Robust ultrathin nanoporous MOF membrane with intra-crystalline defects for fast water transport

Rational design of high-performance stable metal–organic framework (MOF) membranes is challenging, especially for the sustainable treatment of hypersaline waters to address critical global environmental issues. Herein, a molecular-level intra-crystalline defect strategy combined with a selective layer thinning protocol is proposed to fabricate robust ultrathin missing-linker UiO-66 (ML-UiO-66) membrane to enable fast water permeation. Besides almost complete salt rejection, high and stable water flux is achieved even under long-term pervaporation operation in hash environments, which effectively addresses challenging stability issues. Then, detailed structural characterizations are employed to identify the type, chemical functionality, and density of intra-crystalline missing-linker defects. Moreover, molecular dynamics simulations shed light on the positive atomistic role of these defects, which are responsible for substantially enhancing structural hydrophilicity and enlarging pore window, consequently allowing ultra-fast water transport via a lower-energy-barrier pathway across three-dimensional sub-nanochannels during pervaporation. Unlike common unfavorable defect effects, the present positive intra-crystalline defect engineering concept at the molecular level is expected to pave a promising way toward not only rational design of next-generation MOF membranes with enhanced permeation performance, but additional water treatment applications.


S1.1 Raw Materials and Chemical Reagents
Supplementary

S1.3 Schematic of the PV simulation system
The PV simulation system, as depicted in Supplementary Fig. 2, consists of saline solution on the feed side and a vacuum space on the permeate side, separated by a UiO-66/ML-UiO-66 membrane (i.e., as an active PV membrane layer) with a thickness of ~25 Å. Such sandwich simulation setup was also adopted in prior studies by some of us to study PV ethanol/water separation 5,6 . The membrane surface was parallel to the [1 1 1] plane of its crystal structure 7 . The open metal sites resulting from the surface cleavage and missing-linker defects were saturated with acetate group (CH3COO−) 8,9 .
The saline solution containing 20 Na + /Cl − ion pairs solvated by 2000 water molecules, which was bounded by a graphene sheet as a piston to modulate the pressure at 1 atm.
The vacuum condition on the permeate side was also maintained using a graphene sheet as an adsorbing plate to capture all permeated molecules. Each studied active membrane layer (containing hundreds of atoms) was relaxed by the conjugate gradient method using the Forcite module in the Materials Studio package. The convergence criteria for energy, force, and displacement were set to be 2 × 10 −5 kcal mol −1 , 0.001 kcal mol −1 Å −1 , and 1 × 10 −5 Å, respectively. For simplicity, these structures have the same cell parameter as reported in an experimental work 10 . Periodic boundary conditions were applied, and an additional 50 Å-thick vacuum region along z-direction was included to reduce the self-interactions between periodic images.
In these calculations, 12−6 Lennard-Jones (L-J) potential and long-range Coulombic interactions with static point charges were used to describe non-bonded interactions. L-J parameters of the framework atoms were taken from the DREIDING force field 11 except for zirconium atoms whose parameters were instead from the universal force field (UFF) 12 . Atomic charges of the framework atoms were derived from the PM7 calculations based on population analysis 13,14 . The rigid SPC/E model 15 with the SHAKE algorithm was used to model water molecules. Non-bonded potentials developed by Joung et al. 16 were used for salt ions. The Lorentz-Berthelot mixing rule S6 was applied to estimate the cross pairwise L-J parameters between atoms. However, since the UiO-66 membranes should not be influenced by the piston and the adsorbing plate, their pairwise L-J coefficients (i.e., piston-membrane and plate-membrane) were set to zero. The L-J potentials were truncated and shifted to zero at a cutoff distance of 12 Å, while the long-range Coulombic interactions were computed using the particleparticle-particle-mesh (PPPM) algorithm with a precision of 10 −6 .

S1.5 Pore Size Distribution
The mean pore size and pore size distribution of UiO-66 and ML-UiO-66 membranes were experimentally determined by the solute rejection method using a laboratorymade dead-end filtration setup 17,18 . A series of ~200 ppm PEG or glycerol solutions   (2) Then, the solute rejection was plotted against Stokes diameter on a log-normal probability diagram and linear regression was performed. The mean effective pore diameter (μp, nm) is the size of a solute where its rejection is 50%. The geometric standard deviation (σp) of a membrane is the size ratio of solutes with rejections of 84.13% and 50%. The pore size distribution of the membrane was generated using Supplementary Eq. 3: where dp (nm) is the effective pore diameter.

S1.6 Isosteric heat of water adsorption
The isosteric heat of adsorption can be determined by the Clausius-Clapeyron equation as Supplementary Eq. 4: where Qst (kJ mol -1 ) is the isosteric heat of adsorption, R (8.314 J mol -1 K -1 ) is the gas content, T (K) is the absolute temperature, P (bar) is the pressure, and θ (%) is the sorbed amount. Integration of the Clausius-Clapeyron equation (Supplementary Eq.4) gives Supplementary Eq. 5: In this study, adsorption isotherm data measured at 298.15 K and 303.15 K was used to obtain the plots of adsorption heat. The adsorption heat at a given uptake was calculated from the fitted slopes of the Supplementary Eq. 5 19 . S10 S1.7 Measurements of water permeability, adsorption coefficient and diffusivity coefficient 20 For the water adsorption coefficient measurements, the UiO-66 and ML-UiO-66 membranes were immersed into DI water for 2 days to fully hydrate the membranes.
Then, any water droplets on the membrane surface were gently removed with a dry tissue and the wet membrane (Wwet, g) was quickly weighed using an analytical balance.
After drying in a vacuum oven at 80°C for 24 h, the dry membrane (Wdry, g) was weighed.
The volume fraction of water is related to the water adsorption coefficient, Kw(-).
The Kw(-) is defined as Supplementary Eq. 6: where Vdry (cm 3 ) is the volume of the dry membrane, ρ w (g cm -3 ) is the density of water.
The hydraulic water permeability (P w H , L μm m -2 h -1 bar -1 ) was measured using DI water as a feed at room temperature (25°C) during PV process. The hydraulic water permeability was calculated by Supplementary Eq. 7: where V (L) is the volume of the permeated water, A (m 2 ) is the effective membrane areas, t (h) is the test time interval, l (μm) is the hydrated membrane thickness, and P (bar) is the transmembrane pressure difference.
Like the solution-diffusion mechanism in polymeric membranes, water molecules transported through UiO-66 and ML-UiO-66 membranes following the adsorptiondiffusion mechanism during PV process. The intrinsic hydraulic water permeability (Pw, cm 2 s -1 ) of a membrane is associated with P w H , which is calculated as Supplementary Eq. 8: where Dw (-) is the water adsorption coefficient, R (8.314 J mol -1 K -1 ) is the ideal gas constant, and T (K) is the absolute temperature during the permeability measurements.

S2.2 Optimization of the γ-Al2O3 Interlayer
Supplementary Fig. 4 shows that defect-free nanoporous γ-Al2O3 interlayer could be obtained and optimized via a simple dip-coating and sintering technique. The relationship between the thickness of the γ-Al2O3 interlayer and coating time fits well with a classical dip-coating model ( Supplementary Fig. 4h, Supplementary Eq. 9) 23 .
where Lm (m) is the thickness of interlayer membrane, εs is the porosity of interlayer  Supplementary Fig. 6 shows that after introducing the γ-Al2O3 nanoporous interlayer, the ZrO2@γ-Al2O3 substrate has two-fold higher Al-OH group concentration than ZrO2 substrate, which provides more heterogeneous nucleation site for the growth of ML-UiO-66 membranes. The surface properties of substrate are the dominant factor for crystalline MOF membrane growth as the growth of MOF crystals first occurs on the solid-liquid interface (i.e., substrate-solution interface). Specially, besides surface -OH groups, surface roughness also plays an important role in heterogeneous nucleation and subsequent kinetic growth of ML-UiO-66 crystals. This is by providing different energy barriers, which affect the final ML-UiO-66 membrane features, such as integrity (intercrystalline defects), thickness, and surface roughness. Supplementary Fig. 7 shows that the ZrO2@γ-Al2O3 substrate has a much lower surface roughness (Ra = ~10 ± 2 nm) than ZrO2 substrate (Ra = ~27 ± 3 nm).   Supplementary Fig. 9 The load-deflection relationship of membrane substrate. S20

S2.3 Optimization and Performance of ML-UiO-66 Membranes
Supplementary Fig. 10 shows low-quality ML-UiO-66 membranes with poor intergrown morphology and large inter-crystalline defects were obtained on coarse ZrO2 substrates when introducing various amounts of CH3COOH.  In contrast, when using the ZrO2@γ-Al2O3 substrate, the quality of the achieved membrane improved significantly due to the high-density nucleation site with abundant surface -OH groups (Supplementary Fig. 6). CH3COOH can more readily complex with Zr clusters. During the ML-UiO-66 membrane growth, CH3COOH could coordinate with Zr clusters, which plays a competitive role over dicarboxylic acid (BDC) 24 , leading to weakly coordination bonding between BDC and Zr clusters. The amount of nucleation decreases with the increase of CH3COOH, and the morphology of the membrane layer changed from tetrahedron to octahedron (Supplementary Figs. 10 and 11), which is attributed to the coordination modulator mechanism 25 . In our study, when the molar ratio of Zr 4+ /CH3COOH was controlled at ~25, an ultrathin and dense ML-UiO-66 membrane was obtained as the optimum morphology and performance ( Supplementary Fig. 11).    Supplementary Fig. 14 The bulk porosity and surface porosity of ZrO2 substrate and γ-Al2O3   Fig. 15), both of which are between H2O (2.8 Å) and hydrated Na + (7.2 Å). Theoretically, both UiO-66 and ML-UiO-66 membranes are able to reject hydrated Na + . However, low rejection of NaCl can be also similarly observed S31 Supplementary Fig. 17 shows that high-quality ultrathin compact membrane morphology with a thickness of only 120 ± 20 nm could also be obtained on the ZrO2@γ-Al2O3 substrate even without the addition of CH3COOH modulator.  Supplementary Fig. 22d), which implies a more favorable interaction between ML-UiO-66 and water molecules than UiO-66.
That is to say, ML-UiO-66 has better water adsorption ability than UiO-66 19 .

S2.4 Characterization of Missing-linker Defect
The N2 adsorption-desorption isotherms of UiO-66 and ML-UiO-66 powder are shown in Supplementary Fig. 24, where the calculated specific surface area, pore volume and pore size are summarized in Supplementary For quantitative analysis of ML-UiO-66 ( Supplementary Fig. 25b)  Additionally, the number after the underscore refers to the corresponding defect density of each defective structure.