Polyamide nanofiltration membrane with highly uniform sub-nanometre pores for sub-1 Å precision separation

Separating molecules or ions with sub-Angstrom scale precision is important but technically challenging. Achieving such a precise separation using membranes requires Angstrom scale pores with a high level of pore size uniformity. Herein, we demonstrate that precise solute-solute separation can be achieved using polyamide membranes formed via surfactant-assembly regulated interfacial polymerization (SARIP). The dynamic, self-assembled network of surfactants facilitates faster and more homogeneous diffusion of amine monomers across the water/hexane interface during interfacial polymerization, thereby forming a polyamide active layer with more uniform sub-nanometre pores compared to those formed via conventional interfacial polymerization. The polyamide membrane formed by SARIP exhibits highly size-dependent sieving of solutes, yielding a step-wise transition from low rejection to near-perfect rejection over a solute size range smaller than half Angstrom. SARIP represents an approach for the scalable fabrication of ultra-selective membranes with uniform nanopores for precise separation of ions and small solutes.


Chemicals and materials
Piperazine membrane was purchased from Microdyn-Nadir (Germany).

Positron annihilation spectroscopy (PAS)
A slow positron beam (VMSPB) was used to determine the free volume size and distributions of TFC-PA membrane from conventional IP and SARIP with SDS. This radioisotope beam used 50 mCi of 22 Na as the positron source. Two positron annihilation spectroscopies were collected to explore the microstructure of the TFC-PA membrane: Doppler energy spectroscopy (DBES) and positron annihilation lifetime (PAL) spectroscopy. The DBES spectra were determined using PAS with a variable monoenergy slow positron beam (0-30 keV) and recorded using an HP Ge detector (EG&G Ortec). Two parameters, R and S, were reported from the DBES measurement. The S parameter, which was from the o-Ps 2g pick-off annihilation in free volume, yielded information about the depth profile of the free volume (Å to nm) in the polyamide layer. Whereas the R parameter, defined as the 3g to 2g annihilation ratio, indicated the existence of large pores (nm to um) in which ortho-Positrinium (o-Ps) underwent 3g annihilation. The PAL spectra were analyzed using the PATFIT to obtain the o-Ps lifetime ! (1-5 ns), which was used to calculate the mean radius of the free volume (Å to nm) based on a semiempirical equation from a spherical-cavity model. The continuous o-Ps lifetime distribution was obtained from the MELT program to show the corresponding distribution of free volume in the PA network. Detailed descriptions of slow positron beam and PAS data analysis could be found elsewhere 1 .

Scanning electron microscopy (SEM)
Surface morphology of TFC-PA membranes from conventional IP and SARIP with SDS were characterized by a high-resolution Zeiss Merlin scanning electron microscope with GEMINI II column with an accelerating voltage of 3 kV. Samples were sputter-coated with gold (~5 nm thick) to inhibit the charging effect.

X-ray photoelectron spectroscopy (XPS)
Surface elemental composition of polyamide active layers from conventional IP and SARIP was analyzed using a Thermal Fisher Scientific ESCALAB 250 Xi X-Ray photoelectron spectrometer. XPS specimens were prepared by carefully mounting polyamide films onto a silicon wafer. High-resolution scans in the carbon, nitrogen, oxygen, sulfur, and bromine regions were performed at 0.5 eV increments with a sweep time of 5000 s eV -1 and 25 energy sweeps for each region. XPS peak fitting was performed with XPSPEAK41 software.

Transmission electron microscopy (TEM)
Cross-sectional TEM images of TFC-PA membranes prepared from conventional IP and SARIP were obtained using an FEI Tecnai G2 F20 S-twin 200kV field-emission transmission electron microscope. TEM specimens were prepared by embedding TFC-PA membranes into epoxy resins, then ultrathin sections were prepared with a Leika EM UC7/FC7 microtome and carefully mounted onto lacey carbon support grids. The PA layer thickness was obtained by analyzing the TEM image using Image-J. Eight measurements were made at different locations along the PA layer. The reported PA layer thickness represented the average of eight measurements and the error bar represents the standard deviation of eight measurements.

Atomic force microscopy (AFM)
The three-dimensional topography of freestanding PA films from conventional IP and SARIP was measured with a Bruker Dimension Icon atomic force microscopy. Freestanding PA films were prepared using the same receipt in section 2.1, except that no PES support was used. The PA film formed at the water-hexane interface between PIP solution and hexane were transferred to a silicon wafer. The images were captured in tapping mode with RTESP probe (tip radius 8 nm, spring constant 40 N m -1 ). A sampling resolution of at least 256 points per line and a speed of 0.1 to 1 Hz were used.

Contact angle measurement
The contact angle of the PIP aqueous solution with a variety of surfactants on the PES UF substrate was measured on an OCA20 instrument (Data-Physics, Germany) system at ambient temperature. PES membranes were dried before measurement and mounted on glass slides. A drop of PIP aqueous solution (~3 ul) with different concentrations of surfactant was placed on the PES surface with a syringe. An optical image of the drop outline on the PES membrane surface was captured, and the corresponding water contact angle was calculated with a circle fitting method by drop shape analysis software.

Interfacial surface tension measurement
The interfacial surface tension between n-hexane and PIP aqueous solution with and without surfactants was measured using the pendant drop method with OCA20 instrument (Data-Physics, Germany). A transparent cubic container was filled with n-hexane, and one drop of PIP solution was generated from a syringe tip into hexane. An optical image of the drop hanging on the dosing needle was captured and the corresponding IFT value was calculated based on the Young-Laplace equation.

Streaming potential measurement
The surface streaming potential of TFC-PA membranes prepared via conventional IP and SARIP with various surfactants was performed on an electro-kinetic Analyzer (SurPASS, Anton Paar, Ashland, VA) with an adjustable gap cell. The streaming potential values were measured from pH 3 to 10 using 1 mM KCl solution as the background electrolyte at ambient temperature.

Preparation of Poly(piperazine-amide) nanofiltration membrane via conventional interfacial polymerization (IP)
Interfacial polymerization was first discovered in 1959 and remains state-of-the-art method for large-scale fabricating commercial polyamide nanofiltration (NF) and reverse osmosis (RO) thinfilm-composite (TFC) membranes 2,3 . In this process, an ultrafiltration (UF) membrane (as the support layer) is wetted with an aqueous amine solution and then brought into contact with an immiscible organic solution containing acid chloride. Upon contact, amine molecules diffuse from the pores of the support membrane, across the water/oil interface, and react with acid chlorides in the oil phase to form the polyamide network.
In this study, conventional IP was performed using an aqueous solution of 0.25 % w v -1 piperazine and an n-hexane solution of 0.

SARIP with sodium dodecylbenzene sulfonate (SDBS)
Another anionic surfactant, sodium dodecylbenzene sulfonate (SDBS), was investigated because SDBS chemical structure resembles that of SDS and should theoretically lead to qualitatively similar improvement of the properties of the PA layer according to the SARIP theory.
The mechanism was explained in the following contents. The concentrations of SDBS in PIP solution were 0.6 mM (0.5 CMC), 1.2 mM (1 CMC) and 8.2 mM (1 CMC of SDS).

NF performance test of polyamide nanofiltration membranes from conventional IP and SARIP
The performance of the fabricated NF membranes was tested using a system with three parallel The pure water permeability of TFC-PA membrane was calculated by the following equation: where is the pure water permeability of TFC-PA membrane (L m -2 h -1 bar -1 ), ∆ is the permeate water volume (L) collected over the period ∆ (h), is the effective membrane area (m 2 ), and ∆ was the applied pressure (bar), respectively.
The volumetric flux of water, (L m -2 h -1 bar -1 ), was calculated using the following equation: The salt rejection, (%), was calculated using the following equation: where R is the salt rejection (%), " and # are the salt concentrations of the permeate and feed solution (ppm), respectively. The concentration of each organic species solution was 200 ppm and the applied pressure in the filtration experiments was 4 bar. The MWCO of TFC-PA membranes was defined as the molecular weight at which the rejection equals 90%. The pore size distribution curve is expressed as a probability density function (PDF) that was established based on the following assumption: (1) There is no steric or hydrodynamic interaction between these organic solutes and the membrane pores; (2) The mean pore size of the polyamide membrane equals the Stokes radius of the organic solute with a measured rejection of 50%; (3) The distribution of the membrane pore size is characterized by the geometric standard deviation of the PDF curve, which is the ratio between the Stokes radius with a rejection of 84.13% to that with a rejection of 50% 4 .
where " is the mean pore size, " is the geometric standard deviation of the PDF curve and " is the Stokes radius of the organic solute. The Stokes radii of these molecules correlate with their molecular weight 4 : where is the molecular weight of each organic solute. Based on the above equation, the Stokes radii for glycerol, glucose, sucrose, and raffinose are 0.261, 0.359, 0.462, and 0.538 nm, respectively. Separation mechanisms in NF include mainly steric (size sieving) and Donnan (charge) exclusion 7,8 . Solute molecules with a size that is larger than the membrane pore size are sterically blocked, while the transport of solutes with a size similar to that of the membrane pores may also be hindered. A membrane surface with a fixed charge repels ions with the same charge and attracts ions with the opposite charge. Because the poly(piperazine-amide) nanofiltration membrane has a net negative surface charge from the hydrolysis of unreacted TMC groups, it exhibits high rejection of SO4 2but relatively low rejection of Mg 2+ and Ca 2+ . The difference in selectivity for different cations with similar net charges and radii ( Fig. 1d and Supplementary Figure 1) could be further explained based on the dehydration mechanism, i.e., an ion that approaches the membrane pore can strip and readjust its water shells temporarily in order to fit into the membrane pores. In general, smaller ionic size results in higher hydration energy, and ions with higher hydration energy are rejected more effectively by NF and RO membranes 9 . Ion dehydration, which is significant in NF because of the small pore sizes, offers an additional explanation for the differences in the rejection of ions with similar charge and hydrated radii, e.g., Ni 2+ (24%) and Ba 2+ (17%), in the PA-TFC prepared from conventional IP.

Mean free-volume radius and free-volume radius distribution of PA from conventional IP and SARIP (with SDS) as assessed by Positron Annihilation Lifetime Spectroscopy (PALS)
Supplementary

XPS survey spectra of the PA active layer from conventional from SARIP (with SDS)
Supplementary Figure 3. XPS survey of polyamide active layer prepared via SARIP as a function of SDS concentration.

Calculation of degree of cross-linking of polyamide network
Supplementary

High-resolution XPS spectra of poly(piperazine-amide) active layer from conventional IP and SARIP (with SDS)
Supplementary where "+" is the energy of one PIP molecule, /0"+" is the total energy of the system including the PIP molecule and its surrounding, and / is the energy of the system without the PIP molecule, respectively. Figure 7. Binding energy of one PIP molecule to its surrounding in the two MD systems, (a, c) with self-assembled network of SDS at water-hexane interface, (b, d) without SDS network, at three sites: a1, b1, water; a2, b2, water/hexane interface; a3, b3, hexane.

Supplementary
In the presence of an SDS dynamic network, E *+,-+,. at the water/hexane interface (site a2), is calculated to be negative, which indicates that the transport of PIP molecules from bulk solution towards the interface is an energetically favorable process. This result is in good agreement with the locally concentrated population of PIP molecules near the interface. The further transport of a PIP molecule from the water/hexane interface into hexane needs to overcome an additional binding energy penalty of 0.29 eV with the presence of SDS network. Whereas, in the MD system without SDS network, the energy of PIP molecules at the interface is higher than that in the bulk solution, meaning that transport of PIP molecules to the interface is energetically unfavorable. The energy gain for a PIP to transport from the interface into hexane is 1.12 eV in the absence of SDS network, more than three times larger than that with SDS. Therefore, the formation of a self-assembled SDS network at the water/hexane interface reduces the energy required for PIP to diffuse across the water/hexane interface.
While the results presented in Supplementary Figure 7 (c,d) seem to suggest that the diffusion of PIP from the aqueous to the hexane phase is both energetically unfavorable, the MD simulation performed to generate these results only consider the interaction between a PIP molecule and its medium but does not consider the effect of concentration gradient and the polymerization reaction in the hexane phase that depletes the PIP in hexane. The overall diffusion-reaction process is still energetically favorable if both the enthalpic (i.e., binding energy) and entropic contributions are considered. While the MD simulation of the entire diffusion-reaction process is technically highly challenging, the simulation of the binding energy presented in Supplementary Figure 7 is meant to semi-quantitatively show that the presence of the SDS will dramatically reduce the enthalpic gain of the diffusion and thus reduce the barrier of Gibbs free energy for the diffusion-reaction process.

Calculation of surface excess concentration (SEC)
The adsorption of surfactant molecules at the interface is driven by reducing the Gibbs free energy of the system [15][16][17] . Therefore, the concentration of surfactants at the interface is much higher than that of the bulk volume. Such difference of the concentration at the surface and any virtual interface in the bulk volume is called the surface excess concentration (SEC), Г, where the Γ 1 is the interfacial concentration and Γ 2 is the concentration at a virtual interface in the bulk solution.
The surface excess concentration is directly related to the interfacial surface tension (IFT) and can be calculated with the Gibbs adsorption isotherm equation 15 : where the is the interfacial surface tension

Density Functional Theory (DFT) modeling of the interaction between PIP and SDS
To get the insight of how the interaction between a PIP molecule and an SDS molecule changed during the transport of PIP from water to hexane, we also performed a DFT simulation with Dmol modules in Material Studio. The molecular Frontier Orbital of the PIP molecule and SDS molecule was calculated first in order to identify the population of the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO). As shown in Fig S9 ( To simplify the DFT calculation, the transport of one PIP molecule along one SDS molecule was divided into three parts according to the location of PIP relative to SDS (Fig, S10). Part 1 described the attraction between the SDS sulfate group and the PIP molecule in bulk solution (The distance between pip and SDS is around 5Å); Part 2 was the engagement of the PIP molecule with the sulfate group; and in part 3, five different sites along the SDS alkane backbone were selected to discuss the change of interaction between PIP and SDS during transport. The adsorption energy (Eads) of PIP at each site was calculated by the following equation, where "+" was the energy of a single PIP molecule, * 0"+" was the energy of the SDS molecule with the adsorption of PIP, and * was the corresponding energy of the SDS molecule without adsorption of PIP.

Monte Carlo simulation of molecular diffusion across interface with different levels of energy barrier
With the results from the MD and DFT simulations consistently showing that the presence of SDS may reduce the energy barrier for PIP diffusion across the water/hexane interface, we perform simplified Monte Carlo (MC) simulations to illustrate why a lower energy barrier for diffusion can lead to more homogenous diffusive flux. In such an MC simulation, a group of generic particles (mimicking PIP molecules) attempt to pass a grid of cells (10 ´ 10 in this study) with a certain energy barrier, ΔEB. We assume that the intrinsic kinetic energy of these particles follows a Maxwell-Boltzmann distribution as expressed in the following equation where dN/N is the fraction of PIP molecules moving at velocity v to v + dv, m is the mass of the PIP molecule, kB is the Boltzmann constant and T is the absolute temperature. Therefore, the probability of one PIP molecule moving with a speed of v in three dimensions can be expressed as For each "diffusion attempt" across a cell in the grid, we randomly assign kinetic energy to a particle according to the Maxwell-Boltzmann distribution. If the energy of that particle is higher than the energy barrier (i.e., & > 8 ), the attempt is considered as successful and one additional particle is recorded as passing that specific cell. Otherwise, the attempt is considered as a failure and we move onto the next cell for the next "diffusion attempt". Each cell has one diffusion attempt in each round (which comprises 100 attempts). The simulation continues until 1,000 particles have successfully "diffused" across the 10 ´ 10 grids, resulting in an average of 10 particles per grid.
With the cumulative number of successful diffusions for each cell, we create a map of "diffusion flux" for the grid, with an example shown in Fig. 3 (f) in the main text. The value of 8 has an impact on the distribution of diffusion flux, with a higher : leading to a more heterogeneous of diffusion flux and a lower 8 resulting in a more homogeneous diffusion flux.
The heterogeneity can be quantified by calculating the standard deviation of the number of successful diffusions for different grids. We perform such simulations for a range of 8 to obtain the standard deviation and the total number of diffusion attempts (to generate 1,000 successful diffusions) for each 8 . The results presented in Fig. 3 (e) in the main text show that a lower : leads to both faster diffusion (as quantified by fewer diffusion attempts) and a more homogeneous distribution of diffusion flux (as quantified by a lower standard deviation).
Notes: The MC simulations described above are highly simplified and are meant to illustrate qualitatively how reducing energy barrier leads to more uniformly distributed diffusion of molecules across an interface. The impact of the level of energy barrier on diffusion homogeneity may likely be even more significant due to the "positive feedback" mechanism.
Specifically, when a PIP molecule successfully diffuses across an interface and reacts with TMC, a considerable amount of heat will be generated locally as the reaction of PIP and TMC is strongly exothermic. A large fraction of such released heat may propagate back to the water phase near the water/hexane interface (water is significantly more thermally conductive than hexane) and thereby increase the local temperature. The increased local temperature will result in higher thermal energy for the particles attempting to diffuse across and thus enhance the chance of successful subsequent diffusion. In short, a successful diffusion event will facilitate further successful diffusion near the same location, which is a positive feedback mechanism that tends to make the diffusion more heterogeneous. Accurately modeling this positive feedback mechanism is difficult and adds little to the already-highly-simplified MC simulation that is only qualitatively meaningful. We, therefore, do not attempt to perform such a simulation but only discuss the mechanism qualitatively.   Figure 12), which is attributable to a higher degree of crosslinking of the PA layer (Supplementary Table 7) and smaller mean pore size (Supplementary Figure 11 a,c). However, even with the highest PIP concentration (0.5 % w v -1 , twice as the concentration used in SARIP), the rejection of Mg 2+ and Ca 2+ is still moderate as compared to that with TFC-PA membrane obtained using SARIP (with SDS) (Figure 4a). Therefore, even though one of the effects of SDS interfacial network is to enhance the interfacial concentration of PIP, the increase of PIP concentration at the interface is not the only mechanism for achieving a step-wise selectivity (e.g.,  volumes and reduced the surface negative charge. Overall this caused the reduction of rejection of MgSO4 and Na2SO4 and higher selectivity of MgCl2 and CaCl2 at a low concentration of CTAB.
As the concentration of CTAB increased, the more CTAB molecules reacted with TMC in hexane, causing more defects in the polyamide network, leading to the increasing reduction of ion selectivity of the polyamide nanofiltration membrane.     The TFC-PA membrane prepared via SARIP with SDS had much smaller pores than the TFC-PA membrane prepared via conventional IP: the MWCO was reduced to more than one half of the value of the conventional TFC-PA membrane, i.e., the mean pore size decreased from 0.34 nm to 0.29 nm and the distribution of pore size also decreased from 1.345 to 1.217. This provided another evidence of the role of self-assembled SDS dynamic network on the formation of polyamide with smaller and more uniform pore sizes.

TFC-PA NF membrane prepared via SARIP with 2 CMC SDS
Supplementary Figure 34. Rejection of different solutes by TFC-PA membranes fabricated using SARIP with 2 CMC SDS.

MWCO and pore size of TFC-PA membrane from SARIP (with SDS)
Supplementary  Table 3), i.e., the pore size is still widely distributed. In contrast, TFC-PA from SARIP does not only have a smaller mean pore size and MWCO but also a smaller standard deviation (Supplementary Table 7).