1D Continuous Subnanofiltration with Ultrahigh Physical Selectivity for HS− Ion

In almost all cellular phenomena and life activities, transmembrane exchange of signals and metabolites is indispensable, and heavily dependent on high selectivity of membrane pores and channels. The involved principles of natural selectivity are widely inspired and adopted for future membrane design, but often limited by the geometry of those artificial channels. Herein, a smectic liquid crystal polymeric (SmP) membrane embedded with tubular cut‐through pillar[5]arene dimers (P5Ds) by self‐assembly is first constructed. The physical confinement effect of inner subnanosized P5D cavity enables SmP membrane to behave with 1D continuous hydrogen sulfide ion (HS−) flow and ultrahigh physical selectivity for HS−. The simulated calculations and corresponding energy analyses show that it is essentially attributed to the size of ion–water cluster, not its own size. It is anticipated to provide a highly precise platform for separation and detection of human endogenous hydrogen sulfide as representative biomarker.


Introduction
Transmembrane exchange of signals and metabolites is the prerequisite of almost all cellular phenomena and life activities. [1]his transport across membrane pores and channels is characteristic of high efficiency, selectivity, and robustness in the response to environmental and developmental fluctuations. [2]2a] These features and principles for natural precision provide inspirational guidelines for future membrane design.
From a chemical perspective, compensatory interactions provided by functional groups or binding sites at the pore/channel wall act as another determinant factor for high selectivity.Furthermore, operating conditions (such as driving force) and solution chemistry can also greatly affect selection efficiency. [3]From a physical perspective, both pore/channel length to affinity for the target solute, and size to recognization for the correct solute, can be integrated conveniently and efficiently into construction of selective membrane.In particular, the confining geometry of those embedded pore/channels endows the membranes with direct and efficient selectivity.
In this work, pillar[5]arene (P5) dimer (P5D) featuring interior continuous water wire [11] was first uniformly embedded into smectic liquid crystal (LC) polymeric (SmP) membrane by convenient self-assembly.In particular, the physical confinement effect of inner subnanosized P5D cavity enabled SmP membranes to behave with ultrahigh physical selectivity for negative hydrogen sulfide (HS À ) ion.It is anticipated to provide a highly precise platform for separation and detection of human endogenous hydrogen sulfide as representative biomarker.

DOI: 10.1002/sstr.202300002
In almost all cellular phenomena and life activities, transmembrane exchange of signals and metabolites is indispensable, and heavily dependent on high selectivity of membrane pores and channels.The involved principles of natural selectivity are widely inspired and adopted for future membrane design, but often limited by the geometry of those artificial channels.Herein, a smectic liquid crystal polymeric (SmP) membrane embedded with tubular cut-through pillar [5]  arene dimers (P5Ds) by self-assembly is first constructed.The physical confinement effect of inner subnanosized P5D cavity enables SmP membrane to behave with 1D continuous hydrogen sulfide ion (HS À ) flow and ultrahigh physical selectivity for HS À .The simulated calculations and corresponding energy analyses show that it is essentially attributed to the size of ion-water cluster, not its own size.It is anticipated to provide a highly precise platform for separation and detection of human endogenous hydrogen sulfide as representative biomarker.

Results and Discussion
As is well known, self-assembled laminar SmP membrane with high anisotropy provides good orientation for permeable membrane systems.But in practice, horizontal permeation based on interlamellar hydrogen bonds is much superior to vertical permeation, which is unfavorable for efficient and rapid sieving of target molecules and ions. [12]So we tried to spontaneously inset P5s and P5Ds during the formation of SmP membrane through LC molecule-oriented effect, excellent size matching, and hydrophobic interaction with smectic LC molecules.
As shown in Figure 2A, the weak infrared (IR) absorption peak of carbon-carbon double bonds of monomers and cross-linkers (ν C=C : 1633 cm À1 ) completely disappeared after curing.At the same time, the C─O─C symmetrical stretching of carboxylic anhydrides (ν C─O─C : 1200 cm À1 ) appears due to the formation of macromolecules.It proves the formation of homeotropic cross-linked SmP network.At the same time, the characteristic absorbances of free carbonyl groups (ν C=O, free : 1675 cm À1 ) was significantly weakened, and both the ones of hydrogen-bonded carbonyl groups (ν C=O, H-bonded : 1695 cm À1 ) and broad absorbance of hydrogen-bonded hydroxy groups (ω -OH, H-bonded : 935 cm À1 ) emerged, showing the appearance of intermolecular hydrogen bonds between the resulting SmP lamellas.Figure 2B,C further demonstrates the nematic state of the resulting SmP membrane.
On another hand, versatilely functionalable pillar[5]arene (P5) has been widely used for hostÀguest interaction-based supramolecular switches and channels in solution, surface, and nanomaterials. [13]Besides, similar to sulfocalixarenes, [14] both its internal and external hydrophobic surface, and pillar-like cavity with the size of 5.6 Å and the depth of 7.8 Å, [15] greatly facilitate doping in LC layers by hydrophobic interactions and π-π conjugations between the aromatic groups.In order to ensure efficient and continuous selective permeation, pillar[5]arene dimer (P5D) was further synthesized by two-step reactions [11,16] and introduced into the SmP membrane (Figure 5 and 6).According to structural analysis, every two pillar[5]arenes are connected through one flexible methylene in pillar[5]arene dimer, which can better match to these aromatic groups at the end of rod-like LC monomers.This evidently contributes to stabilize the final doping structure without influencing self-assembly of LC monomers.During the preparation process, the appropriate doping ratios of P5 and P5D were determined as 0.8 and 0.4 mol%, respectively.Figure S7, Supporting Information, displays the defect-free 3D surface topography of the 0.4 mol% P5D-doped SmP membrane.And its surface fluctuation did not exceed 30 nm, only 0.6% of the membrane thickness, showing better flatness.The similar situation is also demonstrated in Figure S8, Supporting Information.Compared with the 0.8 mol% P5-doped SmP membrane, the 0.4 mol% P5D-doped SmP membrane still kept low surface roughness and no obvious pore appeared.By comparative analyses on average surface roughness (R a ), root-mean-square roughness (R q ), and maximum height roughness (R max ), an obvious increase in the surface roughness of the P5D-doped SmP membrane is further seen (Figure 3).Particularly after doping, its R max reaches 40.3 nm, which may be the result of the newly appeared pores on the membrane surface.Of course, some pores with the diameter of about 20-30 nm, much larger than P5 and P5D, are found on the surface, and presented funnel-shaped grooves.We believe that those embedded P5Ds will naturally exclude those surrounding rod-like LC units to sacrifice part of the order during the selfassembly process of SmP membrane. [17]And it may also lead to the extra surface fluctuation with increasing surface roughness and large surface pore size.Moreover, the mechanical performances of the SmP membranes before and after doping were also tested by AFM in the mechanical mode as shown in Figure S9, Supporting Information.Obviously, the very low doping concentration of P5 or P5D cannot change the Young's modulus and corresponding stiffness value of the flexible SmP membrane.
As previously known, water molecules (H 2 O) can free pass through P5D, to form continuous water wires. [11]By calculation, we chose three nonmetal ions bit bigger than H 2 O as target ions, namely, negative hydrogen sulfide ion (HS À ; size: 4.3 Â 3.6 Â 3.6 Å 3 ), positive ammonium ion (NH 4 þ ; size: 4.1 Â 3.9 Â 3.8 Å 3 ), and negative bicarbonate ion (HCO 3 À ; size: 5.7 Â 5.2 Â 3.4 Å 3 ) (Table S1, Supporting Information).All of them are common atmogenic ions and representative human endogenous biomarkers.It is found from the comparisons between the three ions that NH 4 þ is slightly smaller than HS À , and HCO 3 À is much larger than the other two.But as a common and predominate anion, HCO 3 À is the smallest in water except HS À .Besides, we also excluded formaldehyde (HCHO; size: 4.5 Â 4.3 Â 3.4 Å 3 ) because HCHO molecules actually exist in the form of much larger oligomer in water. [18]specially, hydrogen sulfide (H 2 S) has been viewed as a crucial signaling molecule with a wide range of physiological functions. [19]In aqueous physiological environment (pH 7.4; 37 °C), more than 80% of H 2 S will exist in its ionized form as HS À . [20]Above all, HS À , rather than H 2 S, regulates the metabolism and redox signaling functions of endogenous electrophiles. [21]So highly selective recognization and sieving of H 2 S derived HS À ion from physiological fluids becomes a very essential and urgent need.
Ion transmittance measurements on HS À , NH 4 þ , and HCO 3 À through the blank, 0.8 mol% P5-doped and 0.4 mol% P5D-doped SmP membranes were performed in a two-compartment electrochemical cell using a picoammeter, just as shown in Figure S10, Supporting Information.It is found that an ionic current across the P5D-doped SmP membrane reached 12.5 nA that is about five times of the one across the blank SmP membrane (2.5 nA; Figure 4A).Distinctly, the undoped SmP membrane remains impervious, and still restricts the flow perpendicular to the SmP lamellas.Similarly, HS À mobility through the SmP membrane is immensely enhanced after P5D doping (Figure 4B,C).After P5 doping, its saturated time and methylene blue (MB) fading time of HS À ion reduced by less than 1/7 and 1/3, respectively.Here, the average filtration rate grew nearly ninefold.Once P5D was doped, its saturated time and MB fading time of HS À ion further reduced by less than 1/8 and 1/7, respectively.In particular, its average filtration rate increased by about 14-fold (Table 1).Just as shown in Figure 4E, P5D is more beneficial than P5 to HS À transmittance.Because in the SmP membrane, P5D with two tubular cavities can stack with a face-to-face manner, to form cut-through organic nanotubes for 1D continuous HS À flow. [11]In contrast, the concentrations of HCO 3 À ions and NH 4 þ ions in the test cell remained basically unchanged, indicating that the two ions are starkly unable to penetrate through the 0.4 mol% P5D-doped SmP membrane (Figure 4D).Why can HS À freely pass through this self-assembled membrane, but "smaller" NH 4 þ not?To evaluate whether an ion can pass through the channel of pillar[5]arene, we calculated the sizes of pillar[5]arene and ions by Multiwfn code, considering the van der Waals radii.In Figure 5A, the diameter of cavity of pillar [5]  arene is approximately equal to 5.2 Å, greater than the diameters of ions.In addition, we calculated the evolution of binding energies between pillar[5]arene and molecule/ion with different relative positions, as presented in Figure 5B.The binding energy is expressed by The neutral H 2 O molecule has weak interaction with pillar[5] arene, whereas the charged ions (HS À , HCO 3 À , and NH 4 þ ) have stronger interaction with pillar[5]arene.All the binding energies of complexes are negative, indicating that the attractive interaction acts as a dominant role.Therefore, from this perspective, the H 2 O molecule or ions can enter the inside of pillar[5]arene.But the experimental results (Figure 4D) display that HCO 3 À and NH 4 þ barely pass through the channel of pillar[5]arene.In Figure 5, NH 4 þ has very strong interaction with pillar[5] arene, especially NH 4 þ locates in the center of pillar[5]arene.One mechanism is that the NH 4 þ can enter the inside of pillar[5]arene but cannot leave due to the very low energy basin.In other words, the NH 4 þ blocks the channel of pillar[5]arene.However, Figure 4D shows that the NH 4 þ concentration monotonously decreased in an extremely low speed within 50 h.If the NH 4 þ blocks the channel of pillar[5]arene, the NH 4 þ concentration should decrease momently and then keep a constant, which is not in accordance with the known experimental result.On the other hand, the HS À and HCO 3 À ions have close energy basin, which cannot explain the experimental phenomenon that HS À can pass through the channel of pillar[5]arene but HCO 3 À cannot.
Table 2 presents the binding energy and H-bond binding energy of dimer complexes, indicating that NH 4 þ and HCO 3 have stronger H-bond interaction with H 2 O than H 2 O and HS À , which can be also proved by the electron density difference maps (Figure S12, Supporting Information) intuitively.As the selected ions can form hydrogen bond with H 2 O molecule, the ion-water cluster could act as an individual.Electron localization function (ELF) topology analysis in Figure S13, Supporting Information, presents the ELF maximum points.Besides the covalent bond between the two atoms, ELF maximum point can also appear in the lone electron pairs of the ─O─ or ─S─ atom, which is required for the formation of hydrogen bonds.Thus, the models of cluster were built based on the ELF schematic.Figure 6 displays the schematic of The ground state up-down-up-down configuration of the water tetramer cluster is particularly one of the most frequently investigated complexes to be close to the experimental ones. [22]The HS À , HCO 3 À , and NH 4 þ ions can form hydrogen bonds with two, three, and four H 2 O molecules, constructing 1D cylindrical, 2D discotic, and 3D tetrahedral clusters, respectively, as displayed in Figure 6.
In particular, based on the calculation of H-bond binding energy and the analysis of independent gradient model based on Hirshfeld partition (IGMH), [23] we can conclude that HCO 3 À and NH 4 þ can form more hydrogen bonds with stronger H-bond interaction than H 2 O and HS À .It indicates that HCO

Conclusion
In summary, a P5D-doped SmP membrane with ultrahigh physical selectivity of HS À ion was self-assembled by means of size matching, hydrophobic interaction, and π-π conjugation between P5D and LC monomer.Hereinto, the laminar SmP network provided well-organized architecture and mechanical support, and the tubular P5D with two stacked face-to-face cavities held and confined 1D continuous HS À flow.It is anticipated to not only propose a facile, precise, and efficient strategy for separation, purification, and sieving of smaller molecules and ions (e.g., sea water desalination and battery separator), but also develop a superprecise separation and even detection approach to HS À ion as a common water-soluble gasotransmitter in diverse pathophysiological processes.All the used SmP membranes had fixed dimensions with the thickness of 30 μm and the area of 3.0 cm Â 3.0 cm; b) Average filtration rate of HS À ion is defined as the transmittance mole number of HS À ion per unit time per unit membrane area; c) Saturated time of HS À subnanofiltration is defined as the time needed at the maximum tuning point of variation rate of MB concentration (i.e., MB decolor rate); d) MB decolor time of MB is defined as the time needed that the MB solution in the test becomes colorless by naked eyes.Table 2. Binding energy and H-bond binding energy of dimer complexes. [19]mer complexes Binding energy
Synthesis and Characterizations of Pillar[5]arene Dimer: Synthesis of Monohydroxy Pillar[5]arene: Monohydroxy pillar[5]arene (P5) was first synthesized according to the previously reported approach shown in the first step of Figure 1A. [24]Typically, 2.0 g of P5 was fully dissolved in 40 mL of ultradry CH 2 Cl 2 under the protection of dry Ar atmosphere.Subsequently, a small amount of CH 2 Cl 2 solution of BBr 3 (0.9 eq.) was added dropwise into the solution and kept stirring for 45 min or 1.5 h at room temperature.Afterward, 20.0 mL of ultrapure water was added to terminate the reaction.The organic phase was separated from the mixed solution through separating funnel, and further dried with anhydrous MgSO 4 powders for the removal of residual moisture.Next, the resulting organic solution was added dropwise into excessive methanol for reprecipitation, to remove redundant by-products (polyhydroxy pillar[5]arene).Finally, the crude product was obtained by filtration and vacuum drying, and further purified by column chromatography (CH 2 Cl 2 :petroleum ether = 6:1) (white powder; yield: 20%).1A. [25]Typically, 1.0 g of P5 and 2 eq. of Cs 2 CO 3 were uniformly dispersed into 10.0 mL of ultradry THF in dry Ar atmosphere.Subsequently, a small amount of ultradry THF solution of 1,6-dibromohexane (0.5 eq.) was added dropwise into the solution, and magnetically stirred with reflux for 6 h at 60 °C.Next, the solution was evaporated to dryness by rotary evaporation, and then redissolved in CH 2 Cl 2 , washed with water.The organic phase was separated from the mixture using separating funnel, and further dried with anhydrous MgSO 4 powders for the removal of residual moisture.Finally, the crude product was obtained by rotary evaporation, and then further purified by column chromatography (CH 2 Cl 2 :petroleum ether = 6:1) (white powder, yield: 20%) The mass spectra of P5 and resulting P5D are shown in Figure S6A and S6B, Supporting Information, respectively.
Mass Spectrometer: The molecular weight of P5 and P5D dimer were characterized by matrix-assisted laser desorption ionization time-of-flight (MALDI-TOF) mass spectrometer(MS; Autoflex III MALDI TOF, Bruker, Germany).Each sample mass is 5 mg.
Preparation and Characterizations of Smectic LC Network (SmP) Membrane: Fabrication of LC Cell: The adopted LC cells were composed of two parallel glass plate (3.0 cm Â 3.0 cm) with the fixed spacing distance determined by the gap control spacer (5 and 30 μm).Hereinto, their inner surfaces were aligned PI layer coated on the glass cover-plate and substrate.
Typically, a right amount of PI 3570 was coated above the treated glass plate, using a spin-coater (KW-4 A, Institute of Microelectronics of the Chinese Academy of Sciences, Beijing, P. R. China) with a fixed rotating speed of 2500 rpm for 60 s.The resulting vertically aligned PI layer was heated to 90 °C for 30 s on a heating stage (HP-303DU, SmartLab, Shanghai, P. R. China), and then placed in a heating chamber (FED 56, BINDER, Neckarsulm, Germany) filled with nitrogen gas, to be heated to 135 °C for 30 min, followed by heating to 230 °C for 90 min.Till returned to room temperature, a right amount of gap control spacer was dripped onto the four corners of the glass substrate with PI alignment layer, and then covered with another PI-aligning glass plate.Finally, the cell was formed through UV curing (FU3228-A, BANGWO, Guangzhou, P. R. China) for 240 s.
Preparation of SmP Membrane: According to the previously reported formula shown in Figure 1B, [12] 0.5 g of 6OBA monomer (85 wt%), 0.05 g of C6H cross-linker (15 wt%), 5.0 mg of photoinitiator (2 wt%), and 0.05 mg of inhibitor (0.01 wt%) were fully codissolved in CH 2 Cl 2 and heated to 60 °C in dark place till the solvent evaporated completely.After the empty LC cell with the predetermined gap was preheated to 96 °C on a heating stage (HP-303DU, SmartLab, Shanghai, P. R. China), the resulting homogeneous LC mixture was poured into the LC cell through capillary force, and kept heating at 105 °C to be vertically aligned for at least 30 min in the yellow room without UV light.Next, each side of the filled cell was irradiated for 5 min, using a spot UV curing system (OmniCure S2000, Lumen Dynamic Group Inc., Mississauga, Canada) with a 365 nm cutoff filter and the fixed irradiation intensity of 5 mW cm À3 .Finally, the cured cell was further fully cured at 120 °C.In addition, the pillar[5]arene-doping SmP membranes were prepared in the same way, in which P5 and P5D were doped into the LC monomer mixture with the fixed mole fractions of 0.8% and 0.4 mol%, respectively.
FT-IR: The LC mixture before and after polymerization was determined by FT-IR (Vertex 70, Bruker, Germany) in a spectral range of 4000-400 cm À1 with the resolution of 2 cm À1 using potassium bromide (KBr) tableting at room temperature.And the SmP membranes were tested in the attenuated total reflection (ATR) mode.
DSC: The thermal analysis was performed by DSC (DSC1, METTLER TOLEDO, Switzerland) in a pure nitrogen atmosphere with the fixed flow rate of 60 mL•min À1 .Typically, 6-10 mg of sample was measured within the temperature range between À30 and 150 °C at constant heating rate of 5 °C min À1 and cooling rate of 10 °C min À1 .
POM: At different temperature, the optical behavior of the crude LC mixture was observed using POM (DM2700p, Leica, Germany) equipped with polarization filters and cooling-heating stage (LTS 120, Linkam, UK).
Scanning Electron Microscope: The surface deposition topographies of the crude and the 0.4 mol% P5D-doped SmP membranes were observed using scanning electron microscope (SEM; ZEISS Ultra 55, Carl Zeiss, Germany; magnification: 80 000Â) operated at extra high tension (EHT) of 2 kV.
D surface topography: The surface topography of the 0.4 mol% P5D-doped SmP membrane was measured by 3D profiler (DCM8, Leica, Biberach, Germany) with a 40-fold objective in confocal mode.
AFM: The surface microtopographies of the crude and the 0.4 mol% P5D-doped SmP membranes were determined precisely using AFM (Multimode 8, Burker, Germany) in tapping mode and mechanical mode.
Performance Evaluation for Ion Permselectivity: Prior to the following measurements, the sample membrane was fixed in the middle of the custom-made sample cell.The internal space of the sample cell was separated into two test cells, as shown in Figure S10A, Supporting Information.
Real-Time Ion Current Measurements: The aqueous solutions of KCl with the settled concentration of 3 and 1 M were poured into the two test cells, respectively.Here, the crude or the 0.4 mol% P5D-doped SmP membrane with the settled thickness of 30 μm was fixed in the middle of the custommade sample cell.On both sides of the membrane, two platinum (Pt) wire electrodes were inserted into the solution through the contact hole, respectively, and connected to a picoammeter (6478, KEITHLEY, USA; Figure S10B, Supporting Information). [26]S-Transmittance Measurements: The HS À transmittances were determined by the color-fading reaction of MB with HS À ion.Typically, the crude, 0.8 mol% P5-doped, or 0.4 mol% P5D-doped SmP membrane with the settled thickness of 30 μm was fixed in the middle of the custom-made sample cell.Next, 3.0 mL of the aqueous solutions of NaHS (concentration: 100 mM) and MB (concentration: 0.2 mg mL À1 ) was poured into the two test cells on both sides of the membrane, respectively (Figure S9C, Supporting Information).During the process of HS À transmittance, a small amount of aqueous MB solution was pipetted once every few minutes or hours, to obtain the residual concentration of unreduced MB by detection of UV-vis spectrophotometer (UV-1750, SHIMADZU, Japan), according to UV absorption-concentration standard curve of MB at the wavelength of 665 nm (Figure S11, Supporting Information).Here, the transmembrane quantity of HS -ions is defined as the decrement of MB in oxidation state.
Typically, the 0.4 mol% P5D-doped SmP membrane with the settled thickness of 30 μm was fixed in the middle of the custom-made sample cell.In the test cell on the side of the membrane, 3.0 mL of the aqueous ion solution of sodium bicarbonate (NaHCO 3 ) or ammonium chloride (NH 4 Cl) with the settled concentration of 100 mM was poured.And in the test cell on another side of the membrane, 3.0 mL of the aqueous solution of hydrochloric acid (HCl; pH = 4) or sodium hydroxide (NaOH; pH = 10) was correspondingly poured (Figure S1C, Supporting Information).During the testing process, the pH value of the acid or base solution was accurately measured by pH meter (PB-10, Sartorius Scientific Instruments Co., Limited, Germany) with PY-ASI as multipurpose electrode once every few hours.Here, the transmembrane quantity of HCO 3 À or NH 4 þ ion is correspondingly defined as the decrement of hydrogen ion (H þ ) or hydroxide ion (OH À ).
Density Functional Theory Calculation: The density functional theory (DFT) calculations were performed using the Gaussian code.M602X exchange-correlation functional with Grimme's DFT-D3 empirical dispersion correction, which is abbreviated as M602X-D3.Geometries of pillar[5]arene/ion dimer complexes were fully optimized using the ma-SVP basis set.The binding energies were evaluated through singlepoint energy calculations using ma-TZVP basis set.For the ion-water clusters, the geometry optimizations and single-point energy calculations were both performed by ma-TZVP basis set.The analyses of independent gradient model based on Hirshfeld partition (IGMH) and electron localization function (ELF) topology analysis were carried out by Multiwfn code. [27]The maps were rendered via the VMD visualization program based on the files exported by Multiwfn.

Figure 1 .
Figure 1.A) Synthetic route of P5D; B) chemical compositions of SmP membrane; C) preparation process of SmP membrane with the fixed thickness, containing the lower left object picture; and D) structural schematic diagrams of blank and P5D-doped SmP membranes.

Figure 2 .
Figure 2. A) Fourier transform infrared spectra (FT-IR) of SmP membrane before and after curing; B) differential scanning calorimetric curves (DSC) of blank, P5-doped and P5D-doped SmP membranes; and C) corresponding polarizing optical microscopic images (POM) of blank SmP membrane; all the scale bars represent 200 μm.

Figure 3 .
Figure 3. A) Atomic force microscopic (AFM) images of the blank and B) 0.4 mol% P5D-doped SmP membranes, and corresponding surface roughness.

Figure 4 .
Figure 4. A) Real-time ion current curves of the blank and 0.4 mol% P5D-doped SmP membranes with the thickness of 30 μm; B) HS À concentration curves and C) corresponding mobilities through the blank, 0.8 mol% P5-doped and 0.4 mol% P5D-doped SmP membranes with the thickness of 30 μm; D) HCO 3 À and NH 4 þ transmittance curves through the 0.4 mol% P5D-doped SmP membrane; and E) principle diagram on physical selectivity of the undoped and doped SmP membranes for ion transport.
clusters are more stable.Moreover, the diameter of 1D cylindrical HS À •2H 2 O cluster (4.2 Å) is smaller than that of cavity of pillar[5]arene (5.2 Å), indicating the HS À •2H 2 O cluster and pass through the channel of pillar[5]arene.The diameters of 2D discotic HCO 3 À •3H 2 O cluster and 3D tetrahedral NH 4 þ •4H 2 O cluster are 8.9 and 8.7 Å, and thus they cannot penetrate the pillar[5]arene due to the size confinement effect.

Figure 5 .
Figure 5. A) Size of pillar[5]arene cavity and permeation ion.B) Binding energies of pillar[5]arene and molecule/ions with different relative positions.

Figure 6 .
Figure 6.H-bond binding energies and their analyses of independent gradient models based on Hirshfeld partition (IGMH) of H 2O þ H 2 O A), HS À þ H 2 O B), NH 4 þ þ H 2 O C) and HCO 3 À þ H 2 O D) clusters.The

HCO 3 À
and NH 4 þ Transmittance Measurements: The HCO 3 À and NH 4 þ transmittances were determined by the acid-base reaction as follows

Table 1 .
Comparison of HS À transmittance performances through different SmP membranes.