentrations and the constant concentration gradient of CHigh / CLow= 10 at pH 5.5. Inset shows the increasing membrane potentials with dilution of the electrolytes (feed molarity cF), associated with the enhancement of the cation selectivity.
S9
11. Voltage drop across bare SiNx scaffold
Figure S10 Ionic current across the bare SiNx membrane without aperture (green line), bare SiNX scaffold with aperture (red line), and GO membrane with SiNX scaffold (blue line). The bare SiNX scaffold contributes 10% or less to the overall resistance of the GO/SiNx membrane for KCl salt, and even less for the other ionic species. Bare SiNx membrane without aperture is completely impermeable to ions, and does not contribute to measured ionic permeability nor selectivity.
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