Layer-by-layer Assembly of Nanosheets with Matching Size and Shape for More Stable Membrane Structure than Nanosheet-Polymer Assembly

Layer-by-layer (LbL) assembly of oppositely charged materials has been widely used as an approach to make two-dimensional (2D) nanosheet-based membranes, which often involves 2D nanosheets being alternately deposited with polymer-based polyelectrolytes to obtain an electrostabilized nanosheet-polymer structure. In this study, we hypothesized that using 2D nanosheets with matching physical properties as both polyanions and polycations may result in a more ordered nanostructure with better stability than a nanosheet-polymer structure. To compare the differences between nanosheet–nanosheet vs nanosheet-polymer structures, we assembled negatively charged molybdenum disulfide nanosheets (MoS2) with either positively charged graphene oxide (PrGO) nanosheets or positively charged polymer (PDDA). Using combined measurements by ellipsometer and quartz crystal microbalance with dissipation, we discovered that the swelling of MoS2–PrGO in ionic solutions was 60% lower than that of MoS2–PDDA membranes. Meanwhile, the MoS2–PrGO membrane retained its permeability upon drying, whereas the permeability of MoS2–PDDA decreased by 40% due to the restacking of MoS2. Overall, the MoS2–PrGO membrane demonstrated a better filtration performance. Additionally, our X-ray photoelectron spectroscopy results and analysis on layer density revealed a clearer transition in material composition during the LbL synthesis of MoS2–PrGO membranes, and the X-ray diffraction pattern suggested its resemblance to an ordered, layer-stacked structure. In conclusion, the MoS2–PrGO membrane made with nanosheets with matching size, shape, and charge density exhibited a much more aligned stacking structure, resulting in reduced membrane swelling under high salinity solutions, controlled restacking, and improved separation performance.


Supporting Table
Table S1.            Figure S17.Filtration performance of nanosheet-based membranes from previous studies.The permeability results were selected from membranes with thickness less than 500 nm.The rejection results were selected for feed molecules with a molecular weight less than 1000 Da.Detailed information are summarized in Table S1.

Text S1. Preparation of GO nanosheets
We prepared GO from graphite using the modified Hummers method 1, 2 .First, graphite flakes were oxidized in a mixture of KMnO4, H2SO4, and NaNO3 (Sigma-Aldrich, St. Louis, MO).The resulting pasty solution was then diluted and sifted through a polyester nonwoven fabric filter (PET, grade 3249, Ahlstrom, Helsinki, Finland) by vacuum filtration.The GO solids retained by the fabric filter were suspended in deionized (DI) water and centrifuged at 8000g-force using a Sorvall RC 6+ (Thermo Scientific, Marietta, OH).The GO solids remaining at the bottom of the centrifuge tube went through at least three cycles of resuspension in DI water and then centrifugation to completely wash out chemical residuals.The washed GO suspension was subsequently ultrasonicated (S-4000, Misonix, Farmingdale, NY) to exfoliate GO particles into GO nanosheets.As the last step, the sonicated solution was centrifuged at 8000g-force to remove any unexfoliated graphite residues, resulting in a pure GO nanosheet suspension.

Text S2. Preparation of XRD samples
After LbL assembly, free standing LbL films can be collected by first drying the membrane in air for 1 min, then resubmerging in water (see an example photo below, the brown colored thin film was the detached LbL film).The floating LbL film was then collected on a silica wafer and dried with nitrogen gas.To obtain thicker layers for XRD analysis, the procedure was repeated multiple times.
The XRD samples for layer stacked PrGO and MoS2 was prepared by drop casting the solutions on silica wafer.

Text S3. Characterizing mass loading during layer-by-layer synthesis using QCM-D and ellipsometry
The mass deposition of the LbL membrane was monitored and characterized in a multi-chamber QCM-D system (E-4, Q-sense, Sweden).A gold-coated QCM-D sensor was cleaned and treated in a UV/ozone chamber to make its surface negatively charged.First, Milli-Q grade water (MQ) was pumped into the chamber to obtain an equilibrated baseline of the vibration frequency of the clean sensor.Then, 0.5 g/L PrGO or PDDA solution was pumped into the chamber with a flow rate of 0.1 ml/min.The positively charged material was therefore deposited in situ on the QCM-D sensor by electrostatic attraction.To ensure a maximized deposition, the solution was not changed until the frequency of the gold sensor was stabilized.MQ water was subsequently pumped into the chamber at the same flow rate to remove excess polycation.Similar procedure was performed for MoS2 deposition.The QCM-D measures the change of frequency and dissipation during deposition and the mass of each layer was later calculated using a viscoelastic model.
To analyze the swelling behavior of the as synthesized membrane, the simultaneous QCM-D and ellipsometry measurements were enabled by mounting a single-chamber QCM-D system (E-1, Qsense, Sweden) onto the sample holder of a multi-wavelength ellipsometer (FS-1Multiwavelength, Film Sense, Lincoln, NE).The mass change was monitored using QCM-D as described previously.During layer deposition, the ellipsometer measures the change of reflected light polarization from the LbL layers.The measured polarization data was used to fit the refractive index "n" with the Cauchy dispersion model that is built-in in the Film-Sense software (Film Sense, Lincoln, NE), and the thickness of the LbL membranes was calculated.

Text S4. Determination of PEG concentration using Dragendorff method
The PEG concentration in membrane feed, retentate and permeate water was determined using Dragendorff method.Dragendorff reagent was prepared by mixing 1) 2.5 mL 16 g/L BiONO3 in 20% acetic acid solution, 2) 2.5 mL 40 g/L potassium iodide solution, and 3) 45 mL 3.88 mol/L acetic acid solution.0.5 ml of sample containing PEG was mixed with 0.6 mL 8.66 mol/L acetic acid solution and 0.1 mL of the Dragendorff reagent in a standard plastic cuvette.The mixed solution should be transparent with light orange color.The solution was tested after 15 min with UV-Vis spectrophotometer (UV160U, Shimadzu Scientific Instruments, Columbia, MD) at 520 nm.The calibration curve for PEG with different molecular weights can be found in Figure S18.

Supporting Calculations Text S5. Calculating the loading of PDDA on PrGO
The chemical composition determined by XPS measurement (Figure S1) was used to estimate the loading of PDDA on PrGO.Using the elemental ratio of C and N measured by XPS, the PDDA can be expressed as (C8.62O0.51N)n(close to the theoretical value of PDDA monomer (C8H16NCl)n 12 , rGO can be expressed as (C37.81O5.24N)n,and PrGO can be expressed as (C16.61O2.69N)n.By using the C/N ratio of each substance, the number of PDDA chains attached to rGO, a, can then be calculated by: is the mass of water between stacked nanosheets; A is the area of the nanosheet; and dcalculated is the interlayer spacing at either dry or hydrated state.The    per unit area (g-nm/cm 2 ) can be calculated from the density of MoS2 and PDDA/PrGO, and the interlayer spacing measured by XRD at dry state: Where  2 is 3.5 g/cm 3 ,   is 1.3 g/cm 3 ; nMoS2 and nPDDA are the weight proportion of each material, which are 0.9 and 0.1 according to the QCM-D results;   is the interlayer spacing of the MoS2-PDDA membrane at dry state that measured by XRD (0.62 nm).
Similarly, the mass of MoS2-PrGO per unit area can be calculated using: is 0.93 nm measured by XRD.
The   can be calculated from the density of water (  =1 g/cm 3 ) and the free spacing between stacked nanosheets.The free spacing is calculated by subtracting the thickness of one nanosheet ( ℎ =0.32 nm) from the interlayer spacing d.The interlayer spacing can now be estimated, and the numbers are tabulated below:

Text S7. Calculating the advection coefficient
The advection coefficient () of the membrane using the solution-diffusion imperfection relationship: = (  −   ) + Where Js is the solute flux, calculated using Js=Jw*Cp; B is the solute permeability coefficient; Cw is the concentration of PEG in the feed (300 mg/L); Cp is the concentration of PEG in the permeate.The equation can be re-written as: 1 −  =  (   −       ) +

Figure S1 .Figure S2 .
Figure S1.XPS results for LbL materials.(A) N 1s scan of rGO.The rGO without PDDA functionalization only has one peak that belongs to the N-H bond (399.3 eV).(B) C 1s scan of PDDA-GO.GO nanosheets functionalized with PDDA without reduction have higher intensity at the C-O peak.(C) Atomic ratio of C, O and N in PDDA, PrGO and rGO.(D) N 1s scan for PDDA, sPSF substrate and PrGO.Only PDDA and PrGO carries the peak from quaternary amine (402.4 eV).

Figure
Figure S6.S 2p scan for MoS2-PDDA membranes with different number of bilayers.The S 2p peak from sPSF at 167.5 eV disappeared after 4 deposited bilayers indicating complete coverage of the sPSF by the bilayers.The S 2p peak from MoS2 at 161 eV was intensified with more bilayers at the same time.

Figure S11 .
Figure S11.XRD of pure A. PrGO and B. MoS2 before and after drying for 10 min under 60C.The interlayer spacing of the materials after drying for 10 min is the same as completely dried condition.

Figure S14 .
Figure S14.Determination of the advection coefficient by correlating rejection and water flux.The the y-intersect is the advection coefficient,, and the slope is the diffusion coefficient, B.

Figure S15 .Figure
Figure S15.Structure of Victoria Blue B (VB) and Rhodamine WT (RWT) drew by MolView.The chemical composition for VB was obtained from Sigma Aldrich.The chemical composition for RWT was from Fisher scientific.

Figure
FigureS14shows the correlating between 1-R and  −     .The value of the slope is the solute permeability coefficient, B, and the value of the y-intercept is the advection coefficient, .
•   +    •   +   =    where Nx is the number of nitrogen atoms of substance x (either PDDA, rGO or PrGO), Cx is the number of carbon atoms of substance x.By plugging in the chemical expression for PDDA, PrGO and rGO, the n can be calculated as   is the density calculated from QCM-D and ellipsometry measurement in either dry or hydrated state;    is the mass of the MoS2 and PDDA/PrGO deposited; Their proportion to total solute flux is: