SO42− selectivity

Accepted Manuscript Layer-by-layer modification of aliphatic polyamide anion-exchange membranes to − 2− increase Cl /SO4 selectivity Muhammad Ahmad, Chao Tang, Liu Yang, Andriy Yaroshchuk, Merlin L. Bruening PII:

S0376-7388(19)30144-9

DOI:

https://doi.org/10.1016/j.memsci.2019.02.018

Reference:

MEMSCI 16843

To appear in:

Journal of Membrane Science

Received Date: 14 January 2019 Revised Date:

7 February 2019

Accepted Date: 8 February 2019

Please cite this article as: M. Ahmad, C. Tang, L. Yang, A. Yaroshchuk, M.L. Bruening, Layer-by-layer − 2− modification of aliphatic polyamide anion-exchange membranes to increase Cl /SO4 selectivity, Journal of Membrane Science (2019), doi: https://doi.org/10.1016/j.memsci.2019.02.018. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.

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Anion-exchange membrane

Receiving Phase

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Source Phase

ClSO42-

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CO32-

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Cl-/SO42- Selectivity of 140 in diffusion dialysis

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Polyelectrolytes

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Layer-by-layer modification of aliphatic polyamide anion-exchange membranes to increase Cl-/SO42- selectivity Muhammad Ahmada, Chao Tangb, Liu Yanga, Andriy Yaroshchukc,d and Merlin L. Brueninga,b * a

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Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, United States Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, United States

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ICREA, pg.L.Companys 23, 08010 Barcelona, Spain

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E-mail: [email protected]

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*Corresponding author: Merlin L. Bruening

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Department of Chemical Engineering, Polytechnic University of Catalonia, av. Diagonal 647, 08028 Barcelona, Spain

Abstract

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Development of anion-exchange membranes (AEMs) with selectivities among anions may expand the applications of these membranes in salt separations. This work shows that layer-by-layer coating of aliphatic polyamide AEMs with poly(4-styrenesulfonate) (PSS)/protonated poly(allylamine) (PAH) films enhances Cl-/SO42- dialysis selectivities, and the extent of this enhancement depends on the source-phase salt concentrations. For a source phase containing 0.01 M NaCl and 0.01 M Na2SO4 and a receiving phase of 0.01 M Na2CO3, a (PSS/PAH)5PSS coating (5 PSS/PAH “bilayers” capped with a layer of PSS) increases the Cl-/SO42- selectivity from 1.7 to 5.3 in diffusion dialysis and from 1.3 to 7.4 in electrodialysis. Remarkably, the diffusion dialysis selectivity of a coated membrane increases to 140 when the salt concentrations in the source phase are 0.1 M. Even with bare membranes, selectivity increases to 13 with 0.1 M sourcephase salt concentrations. Moreover, AEMs coated only on the receiving side show much higher selectivities but lower fluxes than those coated only on the source side. Partitioning experiments and modeling suggest that the increased Cl-/SO42- selectivities at high source-phase salt concentrations stem from enhanced Cl- partitioning and electromigration that disproportionately decreases SO42- flux in the AEM.

Keywords

Ion-exchange membranes; Layer-by-layer; Polyelectrolytes; Dialysis; Selectivity

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1. INTRODUCTION

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In typical electrodialysis (ED), an applied electrical potential difference moves cations and anions from diluate to concentrate compartments for applications such as desalination of brackish water [1-4], concentration of brines [5], recovery of salts from waste-salt solutions [6], treatment of wastewater effluent [7,8] and demineralization of milk byproducts [9,10]. Cations move through cation-exchange membranes (CEMs) toward the cathode, and anions migrate through anion-exchange membranes (AEMs) toward the anode [11,12]. Thus, ion-exchange membranes (IEMs) are at the heart of ED. Typical IEMs are highly selective for cations over anions or anions over cations, but they exhibit relatively low selectivities among cations or among anions. Development of membranes that show high selectivities among cations or anions may extend the utility of IEMs to areas such as separation and purification of salt mixtures [13], removal of Ca2+ and Mg2+ ions to decrease the hardness of water [14], removal of divalent cations to improve the process of reverse electrodialysis [15], recovery of acid from industrial wastewater containing metallic salts [16], prevention of vanadium crossover in redox flow batteries [17], removal of divalent ions from sea water to improve the quality of edible salt [18] and electrochemical acidification of food products [19,20].

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A number of studies explored methods to increase the monovalent-ion permselectivity of IEMs. These strategies mainly focus on increasing the crosslinking density of the membrane matrix or controlling the immobilized charge on the membrane surface [2128]. Increased crosslinking in the membrane hinders the diffusion of ions with larger radii, whereas depositing a polyelectrolyte on the surface may increase the selectivity among counterions with different charge magnitudes [29-33]. Ge and coworkers increased the crosslinking density of a nanofiltration membrane by adding a dense top layer and achieved a Na+/Mg2+ selectivity of 7 in ED [34]. In addition to creating monovalent/multivalent ion selectivity, deposition of a thin charged layer may help to reduce scaling because the electrostatic repulsion decreases the formation of precipitates of oppositely charged multivalent ions on the IEMs [35,36].

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Several research groups employed layer-by-layer deposition of polyelectrolytes to vary the thickness, swelling and charge density of membrane coatings [37-39]. Abdu et al. deposited protonated polyethylenimine (PEI)/poly(4-styrenesulfonate) (PSS) multilayer films on a Neosepta CMX IEM and increased the Na+/Ca2+ selectivity from 0.64 to 1.5 while minimizing the increase in membrane resistance in ED [22]. In another study, a Nafion CEM electrochemically coated with PEI films gave Na+/Cr3+ selectivities >10 [40]. White et al. coated Nafion CEMs with (poly(allylamine hydrochloride) (PAH)/PSS films to achieve remarkable monovalent/multivalent cation selectivities >1000 [23,25]. Zhu et al. reported similar selectivities with less expensive Fujifilm CEMs [24]. In recent work on Nafion CEMs coated with polyelectrolyte multilayers (PEMs), Yang and coworkers reported K+/Li+ selectivities ranging between 8 and 60 [41].

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A few recent studies also examined polyelectrolyte adsorption on AEMs to increase the selectivity among monovalent and multivalent anions. Zhao and coworkers modified an AEM through alternating electrodeposition of PSS and hydroxypropyltrimethyl ammonium chloride chitosan and increased the Cl-/SO42- ED selectivity from 0.66 to 2.90 [42]. Using interfacial polymerization, Zhang et al. grafted a thin electronegative layer onto the surface of an AEM and improved the Cl-/SO42- permselectivity from 1.8 to 10.3 [43]. Pan and coworkers electrochemically deposited and then covalently immobilized a polyethyleneimine layer onto the surface of an AEM to achieve Cl-/SO42selectivities up to 4.3 [44]. Liu et al. modified an AEM with PEMs and then crosslinked the layers to stabilize the film and thus increased the monovalent/divalent anion selectivity from 0.39 to 4.36 [45]. Zhao and coworkers added layers of N-O-sulfonic acid benzyl chitosan and hydroxypropyl trimethyl ammonium chloride chitosan onto an AEM using an electric pulse deposition method. They achieved a Cl-/SO42- selectivity as high as 47 during the first 20 min of ED [46]. In another recent work, AEMs were crosslinked by adding variable amounts of sulfamerazine to partially quaternized chloromethylated polysulfone to achieve Cl-/SO42- selectivities ranging between 4 and 15.9 [47].

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This research examines whether the remarkable monovalent/divalent cation selectivities achieved with (PAH/PSS)5PAH films on CEMs [23,25] are also possible for anions when depositing similar films on AEMs. Moreover, we examine the mechanisms that sometimes lead to dramatic increases in selectivity at high source-phase salt concentrations. We chose to coat Fujifilm type-1 AEMs with these multilayer films because the aliphatic polyamide surface is relatively smooth and may allow formation of a complete coating. Remarkably, the Cl-/SO42- selectivity reaches values as high as 140 when the source phase contains 0.1 M salt concentrations. This work includes measurements of ion partitioning, (electro)dialysis experiments with PEMs on both AEMs and porous alumina, and modeling to explain why selectivity varies significantly with salt concentration. The combination of highly selective AEMs and CEMs in ED may allow purification of salt mixtures containing divalent and/or multivalent ions.

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2. EXPERIMENTAL 2.1. Materials

Poly(sodium 4-styrenesulfonate) (Mw=70,000 Da), poly(allylamine hydrochloride) (Mw= 17,500 Da) and sodium chloride were obtained from Sigma-Aldrich. Sodium sulfate was acquired from Columbus Chemical, and sodium carbonate and sodium bicarbonate were purchased from Jade Scientific. Sodium nitrate was purchased from J.T. Baker, and all salts were used as received. Deionized water (Milli-Q reference Ultra-pure Water Purification System, 18 MΩ cm) was used to prepare all solutions, and the pH values of polyelectrolyte solutions were adjusted with 0.1 M solutions of HCl and NaOH. Fujifilm type-1 CEMs and Fujifilm type-1 AEMs were gifts from Fujifilm, Netherlands.

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2.2. Film formation and characterization

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Fujifilm CEMs and AEMs were punched into 25 mm disks with a mechanical die. For pretreatment, the membrane disks were soaked for >17 h in a room temperature solution containing 0.1 M NaCl. The pretreated AEMs were rinsed with deionized water and modified by dipping them in alternating polyanion (0.025 M PSS in 0.5 M NaCl, pH ∼2.3) and polycation (0.025 M PAH in 1.0 M NaCl, pH ∼2.3) solutions for ∼10 minutes each. The only exception to this was the first PSS layer, whose adsorption employed immersion in the PSS solution for ∼2.5 h. (This long immersion time is likely unnecessary.) The concentrations of the polyelectrolytes are those of the repeat units. After adsorption of each polyelectrolyte “layer”, the membranes were rinsed with deionized water from a squirt bottle for ∼1 min to remove weakly adsorbed polyelectrolytes. One-sided modification of the membranes was performed in a homemade O-ring holder that exposes only one face of the membrane to the polyelectrolyte and rinsing solutions. Images of bare and coated AEMs were obtained with a Magellan 400 FESEM (Field-Emission Scanning Electron Microscope). The membrane samples were dried overnight under vacuum at room temperature and sputter coated with 2 nm of iridium prior to imaging. 2.3. Electrodialysis

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Three homemade 100 mL glass cells clamped together with O-rings (1.8 cm2 of exposed membrane area) were used for ED experiments (Figure 1). The exposed area is defined by the ground glass joint that supports the membranes. In a few prior studies [23-25,41], we overestimated the membrane area by basing it on the O-ring (see the supplementary material, Figure S1 and Table S1; figure and table numbers starting with S refer to the supplementary material). Platinum wire electrodes were inserted into the outer two compartments, and current was applied between these electrodes such that the cathode was in the source phase and the anode was in a phase containing 0.01 M Na2CO3. (We chose CO32- as the anion in the receiving phase because its large excess will not interfere with the analysis of other anions in this phase. Each phase initially contained 90 mL of solution.) A bare pretreated Fujifilm CEM isolated the anode phase from the central compartment, which initially contained 0.01 M Na2CO3 and served as the receiving phase. The isolated anodic compartment avoids the formation of Cl2 due to electrochemical oxidation of Cl- at the anode [48]. The modified AEM was inserted between the source and receiving phases. Thus, the anions migrated to the central (receiving) compartment from the source phase and were blocked from crossing into the anodic compartment by the CEM. Cations migrated toward the receiving phase from the isolated compartment through the CEM. A potentiostat (CH instrument model 604) applied a potential across a 499 Ω resistor (that was connected between working and reference electrodes) to produce a constant 2 mA current (1.13 mA cm-2). The reference terminal of the potentiostat was attached to the Pt anode in the isolated phase, and the

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Anode (+)

Cathode (-)

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Stirrer

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counter electrode terminal was connected to the Pt cathode in the source phase [23]. All three phases were stirred vigorously during ED to limit concentration polarization. During 2 h of ED, 1 mL sample aliquots were collected periodically from the receiving phase to determine the concentration of target anions, and corresponding aliquots were withdrawn from the isolated and source phases to maintain equal volumes. The sourcephase concentration was also verified occasionally. The anion concentrations were determined using ion chromatography (Thermo Dionex ICS-5000 Ion Chromatograph). Calibration curves were obtained by dilution of commercial seven-anion standard solutions (ThermoFisher) with deionized water. To study ion transport under similar conditions without an applied voltage, the same three compartment cell was used to

Isolated Phase

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Coated AEM

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Standard CEM

perform diffusion dialysis.

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Figure 1. ED cell consisting of three 100 mL glass compartments connected by 2.5 cm #15 flat joints with o-rings.

Data were plotted as total moles of target anions permeated through the membrane as a function of time, and the anion fluxes were calculated by dividing the slopes in such plots by the exposed membrane area. The moles in the receiving phase include that which was removed for analyses. The slopes were calculated only from the data acquired after 30 min in a 2 h dialysis. (The concentrations in the receiving compartment were always low, which afforded a pseudo steady state after 30 min.) When the source phase contains equal concentration of both ions, the Cl-/SO42selectivities are simply the ratios of Cl- and SO42- fluxes. Otherwise, fluxes are normalized to the source-phase concentration to determine selectivity. In a few cases,

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the minimum observed selectivities are reported as the smallest selectivity from three different membranes because the selectivities of the three membranes varied greatly due to the challenge of accurately determining the very low multivalent ion fluxes. 2.4. Transmembrane potential measurements

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3. Results and Discussion

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Transmembrane potentials across bare Fujifilm membranes (at zero current) were measured to determine the anion permselectivity of bare AEMs. These measurements used a homemade 2-compartment cell similar to that for electrodialysis. The source and receiving phases were separated by a bare pretreated membrane, and the electrical potential difference across the membrane was measured with a multimeter whose terminals were connected to Ag/AgCl reference electrodes (3 M KCl, CH Instruments) sealed in Haber-Luggin capillaries that approached to within 4 mm of the membrane. The source-phase NaCl concentration varied from 0.002 to 0.1 M, and the receiving phase always contained 0.001 M NaCl. Both phases were stirred strongly to minimize the effect of unstirred diffusion layers. Before measurements, the small potential drop between reference electrodes was determined by keeping both capillaries in the receiving phase, and later this value was subtracted from the multimeter reading. Finally, the potential difference across the membrane was calculated by also subtracting the junction potentials in the capillaries from the multimeter reading [39]. The product of the concentration and activity coefficient gives the activity of NaCl [49,50].

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Fujifilm IEMs consist of an aliphatic polyamide matrix impregnated in a fibrous support. This section initially examines the morphology of bare and modified Fujifilm AEMs and then investigates the increases in monovalent-anion-transport selectivity that result from layer-by-layer deposition of multilayer polyelectrolyte films on these substrates. In addition, we show that selectivities increase greatly with increasing source-phase concentrations, and are also much higher when polyelectrolyte coatings face the receiving rather than the source phase. Modelling of diffusion dialysis confirms these trends and demonstrates that selectivities arise from a combination of less SO42-/Clpartitioning selectivity at high salt concentrations and significant electromigration of SO42- that opposes the diffusive flux. 3.1. Characterization of Fujifilm anion-exchange membranes. Formation of defect-free polyelectrolyte multilayers requires membranes without large pores [51]. Although bare membranes do not show especially rough surfaces, they contain grooves with widths of 10’s of microns. Adsorption of polyelectrolyte films likely covers all of the exposed surfaces. Indeed, one of the attractive features of layer-bylayer films is conformal coverage of complex 3-dimensional shapes [52]. Figure 2 shows an SEM image of a Fujifilm membrane coated with a (PSS/PAH)5PSS film. The small

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nodules are likely polyelectrolyte complexes that form during the deposition (see Figure S2 for other images including bare membranes). The presence of the nodules both in grooves and on plateaus suggests coating of both areas.

Figure 2. SEM image of a Fujifilm anion-exchange membrane coated with a (PSS/PAH)5PSS film.





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To investigate the anion-permselectivity of bare Fujifilm AEMs, we performed transmembrane potential measurements. Equation (1) describes the electrical potential difference, , across a membrane flanked by two solutions with different salt activities  and  . In this equation  and  are the cation and anion transference numbers, and  and  are the cation and anion charges, respectively [49,53]. Equation (2) describes the transference numbers, which for a 1:1 salt depend on the ion mobilities,

 , and local concentrations,  , of the two ions. (1) (2)

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For an ideally permselective AEM,  is one and  is zero, so for salts containing  monovalent ions, a plot of E versus  should yield a slope of 59 mV per decade. !

Figure 3 shows such a plot for Fujifilm AEMs flanked with NaCl solutions. The slope of the plot is 55.3 mV suggesting that the membranes have a low but non-negligible permeability to cations ( = 0.03 - 0.04). Also, the linearity of the plot with source-phase concentrations from 0.002 to 0.1 M suggests nearly ideal anion-exchange behavior.

120 y = 55.31x - 2.26 R² = 0.9998

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1 1.5 Log (a1/a2)

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Figure 3. Transmembrane potential across a Fujifilm anion-exchange membrane as a function of the ratio of NaCl activities in the source (a1) and receiving (a2) phases. Error bars represent standard deviations from measurements with three different membranes.

3.2. Attainment of steady state in electrodialysis and diffusion dialysis with bare and (PAH/PSS)5PSS-coated Fujifilm anion-exchange membranes

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Adsorption of (PSS/PAH)5PSS films on Fujifilm AEMs leads to significant increases in ED selectivity for monovalent over divalent anions, but this selectivity also results in large lag times before reaching steady state. Figure 4 shows the total moles of Cl- and SO42- that passed into the receiving phase as a function of time during consecutive 2 h periods of ED from a source phase containing 0.01 M NaCl and 0.01 M Na2SO4 to a receiving phase of 0.01 M Na2CO3. Initially, the SO42- flux was negligible, but it started increasing after 70 min. After the first 2 h of ED, we emptied and rinsed the cells and added fresh source and receiving phases. During the second 2 h of ED, the SO42- flux was essentially constant after 30 min, and the Cl-/SO42- selectivity was 9.6 ± 3.3 with three different membranes. Polyelectrolyte adsorption occurs in solutions containing 0.5 M or 1.0 M NaCl, so anion-exchange sites in modified membranes initially contain only Cl- counterions. Sulfate from the source phase or CO32- from the receiving phase must replace some of the Cl- to achieve steady state, and this requires more than 1 h due to the low permeability of the (PSS/PAH)5PSS films to SO42- and CO32-. Experiments with a source phase containing 0.01 M NaNO3 and 0.01 M Na2SO4 confirm the displacement of Cl- (see the supplementary material, Figure S3 and Tables S2-S3 for details).

Chloride ions (1st 2h) Chloride ions (2nd 2h) Sulfate ions (1st 2h) Sulfate ions (2nd 2h)

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Figure 4. Amounts of Cl (triangles) and SO4 (squares) passed to the receiving phase vs time during ED with a source phase containing 0.01 M NaCl and 0.01 M Na2SO4. The filled and open symbols represent ED through (PSS/PAH)5PSS-coated membranes during the first and second 2 h experiments, respectively, at a current density of 1.13 mA cm-2. The receiving phase and isolated anode compartments 2initially contained 0.01 M Na2CO3. Note the different scales for Cl and SO4 .

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We examined diffusion dialysis (DD) to make sure that the decrease in selectivity over the first few h is not due to film instability under an applied current. Trends in DD and ED are similar. In DD the SO42- flux is undetectable during the first 2 h of dialysis, but it increases during a second 2 h, where the Cl-/SO42- selectivity is ∼23 (See Figure S4 and Table S4 of the supplementary material). Thus, the decrease in selectivity with time is not due to the applied current (and resulting potential gradient) but likely indicates that transport through the membrane does not reach a steady state within 2 h. In contrast, bare membranes show a Cl-/SO42- selectivity of only 1.3 and reach steady state within ~10 min (see Figure S4) [54].

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To avoid the long lag times, we soaked the coated AEMs in the feed solution for ∼24 h and rinsed them with deionized water prior to dialysis. Table 1 shows the Cl-/SO42fluxes and selectivities for bare and coated membranes equilibrated with the feed solution for 24 h. For (PSS/PAH)5PSS-coated membranes, the resistance to the passage of SO42- is more than to Cl-, which gives rise to a selectivity of 7.4 in ED and 5.3 in DD, whereas bare membranes show selectivities of only 1.3 in ED and 1.7 in DD. After equilibration with the feed solution, the Cl- and SO42- fluxes are essentially constant (Figure S5) and similar to those after several h of dialysis when using membranes that were not equilibrated with the feed solution (compare Table 1 and Tables S5 and S6). Overall, the Cl-/SO42- selectivities are orders of magnitude lower than the K+/Mg2+ selectivities we determined previously with coated membranes [24,25].

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Table 1. Cl and SO4 fluxes and Cl /SO4 selectivities during ED and DD through (PSS/PAH)5PSScoated and bare Fujifilm AEMs equilibrated for 24 h with the source-phase solution, which contained 0.01 M NaCl and 0.01 M Na2SO4. The receiving phase was initially 0.01 M Na2CO3, and the current density -2 was 1.13 mA cm in ED.

ED DD

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SO42- Flux (nmol cm-2 s-1) 5.57 ± 0.26 0.91 ± 0.09 3.70 ± 0.22 0.31 ± 0.16

Selectivity

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Cl- Flux (nmol cm-2 s-1) 7.38 ± 0.31 6.72 ± 0.13 6.12 ± 0.12 1.47 ± 0.20

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We confirmed the attainment of steady-state transport through the equilibrated AEMs (coated with (PSS/PAH)5PSS films and subsequently soaked in feed solution for 24 h) during 6 h of ED under a constant applied current. In these experiments, we changed the solutions in the source, receiving and isolated phases after every 2 h of electrodialysis. Fluxes increase marginally over the course of the experiment, whereas the selectivity shows no significant change (see Figure S6). The supplementary material shows that previously reported high K+/Mg2+ selectivities of PEM-coated membranes [23-25] are not an artefact of lag times.

3.3. Effect of source-phase concentrations on Cl- and SO42- transport through bare and (PAH/PSS)5PSS-coated Fujifilm anion-exchange membranes

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If charge screening or ion adsorption in polyelectrolyte films affects anion transport through (PAH/PSS)5PAH coatings, Cl-/SO42- selectivities may vary significantly with source-phase ion concentrations [23,55,56]. Moreover, limiting currents and partitioning into the underlying IEM will also vary with concentration [12,22,57]. To investigate the effect of source-phase concentration on fluxes and selectivity, we performed DD and ED with Cl- and SO42- source-phase concentrations ranging from 0.005 to 0.1 M, but the receiving and isolated phases always contained 0.01 M Na2CO3, and in ED the current density was always 1.13 mA cm-2. We did not investigate higher source-phase salt concentrations because of the low solubility of Na2SO4. Figure 5(A) plots steady-state DD anion fluxes through bare AEMs as a function of the feed concentration. The Cl- flux increases monotonically from 4.0 to 30 nmol cm-2 s-1 as the source-phase concentrations of NaCl and Na2SO4 rise from 0.005 to 0.1 M. In contrast, the SO42- flux is relatively invariant with concentration, so the Cl-/SO42selectivity increases from 1.3 to 13 over this source-phase concentration range, even with a bare membrane (see Table S7 for flux values).

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(B) 10

Chloride Ions 137 9 Sulfate Ions 8 7 6 5 27 4 3 5.3 2 3.9 1 0 0 0.02 0.04 0.06 0.08 0.1 0.12 Source-Phase Cl- and SO42- Concentration (M)

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Ion Flux (nmol/cm2/s)

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Figure 5. Plots of ion fluxes versus source-phase concentrations for DD through (A) bare AEMs and (B) AEMs coated with (PAH/PSS)5PSS films. The source phase contained equal concentrations of Cl and SO42-, and the receiving and isolated phases contained 0.01 M Na2CO3. Numbers above the data points indicate the selectivity at that concentration.

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In DD through (PAH/PSS)5PSS-coated AEMs, Cl- fluxes are around 25% of those through bare AEMs (compare Figures 5(A) and 5(B)), and the Cl- flux again increases monotonically with concentration. Thus, the coating provides significant resistance to Cltransport. However, SO42- flux through the coated membranes declines significantly at high concentrations (see Table S7). Thus, the Cl-/SO42- selectivity increases from 3.9 to 140 on going from source-phase salt concentrations of 0.005 M to 0.1 M, and selectivity is an order of magnitude higher than with bare membranes at the highest source-phase salt concentrations.

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ED shows trends similar to those in DD (see Figure S7 and Table S8). The Cl-/SO42selectivity rises from 1.1 to 11 for bare membranes and from 7.2 to 70 for (PAH/PSS)5PSS-coated membranes when the source-phase salt concentrations increase from 0.005 to 0.1 M. For the bare membrane, however, the applied current in ED does not greatly increase fluxes relative to DD, so most of the transport likely occurs due to diffusion even with the applied current. In contrast, for the coated membranes ED fluxes are 2 to 7 times the fluxes in DD. Despite higher fluxes in ED, at source-phase salt concentrations of 0.005 or 0.01 M, Cl-/SO42- selectivities are higher in ED than in DD through (PAH/PSS)5PSS-coated membranes. This is not the case at the higher concentrations, however. We also investigated the selectivity in DD and ED with source-phase solutions containing unequal concentrations of NaCl and Na2SO4 (Table 2). When the source phase contained 0.01 M NaCl and 0.1 M Na2SO4, in ED the Cl-/SO42- flux ratio was 1.7, which implies a Cl-/SO42- selectivity of 17. Bare AEMs show a selectivity of only 3.2 with this source phase. We performed DD with the same source phase, and the Cl-/SO42selectivity was 28 for a coated membrane and 4.3 for a bare membrane.

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Table 2. Cl /SO4 selectivities in DD and ED through bare and (PSS/PAH)5PSS-modified Fujifilm AEMs for source phases containing unequal concentrations of NaCl and Na2SO4. Each of the receiving and -2 isolated phases contained 0.01 M Na2CO3, and the current density in ED was 1.13 mA cm . Membranes were soaked in the source phase solution for 24 h and rinsed with water prior to the experiment.

0.01 M Cl-, 0.1 M SO42-

DD ED DD

0.1 M Cl-, 0.01 M SO42-

ED

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Selectivity

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4.3 ± 0.1 27.9 ± 5.0 3.2 ± 0.1 17.3 ± 2.4 9.9 ± 1.0 >200 8.4 ± 1.1 >81

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In the reciprocal ED experiment, when the source phase contained 0.1 M NaCl and 0.01 M Na2SO4, the Cl-/SO42- flux ratio was always >810 so the Cl-/SO42- selectivity was >81. The bare AEMs show an ED selectivity of 8.4 under these conditions. In DD with excess Cl-, the SO42- flux through coated membranes was undetectable giving a Cl-/SO42selectivity of >200. Overall, selectivities are much higher with excess Cl- in the source phase than with excess SO42- in the source phase. Table S9 gives Cl- and SO42- fluxes for experiments with unequal concentrations in the source phase.

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3.4. Effect of source-phase concentrations on Cl- and SO42- partitioning in bare and (PAH/PSS)5PSS-coated AEMs

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Figure 5 and Figure S7 show that both ED and DD Cl-/SO42- selectivities increase with increasing source-phase salt concentrations. One possible mechanism for this trend is that higher salt concentrations favor Cl- partitioning into the membrane. To examine partitioning in bare and coated AEMs, we immersed membranes for 3 days in the feed solution (including changing to fresh solutions every 24 h) to reach equilibrium partitioning. After equilibration, we rinsed the membranes with deionized H2O from a squirt bottle for ∼5-7 seconds to remove excess solution and then placed the membranes in 50-mL solutions containing 0.1 M Na2CO3 and 0.01 M NaHCO3 for 2 days to displace the Cl- and SO42- from membranes into the solution. We then determined the concentrations of Cl- and SO42- with ion chromatography and divided the amount of each ion in the membrane by the swollen membrane volume. The volume of the swollen membrane was determined from the thickness (∼110 µm from optical microscopy) and diameter (∼2.6 cm) of the wet membrane.

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Figure 6. Chloride (blue squares) and sulfate (red circles) concentrations in AEMs after immersion in solutions containing different concentrations of equimolar NaCl and Na2SO4. Dashed and solid lines show simulated concentrations in the membrane calculated using the Donnan and extended Donnan models, respectively (see below). Table S10 gives original data for coated and bare membranes.

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Figure 6 shows the extent of Cl- and SO42- partitioning into AEMs from different solutions. At equimolar salt concentrations of 0.005 M in solution, the ratio of SO42- to Cl- is around 4.5 in the membrane. In contrast, with 0.1 M NaCl and 0.1 M Na2SO4 in solution, the ratio of SO42- to Cl- in the membrane is only 0.6. The number of anions in the substrate AEM is much greater than in the (PAH/PSS)5PSS film because the AEM is 3 orders of magnitude thicker than the coating. Thus, partitioning into coated and bare membranes is the same (see Table S10 for data) because the AEM is in equilibrium with the external solution with or without the coating. Moreover, the equal partitioning in bare and coated membranes suggests that slow diffusion through the coating did not prevent attainment of equilibrium. Increased Cl-/SO42- partitioning ratios at higher salt concentrations are consistent with trends in Cl-/SO42- transport selectivities. However, the ratio of Cl- to SO42- partitioning into the membranes increases 7.5-fold on going from 0.005 M to 0.1 M salts in the solution, whereas the DD Cl-/SO42- selectivity through a coated membrane increases 35-fold under the same conditions.

3.5. Selectivities of membranes coated on only one side. Coating membranes on only one face (rather than on both sides) may decrease their resistance to mass transport. Thus, we examined the DD and ED ion fluxes through one-side-coated membranes with the coating facing toward either the source or

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receiving phases. The difference in selectivities for the two configurations is dramatic. In DD, the Cl-/SO42- selectivity increases from 27 to 140 when the coating faces the receiving phase rather than the source phase (Figure 7). Unfortunately, lower fluxes accompany higher selectivities. ED also shows higher Cl-/SO42- selectivities and lower fluxes when the coating faces the receiving phase (Figure S8). Moreover, AEMs with the coating only on the receiving side show similar fluxes and selectivities as membranes with the coating on both sides. Modeling studies (next section) are consistent with these trends.

27.1 ± 1.6

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Figure 7. Cl and SO4 fluxes through AEMs in DD experiments with different configurations of (PAH/PSS)5PSS coating. The source phase contained 0.1 M NaCl and 0.1 M Na2SO4, whereas receiving 2and isolated phases contained 0.01 M Na2CO3. The numbers above the bars are the Cl /SO4 2selectivities. Note the different scales for Cl and SO4 fluxes. Membranes were soaked in the sourcephase solution for 24 h and rinsed with water prior to the experiments.

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3.6. Modelling of transport in DD

Modelling of transport through bare and coated membranes is vital to understanding the mechanisms behind trends in partitioning, fluxes, and selectivities. The transport model should explain the following phenomenon: 1. The ratio of Cl- to SO42- partitioning in the membrane increases with the concentrations of NaCl and Na2SO4 in solution. 2. The Cl-/SO42- selectivity in DD is an even stronger function of source-phase solution concentration than the partitioning selectivity. 3. Selectivities are higher in excess chloride than in excess sulfate. 4. Placing the coating on the receiving-phase side leads to higher transport selectivities than placing the coating on the source-phase side.

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Such transport phenomena are interesting yet difficult to understand because ion transport through a coated membrane includes diffusion in solution boundary layers, permeation through the coatings, and partitioning and diffusion in the ion-exchange membrane. Moreover, spontaneously arising potentials give rise to significant electromigration even under conditions of zero electric current (DD). Figure 8 describes the transport model.

Electromigration / ,2 *  - + 01 ,.

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Figure 8. Qualitative drawing of the simulated Cl (red lines) and SO4 (black lines) concentration profiles in the solution boundary layers, polyelectrolyte multilayers (PEMs), and anion-exchange membrane (AEM) during diffusion dialysis through a (PSS/PAH)5PSS-coated membrane. The source phase contained 0.1 M NaCl and 0.1 M Na2SO4, and the receiving phase was 0.01 M Na2CO3. We considered ion transport from diffusion and electromigration in each layer of the system. Simulations show that the spontaneously arising electric field causes electromigration fluxes that are opposite in direction to the 2diffusive fluxes for Cl and SO4 . We used a virtual solution to model ion transport in PEMs and an extended Donnan model to describe partitioning behavior at the PEM/AEM interface. Transport modelling within the boundary layers and AEM employed the Nernst-Planck equation. Figure S12 of the 2supporting information quantitatively shows the simulated concentration profiles, including those for CO3 + and Na .

The parameters needed to describe transport include ion diffusion coefficients in solution boundary layers [58,59], the solution boundary-layer thicknesses, permeability coefficients in the coatings, partition coefficients in the ion-exchange membrane, and diffusion coefficients in the ion-exchange membrane. We used an extended Donnan model to describe ion partitioning at the two sides of the AEM, and we roughly estimated diffusion coefficients in the AEMs using literature values [60]. The simulations employ solution ion-diffusion coefficients at infinite dilution and assume a boundary layer thickness of 100 µm in the stirred solutions. We also performed

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diffusion dialysis through (PAH/PSS)5PSS coatings on porous alumina membranes to estimate ion permeability coefficients in the coatings (see the supplementary material for details).

3.6.1. Modelling of partitioning phenomena with an extended Donnan model

$"7 $"8

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The Donnan model of ion partitioning into AEMs assumes that (a) the ion electrochemical potentials are the same in the exterior solution and in the membrane, (b) activity coefficients are unity, and (c) standard-state ion chemical potentials are equal inside and outside the membrane [61,62]. Equation (3) defines the partition coefficient, Γ , for a specific ion 4 , where 5 is the ion concentration in the membrane and 6 is the ion concentration in solution. (3)

The assumptions of the Donnan model (see the supplementary material) lead to the equation 9"

Γ Γ 9

(4)

where  is the charge on ion 4 and  is the charge on ion 1. For a three-ion system, substituting the expressions from equations (3 and 4) into the electroneutrality condition inside the ion-exchange membrane leads to 9!

9;

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In equation (5) <5 is the concentration of fixed-charge sites in the membrane, and < is the charge on these sites. For mixtures of NaCl and Na2SO4, this is a cubic equation that yields Γ . Subsequently, one can determine Γ and Γ from equation (4) and all of the concentrations in the membrane from equation (3). With a fixed charge concentration of 1.03 M in the membrane (as estimated from the total counterion charge in the membrane in Figure 6 at the lowest concentration), the Donnan model gives the estimates in Figure 6 (dashed lines) for Cl- and SO42- concentrations in the membrane as a function of the solution concentrations of NaCl and Na2SO4. Although the model shows increased partitioning of Cl- and decreased partitioning of SO42- at higher salt concentrations in solution, it always shows preferential SO42- partitioning and significantly underpredicts the Cl-/SO42- ratio in the membrane. As Figure 6 shows, the Donnan model is insufficient to fit the experimental data. The deviations of experimental partitioning data from the Donnan model are especially large for Cl-, which shows a ~2-fold higher level of partitioning than the model predicts. To account for this difference, we chose to relax the constraint of equal ion standard-state chemical potentials in the membrane and the solution. Physically this means that for a given ion, solvation energies are not the same in the membrane and the solution. Relaxing this assumption gives rise to equation (6) where > is the partition coefficient for ion 4 based only on standard state chemical potentials (see the supplementary material).

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9" 9

Γ ?Γ @

A

9  " 9

(6)

A"

Substituting this expression into the electrical neutrality condition gives 9

9  !

! A 9   6 Γ 9 A!



9

9  ;

; A 9  6 Γ 9 A;

 < <5 0

(7)

Because we do not know the values of > , >, and >, we used

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 : Γ

A

9  ! 9

A!

and

A

9  ; 9

A;

as two fitting

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parameters to match this extended Donnan model to the experimental partitioning data, which include 4 points each for Cl- and SO42-. Figure 6 shows the fit of this model to the experimental data. Clearly the extended Donnan model fits the data better than the classical Donnan model, which one would expect with the addition of two fitting parameters. (Because of the low amount +

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of Na in the membrane, the fitting is not very sensitive to the value of +

A

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A;

when ions 1, 2, and

and Na , respectively, so there is essentially one fitting parameter

A

9  ! 9

A!

.) In

summary, an extended Donnan model is crucial to fit the partitioning data, but it underpredicts the Cl- concentration in the membrane at the highest solution concentration. Other models may also describe the partitioning data [63-65].

3.6.2. Selectivity as a function of source-phase concentration

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With approximate parameters in hand, we simulated DD fluxes through bare and coated membranes as a function of source-phase Cl- and SO42- concentrations and compared trends in calculated and experimental data. For bare membranes (Figure 9), calculated and experimental Cl- and SO42- fluxes usually agree to within 20%, suggesting that the simulation parameters including boundary layer thicknesses, the extended Donnan model, and the ion diffusion coefficients in the AEM are reasonable first-order approximations. However, the model underestimates the Cl- flux when source-phase Cland SO42- concentrations are 0.1 M, in large part because the extended Donnan model underestimates Cl- partitioning into the AEM at this concentration (see Figure 6).

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0 0.02 0.04 0.06 0.08 0.1 2Source-Phase Cl and SO4 Concentration (M) Figure 9. Chloride (blue squares) and sulfate (red circles) DD fluxes through bare AEMs as a function of 2source-phase Cl and SO4 concentrations. Dashed lines show fluxes simulated using a solutiondiffusion/electromigration model. The receiving phase contained 0.01 M Na2CO3.

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For coated membranes (Figure 10), the model again underestimates Cl- fluxes at higher concentrations, probably due to the aforementioned underprediction of Cl- partitioning at high salt concentrations. In contrast, calculated SO42- fluxes match experimental data well at 0.1 M concentrations of Cl- and SO42- in the feed, but at low concentrations simulated SO42- fluxes are only 20% of the experimental value. This may suggest a concentration-dependent sulfate permeance in the polyelectrolyte film or perhaps underestimation of the SO42- permeance (see the supplementary material surrounding Table S11 for further discussion). Additionally, the film structure and, hence, the ion permeances may differ for coatings on porous alumina and on an AEM. Simulations with a 2-fold increase in the sulfate (and carbonate) PEM permeances show much better agreement with experimental sulfate fluxes (Figure 10). Given the much better agreement with experiment, the rest of this section describes simulations with the doubled sulfate (and carbonate) permeance.

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Cl Cl⁻⁻ 2SO SO₄4₄ ²⁻⁻

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0 0.02 0.04 0.06 0.08 0.1 Source-Phase Cl- and SO42- Concentration (M) Figure 10. Chloride (blue squares) and sulfate (red circles) DD fluxes through (PAH/PSS)5PAH-coated 2AEMs as a function of source phase Cl and SO4 concentrations. Dashed lines show fluxes simulated using a solution-diffusion-electromigration model. Solid lines show fluxes simulated using the same model 22but with a 2-fold increase in the SO4 and CO3 permeance in the coating. The receiving phase contained 0.01 M Na2CO3.

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Figure 11. Concentration dependence of experimental and calculated Cl /SO4 selectivities in DD through (PAH/PSS)5PSS-coated membranes. The error bars in experimental data represent standard deviations of experiments with at least 3 membranes. At 0.1 M salt concentrations, the error bar is relatively large 2because the SO4 flux is small and the selectivity is high.

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As Figure 11 shows, although calculations and experiment do not provide quantitative agreement in selectivities, trends are the same. Thus, the simulations may provide insight into why selectivity increases at higher salt concentrations. The ratios of the assumed Cl- and SO42- diffusion coefficients were only 2 in the boundary layers and AEM, and Cl-/SO42- partitioning selectivities in the AEM are at most 1.2. Additionally, polyelectrolyte coatings show a Cl-/SO42- permeance ratio of only 15 (and this is only 8 when we use the doubled SO42- permeance), so based on a series resistance model, one would expect an overall selectivity <15. Nevertheless, simulated Cl-/SO42selectivities reach 48 with a feed containing 0.1 M NaCl and 0.1 M Na2SO4, and the experimental selectivity is 140 (Figure 11).

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In the AEM, the higher-than-expected selectivities stem largely from the spontaneously arising electric fields that induce electromigration, which decreases the net Cl- and SO42fluxes and increases the magnitudes of the Na+ and CO32- fluxes to maintain zero current in DD. Figure 12 shows the simulated Cl- and SO42- diffusive and electromigration flux components as well as net fluxes in the AEM. Although electromigration flux components are negative for both Cl- and SO42-, the absolute value of the ratio of electromigration to diffusion flux is higher for SO42-. Electromigration affects SO42- especially strongly because it is a divalent anion with a concentration (in the AEM) that is high compared to its concentration gradient. When the source phase contains 0.005 M NaCl and 0.005 M Na2SO4, the simulation shows a Cl-/SO42- diffusive flux ratio of ~5 and an overall selectivity of ~7. Such an enhancement of selectivity due to electromigration is more evident at higher source-phase concentrations. With 0.1 M NaCl and Na2SO4 source-phase concentrations, electromigration increases the selectivity from 7 to 48. The higher source-phase salt concentrations lead to higher Cland SO42- diffusive flux components (Figure 12) that require larger electric fields to maintain zero current. Importantly, the high electric fields at high concentrations result in very low SO42- fluxes. In the coatings and solution-boundary layers, the combination of different concentration gradients and electromigration maintain the same selectivity and flux as in the AEM (see Table S13 and Figures S9-S12).

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N Axis Title N Figure 12. Simulated average diffusion (jC ) and electromigration (jDE ) flux components, and net fluxes (j) 2for Cl and SO4 in the AEM. The source phases contained (A) 0.005 M NaCl and Na2SO4 (B) 0.01 M NaCl and Na2SO4 (C) 0.03 M NaCl and Na2SO4 or (D) 0.1 M NaCl and Na2SO4. The receiving phase always contained 0.01 M Na2CO3.

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3.6.3. Changes in selectivity with different ratios of Cl- and SO42- in the source phase.

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In experiments with 0.01 M NaCl and 0.1 M Na2SO4 in the source phase, the Cl-/SO42flux ratio was 2.8 in DD, which implies a Cl-/SO42- selectivity of 28. However, when the source phase contained 0.1 M NaCl and 0.01 M Na2SO4, the Cl-/SO42- flux ratio was ≥ 2000, which gives a Cl-/SO42- selectivity ≥ 200. Simulations shows a similar trend, in large part due to electromigration. When comparing Cl- and SO42- transport with excess Cl- in the source phase, in the AEM electromigration offsets a much larger fraction of the diffusive flux component for SO42- than for Cl- (Figure 13A). Thus, the overall simulated selectivity (using concentration-normalized fluxes) is 69 whereas the diffusive flux selectivity is only 25. With excess SO42- in the source phase, the spontaneously arising electric field becomes smaller and electromigration increases overall selectivity only moderately (from 11 to 15). In the solution and coating layers, the combination of different concentration gradients and electromigration leads to the same fluxes as in the AEM. Table S14 lists the simulated diffusive, electromigration, and net fluxes in the coatings, AEM, and solution boundary layers. Figures S13 and S14 provide calculated concentration profiles.

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Figure 13. Simulated average diffusive and electromigration flux components, and net fluxes for Cl and 2SO4 in the AEM when the source phase contains (A) 0.1 M NaCl and 0.01 M Na2SO4 or (B) 0.01 M NaCl and 0.1 M Na2SO4.

Why is the electric field in the AEM smaller with excess SO42- in the source phase? The electric field arises to push Cl-, CO32-, and SO42- toward the source phase and Na+ toward the receiving phase to maintain zero-current in DD. In the case of excess Cl- in

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3.6.4. Coating only one face of the membrane.

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the source phase (and in the AEM), the electric field must be high to counteract its diffusion. Note that Cl- has a higher diffusion coefficient than both SO42- and CO32- (we assumed that the two divalent anions have the same partitioning and diffusion coefficients in the AEM). With excess SO42- in the source phase (and an even higher concentration of Na+ in this phase), a smaller electric field is needed to achieve zero current because SO42- is a divalent ion and the membrane also contains more Na+. This is an oversimplification because transport depends on the boundary layer, coatings, and AEM, and other layers affect concentrations in the AEM.

4. Conclusions

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For membranes coated on only one side, the experimental selectivity when the coating faces the receiving phase is 5 times that when the coating faces the source phase. This drastic difference is unexpected for a resistance in series model. Modelling results show the same trends as the experiment and again suggest that spontaneously arising electric fields underlie the drastically different transport phenomena. Figure S15 shows the simulated diffusive and electromigration flux components along with the net flux in the AEM. When the (PSS/PAH)5PSS coating is only on the receiving phase side, electromigration increases the selectivity in the AEM from 6 to 54. However, when the (PSS/PAH)5PSS coating is only on the source phase side, enhancement of selectivity by electromigration is modest (from 6 to 10). Figures S16-S17 show the concentration profiles for the coating facing the receiving and the source phase, respectively, and Table S15 gives average flux components in the different regions of the membrane.

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Alternating adsorption of PSS and PAH on Fujifilm AEMs significantly increases Cl/SO42- transport selectivities to values as high as 140 in diffusion dialysis. For (PAH/PSS)5PAH-coated membranes initially loaded with Cl-, attainment of steady-state transport requires several hours because of the low film permeability to SO42-. Steadystate transport selectivities increase an order of magnitude on increasing the NaCl and Na2SO4 concentrations from 0.005 to 0.1 M. Moreover, selectivities are an order of magnitude higher when the source phase contains an excess of Cl- rather than an excess of SO42-. Finally, with membranes coated on only one face, selectivity is an order of magnitude higher when the coating faces the receiving rather than the source phase. Modelling such phenomena is complicated because it includes transport through two boundary layers, two coatings, and the AEM, and partitioning into the AEM is a function of concentration. Nevertheless, trends in fluxes and selectivities are the same in simulations and experiments. Simulations suggest that under conditions of high selectivity, electromigration disproportionately decreases SO42- flux in the AEM due to the 2- charge and a high concentration of SO42- in the AEM. These results indicate the need to consider the specific feed and permeate concentrations when designing

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separations with both bare and coated AEMs and CEMs. The high selectivities of coated membranes may potentially prove useful in separations such as purification of acids [66,67], recovery of phosphate [68-70], or removal of SO42- to improve the quality of edible salt [18]. In addition, the combination of highly selective CEMs and AEMs could allow separation of salt mixtures containing divalent and/or multivalent ions [7173]. 5. Acknowledgments

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We gratefully acknowledge funding from the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences of the U.S. Department of energy through Grant DE-SC0017618. We also thank the Center for Environmental Science & Technology, University of Notre Dame for help with the anion analysis. AY acknowledges funding from the Spanish Ministry of Economy and Competitiveness through project CTM2017-85346-R. References

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26. J. Li, J. Zhu, J. Wang, S. Yuan, J. Lin, J. Shen, B. Van der Bruggen, Charge-assisted

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Prefractionation of LiCl from concentrated seawater/salt lake brines by electrodialysis with monovalent selective ion exchange membranes, J. Clean. Produc. 193 (2018), 338-350. 73. H. –F. Xiao, Q. Chen, H. Cheng, X. –M. Li, W. –M. Qin, B. –S. Chen, D. Xiao, W. –M. Zhang, Selective removal of halides from spent zinc sulfate electrolyte by diffusion dialysis, J. Membr. Sci. 537 (2017) 111-118.

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Layer-by-layer modification of aliphatic polyamide anion-exchange membranes to increase Cl-/SO42- selectivity Muhammad Ahmada, Chao Tangb, Liu Yanga, Andriy Yaroshchukc,d and Merlin L. Brueninga,b * a

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Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, United States b

Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, United States c

ICREA, pg.L.Companys 23, 08010 Barcelona, Spain

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E-mail: [email protected]

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*Corresponding author: Merlin L. Bruening

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Department of Chemical Engineering, Polytechnic University of Catalonia, av. Diagonal 647, 08028 Barcelona, Spain

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Figure S1. Dialysis apparatus diagram…………………………………………………………………………S-4 -

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Table S1. Cl and SO4 fluxes during DD through bare AEMs when using o-rings of different sizes……S-4 Figure S2. SEM images of bare (A) & (B), and (PSS/PAH)5PSS-modified (C) & (D) Fujifilm AEMs….…S5 -

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Figure S3. Amounts of Cl , NO3 , and SO4 passed to the receiving phase vs time during ED with a source phase containing 0.01 M NaCl and 0.01 M Na2SO4…………………………………………………………...S-6 2-

Table S2. NO3 and SO4 fluxes and NO3 /SO4 selectivities during ED and DD through coated Fujifilm membranes………………………………………………………………………………………………………...S-6

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Table S3. NO3- and SO42- fluxes and NO3-/SO42- selectivities through a (PSS/PAH)5PSS-coated AEM from the first to the fourth 2-h cycle of DD………………………………………………………………………..…...S-6

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Figure S4. Amounts of Cl- (triangles) and SO42- (squares) passed to the receiving phase vs time during DD through (A) a bare AEM and (B) an AEM coated with a (PSS/PAH)5PSS film……………………………..S-7 Table S4. Cl- and SO42- fluxes and Cl-/SO42- selectivities during ED and DD through coated and bare Fujifilm membranes………………………………………………………………………………………………………...S-7 -

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Table S5. Cl and SO4 fluxes and Cl /SO4 selectivities through a (PSS/PAH)5PSS-coated AEM from the first to the fourth 2-h cycle of ED……………………………………………...…………………………….…...S-8 2-

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Table S6. Cl and SO4 fluxes and Cl /SO4 selectivities through a (PSS/PAH)5PSS-coated AEM from the first to the fourth 2-h cycle of DD…………………………………………………………….…………………..S-8 -

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Figure S5. Amounts of Cl (triangles) and SO4 (squares) passed to the receiving phase vs time during ED after equilibration with the source phase………………………………………………………………………..S-8 2-

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Figure S6. Cl and SO4 fluxes for a series of three 2-h ED experiments with the same (PAH/PSS)5PSScoated AEMs……………………………………………………………………………………………………….S-9 Accounting for Lag Times in Cation-selective Membranes………………………………………………S9 -

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Table S7. Cl and SO4 fluxes and Cl /SO4 selectivities in DD through bare and (PSS/PAH)5PSSmodified Fujifilm AEMs using different source-phase concentrations…………………………………………….…….S-9 -2

Figure S7. Plots of ion fluxes versus source-phase concentrations for ED (i = 1.13 mA cm ) through (A) bare AEMs and (B) AEMS coated with (PAH/PSS)5PSS films………………………………………….......S10

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Table S8. Cl and SO4 fluxes and Cl /SO4 selectivities in ED through bare and (PSS/PAH)5PSS-coated AEMs using different source-phase concentrations…………………………………………………….....…S10 Table S9. Cl and SO4 fluxes in DD and ED through bare and (PSS/PAH)5PSS-modified Fujifilm AEMs with source phases containing unequal concentrations of NaCl and Na2SO4…………………………….S-11 -

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Table S10. Cl and SO4 concentrations and Cl /SO4 partitioning selectivities in bare and (PSS/PAH)5PSS-coated Fujifilm AEMs equilibrated with different external solutions……………………………………...….S-11 Figure S8. Cl and SO4 fluxes in ED with different configurations of (PAH/PSS)5PSS-coating………..S12

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Table S11. NaCl and Na2SO4 fluxes in single-salt diffusion dialysis through bare and (PSS/PAH)5PSScoated porous alumina membranes……………………………………………………………………………S-13 Table S12. Parameters used in the solution-diffusion/electromigration model………………...…….……S14 Donnan and Extended Donnan Models of Partitioning into Ion-exchange Membranes……..….…S15

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Figure S9. Simulated ion concentration profiles in the boundary layers, polyelectrolyte multilayers, and anion exchange membrane. The source phase contained 0.005 M NaCl and 0.005 M Na2SO4…..…..S-20

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Figure S10. Simulated ion concentration profiles in the boundary layers, polyelectrolyte multilayers, and anion exchange membrane. The source phase contained 0.01 M NaCl and 0.01 M Na2SO4………......S20 Figure S11. Simulated ion concentration profiles in the boundary layers, polyelectrolyte multilayers, and anion exchange membrane. The source phase contained 0.03 M NaCl and 0.03 M Na2SO4…………...S21 Figure S12. Simulated ion concentration profiles in the boundary layers, polyelectrolyte multilayers, and anion exchange membrane. The source phase contained 0.1 M NaCl and 0.1 M Na2SO4……………...S21 Table S14. Simulated average diffusive, average electromigration, and net fluxes in the coatings, AEM, and boundary layers for source phases containing unequal concentrations of NaCl and Na2SO4………S22

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Figure S13. Simulated ion concentration profiles in the boundary layers, polyelectrolyte multilayers, and anion exchange membrane. The source phase contained 0.1 M NaCl and 0.01 M Na2SO4………….…S23

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Figure S14. Simulated ion concentration profiles in the boundary layers, polyelectrolyte multilayers, and anion exchange membrane. The source phase contained 0.01 M NaCl and 0.1 M Na2SO4………….…S23 Figure S15. Simulated average diffusive flux and average electromigration flux components and net fluxes in the AEM when the (PSS/PAH)5PSS coating faces the (A) source and (B) receiving phase……….…S-24

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Table S15. Simulated average diffusive, average electromigration, and net fluxes in the coatings, AEM, 2and boundary layers for Cl and SO4 with different configurations of (PAH/PSS)5PSS-coating………..S25

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Figure S16. Simulated ion concentration profiles in the boundary layers, polyelectrolyte multilayers, and anion exchange membrane. The PEM is only on the side facing toward the source phase …….………S26 Figure S17. Simulated ion concentration profiles in the boundary layers, polyelectrolyte multilayers, and anion exchange membrane. The PEM is only on the side facing toward the receiving phase ……….…S26 MATLAB Code……………………………………………………………………………………………….….S-27

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Figure S1 illustrates the connection between two cells separated by a membrane. To decide whether the supporting ground glass or the o-ring defines the active membrane area, we measured DD ions fluxes through bare AEMs using two o-rings of different sizes. The source phase contained 0.01 M NaCl and 0.01 M Na2SO4. One o-ring had an inside diameter approaching the diameter of the hole in the ground glass joint, i.e. 1.5 cm. In a separate experiment the o-ring had a diameter of 2 cm. Table S1 gives the average fluxes (calculated using the area of the hole in the ground glass joint) when using the two different o-rings. If the o-rings define the active areas of the membranes, the ratio of the fluxes should be 1.8, but the experimental data show a ratio of only 1.11. Thus, although the ground glass joint may not seal perfectly against the back of the membrane, it defines the membrane area more accurately than the o-ring diameter. The experiments reported in the paper used an o-ring with an inside diameter of 2 cm but used the area of the glass joint when calculating flux. Future studies should use the smaller o-ring, but even it does not define exactly the same area as the ground glass.

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Figure S1. In the dialysis apparatus, 100 mL glass cells are clamped together with an interior o-ring, and a ground glass joint supports the membrane. -

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Table S1. Cl and SO4 fluxes during DD through bare AEMs when using o-rings of different sizes. The source phase contained 0.01 M NaCl and 0.01 M Na2SO4, and the receiving phase was initially 0.01 M Na2CO3. In both cases, the fluxes are based on the area of the opening in the ground glass.

Inside diameter of oring 2.0 cm 1.5 cm

Cl- Flux (nmol cm-2 s-1) 6.62 ± 0.26 5.98 ± 0.36

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Figure S2. SEM images of bare (A) & (B), and (PSS/PAH)5PSS-modified (C) & (D) Fujifilm anionexchange membranes

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Experiments with a source phase containing NaNO3 and Na2SO4 (rather than NaCl and Na2SO4) illustrate the replacement of Cl- to attain steady state. Figure S3 suggests that the lag time for NO3- transport through the membrane is around 5-8 min. The Clconcentration in the receiving phase increases rapidly over the first 30 min of ED as NO3- and SO42- displace these ions from the membrane. Afterward, the Cl- concentration in the receiving phase increases very slowly. In contrast, SO42- ions are detectable only during a second 2-h period of electrodialysis. Table S2 shows the measured NO3- and SO42- fluxes. During the second 2-h of electrodialysis the NO3/SO42- selectivity is 21.6 ± 4.1. The NO3- and SO42- induction times differ by more than an order of magnitude [1].

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Figure S3. Amounts of Cl (triangles), NO3 (circles) and SO4 (squares) in the receiving phase vs time during ED with a source phase containing 0.01 M NaNO3 and 0.01 M Na2SO4. The open and filled symbols represent ED through (PSS/PAH)5PSS-coated membranes during the first and second 2-h -2 experiments respectively, at a current density of 1.13 mA cm . The receiving phase and isolated anode compartments initially contained 0.01 M Na2CO3. Note the primary vertical axis is for Cl and NO3 and the 2secondary (right) vertical axis is for SO4 . The cells were emptied, rinsed and refilled with fresh solutions after the first 2 h of dialysis. -

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NO3- Flux (nmol cm-2 s-1) 8.68 ± 1.27 8.59 ± 0.54 2.59 ± 0.40 1.75 ± 0.29

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Table S2. NO3 and SO4 fluxes and NO3 /SO4 selectivities during ED and DD through coated Fujifilm membranes. The source phase contained 0.01 M NaNO3 and 0.01 M Na2SO4, the receiving phase was -2 initially 0.01 M Na2CO3, and the current density was 1.13 mA cm in ED. The cells were emptied, rinsed and refilled with fresh solutions after the first 2 h of dialysis.

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NO3- flux (nmol cm-2 s-1) 2.55 1.92 1.64 1.53

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Figure S4. Amounts of Cl (triangles) and SO4 (squares) passed to the receiving phase vs time during DD through (A) a bare AEM and (B) an AEM coated with a (PSS/PAH)5PSS film. The source phase contained 0.01 M NaCl and 0.01 M Na2SO4, and the receiving phase was initially 0.01 M Na2CO3. The filled and open symbols in (B) represents results during the first and second 2-h DD experiments, respectively. The cells were emptied, rinsed, and refilled after the first 2 hour DD. Please note different scales for Cl- and SO42- in (B). Table S4. Cl- and SO42- fluxes and Cl-/SO42- selectivities during ED and DD through coated and bare Fujifilm membranes. The source phase contained 0.01 M NaCl and 0.01 M Na2SO4, the receiving phase was initially 0.01 M Na2CO3, and the current density was 1.13 mA cm-2 in ED. These membranes were not equilibrated with the source phase prior to the experiment, and the initial selectivity of coated membranes does not represent a steady state.

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To reach a steady state, we performed several consecutive 2-h ED and DD experiments with the same membrane. With a source phase containing 0.01 M NaCl and 0.01 M Na2SO4, the observed Cl-/SO42- selectivity decreased from 65 to 8 on going from the 1st to 4th 2-h of ED (see Table S5). Similar trends appeared in DD, where the Cl-/SO42selectivity declined from >200 to 10 at the end of 8 h of DD (See Table S6). In DD with a source phase containing 0.01 M NaNO3 and 0.01 M Na2SO4, the NO3-/SO42- selectivity declined from >200 to 14 at the end of the 4th 2h of DD (see Table S3).

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Table S5. Cl and SO4 fluxes and Cl /SO4 selectivities through a (PSS/PAH)5PSS-coated AEM from the first to the fourth 2-h cycle of ED. The source phase contained 0.01 M NaCl and 0.01 M Na2SO4, whereas -2 receiving and isolated phases were initially 0.01 M Na2CO3. The applied current was 1.13 mA cm . The cells were rinsed and fresh solutions were refilled after every 2 h of dialysis.

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Total µMoles (Receiving)

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Table S6. Cl and SO4 fluxes and Cl /SO4 selectivities through a (PSS/PAH)5PSS-coated AEM from the first to the fourth 2 h cycle of DD. The source phase contained 0.01 M NaCl and 0.01 M Na2SO4, whereas receiving and isolated phases contained 0.01 M Na2CO3 in a 3-compartment cell. The cells were rinsed and fresh solutions were refilled after every 2 h of dialysis.

60

AC C

40 20 0

0

-

20

40

60

80

100

120

Time (min) 2-

Figure S5. Amounts of Cl (triangles) and SO4 (squares) passed to the receiving phase vs time during ED with a source phase containing 0.01 M NaCl and 0.01 M Na2SO4. The filled and open symbols represent ED through (PAH/PSS)5PSS-coated and bare AEMs, respectively, at a current density of 1.13 -2 mA cm . Coated membranes were soaked overnight in 0.01 M NaCl, 0.01 M Na2SO4 and rinsed with deionized water prior to dialysis. The receiving phase and isolated anode compartments initially contained 0.01 M Na2CO3.

S-9

ACCEPTED MANUSCRIPT

Chloride ions Sulfate ions 62.8 ± 5.5 70.7 ± 5.4

25 20

0.6 0.5

64.9 ± 4.4

0.4 0.3

10

0.2

5

0.1

0

0

1st 2h

2nd 2h

3rd 2h

SC

Electrodialysis Experiment -

RI PT

15

SO42- Flux (nmol/cm2/s)

Cl- Flux (nmol/cm2/s)

30

2-

M AN U

Figure S6. Cl and SO4 fluxes for a series of three 2 h ED experiments with the same (PAH/PSS)5PSScoated AEMs. Source-phase, receiving-phase, and isolated-phase solutions were replaced after every 2 h. The source phase contained 0.1 M NaCl and 0.1 M Na2SO4, and the applied current density was 1.13 -2 2mA cm . The numbers above the bars are the Cl /SO4 selectivities for experiments with three different membranes. Note the different scales for Cl- and SO42- fluxes.

Accounting for Lag Times in Cation-selective Membranes

TE D

The slow approach to steady-state in anion transport made us concerned as to whether some of our previously reported high selectivities with coated CEMs represented a steady-state selectivity [2-4]. Thus, we also performed ED with Nafion CEMs coated with (PAH/PSS)5PAH films. In these ED experiments, we equilibrated membranes with the feed solution (0.01 M KNO3, 0.01 M Mg(NO3)2) for 3 days. The receiving phase was 0.01 M HNO3. Even after 3 days of equilibration with the feed solution, in ED the Mg2+ flux was undetectable, whereas the K+ flux was 5.5 ± 0.4 nmol cm-2 s-1, yielding a K+/Mg2+ selectivity of >1000.

AC C

EP

Table S7. Cl- and SO42- fluxes and Cl-/SO42- selectivities in DD through bare and (PSS/PAH)5PSSmodified Fujifilm AEMs. Each of the receiving and isolated phases contained 0.01 M Na2CO3. The membrane was soaked in the source-phase solution for 24 h and rinsed with deionized water prior to the experiment.

Cl- and SO42Source-Phase Concentrations 0.005 M 0.01 M 0.03 M 0.1 M

Membrane

Cl- Flux (nmole cm-2 s-1)

SO42- Flux (nmole cm-2 s-1)

Selectivity

Bare Coated Bare Coated Bare Coated Bare Coated

4.00 ± 0.08 0.89 ± 0.08 6.12 ± 0.12 1.47 ± 0.20 13.70 ± 1.84 3.14 ± 0.15 30.0 ± 1.9 8.14 ± 0.39

3.02 ± 0.03 0.23 ± 0.02 3.70 ± 0.22 0.31 ± 0.16 3.51 ± 0.54 0.13 ± 0.04 2.30 ± 0.19 0.06 ± 0.01

1.32 ± 0.02 3.9 ± 0.7 1.66 ± 0.08 5.3 ± 1.7 3.91 ± 0.10 27.2 ± 9.8 13.0 ± 0.4 137 ± 31

S-10

ACCEPTED MANUSCRIPT

30

Sulfate Ions

(B)

11

25 2.8

20 15

1.3 10 1.1 5

20

Sulfate Ions 15 12 10 5 0

0

69

Chloride Ions

7.4 7.2

RI PT

35

Chloride Ions

Ion Flux (nmol/cm2/s)

Ion Flux (nmol/cm2/s)

(A) 40

0 0.02 0.04 0.06 0.08 0.1 0.12 Source-Phase Cl- and SO42- Concentration (M)

0 0.02 0.04 0.06 0.08 0.1 0.12 Source-Phase Cl- and SO42- Concentration (M)

-2

-

2-

-

2-

M AN U

SC

Figure S7. Plots of ion fluxes versus source-phase concentrations for ED (i = 1.13 mA cm ) through (A) bare AEMs and (B) AEMs coated with (PAH/PSS)5PSS films. The source phase contained equal 2concentrations of Cl and SO4 , and the receiving and isolated phases containing 0.01 M Na2CO3. Numbers above the data points indicate the selectivity at that concentration.

Table S8. Cl and SO4 fluxes and Cl /SO4 selectivities in ED through bare and (PSS/PAH)5PSS-coated AEMs. The source-phase concentration varied as shown, but each of the receiving and isolated phases -2 contained 0.01 M Na2CO3. The applied current density was 1.13 mA cm . The membrane was soaked in the source-phase solution for 24 h and rinsed with deionized water prior to the experiment.

0.01 M 0.03 M

Bare Coated Bare Coated Bare Coated Bare Coated

AC C

0.1 M

Cl- Flux (nmole cm-2 s-1)

TE D

0.005 M

Membrane

EP

Cl- and SO42Source-Phase Concentrations

5.17 ± 0.41 6.39 ± 0.06 7.38 ± 0.31 6.72 ± 0.13 17.1 ± 1.7 10.06 ± 0.46 34.11 ± 1.63 19.37 ± 0.37

S-11

SO42- Flux (nmole cm-2 s-1)

Selectivity

4.74 ± 0.47 0.88 ± 0.05 5.57 ± 0.26 0.91 ± 0.09 6.04 ± 0.42 0.87 ± 0.13 3.13 ± 0.12 0.28 ± 0.02

1.09 ± 0.02 7.2 ± 0.3 1.32 ± 0.01 7.4 ± 0.6 2.82 ± 0.16 11.8 ± 2.2 10.9 ± 0.2 69.3 ± 5.2

ACCEPTED MANUSCRIPT

-

2-

Table S9. Cl and SO4 fluxes in DD and ED through bare and (PSS/PAH)5PSS-modified Fujifilm AEMs with source phases containing unequal concentrations of NaCl and Na2SO4. Each of the receiving and isolated phases contained 0.01 M Na2CO3. The membrane was soaked in the source-phase solution for 24 h and rinsed with deionized water prior to the experiment.

DD

0.1 M Cl- + 0.01 M SO42-

DD

-

Bare Coated Bare Coated Bare Coated Bare Coated

ED

ED

2-

-

2-

Flux (nmol cm-2 s-1) 6.61 ± 0.12 0.57 ± 0.09 11.34 ± 0.57 2.65 ± 0.28 0.361 ± 0.064 No Detected 0.695 ± 0.11 0.018 ± 0.008

RI PT

0.01 M Cl- + 0.1 M SO42-

Flux (nmol cm-2 s-1) 2.85 ± 0.07 1.55 ± 0.06 3.62 ± 0.29 4.54 ± 0.21 35.16 ± 3.17 7.40 ± 0.53 57.76 ± 5.04 18.38 ± 0.77

SC

Source-Phase Conc.

M AN U

Table S10. Cl and SO4 concentrations and Cl /SO4 partitioning selectivities in bare and (PSS/PAH)5PSS-coated Fujifilm AEMs equilibrated with different external solutions.

AC C

EP

TE D

ClSO42Cl- and SO42Concentration Concentration Concentrations Membrane in Membrane in Membrane in Solution (mM) (mM) Bare 106.8 ± 11.4 465.8 ± 37.3 0.005 Coated 100.4 ± 8.4 442.3 ± 27.0 Bare 148.0 ± 13.1 448.1 ± 37.2 0.01 Coated 140.8 ± 10.3 426.4 ± 23.0 Bare 260.8 ± 17.5 388.1 ± 26.1 0.03 Coated 246.6 ± 11.7 365.1 ± 17.3 Bare 479.7 ± 40.2 294.4 ± 18.7 0.1 Coated 470.8 ± 29.6 281.9 ± 14.6

S-12

Cl-/SO42Selectivity 0.23 ± 0.01 0.23 ± 0.00 0.33 ± 0.01 0.33 ± 0.01 0.67 ± 0.01 0.68 ± 0.01 1.63 ± 0.06 1.67 ± 0.06

10.9 ± 0.2

35

Chloride Ions

17.6 ± 2.5

4

Sulfate Ions

30

3 58.6 ± 5.7

20

69.3 ± 5.2

RI PT

25

2

15 10

1

5 0 1

Bare AEM

2 Source Side

SC

Cl- Flux (nmol/cm2/s)

40

3 Receiving

Side

SO42- Flux (nmol/cm2/s)

ACCEPTED MANUSCRIPT

0

4 Both Sides

-

M AN U

Configuration of (PSS/PAH)5PSS-Coating 2-

Figure S8. Cl and SO4 fluxes in ED experiments with different configurations of (PAH/PSS)5PSScoating. The source phase contained 0.1 M NaCl and 0.1 M Na2SO4, whereas the receiving and isolated -2 phases contained 0.01 M Na2CO3. The applied current was 1.13 mA cm . The numbers above the bars 22are the Cl /SO4 selectivities. Note the different scales for Cl and SO4 fluxes.

TE D

Permeance Measurements and Determination of Permeability Coefficients

To estimate the ion permeability coefficients in (PAH/PSS)5PSS coatings, we prepared such films on porous alumina membranes. Ion fluxes in diffusion dialysis through these composite membranes depend on both the PEM and the alumina support. In each of these membrane regions, equation (S-1) describes the salt flux, P, where ∆ is the concentration gradient across the region and R is the local permeance. (S-1)

EP

P R∆

AC C

According to the series resistance model, equation (S-2) describes the permeance of the PEM, RSTU , where RVWUXW:Y is the permeance of the PEM-coated membrane and R:ZXXW[ is the permeance of the bare alumina. RSTU

\]^_`^a"bc \ad``^eb

(S-2)

\ad``^eb \]^_`^a"bc

We calculated the values of RVWUXW:Y and R:ZXXW[ for NaCl and Na2SO4 using equation (S-2) and the experimental data in Table S11. Equation (S-2) then reveals that the permeance of the PEM, RSTU , is 6.15 µm/s for NaCl. In contrast, the PEM permeance to Na2SO4 is 1.42 µm/s. To calculate ion permeance coefficients from salt permeance values, we used equation (S-3), which describes the salt permeance, R:T , in terms of the anion permeance, Rf, and cation permeance, RV . In this equation, f is the charge on the anion and V is the charge on the cation.

S-13

ACCEPTED MANUSCRIPT

R:T

g& \g& \]gb ]gb \g& \]gb ]gb \]gb g& \g&

(S-3)

RI PT

Equation (S-3) provides 2 independent equations to describe Rh$T and Rh! 6ij in terms of R$T , R6ij! , and Rh . We need one more independent equation to solve for those ion permeances. Previous work in our group suggests that (PAH/PSS)5PSS coatings are selective for transport of anions over cations [5]. More specifically, the transference number of Cl- was ~0.65 through PEM coatings, whereas the cation (K+) transference number was only 0.35. We assumed the same behavior for Na+ and Cl-, which provides us another independent equation to solve for R$T , R6ij! , and Rh . We determined ion permeability coefficients of 2.64 x10-11 dm2/s, 1.77 x10-12 dm2/s, and 1.42 x10-11 dm2/s for Cl-, SO42-, and Na+, respectively (previous work showed a swollen PEM coating thickness of ~30 nm). We assumed CO32- to have the same permeability coefficient as SO42.

TE D

M AN U

SC

As Figure 10 shows, the transport model significantly underestimates SO42- fluxes at lower source-phase concentrations. We suspect that we may have underestimated the SO42permeability coefficients in coatings due to possible osmosis that occurred in the ion permeance experiments. Since porous alumina membranes were used instead of AEMs, osmosis is much stronger and draws water from the receiving phase to the source phase, decreasing SO42- flux due to convection [6]. Moreover, osmosis is strongest with Na2SO4 due to the high concentration of ions and the low permeance of SO42-. We did not take osmosis into account when calculating the SO42- permeance and therefore could have underestimated its value. We arbitrarily doubled the SO42- and CO32- permeability coefficients to give better agreement with experimental data (see Figure 10). (SO42- and CO32- permeabilities in Table S12 are the doubled values.) We also tried to determine the sulfate permeability coefficient using lower source-phase concentrations in diffusion dialysis through coated porous alumina. Indeed at lower concentrations the Na2SO4 permeance of the coating was higher, but the above treatment gave negative R6ij! , so we could not use it. Table S11. NaCl and Na2SO4 fluxes in single-salt diffusion dialysis through 3 replicate bare and (PSS/PAH)5PSS-coated porous alumina membranes. The experiments employed 0.1 M salt in the source phase and deionized water in the receiving phase.

EP

Membrane

AC C

Bare Alumina 1 Bare Alumina 2 Bare Alumina 3 Coated Alumina 1 Coated Alumina 2 Coated Alumina 3

NaCl Flux (nmol/cm2/s) 57.0 54.4 58.8 31.4 28.1 29.0

S-14

Na2SO4 Flux (nmol/cm2/s) 41.5 41.0 41.8 10.5 10.6 10.8

ACCEPTED MANUSCRIPT

Table S12. Parameters used in the solution-diffusion/electromigration model.

8l! j   mn

>$T >6ij!

   og  mn

>$T >h

ml! ; 

SC

RI PT

2.03 x 10-7 1.07 x 10-7 0.96 x 10-7 1.33 x 10-7 4.61 x 10-8 2.43 x 10-8 2.18 x 10-8 3.02 x 10-8 2.64 x10-11 3.54 x10-12 3.54 x10-12 1.42 x10-11 100 30 110 1.03

M AN U

+$T (dm2 s-1) +6ij! (dm2 s-1) +$i;! (dm2 s-1) +h (dm2 s-1) k$T (dm2 s-1) + k6i! (dm2 s-1) + j k$i! (dm2 s-1) + ; k h (dm2 s-1) + R$T (dm2 s-1) R6ij! (dm2 s-1) R$i;! (dm2 s-1) Rh (dm2 s-1) Boundary layer thickness (µm) PAH/PSS coating thickness (nm) AEM swollen thickness (µm) -< (M)

a

0.178

0.122

TE D

>$T mn >$i;!

0.178

Values of +$T  , +6ij! , +$i;! , and +h are those determined in solution at infinite dilution [7,8]. k$T  was based from literature data for other AEMs [9]. We assumed that the ratios The value of + k6i! , + k $i! , and + kh to + k$T were the same as the ratios of the aqueous diffusion of + a

j

;

EP

coefficients at infinite dilution. -< was estimated from partitioning data at the lowest concentration where Na+ exclusion should be strongest.

AC C

Donnan and Extended Donnan Models of Partitioning into Ion-exchange Membranes The Donnan model. In equilibrium partitioning of an ion between two phases, the ion’s electrochemical potentials should be equal in the two phases [10,11]. Considering membrane, M, and solution, S, phases, this gives equation (S-4),

̅ 5 ̅ 6

(S-4)

where ̅ 5 and ̅ 6 are the electrochemical potentials in the membrane and solution, respectively. Substituting for the electrochemical potentials leads to

W5  01r5   /2 5 W6  01r6   /2 6

S-15

(S-5)

ACCEPTED MANUSCRIPT

In these equations W is the standard state chemical potential,  is the ion activity, and 2 is the electrical potential for the denoted phase. Further,  is the ion charge, 0 is the gas constant and 1 is temperature. The Donnan model assumes that W5 = W6 and that activity coefficients are unity so activities equal concentrations. These assumptions lead to $"8  r 7 "  $"

(S-6)

RI PT

25 * 2 6

For a system with three ions, we can equate the potential differences for all three ions.

 $!8 r 7 $! ! 

 $;8 r 7 $; ; 

$7

/

or s 8 t $

/! $!7 t $!8

s

s

We define a partition coefficient Γ

Γ

$"7 $"8

Γ

$!7 $!8

9!

Γ 9 and Γ

M AN U

Substituting this definition into equation (S-7) yields 9;

$;7 $!8

/; $;7 t $;8

SC

 $8 r 7 $  

Γ 9

(S-7)

(S-8)

(S-9)

For a three-ion system, the electrical neutrality condition inside the membrane is

 5   5   5  < <5 =0.

(S-10)

TE D

Using equations (S-8 and S-9) to define the concentrations in the membrane, equation (S-10) becomes 9!

9;

 : Γ   6 Γ 9   6 Γ 9  < <5 =0

(S-11)

EP

Knowing the ion concentrations in solution, for a mixture of NaCl and Na2SO4 this is a cubic equation that one can solve for Γ . Subsequently equations (S-8) and (S-9) allow calculation of other ion partition coefficients and the concentrations of each ion in the membrane.

AC C

The extended Donnan model. To better model partitioning, we relax the assumption that

W5 = W6 , but we retain the assumption of activity coefficients of 1 (or at least equal activity coefficients in the solution and membrane) [12]. Under these assumptions, equating electrochemical potentials leads to 25 * 2 6

$"8  r 7 "  $"



#"^8 #"^7

(S-12)

" 

For a system with three ions, we can equate the potential differences for all three ions to obtain equation (S-13).  

$8

r $ 7 

#^8 #^7  



$8

!

 r $ 7  !

!

#!^8 #!^7 ! 



$8

;

 r $ 7  ;

;

#;^8 #;^7 ; 

S-16

(S-13)

ACCEPTED MANUSCRIPT

Rearranging leads to $8 9

s$ 7t v.w s

#^8 #^7 t  

$8 9

#^8 #!^7 t ! 

!

s$ 7 t v.w s !

$8 9

;

s$ 7 t v.w s ;

#^8 #!^7 t ! 

(S-14)

> v.w x

#"^8 #"^7 

RI PT

We define the constant >

y

(S-15)

Substituting equation (S-15) into equation (S-14) and rearranging yields 

9

$ 7 9!

=s $!8 t > !



9!

$ 7 9;

s $;8 t >



;

9;

(S-16)

SC

$7 9

s $ 8 t >

9! 9

Γ ?Γ @

A

9  ! 9

A!

9; 9

and Γ ?Γ @

A

9  ; 9

A;

M AN U

The value of > depends on differences in the solvation energies of the ion in the membrane and the solution as reflected in W6 and W5 values. Noting the definition of Γ , equation (S-16) gives (S-17)

Finally, substituting equation (S-17) into the condition for electroneutrality in the membrane yields 9

9  !

! A 9   6 Γ 9 A!



9

9  ;

; A 9  6 Γ 9 A;

 < <5 =0

TE D

 : Γ

(S-18)

AC C

EP

The expressions in red serve as fitting parameters. Similar to the Donnan model, for a given set of fitting parameters we solve equation (S18) to obtain Γ and then use equation (S-17) and the definition of Γ to obtain the values of 5 . We vary the two parameters (in red in equation S18) to minimize the sum of squares of z 5 * 5∗ |/ 5∗ where 5∗ is the experimental value. In this fitting, we only minimized the sum of squares for the anions because cation concentrations in the membrane are low and difficult to determine.

S-17

ACCEPTED MANUSCRIPT

Modeling of Transport in Membranes

*

}" ~"

V" <

  -

RI PT

The model for ion transport includes diffusion and electromigration in the solution boundary layer, permeation (taking into account electromigration) through the polyelectrolyte coating, partitioning into the AEM, diffusion and electromigration in the AEM, permeation through a second polyelectrolyte coating, and diffusion in the second solution boundary layer. Equation (S-19) describes the fluxes, P , of specific ions in the boundary layer. € <

(S-19)

In this equation, + is the diffusion coefficient in solution, - is the ion concentration, which depends on the coordinate . ,  is the ion charge, and  is dimensionless (in F/RT units) electrical potential. In the polyelectrolyte coating, equation (S-20) describes the }" \" ∗

V"∗ < ∗

  -∗

€∗ < ∗

SC

*

(S-20)

M AN U

ion flux, where R ∗ is the ion permeability in the coating,  ∗ is the dimensionless (in F/RT units) electrostatic potential in a virtual solution, -∗ is the concentration of ion 4 in this solution, and . ∗ is the coordinate on the coating. The virtual (or reference) solution is a bulk electrolyte solution that could be in thermodynamic equilibrium with a given plane inside the coating [13]. Similarly, equation (S-21) describe ion fluxes, P , through the Fujifilm AEM. }

* k" ~"

V̅" <̅

  -̅

k € <̅

(S-21)

TE D

The overbars denote that the specific variables apply to the Fujifilm AEM. In equation (S-21), concentrations and electrical potential are real, rather than virtual, quantities because we use a diffusion coefficient rather than a permeability coefficient. Thus, we also need to determine partitioning at the interface of the coating and the AEM. The partitioning occurs from the virtual solution at the edge of the coating into the AEM according to the extended Donnan model in equation (S-18). The simulations include four ions (Cl-, SO42-, CO32-, and Na+), so we include another term in equation (S-18) for CO3 and assume that the values of Γ

EP

2-

are the same, where ions 2 and 4 are sulfate and carbonate.

9! 9

A

9  ! 9

A!

9j

and Γ 9

A

9  j 9

Aj

„V"∗ „< ∗ Vk‡ <̅

V" <

AC C

Equations (S-19 to S21) are systems of four equations (one equation for each ion). We assume V that the AEM is homogeneous ( ‚ 0@. With the assumption of electroneutrality <̅ (∑  - 0, ∑  -∗ 0, r, ∑  -kƒ *-< @, one can transform equations (S-19 to S21) into: }

… ∑" " "

†" ! ∗ " " V"

* \"   -∗ ∑

"

} * k" ~"

*

}"

~"

  -kƒ

(S-22)

… ˆ" ∑" "! V̅"

∑" " k"

(S-23)

… ∑" " "

  - ∑

ˆ"

(S-24)

! " " V"

S-18

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

We assumed -∗ - at the boundary layer/coating interfaces because we use virtual solution to model ion transport in coatings. We employed the extended Donnan model to relate -∗ and -kƒ at the coating/AEM interfaces. We treated equations (S-22 to S24) as initial value problems by specifying the source-phase concentrations as initial conditions. By inputting three ion fluxes (the fourth flux is specified by the zero-current condition, ∑  P 0), we solved equations (S-22 to S24) using a differential equation solver that is based on an explicit Runge-Kutta formula to get the ion concentration profiles in the boundary layers, coatings, and AEM. Equations (S-22 to S24) can also be solved using the receiving phase concentrations as initial conditions instead. Correct input fluxes must give the same ion concentration profiles using either the source-phase concentrations or the receiving-phase concentrations as initial conditions. In the MATLAB program, we performed iterations until the AEM concentrations at the boundary near the receiving phase, obtained with either the source-phase or receiving-phase concentrations as initial conditions, converged. Table S12 gives the modeling parameters, and we are including the MATLAB code that we used to solve the equations.

S-19

ACCEPTED MANUSCRIPT

Table S13. Simulated average diffusive (jC ), average electromigration (jDE ), and net fluxes (j) in the 2coatings, AEM, and boundary layers for Cl and SO4 in DD experiments. The source-phase concentration varied as shown, but the receiving phase always contained 0.01 M Na2CO3.

AEM Fluxes (nmol/cm2/s)

j‰Š

EP

Boundary Layer 2 Fluxes (nmol/cm2/s)

2.05 -0.24

0.34

0.45

-0.17

-0.26

1.73 -0.55

2.76 -0.95

5.93 -0.57

0.55

0.72

-0.41

-0.61

4.74 -1.74

7.78 -2.42

0.45

0.00

0.78

-0.26

0.00

-0.67

1.89 -0.08

3.31 -0.30

6.34 -0.98

0.26

0.39

0.63

0.93

-0.09

-0.21

-0.49

-0.81

1.18 -0.01

2.34 -0.53

4.63 -1.63

8.66 -3.30

0.17

0.26

0.25

0.23

0.00

-0.08

-0.12

-0.11

1.37 -0.19

1.83 -0.02

3.04 -0.04

5.47 -0.11

0.20

0.19

0.14

0.12

-0.04

0.00

0.00

0.00

1.18 0.17

1.81 0.19

3.00 0.14

5.36 0.12

0.31 -0.15 1.21 -0.03

j‹Œ! j

AC C

Net Fluxes (nmol/cm2/s)

0.1 M

3.38 -0.38

TE D

PEM Coating 2 Fluxes (nmol/cm2/s)

1.34 -0.16

0.03 M

RI PT

PEM Coating 1 Fluxes (nmol/cm2/s)

0.01 M

SC

j

jDE ‹Œ! j jC ‰Š jDE ‰Š C j‹Œ! j jDE ‹Œ! j jC ‰Š jDE ‰Š C j‹Œ! j jDE ‹Œ! j jC ‰Š jDE ‰Š C j‹Œ! j jDE ‹Œ! j jC ‰Š jDE ‰Š C j‹Œ! j jDE ‹Œ! j

0.005 M

M AN U

Boundary Layer 1 Fluxes (nmol/cm2/s)

Cl- and SO42Source-Phase Concentrations jC ‰Š jDE ‰Š C j‹Œ!

S-20

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

Figure S9. Simulated ion concentration profiles in the boundary layers (BLs), polyelectrolyte multilayers (PEMs), and anion exchange membrane (AEM). The source phase (left) contained 0.005 M NaCl and 0.005 M Na2SO4, and the receiving phase contained 0.01 M Na2CO3.

Figure S10. Simulated ion concentration profiles in the boundary layers (BLs), polyelectrolyte multilayers (PEMs), and anion exchange membrane (AEM). The source phase (left) contained 0.01 M NaCl and 0.01 M Na2SO4, and the receiving phase contained 0.01 M Na2CO3.

S-21

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

Figure S11. Simulated ion concentration profiles in the boundary layers (BLs), polyelectrolyte multilayers (PEMs), and anion exchange membrane (AEM). The source phase (left) contained 0.03 M NaCl and 0.03 M Na2SO4, and the receiving phase contained 0.01 M Na2CO3.

Figure S12. Simulated ion concentration profiles in the boundary layers (BLs), polyelectrolyte multilayers (PEMs), and anion exchange membrane (AEM). The source phase (left) contained 0.1 M NaCl and 0.1 M Na2SO4, and the receiving phase contained 0.01 M Na2CO3.

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Table S14. Simulated average diffusive (jC ), average electromigration (jDE ), and net fluxes (j) in the 2coatings, AEM, and boundary layers for Cl and SO4 for source phases containing unequal concentrations of NaCl and Na2SO4, but each of the receiving and isolated phases contained 0.01 M Na2CO3.

AEM Fluxes (nmol/cm2/s)

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Boundary Layer 2 Fluxes (nmol/cm2/s)

11.17 -7.18

j‰Š

j‹Œ! j

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Net Fluxes (nmol/cm2/s)

0.17 -0.16

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PEM Coating 2 Fluxes (nmol/cm2/s)

j

jDE ‹Œ! j jC ‰Š jDE ‰Š C j‹Œ! j jDE ‹Œ! j jC ‰Š jDE ‰Š C j‹Œ! j jDE ‹Œ! j jC ‰Š jDE ‰Š C j‹Œ! j jDE ‹Œ! j jC ‰Š jDE ‰Š C j‹Œ! j jDE ‹Œ! j

0.01 M NaCl and 0.1 M Na2SO4 1.39 -0.02 1.14

-0.20

1.39 -0.02

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PEM Coating 1 Fluxes (nmol/cm2/s)

0.1 M NaCl and 0.01 M Na2SO4 5.53 -1.54

0.20

1.01

-0.19

-0.07

5.68 -1.69

1.39 -0.02

0.23

1.22

-0.22

-0.28

7.78 -3.79

1.41 -0.04

0.02

0.98

-0.01

-0.03

4.06 -0.07

1.37 -0.01

0.01

0.95

0.00

-0.01

3.99 0.01

1.37 0.94

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Boundary Layer 1 Fluxes (nmol/cm2/s)

Source-Phase Concentrations jC ‰Š jDE ‰Š C j‹Œ!

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Figure S13. Simulated ion concentration profiles in the boundary layers (BLs), polyelectrolyte multilayers (PEMs), and anion exchange membrane (AEM). The source phase (left) contained 0.1 M NaCl and 0.01 M Na2SO4, and the receiving phase contained 0.01 M Na2CO3.

Figure S14. Simulated ion concentration profiles in the boundary layers (BLs), polyelectrolyte multilayers (PEMs), and anion exchange membrane (AEM). The source phase (left) contained 0.01 M NaCl and 0.1 M Na2SO4, and the receiving phase contained 0.01 M Na2CO3.

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24.0

8.0

(B)

(A) 19.36

-1.12 4.0

2.0

18.0

12.0

6.0

1.01 -0.91 0.10

0.0

JK FI LM O FLM O FLMO N

Em

N

D

N

Em N

N

N JK FDIGH FEm GH FGH

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5.43

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6.0

Flux (nmol/cm2/s)

Flux (nmol/cm2/s)

6.55

3.51

1.71 -1.79 D Em N JK FILM O F O FLM O LM N N

N

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Figure S15. Simulated average diffusive flux (P~ ) and average electromigration flux (PU ) components 2and net fluxes for Cl and SO4 in the AEM when the (PSS/PAH)5PSS coating faces the (A) source and (B) receiving phase. The source phase contained 0.1 M NaCl and 0.1 M Na2SO4, and the receiving phase was 0.01 M Na2CO3.

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Table S15. Simulated average diffusive (jC ), average electromigration (jDE ), and net fluxes (j) in the 2coatings, AEM, and boundary layers for Cl and SO4 with different configurations of (PAH/PSS)5PSScoating. The source phase contained 0.1 M NaCl and 0.1 M Na2SO4, whereas receiving and isolated phases contained 0.01 M Na2CO3.

jC ‹Œ!

4.05

j

-2.34 25.48 -8.34 4.04 -2.32

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j‹Œ! j

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Net Fluxes (nmol/cm2/s)

0.72

-0.62

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NA

19.36 -2.22

6.55 -1.12

3.51

1.01

-1.79

-0.91

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AEM Fluxes (nmol/cm2/s)

jDE ‹Œ! j jC ‰Š jDE ‰Š C j‹Œ! j jDE ‹Œ! j jC ‰Š jDE ‰Š C j‹Œ! j jDE ‹Œ! j jC ‰Š jDE ‰Š C j‹Œ! j jDE ‹Œ! j jC ‰Š jDE ‰Š C j‹Œ! j jDE ‹Œ! j

6.01 -0.58

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PEM Coating 1 Fluxes (nmol/cm2/s)

Boundary Layer 2 Fluxes (nmol/cm2/s)

19.29 -2.16

Coated on Receiving Phase Side

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jC ‰Š jDE ‰Š

Boundary Layer 1 Fluxes (nmol/cm2/s)

PEM Coating 2 Fluxes (nmol/cm2/s)

Coated on SourcePhase Side

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(PAH/PSS)5PSS Coating Configurations

8.99 -3.56 0.21 -0.11

18.64 -1.50

5.54 -0.11

2.03

0.11

-0.32

0.00

17.14 1.71

5.43 0.10

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Figure S16. Simulated ion concentration profiles in the boundary layers (BLs), polyelectrolyte multilayer (PEM), and anion exchange membrane (AEM). The source phase (left) contained 0.1 M NaCl and 0.1 M Na2SO4, and the receiving phase contained 0.01 M Na2CO3. The AEM is only coated with the PEM on the side facing toward the source phase.

Figure S17. Simulated ion concentration profiles in the boundary layers (BLs), polyelectrolyte multilayer (PEM), and anion exchange membrane (AEM). The source phase (left) contained 0.1 M NaCl and 0.1 M Na2SO4, and the receiving phase contained 0.01 M Na2CO3. The AEM is only coated with the PEM on the side facing toward the receiving phase.

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MATLAB Code clear all close all

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z1=-1; %Charge on Clz2=-2; %Charge on SO42z3=-2; %Charge on CO32z4=1; %Charge on Na+ A=0.177531090415446; %Extented Donnan model parameter for SO42B=A; %Extented Donnan model parameter for CO32C=0.122129889612291; %Extented Donnan model parameter for Na+ c1L=0.1; %Source phase Cl- concentration in M c2L=0.1; %Source phase SO42- concentration in M c3L=0; %Source phase CO32- concentration in M c4L=(z1*c1L+z2*c2L+z3*c3L)/-(z4); %Source phase Na+ concentration in M cx=1.03; %Swelled membrane fixed charge concentration in M l1=100*10^-5; %Boundary layer thickness in dm l2=30*10^-8; %Coating thickness in dm l3=110*10^-5; %Membrane thickness in dm D1=2.03*10^-7; %Cl- Bulk diffusion coefficients in dm^2/s D2=1.07*10^-7; %SO42- Bulk diffusion coefficients in dm^2/s D3=0.96*10^-7; %CO32- Bulk diffusion coefficients in dm^2/s D4=1.33*10^-7; %Na+ Bulk diffusion coefficients in dm^2/s D1_m=4.61*10^-8; %Cl- membrane diffusion coefficients in dm^2/s D2_m=D1_m*D2/D1; %SO42- membrane diffusion coefficients in dm^2/s D3_m=D1_m*D3/D1; %CO32- membrane diffusion coefficients in dm^2/s D4_m=D1_m*D4/D1; %Na+ membrane diffusion coefficients in dm^2/s P1=2.637*10^-11; %Cl- permeability in dm^2/s P2=3.54*10^-12; %SO42- permeability in dm^2/s P3=P2; %CO32- permeability in dm^2/s P4=1.419*10^-11; %Na+ permeability in dm^2/s c1R=0; %Receiving phase Cl- concentration in M c2R=0; %Receiving phase SO42- concentration in M c3R=0.01; %Receiving phase CO32- concentration in M c4R=(z1*c1R+z2*c2R+z3*c3R)/-(z4); %Receiving phase Na+ concentration in M

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j1=2.997e-08; %Initial guess of Cl- flux in mol/dm^2/s j2=1e-09; %Initial guess of SO42- flux in mol/dm^2/s j3=-1.670E-08; %Initial guess of CO32- flux in mol/dm^2/s options = optimset('TolX',1e-15,'TolFun',1e-15,'MaxFunEvals',1e15,'MaxIter',1e15); sol = fminsearch(@(j) funcSolve(j, z1,z2,z3,z4,A,B,C,c1L,c2L,c3L,c4L,c1R,c2R,c3R,c4R,cx,l1,l2,l3,D1,D2,D3,D4,D1_m,D2_m,D3 _m,D4_m,P1,P2,P3,P4), [j1,j2,j3],options); % plot and return new results j1=sol(1) %Final Cl- flux in mol/dm^2/s j2=sol(2) %Final SO42- flux in mol/dm^2/s j3=sol(3) %Final CO32- flux in mol/dm^2/s

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% This function is built to solve the system and calculate residuals function [res] = funcSolve (j, z1,z2,z3,z4,A,B,C,c1L,c2L,c3L,c4L,c1R,c2R,c3R,c4R,cx,l1,l2,l3,D1,D2,D3,D4,D1_m,D2_m,D3 _m,D4_m,P1,P2,P3,P4) j1 = j(1); %Input Cl- flux in mol/dm^2/s j2 = j(2); %Input SO42- flux in mol/dm^2/s j3 = j(3); %Input CO32- flux in mol/dm^2/s j4=(-z1*j1-z2*j2-z3*j3)/z4; %Na+ flux in mol/dm^2/s specifed by zero-current condition

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%This part solves the boundary layer 1 concentration profiles a1=0; b1=1; alpha1=[c1L,c2L,c3L,c4L]; %Source phase concentrations as initial conditions

[t1,c1]=ode45(@(t1,c1) func1(c1, D1,D2,D3,D4,z1,z2,z3,z4,j1,j2,j3,j4,l1), [a1 b1], alpha1); %Cl- concentration at the boundary layer 1 edge towards the

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c1_int1=c1(end,1); coating c2_int1=c1(end,2); coating c3_int1=c1(end,3); coating c4_int1=c1(end,4); coating

%SO42- concentration at the boundary layer 1 edge towards the %CO32- concentration at the boundary layer 1 edge towards the %Na+ concentration at the boundary layer 1 edge towards the

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%This part solves the PEM coating 1 concentration profiles a2=0; b2=1; alpha2=[c1_int1,c2_int1,c3_int1,c4_int1]; %Boundary layer 1 edge concentrations as initial conditions

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[t2,c2]=ode45(@(t2,c2) func1(c2, P1,P2,P3,P4,z1,z2,z3,z4,j1,j2,j3,j4,l2), [a2 b2], alpha2); %Cl- concentration at the PEM coating 1 %SO42- concentration at the PEM coating %CO32- concentration at the PEM coating %Na+ concentration at the PEM coating 1

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c1_int2=c2(end,1); c2_int2=c2(end,2); c3_int2=c2(end,3); c4_int2=c2(end,4);

edge towards the AEM 1 edge towards the AEM 1 edge towards the AEM edge towards the AEM

%This part uses the extened Donnan model to solve for AEM boundary conditions func2 = @(gamma)z1*c1_int2*gamma+z2*c2_int2*(gamma^(z2/z1))*A+z3*c3_int2*(gamma^(z3/z1))*B+z4* c4_int2*(gamma^(z4/z1))*C+cx; gamma1 = fzero(func2,4); co1=gamma1*c1_int2; source phase co2=(gamma1^(z2/z1))*A*c2_int2; source phase

%Cl- concentration at the AEM edge towards the %SO42- concentration at the AEM edge towards the

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co3=(gamma1^(z3/z1))*B*c3_int2; source phase co4=(gamma1^(z4/z1))*C*c4_int2; source phase

%CO32- concentration at the AEM edge towards the %Na+ concentration at the AEM edge towards the

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%This part solves the AEM concentration profiles a3=0; b3=1; alpha3=[co1,co2,co3,co4]; %AEM edge concentrations as initial conditions

[t3,c3]=ode45(@(t3,c3) func1(c3, D1_m,D2_m,D3_m,D4_m,z1,z2,z3,z4,j1,j2,j3,j4,l3), [a3 b3], alpha3);

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%Cl- concentration at the AEM edge towards the receiving phase %SO42- concentration at the AEM edge towards the receiving phase %CO32- concentration at the AEM edge towards the receiving phase %Na+ concentration at the AEM edge towards the receiving phase

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ce1=c3(end,1); ce2=c3(end,2); ce3=c3(end,3); ce4=c3(end,4);

%This part solves the boundary layer 2 concentration profiles a4=1; b4=0; alpha4=[c1R,c2R,c3R,c4R]; %Receiving phase concentrations as initial conditions [t5,c5]=ode45(@(t5,c5) func1(c5, D1,D2,D3,D4,z1,z2,z3,z4,j1,j2,j3,j4,l1), [a4 b4], alpha4);

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%Cl- concentration at the boundary layer 2 edge towards the %SO42- concentration at the boundary layer 2 edge towards the %CO32- concentration at the boundary layer 2 edge towards the %Na+ concentration at the boundary layer 2 edge towards the

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c1_int4=c5(end,1); coating c2_int4=c5(end,2); coating c3_int4=c5(end,3); coating c4_int4=c5(end,4); coating

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%This part solves the PEM coating 2 concentration profiles a5=1; b5=0; alpha5=[c1_int4,c2_int4,c3_int4,c4_int4]; %Boundary layer 2 edge concentrations as initial conditions [t4,c4]=ode45(@(t4,c4) func1(c4, P1,P2,P3,P4,z1,z2,z3,z4,j1,j2,j3,j4,l2), [a5 b5], alpha5); c1_int3=c4(end,1); c2_int3=c4(end,2); c3_int3=c4(end,3); c4_int3=c4(end,4);

%Cl- concentration at the PEM coating 2 %SO42- concentration at the PEM coating %CO32- concentration at the PEM coating %Na+ concentration at the PEM coating 2

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edge towards the AEM 2 edge towards the AEM 2 edge towards the AEM edge towards the AEM

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%This part uses the extened Donnan model to solve for AEM boundary conditions (at the edge towards the receiving phase) func3 = @(gamma)z1*c1_int3*gamma+z2*c2_int3*(gamma^(z2/z1))*A+z3*c3_int3*(gamma^(z3/z1))*B+z4* c4_int3*(gamma^(z4/z1))*C+cx; x0=[-0.1 1000]; gamma2 = fzero(func3,x0);

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ce1_target = gamma2*c1_int3; %Cl- concentration at the AEM edge towards the receiving phase (calculated from the receiving phase side) ce2_target = (gamma2^(z2/z1))*A*c2_int3; %SO42- concentration at the AEM edge towards the receiving phase (calculated from the receiving phase side) ce3_target = (gamma2^(z3/z1))*B*c3_int3; %CO32- concentration at the AEM edge towards the receiving phase (calculated from the receiving phase side) ce4_target = (gamma2^(z4/z1))*C*c4_int3; %Na+ concentration at the AEM edge towards the receiving phase (calculated from the receiving phase side)

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%This calculates the residual between AEM boundary conditions calculated from both sides res = (ce1/ce1_target-1)^2+(ce2/ce2_target-1)^2+(ce3/ce3_target-1)^2+(ce4/ce4_target1)^2;

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function dc = func1(c, D1,D2,D3,D4,z1,z2,z3,z4,j1,j2,j3,j4,l1) dc =[j1*l1/D1+(z1*c(1)*l1*((z1*j1/D1)+(z2*j2/D2)+(z3*j3/D3)+(z4*j4/D4))/(z1*z1*c(1)+z2*z2*c (2)+z3*z3*c(3)+z4*z4*c(4))); j2*l1/D2+(z2*c(2)*l1*((z1*j1/D1)+(z2*j2/D2)+(z3*j3/D3)+(z4*j4/D4))/(z1*z1*c(1)+z2*z2*c (2)+z3*z3*c(3)+z4*z4*c(4))); j3*l1/D3+(z3*c(3)*l1*((z1*j1/D1)+(z2*j2/D2)+(z3*j3/D3)+(z4*j4/D4))/(z1*z1*c(1)+z2*z2*c (2)+z3*z3*c(3)+z4*z4*c(4))); j4*l1/D4+(z4*c(4)*l1*((z1*j1/D1)+(z2*j2/D2)+(z3*j3/D3)+(z4*j4/D4))/(z1*z1*c(1)+z2*z2*c (2)+z3*z3*c(3)+z4*z4*c(4)))]; end end

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References:

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1. A. E. Yaroshchuk, M. A. Glaus, L. R. Van Loon, Diffusion through confined media at variable concentrations in reservoirs, J. Membr. Sci. 319 (2008) 133-140. 2. N. White, M. Misovich, A. Yaroshchuk, M. L. Bruening, Coating of Nafion membranes with polyelectrolyte multilayers to achieve high monovalent/divalent cation electrodialysis selecttivities, ACS Appl. Mater. Interfaces 7 (2015) 6620-6628. 3. Y. Zhu, M. Ahmad, L. Yang, M. Misovich, A. Yaroshchuk, M. L. Bruening, Adsorption of polyelectrolyte multilayers imparts high monovalent/divalent cation selectivity to aliphatic polyamide cation-exchange membranes, J. Membr. Sci. 537 (2017) 177-185. 4. N. White, M. Misovich, E. Alemayehu, A. Yaroshchuk, M. L. Bruening, Highly selective separation of multivalent and monovalent cations in electrodialysis through Nafion membranes coated with polyelectrolyte multilayers, Polymer 103 (2016) 478-485. 5. C. Cheng, A. Yaroshchuk, M. L. Bruening, Fundamentals of selective ion transport through multilayer polyelectrolyte membranes, Langmuir 29 (2013) 1885-1892. 6. A. Yaroshchuk, Influence of osmosis on the diffusion from concentrated solutions through composite/asymmetric membranes: Theoretical analysis, J. Membr. Sci. 355 (2010) 98-103. 7. Y.–H. Li, S. Gregory, Diffusion of ions in sea water and in deep-sea sediments, Geochim. Et. Cosmochim. Acta 38 (1974) 703-714. 8. W. M. Haynes, CRC Handbook of Chemistry and Physics (96th ed.), CRC Press, Taylor & Francis Group, Boca Raton, London, New York (2015–2016). 9. E. Fontananova, W. J. Zhang, I. B. Nicotera, C. Simari, W. van Baak, G. D. Profio, E. Curcio, E. Drioli, Probing membrane and interface properties in concentrated electrolyte solutions, J. Membr. Sci 459 (2014) 177-189. 10. F. G. Donnan, The theory of membrane equilibria, Chem. Rev. 1 (1924) 73-90. 11. H. Strathmann, Chapter 2 - Electrochemical and Thermodynamic Fundamentals in Membrane Science and Technology 9 (2004) 23-88. 12. L. Dammak, C. Larchet, B. Auclair, Theoretical study of the bi-ionic potential and confrontation with experimental results, J. Membr. Sci. 155 (1999) 193-207. 13. A. Yaroshchuk, M. L. Bruening, E. E. Licón Bernal, Solution-Diffusion–Electro-Migration model and its uses for analysis of nanofiltration, pressure-retarded osmosis and forward osmosis in multi-ionic solutions, J. Membr. Sci. 447 (2013) 463-476.

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Highlights

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Polyelectrolyte films increase Cl-/SO42- selectivity in anion-exchange membranes Selectivity increases with an increase in Cl- and SO42- concentrations Cl-/SO42- selectivities reach values as high as 140 Partitioning and electromigration contribute to selectivities at high concentrations Modeling describes variations in transport with source-phase salt concentrations

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• • • • •