The pH as a tool to tailor the performance of symmetric and asymmetric layer-by-layer nanofiltration membranes

Layer-by-layer assembly of polyelectrolyte layers is a versatile method to produce nanofiltration membranes. The membrane formation and subsequently performance is easily tailored with pH as it varies the polyelectrolyte charge density. Here, membranes are fabricated at different pH (4,8, and 9) with branched polyethyleneimine (PEI)/poly(sodium-4-styrenesulfonate) (PSS) layers (symmetric membranes) or a combination of poly(dia-llyldimethylammonium chloride) (PDADMAC)/PSS base layers terminated with PEI/PSS layers (asymmetric membranes). Overall, increasing the pH lowers the PEI charge density, which increases PEI adsorption, as measured by optical reflectometry and positive zeta potential. For symmetric systems, decreasing the charge density decreases the salt retention, because fewer intrinsic linkages are formed. Contrarily, asymmetric membranes, independent of charge density, show retentions > 90% for MgSO 4 and Na 2 SO 4 . Additionally, the benefit of asymmetric membrane formation is proven by comparing the best membrane performances. Asymmetric membranes prepared at pH = 4 form an open base layer and defect-free dense selective layer, resulting in much higher permeabilities compared to symmetric membranes (~13 and ~9 L/ (m 2 hbar)), and significantly improving MgSO 4 and Na 2 SO 4 retentions ( > 95% compared to > 90%). By combining two well-known polycations and tailoring the pH, versatile membranes are produced, without the need for synthesis or modification steps while obtaining improved water fluxes and salt retentions.


Introduction
Membrane separation technologies are one of the most promising and sustainable solutions to meet the increasing demands concerning sanitation and water supply [1,2].Commercial nanofiltration (NF) membranes show good performance in rejecting micropollutants and multivalent ions while operating at lower pressures and higher permeate fluxes compared to reverse osmosis membrane systems [3,4].Unfortunately, the production pathway for nanofiltration membranes commonly involves the use of organic, toxic solvents and approaches to precisely tailor the membrane properties are scarce [5,6].
A much more sustainable and tunable alternative is the production of nanofiltration membranes by alternating sequential adsorption of watersoluble polycations (PCs) and polyanions (PAs) on a charged porous support [7].This so-called layer-by-layer (LbL) technique results in the self-assembly of oppositely charged polyelectrolytes (PEs) forming a thin NF membrane layer on a porous membrane support with high permeabilities compared to commercial polyamide nanofiltration membranes and thus a decrease in the energy demand associated with the separation [8][9][10].Moreover, these LbL membranes are in general more stable towards chemical cleaning and backflushing [11].However, there are challenges to create a defect-free membrane, the layers should not be too thin as these layers will not completely close the pores of the porous support [12].The formation and ultimately the performance of these LbL membranes is versatile and can be tuned with several parameters such as the number of adsorption cycles, the chemical composition of the PEs, the ionic strength and the pH of the coating solutions [13].Two frequently used PCs in LbL membranes are poly (diallyldimethylammonium chloride) (PDADMAC) and polyethyleneimine (PEI) [14][15][16][17][18][19][20].
Tuning the NF membrane chemistry also influences the salt retention of the membrane, as the salt retention is based on size as well as on charge exclusion [21].When size exclusion occurs, the transport of solutes through the layers is affected by steric hindrance which is stronger when the solute size is comparable to or larger than the membrane pore size [22].Solutes that are smaller than the membrane pores do not always enter the pores, but rather have a size-dependent probability of successful entry [23].When charge exclusion occurs, ions with the same charge as the membrane are repelled, while ions with opposite charges are attracted [21].The ionic concentrations in the membrane phase are not equal to the concentrations in the bulk solution due to a fixed membrane charge [24].This inequality arises as the charge (e.g.negative) of a membrane restricts the permeation of co-ions (i.e.negatively charged ions), while it facilitates the transport of counter ions (i.e.positively charged ions), resulting in a potential difference over the membrane.This potential difference dictates both counter-ion and co-ion transport through the membrane.The retention of multivalent counter-ions is lower in comparison with monovalent counter-ions.Oppositely, multivalent co-ions result in higher retentions in comparison with monovalent co-ions [24,25].
The effect of various LbL coating parameters on the ultimate membrane formation and performance has been extensively investigated [6,7,[26][27][28].One of the most important control parameters is the charge density (CD) of the PEs [28][29][30].In this context CD is defined as the number of charges per carbon atom in the monomer unit, essentially representing how much charge is stored in a PE [20].The CD of strong PEs is independent of pH, whereas the charge of weak PEs depends strongly on the pH of the solution [30].For weak PEs, the pH of the coating solution can thus be used to tune the membrane properties as it determines how the PE chains adsorb on the charged surface [31].A low pH results in a strong positive charge of the weak PC.So the electrostatic repulsive force between the different polymer chain segments is high, resulting in a stretched and rigid chain conformation [32].As a result, a lower number of polymer chains can adsorb on the surface, as a single chain can compensate for a higher number of available surface charges [31].Due to the stretched conformation of the chains, thin layers are formed.When the pH of the coating solution increases, the functional groups of the weak PC will deprotonate resulting in a lower effective CD.Due to this, the electrostatic repulsive force between the chain segments is lower, resulting in a coiled chain conformation on the surface ensuing in thicker but more open layers [30].
The earlier mentioned PDADMAC is a strong PE, whereas, for example, PEI is a weak PE.It is well known that in the ideal case the maximum CD of PEI is higher than that of PDADMAC (1:2 and 1:8 charged group per number of carbon atoms, respectively) [20].Depending on the pH, PEI can thus form dense, thin bilayers (at low pH) or more open, thicker layers (at high pH).Several PE membranes have already been produced with unmodified [20,33,34] and modified layers of PEI [14,15,35,36].These dense membranes result in very high salt and micropollutant retentions, but at the cost of permeability, the high number of PE layers or extra processing steps, such as the addition of polydopamine, crown ethers or chemical crosslinking [14,15,20,[33][34][35][36].
A promising solution to improve the permeability of LbL membranes without compromising their retention too much is the construction of asymmetric LbL membranes [8,10,12,19].This strategy allows the formation of an effective separation layer for nanofiltration purposes while maintaining a high pure water permeability.With asymmetric membranes, first, a relatively thick but open amount of base PE layers is applied that close the pores of the membrane support.Then a few terminating PE layers of a different material are coated on top of this base case assembly forming thin but dense layers responsible for high retentions [8,12].Asymmetric layer formation can reduce the amount of BLs to reach a similar membrane performance and/or can improve the performance [8,10,12].This concept was shown for several PE couples, such as PDADMAC, P(AM-co-DADMAC) or PAH as PCs, and PAA or PSS as PAs [8,10,12,19].PEI, however, has not been included so far, while it is known to give the highest salt retentions and micropollutant rejections among several PCs tested [20] and moreover, due to its sensitivity to pH, allows precise control over the layer structure and properties.
In this research, PEI is used as PC to tailor the performance of LbL NF membranes.The pH of the coating solution is used to change the PEI CD and thus tune the membrane formation and performance of both symmetric and asymmetric membranes with PEI/PSS.For the symmetric system, only PEI and PSS are used as PEs, whereas for the asymmetric systems first layers of PDADMAC/PSS are coated, which are subsequently terminated with PEI/PSS layers.This is done for three different pH values of the PEI coating solution (pH of 4,8,9), to investigate the influence of pH and thus PEI CD.PE adsorption at different pHs and thus CD and its effect on the surface charge, the pure water permeability, molecular weight cut-off value and a series of different salt retentions of the membrane are measured to quantify the membrane performance.

Polyelectrolyte adsorption
Optical fixed angle reflectometry was used to study the alternating adsorption of various PEs onto a flat, reflective model surface.The reflectometer set-up is custom-made by Wageningen University & Research (The Netherlands).Using a stagnation point flow cell, the PE solution was flown to a silicon wafer with a silica layer on top of 67.6 nm until a stable adsorption plateau was reached.PE solutions containing the PC or PA (0.01 wt% PE) with ionic strengths of 0.05 M NaCl were prepared and alternately adsorbed at room temperature onto the wafer.After each PE adsorption step, the wafer was rinsed using a 0.05 M NaCl solution.By using the stagnation point flow cell, the PE transport at the measuring spot on the wafer is purely diffusion-based as the solution is stagnant [37].Therefore, the PE adsorption is determined by the electrostatic interactions between the substrate and the PE solution.Under these hydrodynamic conditions, each subsequent depositing step is stabilized within minutes.
Polarized monochromatic light (He/Ne laser 1108P, 632.8 nm, power < 1 mW) hit the wafer at approximately the Brewster angle and was reflected towards a detector.This reflected light was split into parallel (p) and perpendicular (s) polarized components, and the ratio between the change in these components i.e.ΔS, was directly proportional to the mass adsorbed onto the wafer, as shown in equation (1).
Here, Γ is the amount of mass adsorbed onto the wafer (mg/m 2 ).S 0 is the initial output signal of the bare silicon wafer (− ), where S is defined as the ratio between the intensities of the two components p and s, and finally, Q is the sensitivity factor.This factor is dependent on the configuration of the setup (calculated using the software program Prof. Huygens, version 1.3) [38].

Membrane support
Hollow fiber tight ultrafiltration inside-out HFS membranes with a molecular weight cut-off (MWCO) value of 10 kDa were kindly provided by Pentair X-Flow (The Netherlands) and used as support for LbL deposition.The hollow fiber support consists of polyethersulfone (PES) and modified PES (negatively charged).The modified PES is predominantly present at the inside of the fibers [39].These fibers have a length of 154 cm and an inner diameter of 0.8 mm [39].Before coating, the support was cut into lengths of 30 cm, as fibers with these lengths have been successfully coated before with the LbL technique [6,10,27,28].

Membrane preparation
Before coating the PE layers, the hollow fiber supports were submerged in an ethanol/water mixture overnight to remove impurities on the support.Because of its negatively charged nature at the inner side, the PE layers were coated on the inside of the support.Also, for the same reason, the PC layer was applied first.This was followed by a PA layer and this approach was repeated until the required number of bilayers was applied.During coating, the support was completely immersed in the PE solution with a manual refreshment every 5 min and a total immersion time of 30 min.Afterward, the membranes were immersed in an NaCl solution with equivalent ionic strength as the PE solution.This was done for 10 min to remove any weakly bound PE present.The NF membranes were coated using 0.01 wt% PE in 0.05 M NaCl solutions at room temperature.These coating conditions were chosen according to the optical reflectometry data which showed stabilization of the adsorption within 1 min (Fig. S2).The PDADMAC and PSS solutions were used unmodified (pH = 5.8), whereas the PEI solution was adjusted to a pH of 4, 8 or 9 with HCl solutions of 1 M.
Firstly, different (symmetric) membrane sets were coated solely using PEI/PSS layers at a pH of 4,8, or 9. Next, for the formation of asymmetric membranes, four different base layers were produced.This was done with one, three, five or seven bilayers of PDADMAC/PSS each of these subsequently terminated with two PEI/PSS bilayers.After each subsequent PE layer coating, a sample of seven membranes was taken: one sample for surface charge characterization and six samples for the pure water permeability and retention measurements.This was conducted for PEI as well as PSS terminated membranes.

Membrane charge
The surface charge of the support and the LbL coated membranes was determined using an electrokinetic analyzer (SurPASS™ 3, Anton Paar, Austria).The zeta potential is derived from the streaming current generated by flowing an electrolyte solution along the membrane.The electrolyte solution consisted of a 1 mM KCl solution.Two membrane samples per layer were measured for 20 measurement cycles at room temperature at a constant pH of 5.8.

Membrane performance
The performance of the prepared membrane sets was characterized by their pure water permeability (PWP), MWCO, and retention of 5 mM MgSO 4 , MgCl 2 , Na 2 SO 4, or NaCl solutions.To ensure reproducibility, 6 different membranes of each set were measured.The membranes were fixated with the use of chromatographic connectors (Inacom Instruments, The Netherlands), such that 18 membranes could be measured simultaneously.After fixation, a crossflow through the membranes was employed with the use of a diaphragm pump (KNF, Switzerland), with a nominal flow of 6 L/min at atmospheric pressure.The transmembrane pressure was 3 bar, resulting in a crossflow velocity of 6.6 m/s, and was controlled with a pressure regulator (Swagelok).The permeability and retention were measured as described in our previous work [28].
The MWCO was determined by measuring at which molecular weight of PEG 90% is retained by the membrane.PEG solutions were prepared with an average M w of 200, 300, 400, 600, 1000 and 1500 g/ mol.The concentration of each PEG size was 1 g/L in the feed solution.The concentration of each PEG in the permeate and retentate samples were analyzed with Gel Permeation Chromatography (GPC) (Shimadzu LC-2050C 3D series) and one size exclusion column (Shodex OHpak SB-802.5 HQ 8 × 300 mm 2 column 200 Å, 6 μm).The flow rate of the PEG sample solutions was 1 mL/min, and the eluent was ultrapure water PURELAB Option.

PEI charge density
PEI is one of the most commonly used weak PCs, where the amine groups of this branched PEI are either primary, secondary or tertiary.These amine groups (NH x ) are protonated at different pH, resulting in a positively charged PE [40].This protonation degree is referred to as the charge density of PEI, hence the charge density decreases with increasing pH and is directly proportional to the zeta potential of the polyelectrolyte solution (the method to determine the zeta potential and obtained data are reported in the supplementary information (Fig. S1)).The ratio between the maximum and minimum zeta potential represents the relative charge density of PEI.At pH 4 approx.100% of the functional groups are charged, whereas at pH 8 and pH 9, this is respectively ~70% and ~45%.Additionally, at a pH of 5.8, which is the pH of the rinsing solution and the PA solution, ~85% of the PEI functional groups are charged.This is in accordance with trends reported earlier in literature [40].However, due to the buffer capacities of PEI, it is disputable whether at pH 4 all available charges are indeed ionized [32,41,42].Nevertheless, this leaves unchanged that PEI at pH 4 has a significantly higher charge density than PEI at pH 8 or 9. Hence, PEI with 100% CD is defined as the highest possible charge of PEI.

Polyelectrolyte adsorption
The growth behavior on silicon wafers using optical fixed angle reflectometry is investigated for PEI/PSS layers at the three different PEI CDs.The multilayer growth signals can be found in the supplementary information (Fig. S2).The adsorption begins when the negatively charged silicon wafer is exposed to the PC solution (BL = 0.5), further exposure to the PA solution (BL = 1) leads to an additional increase in the amount of adsorbed PE.The repetitive alternation between PCs and PAs causes a stepwise growth in the signals over time, which quickly stabilizes within 1 min.This indicates that these PE layers adsorb steadily and result in consistent layer-by-layer build-up.Fig. 2 shows the overall polyelectrolyte adsorption at three different PEI CDs of 45, 70 and 100%.
The PE adsorption increases for all charge densities with an increasing number of layers.This growth, which slightly increases with every BL, is determined by measuring the adsorbed mass after each BL as can be seen in the supplementary information (Fig. S3).The growth regime of PE layers can be either exponential or linear depending on the coating conditions [43].The buildup shown here is slightly exponential, which is caused by the diffusion of single chains into the film during each adsorption step, causing an extra adsorbed amount of polyelectrolyte at every step.
Additionally, the overall mass adsorbed follows the order PEI CD = 45% /PSS > PEI CD = 70% /PSS > PEI CD = 100% /PSS.It is well established that the charge density of PEs influences the amount and type of adsorption of the PE [44].A higher charge density indicates a higher number of charged groups, hence less PE adsorption is necessary to compensate for opposite charges already present on the surface.Therefore, a higher PEI charge density results in a decreasing amount of PEI adsorption.For the subsequent adsorption step of PSS, the same trend is visible, where the PSS adsorption decreases with increasing PEI charge density.The original adsorbed mass of PEI is lowest at the highest charge density resulting in the least free positive charges.The low number of free positive charges determines the possible intrinsic linkages between PC and PA in the next step, which thus limits the adsorption of PSS.Hence, the adsorption of PSS is determined by the underlying charge density of PEI, resulting in the highest adsorption of PSS at the lowest charge density of PEI.

Membrane surface charge
The effect of the terminating layer and the charge density of PEI on the membrane surface charge in terms of the apparent zeta potential of the membrane is shown in Fig. 3 for the last two layers, BL 6.5 and 7 (PEI and PSS terminating layer, respectively).
As expected, the PEI terminated membranes (BL 6.5) are more positively charged compared to the PSS terminated membranes (BL 7).The difference between a PC and a PA terminated membrane (so-called odd-even effects) is often an indication of successful adsorption of the PC as well as the PA layer [6,10].
Additionally, a less positive or more negative apparent zeta potential is seen with an increasing CD (ζ CD 100% < ζ CD 70% < ζ CD 45% ).This is seen for the zeta potential of PEI as well as PSS terminated layers measured at a constant pH of 5.8.The membranes coated with a lower charge density are more positively charged due to the excess of PEI that is adsorbed, as seen from the reflectometry data.There, it is apparent that PE adsorption decreases with increasing CD.Consequently, the PEI terminated membranes with a CD of 45% (coated at a pH of 9) have the highest amount of PEI adsorbed.These layers, at the measurement pH of 5.8, have the most free positive charges.Hence, this results, as confirmed by the apparent zeta potential, in the most positively charged membrane.The opposite is true for the membranes with 100% charge density.These membranes adsorbed the least amount of PEI, due to its high charge density.Moreover, during the measurement at a pH of 5.8, this layer becomes even less charged.This results in a slightly negatively charged membrane for 6.5 BLs and highly negatively charged at 7 BLs.

Pure water permeability
To investigate the effect of PE adsorption and surface charge on the membrane performance, the permeability for PEI/PSS membranes at different charge densities is measured as well.The pure water permeability (PWP) of membranes coated with several BLs (1, 3, 5, 7) is given in the supplementary information (Fig. S4).Fig. S4 shows a decreasing permeability with an increasing amount of BLs as expected.A decreasing permeability with the number of BLs indicates additional adsorption of PE with every coating step [6].This is a result of the thicker selective layer and thus higher resistance to permeate with every layer.The pure water permeability of the membranes with 6.5 and 7 BLs is given in Fig. 4 to show the influence of PEI compared to PSS terminated layers.
For the membranes coated with 45 and 70% CD, the permeability is clearly lower with 7 BLs, compared to 6.5 BLs, whereas at 100% charge density the permeabilities are very similar.This difference is partially attributed to the adsorption of extra material with a lower charge density, as seen in Fig. 2. Furthermore, weak PEs such as PEI are known to be more prone to swelling compared to PSS [14,15,45].For example, another weak polycation (PAH) shows significant swelling when exposed to low pH solutions [45].Therefore, PEI terminated membranes show more swelling resulting in a more fluffy membrane structure, hence higher permeabilities.The formation of intrinsic linkages suppresses swelling, hence the higher the charge density the least difference in permeability is seen between BL 6.5 and 7.
PEI, as well as PSS, terminated membranes have the highest permeability at the lowest CD (45%) and the lowest permeability for a CD of 70% (PWP CD = 45% > PWP CD = 100% > PWP CD = 70% ).The permeability of a membrane is determined by the membrane resistance.Normally, an increased membrane resistance is caused by either a decreasing pore size or an increasing membrane thickness [8].The lowest CD favors the formation of a fluffy, more open and more permeable multilayer, whereas a CD of 100% favors the formation of a thin but denser layer [46].The moderate CD of 70% balances both of these effects creating a thick and dense layer resulting in the lowest permeability of all.
For the systems coated at the lowest charge density (~45%), the highest pure water permeabilities are generally observed.Low charge density PEI has a low degree of protonation, resulting in limited intrachain repulsion and thus a more coiled conformation [30,47].It is expected that these conditions induce the formation of the thickest but most open multilayers [43,44].
The low pure water permeability for the system coated with PEI with a CD of 70% can be explained by the high amounts of adsorbed PE.Due to the coiled conformation of the polymer chains caused by incomplete ionization of the amine groups, thicker multilayers are formed resulting in more resistance toward permeation [48].Furthermore, during the subsequent PSS assembly step at a lower pH value of 5.8, part of the uncharged amines become protonated, resulting in expansion of the PEI chains and a higher PSS adsorption to cover all the positively charged groups [29,47,49].
Adsorption of PEI with a CD of 100% results in the formation of thinner but denser multilayers, with less adsorbed PE in every coating step.This is caused by the stretched, elongated conformation of the high charge density PEI and PSS chains [47,50,51].Even though PEI has a branched structure, it still behaves as a worm-like chain, where at higher CDs, more elongation of the chain is observed [47,51].Therefore, only a small amount of PE is required to compensate for all charges from the previously deposited negatively charged layer, resulting in less adsorption of material and thinner adsorbed layers [52].This, as the results show, gives rise to lower resistance towards permeation, despite the higher density of the layers.

Molecular weight cut-off
A parameter that gives information about the ability of the membranes to separate uncharged species based on size is the molecular weight cut-off (MWCO).The MWCO is defined as the smallest molecular weight of which 90% is retained by the membrane.The lower the MWCO, the better it retains smaller pollutants and MWCOs of most commercial NF membranes lay between 200 and 1000 g/mol [53].The experimentally determined MWCO values of the symmetric PEI/PSS coated membranes are given in Fig. 5.
Clearly, the MWCO of the PEI/PSS membranes with a CD of 45% is not in the NF regime.This is a confirmation that this CD forms the most open multilayers.Moreover, the MWCO of the other membranes all lay in the same range between 200 and 300 g/mol, which is the lower region of NF membranes.The small MWCO differences compared to the big differences in permeability are a result of the difference in membrane resistance and size exclusion.The system coated with PEI CD=70% has thicker multilayers compared to the system coated with PEI CD=100% resulting in more resistance toward permeation (see Fig. 4).However, this does not result in a lower MWCO, as the increased membrane resistance is caused by an increasing membrane thickness and not by a decreasing pore size, which in fact would be undesired.
Additionally, the membranes coated with a CD of 70% show an oddeven effect, as was also seen for the pure water permeability.At a higher Fig. 4. Pure water permeability for nanofiltration membranes coated with PEI/ PSS layers with a PEI charge density of 45, 70 and 100% for 6.5 bilayers and 7 bilayers, measured at a constant pH of 5.8.pH, PEI has a lower polymer charge which makes it more prone to significant swelling [45,54].Therefore, a more open membrane structure is obtained with PEI terminated membranes compared to PSS terminated membranes, hence higher MWCOs are found.

Salt retentions
To investigate the effect of PE adsorption on the final membrane performance, the retentions of several salts for membranes with 6.5 and 7 bilayers have been determined and are depicted in Fig. 6.
In general, for BL 6.5 as well as BL 7, the MgSO 4 , Na 2 SO 4, and NaCl retentions all increase with increasing charge density.For MgCl 2 however, a maximum is observed and the retention is found for membranes prepared with PEI with a charge density of 70%, followed by 100% and 45% (R MgCl2 70% > R MgCl2 100% > R MgCl2 45% ).The salt retention of the membranes with less BLs (1, 3, 5, 7) is given in the supplementary information (Fig. S5).Those data show that all salt retentions are low for membranes prepared with PEI with a CD of 45%, as is also visible for BL 6.5 and 7.For the membranes prepared with PEI with a CD of 70 and 100%, an increasing salt retention with an increasing amount of bilayers is found as expected.This is in accordance with the permeabilityretention trade-off [55].
Additionally, the salt retentions at a CD of 70 and 100% are clearly affected by charge exclusion, as charged ions are significantly smaller compared to PEGs.The stokes radii of PEG 200 and 400 (in which the MWCOs lay) are 4.3 and 5.4 Å, respectively, whereas Mg 2+ and SO 4 2− radii are 3.5 and 2.3 Å [56,57].Giving this, if no contribution of the solute charges would be relevant to the rejection behavior of the membranes prepared, the retention towards Mg 2+ or SO 4 2− would be significantly lower.
For the membranes coated with PEI with a CD of 45% all retentions are very low (<20%).This is in accordance with the highest permeability values observed, following the permeability-retention trade-off [22,58].Commercial NF permeability values are around 10 L/m 2 hbar with higher retentions than the values reported here [59][60][61].However, LbL layers are usually 'looser' layers due to the low charge density of the adsorbed polymer chains than the selective interfacial polymerization layer of commercial membranes prepared via interfacial polymerization [43,44,62], thus explaining these lower retentions.Additionally, slight negative retentions are measured for MgCl 2 and NaCl at BL 7. The openness of the layers result in high adsorption of PEI as well as PSS with every adsorption step (See Fig. 2).Therefore, membrane charge and corresponding charge exclusion effects shift between BL 6.5 to 7 from a positive to a negative charge.
For the membranes prepared with PEI with a CD of 70%, clear oddeven effects are visible: All salt retentions are higher for BL 7 compared to BL 6.5.At BL 7, less swelling occurs resulting in more size exclusion, hence an increase in all retentions, as confirmed by the lower MWCO at BL 7 (Fig. 5).Interestingly, at BL 6.5 the salts are retained in the order MgCl 2 >MgSO 4 >NaCl > Na 2 SO 4 , whereas at BL 7 this is MgSO 4 >MgCl 2 >Na 2 SO 4 >NaCl.This demonstrates the influence of size as well as charge exclusion: With size exclusion, the salt ions with a higher stokes radii are easier retained, which from highest to lowest radius is Mg 2+ >SO 4 2− > Na + >Cl − [56].This would result in the retention order of: MgSO 4 >MgCl 2 >Na 2 SO 4 >NaCl, as is the case for BL 7.However, considering charge exclusion, the membrane charge determines the repulsion and attraction of ions.The membrane terminated with PEI CD = 70% has significantly more positive surface charge compared to the PSS terminated membrane, as seen in Fig. 3. Therefore, the PEI terminated membrane attracts anions and repels cations [27].
That the charge exclusion for the PEI terminated membrane significantly impacts the salt retentions is clearly visible in the higher NaCl retention compared to the Na 2 SO 4 retention as well as the slightly higher MgCl 2 compared to the MgSO 4 retention.
The highest retentions overall are found for the PEI/PSS membranes coated with PEI with a CD of 100%.The order of retentions is Na 2 SO 4 >MgSO 4 >NaCl > MgCl 2 and follows the results from Dizge et al. for membranes with two BLs of PEI/PSS [63].The results for BL 6.5 and 7 show only small differences visible for BL 6.5 and 7, which is a confirmation of the formation of thin layers with high charge density PEs, as was already proven by the limited amount of PE adsorbed in each step with reflectometry (Fig. 2), combined with the small permeability and MWCO differences between BL 6.5 and 7. Additionally, a significant difference in the measured zeta potentials for BL 6.5 and 7 exists: The membrane with BL 7 has a more negative zeta potential than that with BL 6.5.Charge exclusion due to the negative surface charge of the membrane results in the overall high MgSO 4 and Na 2 SO 4 retentions, which are slightly higher for BL 7 compared to 6.5.
From these results, it can be concluded that all PEI solutions, despite the difference in CD, adsorb on both the model surface as well as the porous support.However, a CD of 45% results in a more open membrane layer, which is unable to retain salt ions.A CD of 70%, as well as 100%, gives rise to moderate pure water permeabilities, with MgSO 4 retentions surpassing 80%.With a CD of 70%, a more positively charged membrane is produced, whereas for 100% a more negatively charged membrane is obtained.The effect of this is especially visible when comparing the difference in retention for Na 2 SO 4 and MgCl 2 .

Asymmetric PEI/PSS membranes
To be able to decouple to a certain extent the membrane permeability/retention trade-off, as a next approach the properties and performance of asymmetric membranes are investigated.This approach introduces next to the CD of the PEs and the charge of the terminating layer another parameter to tune membrane performance: i.e. the PE chemistry.This allows the combining of different PE chemistry properties in one single membrane assembly.Here we compare the data of membranes all made with 5 base BLs PDAMAC/PSS followed by layers of PEI/PSS/PEI (i.e.(PDADMAC/PSS) 5 + (PEI/PSS) 1.5 ) or PEI/PSS/PEI/ PSS (i.e.(PDADMAC/PSS) 5 + (PEI/PSS) 2 ).The base membrane is suited for asymmetric layer-by-layer formation as it has a significantly higher PWP of ~50 L/(m 2 hbar) compared to PWPs of ~31, 11 and 16 for PEI/ PSS (5 BLs) with a CD of 45, 70 and 100% (See Fig. S5) [10].Moreover, PDADMAC/PSS is a stable PE couple as can be seen by the PE adsorption in the supplementary information (SI Fig. S6).

Membrane surface charge
The surface charge of the asymmetric membranes is given in Fig. 7. Here, the PEI terminated membranes are positively charged, whereas the PSS terminated membranes are negatively charged.This behavior is similar to the symmetric membranes in Fig. 3. Hence the membrane surface charge is mainly determined by the terminating layer and not by the underlying layers.

Pure water permeability
The permeabilities of membranes with different base layers of PDADMAC/PSS (1, 3, 5, and 7) and two terminating BLs of PEI/PSS, are given in the supplementary information (Fig. S7), for the three different charge densities.Here a consistent trend is observed: The asymmetric membranes show the highest permeability at a PEI CD of 100% followed by 70% and 45%.To look in more detail, Fig. 8 shows the PWP for assemblies that consist of 5 base bilayers of PDADMAC/PSS terminated with 1.5 (BL 6.5) or 2 (BL 7) bilayers of PEI/PSS.
In previous research, we showed that membranes with a base layer of PDADMAC/PSS (5 BLs) have a PWP of ~50 L/(m 2 hbar) [10].The addition of the extra PEI/PSS layers significantly decreases the permeability for all CDs.For BL 6.5 (i.e. the base membrane coated with PEI/PSS/PEI) as well as BL 7 (i.e. the base membrane coated with PEI/PSS/PEI/PSS) an increasing permeability with an increasing charge density is seen.Moreover, the addition of an extra PSS layer (BL 7) results in a decrease in permeability for all charge densities.This decreasing permeability for PSS terminated layers was also observed for the symmetric PEI/PSS systems in Fig. 4.
The obtained order of the permeability (PWP CD = 45% < PWP CD = 70% < PWP CD = 100% ) is contrary to what is observed for the symmetric PEI/ PSS coated membranes: In that case the order was PWP CD = 70% < PWP CD = 100% < PWP CD = 45% (Fig. 4).This difference is attributed to the difference between the amount of PE adsorption and the formed structure of the formed layers.The PEI/PSS adsorption results showed that the highest amount of PE is adsorbed for the lowest CD (45%), but that the structure remains relatively open and is unable to retain any salts, as indicated by the low retentions (Figs. 2 and 6).The lower pure water permeability obtained for the asymmetric membranes is an indication of an additional resistance of the membrane, which is hypothesized to stem from the thickness of the PEI/PSS layers, due to the extra PE material that is adsorbed.

Molecular weight cut-off
The experimentally determined MWCO values of the asymmetric membranes are given in Fig. 9.All these membranes have MWCO values in the NF range, i.e. between 200 and 1000 g/mol [53].Hence, in terms   of size exclusion, the base layers of PDADMAC/PSS are of great benefit as previously with symmetric membranes prepared with PEI with a CD of 45% MWCOs above 1000 g/mol were obtained.
In general, the MWCO of PEI terminated membranes is higher compared to PSS terminated membranes.Moreover, the difference between PEI and PSS terminated membranes decreases with increasing CD.PEI swells more at a lower CD and also more than PSS resulting in a more open membrane structure at lower CDs and when PEI terminated membranes are used, hence higher MWCOs are obtained [14,45].Moreover, a lower CD of PEI results in more PSS adsorption resulting in higher membrane resistance and a denser membrane at 7 BLs (as previously seen in Figs. 2 and 8).This explains the increase in MWCO with increasing CD for BL 7.

Salt retention
To investigate the effect of PE adsorption on the final membrane performance, the retentions of several salts for the systems with 6.5 and 7 bilayers were measured and are depicted in Fig. 10.All the salt retentions of the base membrane with five PDADMAC/PSS layers are lower than 35%.The retentions for the different PSS terminated membranes are given in the supplementary information (Fig. S8).
Clear differences between 6.5 or 7 bilayers are observed in membrane retention.In general, the salt retentions are higher for the membranes terminated with PSS, compared to PEI terminated membranes.This is in accordance with the permeability-retention trade-off, where lower permeabilities are correlated to higher retentions caused by the swelling of PEI (Fig. 7).For BL 6.5 and PEI with the lowest charge density (CD = 45%), moderate retentions are measured for MgSO 4 , Na 2 SO 4 and MgCl 2 , which increase tremendously with the addition of the PSS layer (BL 7).For membranes coated with PEI with a CD of 45 and 70%, clear odd-even effects are visible.At BL 6.5 the salts are retained in the order MgSO 4 >MgCl 2 >Na 2 SO 4 >NaCl, whereas at BL 7 this is Na 2 SO 4 >MgSO 4 >MgCl 2 >NaCl.This is an important observation, as it also demonstrates the influence of charge as well as size exclusion.The membrane terminated with PEI has a positive charge, whereas the PSS terminated membrane is more negatively charged.Therefore, the PSS terminated membranes repel multivalent anions more than PEI terminated membranes.This explains why for the PEI terminated membranes the Na 2 SO 4 retention is significantly lower.

Comparison of symmetric and asymmetric membranes
To be able to compare the effect of layer build-up of symmetric and asymmetric membranes, the permeability and salt retention of 7 BLs for all these membranes are shown in Fig. 11.Only results for membranes coated with PEI with a CD of 45 and 100% are shown, as these show the most interesting differences.For the membranes coated with PEI CD = 45%, the membrane performance differs significantly between symmetric and asymmetric membranes.For the symmetric membrane, the low charge density of PEI results in limited intrinsic linkages between the polyelectrolytes, which favors the formation of a fluffy, more open and more permeable multilayer, giving low salt retentions.Asymmetric membranes, however, show a significantly lower permeability, but with retentions over 90% for MgSO 4 and Na 2 SO 4 .The base membrane is less positively charged compared to the fully symmetric membrane, causing PEI and PSS to interdiffuse into the base structure, resulting in a denser membrane.
For the membranes prepared with PEI with a CD of 100%, the asymmetric membranes have a lower membrane resistance compared to the symmetric membrane.As previously mentioned, a lower membrane resistance is caused by either a more open or a thinner selective layer [8].The asymmetric membrane has a slightly more open layer, as seen by the lower MgCl 2 and NaCl retentions, as well as a thinner selective layer, as seen by the much higher PWP.

Conclusions
Symmetric and asymmetric NF membranes are produced by layerby-layer assembly of PEI/PSS on a model surface as well as on a porous support using different charge densities of PEI.The PEI CD is varied by changing the pH of the coating solution.Overall, at a lower CD, more PE is adsorbed due to the lower surface CD induced by PE deprotonation.The PE deprotonation results in fewer intrinsic linkages that are formed resulting in thicker but more open layers.
For symmetric systems, with a CD of 45%, this results in a high pure water permeability, but with very high MWCOs as well as salt retentions of only 20%.The membranes with a CD of 70% and 100% have moderate pure water permeabilities with MgSO 4 retentions surpassing 80%.With a CD of 70% a more positively charged membrane with high MgCl 2 retentions is produced, whereas for 100% a more negatively charged membrane with high Na 2 SO 4 retentions is obtained.
Contrarily, for asymmetric systems, nanofiltration membranes are formed for all charge densities due to the already deposited base layers of PDADMAC/PSS.For all PSS terminated membranes (BL 7), we have MgSO 4 and Na 2 SO 4 retentions of over 90%.Between the different charge densities, clear differences are visible due to less swelling of PEI at high Additionally, the benefits of the thin layer formation with asymmetric membranes are proven by comparing the best membrane performances measured with the highest CD (100%) during coating.For symmetric systems, permeabilities of ~9 L/(m 2 hbar) could be achieved, while reaching retentions for MgSO 4 and Na 2 SO 4 of 90 and 95%, respectively due to the thin layers formed.For asymmetric membranes, the thickness of the selective layer is even further decreased, resulting in significantly higher permeabilities (~12 L/(m 2 hbar)) while reaching even higher MgSO 4 and Na 2 SO 4 retentions (94 and 97%, respectively).The asymmetric approach resulted in the successful production of LbL membranes, with higher permeabilities and retentions compared to the symmetric approach.Therefore, it can be concluded that asymmetric layer-by-layer formation, especially with high charge densities, has a lot of potential to improve the NF membrane performance for different applications, such as desalination.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 2 .Fig. 3 .
Fig. 2. Adsorption of PEI/PSS layers on silicon wafers monitored via optical fixed angle reflectometry for three different charge densities of PEI (45, 70 and 100%).PE concentration of 0.01 wt% and ionic strength of the coating solution of 0.05 M NaCl.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 5 .
Fig.5.Influence of the charge density of PEI (45, 70 and 100%) on the MWCO for 6.5 and 7 bilayers of PEI/PSS membranes.The two membranes coated with a CD of 45% exceed the NF MWCO range of 1000 g/mol and cannot be determined experimentally.Therefore, these data points are plotted with shaded bars.

Fig. 7 .
Fig. 7. Influence of the charge density of PEI (45, 70 and 100%) on the apparent zeta for asymmetric coated membranes with five BLs of PDADMAC/ PSS and 1.5 or 2 BLs of PEI/PSS.

Fig. 11 .
Fig. 11.a) Pure water permeability and b) salt retention of nanofiltration membranes with either 7 BLs of PEI/PSS (symmetric) or 5 BLs of PDADMAC/PSS and 2 BLs of PEI/PSS (asymmetric), for two different charge densities of 45 and 100%.