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Mechanistic formulation of inorganic membranes at the air–liquid interface

Nature volume 616, pages 293–299 (2023)Cite this article

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Abstract

Freestanding functional inorganic membranes, beyond the limits of their organic and polymeric counterparts1, may unlock the potentials of advanced separation2, catalysis3, sensors4,5, memories6, optical filtering7 and ionic conductors8,9. However, the brittle nature of most inorganic materials, and the lack of surface unsaturated linkages10, mean that it is difficult to form continuous membranes through conventional top-down mouldings and/or bottom-up syntheses11. Up to now, only a few specific inorganic membranes have been fabricated from predeposited films by selective removal of sacrificial substrates4,5,6,8,9. Here we demonstrate a strategy to switch nucleation preferences in aqueous systems of inorganic precursors, resulting in the formation of various ultrathin inorganic membranes at the air–liquid interface. Mechanistic study shows that membrane growth depends on the kinematic evolution of floating building blocks, which helps to derive the phase diagram based on geometrical connectivity. This insight provides general synthetic guidance towards any unexplored membranes, as well as the principle of tuning membrane thickness and through-hole parameters. Beyond understanding  a complex dynamic system, this study comprehensively expands the traditional notion of membranes in terms of composition, structure and functionality.

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Fig. 1: SLIS-induced conversion of the nucleation preference in aqueous solution.
Fig. 2: From the pilot Ag membrane to unlocking a colourful membrane library.
Fig. 3: Kinematic-controlled membrane growth in the SLIS system.
Fig. 4: General synthetic methodology and extension of complexity for the SLIS-mediated membrane.

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Data availability

The data that support the findings of this study are available from the corresponding author on reasonable request. Source data are provided with this paper.

Code availability

The codes used to solve the kinematic equation, calculate the collision energy and perform dynamic GT-phase simulation are available in the repository at https://github.com/jokerxy624/membrane.

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Acknowledgements

This research is supported by A*STAR under its 2019 AME IRG & YIRG Grant Calls, A2083c0059, as well as the National Research Foundation Central Gap Fund NRF2020NRF-CG001-023 and National University of Singapore TAP25002021-01-01.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore

    Chen Zhang, Wanheng Lu, Yingfeng Xu & Ghim Wei Ho

  2. Department of Mechanical Engineering, National University of Singapore, Singapore, Singapore

    Kaiyang Zeng

  3. Department of Materials Science and Engineering, National University of Singapore, Singapore, Singapore

    Ghim Wei Ho

  4. Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), Singapore, Singapore

    Ghim Wei Ho

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Contributions

C.Z. and G.W.H. conceived the idea. C.Z. designed and performed most of the experiments and theoretical derivations. Y.X. assisted in some membrane characterizations as well as the video editing. W.L. and K.Z. supported the AFM experiments. G.W.H. supervised the project. C.Z. and G.W.H. analysed all the data and wrote the manuscript. All authors commented on the manuscript.

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Correspondence to Ghim Wei Ho.

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Extended data figures and tables

Extended Data Fig. 1 Universality of the SLIS strategy for diverse types of vessel routinely used in the lab to perform aqueous reactions.

The polymer-based substrates include polyethylene (PE) (a), polytetrafluoroethylene (PTFE) (b), polypropylene (PP) (c), polystyrene (PS) (d) and polyethylene terephthalate (PET) (e). The ceramic-based substrates include silicon (f) and sapphire (g). The metal-based substrate includes platinum (h). Their molecular or crystalline structures are shown in a1–h1, respectively. a2–h2, Contact-angle images for a sessile water droplet on the substrates, visually showing their relative hydrophilicity. a3–h3, AFM force–distance curves for bare and PVAAc-coated substrate surfaces measured in air and under water, respectively. The insets zoom in on the force-sensing regions in the force–distance curve for the bare substrate–liquid water interface during approach and withdraw processes and present the related potential energy changes (ΔE).

Source Data

Extended Data Fig. 2 Further information on the inorganic membrane library constructed by the SLIS strategy.

a, Digital photos of the reaction systems with freshly prepared membrane floating on the solution surface. b, Chemical elements involved in the inorganic membrane library constructed using the SLIS strategy. The yellow colour indicates that the element has been involved to constitute specific membrane in the presented membrane library. The blue colour denotes all the potential elements that can be theoretically further incorporated into the membrane library because each of them can find the analogue in chemical property in the as-involved ones. The grey colour indicates all the elements that are not available for SLIS synthesis owing to their extremely expensive price, chemical inertness and/or radioactive hazard. c, Chord diagram showing the potential multifield-coupling energy-conversion pathways among these functional membranes presented in the library (for details, see Supplementary Table 2). The available energy forms are mechanical, light, thermal, electric, magnetic and chemical energy.

Source Data

Extended Data Fig. 3 Critical developments of structural evolution during Ag membrane growth in the SLIS system.

a, Voronoi texture-meshed typical SEM images of the floating solid collected at 4.32, 17.1 and 53.5 s. The red dot indicates the centre of each Brownian cluster. The colour of each cell denotes the coordination number, as indicated in the right colour bar. The colour of the boundary highlights the connectivity between the adjacent cells, that is, blue denotes unconnected cells and yellow denotes connected cells that are caused by the cross-domain growth of the Brownian cluster. b, Typical SEM images with pseudo colours of the floating Ag membrane collected at 15, 20.5, 25.5 and 30 min. The numbers above these images (a and b) help to identify the corresponding critical moments as indicated in Fig. 3a. c, Statistical map of the circularity against the logarithmic area for the through holes extracted from the typical SEM images in b. The top and right plots are the density distributions along the axes of the through-hole area and the circularity, respectively. d, Violin plots to show the statistical changes in the solidity (left) and the minimum Feret diameter (right) of the through holes after the formation of the (quasi-)bicontinuous framework. The scatter line in right plot shows the corresponding evolution in the coverage factor of the floating Ag membrane. e, Typical structures of the extracted through holes forming at the corresponding critical moments. Starting from the highly connected network structure, the through holes can gradually evolve into a low-circularity closed-hole structure, then to a high-circularity closed-hole structure and an eventual compact structure, accompanied by the continuously sharpened size distribution and increased geometrical convexity. To aid in visual identification, all the scatters, rugs, lines, violins and the extracted hole structures are respectively coloured with the same colours of the corresponding SEM images in b. Scale bars are 1 μm (a,b and e).

Source Data

Extended Data Fig. 4 Confirmation of the actual position of the as-prepared floating Ag membrane on the aqueous surface.

a–f, 2D maps of the local adhesion force (a,d), interfacial stiffness (b,e) and rupture distance (c,f) for the interface between air and the on-site floating Ag membrane (d–f, 30 min after igniting the silver mirror reaction in the SLIS system) in comparison with that of the air–deionized water interface (a–c). The maps represent the results of AFM indentation measurements performed at 25 different positions on the two kinds of interface. The colour-coded plots represent variations of the parameters of interest as indicated in the left colour bars. g–i, Statistical variations for the measured adhesion force (g), interfacial stiffness (h) and rupture distance (i) extracted from the corresponding 2D maps. All the points are presented in scatters along with a Gauss function fitting line. The corresponding box plot shows the interquartile range with the marked mean value (open square inside), the median (transverse line inside) and the error bar. The air-floating Ag membrane interface presents a well-defined mechanical characteristic of the typical air–solid interface (Supplementary Fig. 52), featuring a much smaller AFM tip–interface adhesion force, a notably increased interfacial stiffness and a substantially shorter rupture distance in comparison with that of the air–water interface. These evidences confirm that the as-prepared Ag membrane is definitely floating on the aqueous surface with no liquid-water layer above it.

Source Data

Extended Data Fig. 5 Structural characterizations of the (quasi-)bicontinuous Ag membrane.

a,b, Digital photo (a) and transmission optical microscopic image (b) of the (quasi-)bicontinuous Ag membrane suspended by a varnished wire ring. Under transmission white light, the membrane with sub-visible-wavelength holes exhibits a selective optical transmittance of short-wavelength light, giving it a blue–violet appearance. The consistent colour without any detectable chromatic aberration demonstrates the large-scale homogeneity of the (quasi-)bicontinuous structure. c–e, TEM images of the Ag membrane suspended on the TEM copper grid obtained under different magnifications, evidently confirming its multiscale structural homogeneity. The inset in e is the corresponding selected-area electron diffraction pattern, showing the polycrystalline nature. f, Illustration of the image-processing procedure for anisotropic analysis of the (quasi-)bicontinuous structure in a typical TEM image (d). Binary conversion was first performed on the image with the empty portions set to transparent. A copy of the processed image was then stacked on the original one and allowed to undergo a continuous clockwise rotation around the image centre. Through our customized Python image-processing code, the stacked part of the two square images at a specific rotation angle of θ was extracted by using their inscribed circle to calculate the geometric permeability (the ratio of the area of the overlapped through holes to the whole circle area). g, Rotation angle θ-dependent geometric permeability of the stacked (quasi-)bicontinuous structure. The step size of θ is 0.5°. The real-time analysis of the geometric permeability with the corresponding stacked configuration is visually presented in Supplementary Video 1. h, Area distribution of the projected through holes of the stacked structure at the selected rotation angles. The density of the strips represents the frequency and the right curve shows the result of the frequency statistic. The dashed red line indicates the peak position of each distribution curve, highlighting the structural isotropy. i, TEM image of the practical stacked two-layer (quasi-)bicontinuous Ag membrane (right) compared with the single-layer counterpart (left). The stacking operation demonstrates a simple strategy to adjust the through-hole sizes in the membrane by using the (quasi-)bicontinuous structure. j, Statistical map of the circularity against the logarithmic area for the through holes in the one-layer and two-layer regions in i. The top plot is the density distribution along the axis of the through-hole area, showing a substantial decrease in both the hole size and the size dispersion after the stacking operation. The right box charts show the statistical result of the circularity of the through holes. The caps indicate the 3× interquartile range. Every box shows 25th–75th percentiles, with the marked median (transverse line inside) and mean (dot inside). Scale bars are 5 mm (a), 100 μm (b), 20 μm (c), 2 μm (d), 200 nm (e) and 10 μm (i).

Source Data

Extended Data Fig. 6 Typical twist boundaries in the (quasi-)bicontinuous Ag membrane viewed from a direction parallel to the boundary.

a, TEM image of the overall membrane network. b, Size distribution of the grains in the membrane compared with that of the initial floating particles. Two hundred well-defined grains distinguished by the diffraction contrast were counted. The two distributions are nearly identical, evidently confirming that the membrane is derived from the assembly of the initial isolated particles instead of an epitaxial growth based on the sliver atom deposition. c, Magnified TEM image of the marked region in a, visually showing the plentiful grain boundaries in the membrane network. d,e, High-resolution transmission electron microscopy image (d) of the marked region with small curvature in c and its corresponding pseudo-coloured counterpart (e), which highlights the three grains (A, B and C) with two visual grain boundaries (60°/[0-11] between grains A and B, 60°/[-1-10] between grains B and C). The two dashed squares in d mark the well-defined cross-boundary regions (that is, square 1 marks the boundary between grains A and B and square 2 marks that between grains B and C). The black arrows indicate the reactive amorphous surface with about 2 nm thickness. f–i, FFT images (f,h) and the corresponding Fourier-mask-filtered (twin-oval pattern, edge smoothed by five pixels) images (g,i) for the square-marked regions 1 and 2 in d, respectively. The reciprocal vectors in the FFT image were labelled by using the same colours with their mother grains. Note the crystal indices labelled with ‘’ denote that these lattice planes should be absent in the reciprocal space owing to the crystallographic extinction rule, which are identifiable in the direct space in the high-resolution transmission electron microscopy image obtained under an appropriate Scherzer defocus. The white lines in g and i depict the twist boundary plane. Scale bars are 500 nm (a), 50 nm (c) and 5 nm (d).

Source Data

Extended Data Fig. 7 Various factors that influence the capillary-attraction-driven kinematics between two floating particles.

a–d, Influence of the particle size (variable R1 is from 10 to 99.99 μm) on the kinematics at L0 = 400 μm, k = 3, ρ = 8,000 kg m−3 and ε = 0.05. e–h, Influence of the initial distance (variable L0 is from 100 to 1,000 μm) on the kinematics at R1 = 20 μm, k = 3, ρ = 8,000 kg m−3 and ε = 0.05. i–l, Influence of the diversity factor (variable k = R2R1−1 is from 1 to 10) on the kinematics at L0 = 500 μm, R1 = 40 × 10−6, ρ = 8,000 kg m−3 and ε = 0.05. a,e,i, Time-dependent distance between the two floating particles in the capillary-attraction-driven acceleration process. b,f,j, Proportion of the displacement of the smaller particle to the initial distance when the two particles mutually collide. c,d,g,h,k,l, Time-dependent velocity for smaller particle (v1; c,g,k) and bigger particle (v2; d,h,l). Note that v1 and v2 are in opposite sign, indicating their relative movement under capillary attraction.

Source Data

Extended Data Fig. 8 Further evolution of the membrane after the formation of the bicontinuous 2D network.

a, Digital photograph of the aqueous system for AgCl membrane synthesis at the emergence of a whole (quasi-)bicontinuous network. The marked regions 1 and 2 highlight the marginal and internal regions of the floating solid network, respectively. b,c, Representative digital photograph of the marginal region of the (quasi-)bicontinuous AgCl network (b) and the corresponding map from the velocity-field analysis (c) (see the dynamic process in Supplementary Video 3). The colour shows the local vorticity direction and intensity as indicated in the right colour bar. d,e, Digital photographs (d) recording the change of the internal region in the bicontinuous network after continuous particle trapping in 36 s and the time-course spatial distribution of these trapped nascent AgCl particles (e) (see the whole process in Supplementary Video 4). Scale bars are 1 cm (a), 500 μm (b) and 200 μm (d).

Extended Data Fig. 9 Evolution of the through holes in connectivity and geometry during membrane network growth.

a, Sequential microscopic images (obtained 6, 10, 26 and 35 min from the beginning of the reaction) recording the evolution of the AgCl membrane from the moment of forming (quasi-)bicontinuous structure (about 6 min). Scale bar, 200 μm. b, Connectivity analysis of seven selected holes in the corresponding images in a. These selected regions are coloured and numbered as indicated on the right for the convenience of observation on the evolution in the hole’s geometry and connectivity. Note that almost all the holes are interconnected and impartible in the original (quasi-)bicontinuous structure. c, Calculated map obtained from the difference set between the microscopic images taken at 35 and 26 min, showing the locations of these trapped AgCl nascent particles during this period. The image is coloured blue to improve the visual contrast. Macroscopically, all of the hole boundaries have a nearly identical rise in thickness, implying that the new AgCl particles are randomly trapped by the solid network and there is little possibility of generating new Brownian clusters in the hole region. d, Spatial evolution mapping of a representative hole (no. 1) during 26 to 35 min. The length and direction of the black arrows representatively show the maximum shrink rate and orientation of the hole at different boundary regions. The hot colour map highlights the vorticity of the shrink rate caused by the difference in the shrink orientation. The inset is the thin-plate spline analysis of differential evolution of the hole to visualize its shape changes in different areas. e, Distributions of the velocity magnitude and the tangent velocity along the hole boundary in d. These parameters were extracted clockwise along the hole boundary from the start point indicated by the white arrow in d.

Source Data

Extended Data Fig. 10 Foolproof synthetic guidance to an unexplored inorganic membrane in our proposed SLIS system.

a, Step-by-step flow chart to guide the synthesis of an inorganic membrane. b, Summary of the initial conditions for creating the membranes in the presented library and the corresponding distributions based on 2D kernel density estimation, offering experiential choice of the initial concentration and temperature for different reaction categories. c–f, Results of the kinematic simulations for the CN (c), ON (d), NI (e) and CI (f) phases (see the dynamic evolutions in Supplementary Video 5). Note that these isolated particles are in grey and turn into blue once they are physically connected. g, 2D kernel density estimation map of the membrane locations in a customized space, which consists of the terminal reaction time-to-critical time ratio and the membrane thickness-to-building unit size (vertical dimension) ratio. All the data were derived from the 40 kinds of membrane in the presented library. The dot density is indicated by the top colour bar. The box chart shows the statistical result of the membrane thickness-to-building unit size (vertical dimension) ratio. The caps indicate the 1.5× interquartile range. The diamond box shows 10th–90th percentiles, with the marked median (transverse line inside) and mean (dot inside). The empirical deviation coefficient ω, which represents the statistical ratio of the SLIS-mediated membrane thickness to the building unit size (vertical dimension), is determined to be between 1.06 and 5.94 by the box range. The detailed description of the general synthesis of an unexplored inorganic membrane is included in Supplementary Section 8.1.

Source Data

Supplementary information

Supplementary Information

This file contains Supplementary Sections 1–10, Supplementary Figs. 1–71, Supplementary Tables 1–3 and References.

Supplementary Video 1

Geometric isotropy of the critical (quasi-)bicontinuous Ag network. This video corresponds to Extended Data Fig. 5f,g. A duplicated (quasi-)bicontinuous pattern layer is stacked on top of its mother layer and rotated continuously. The dynamic change of the stacked structure is shown in the left split screen and the corresponding through-hole ratio against the rotation angle is simultaneously quantified in the right split screen. The (quasi-)bicontinuous pattern was extracted from a typical TEM image of the bicontinuous Ag membrane (Extended Data Fig. 5d). The angle-dependent network pattern snapshot and the corresponding geometric permeability analysis were performed every 0.5° by using a customized Python image-processing code. A split-screen video with synchronous display was then created by combining all the sequential frames.

Supplementary Video 2

Dynamic formation of the (quasi-)bicontinuous network in various reaction systems. This video corresponds to Fig. 3h. The three split screens record the independent microscopic videos corresponding to the dynamic formations of the (quasi-)bicontinuous network for AgCl (left), BiVO4 (middle) and Ag2CrO4 (right) membranes, respectively. In spite of the different components, sizes and morphologies of the building blocks, all the processes successively experience four well-defined steps, that is, explosive emergence of particles with intrinsic Brownian motion, random-collision-induced Brownian cluster formation, Cheerios-effect-driven aggregation among clusters and the final formation of the critical (quasi-)bicontinuous network. Each split-screen video was recorded from the beginning of the reaction to the moment of forming the critical (quasi-)bicontinuous network. They were then sped up (by factors of 8, 3.5 and 6 from real time for AgCl, BiVO4 and Ag2CrO4, respectively), normalized to 35 s and played synchronously to show the kinematic similarities among the three cases.

Supplementary Video 3

Trapping of the floating AgCl particles/Brownian clusters by the outer margin of the (quasi-)bicontinuous network. This video corresponds to Extended Data Fig. 8b,c. The upper split screen shows the kinematics of the AgCl particles/Brownian clusters at the outer margin of the (quasi-)bicontinuous AgCl network. The synchronous velocity-field analysis result is presented in the bottom split screen. Notably, the large (quasi-)bicontinuous network constantly attracts and traps these outside particles and small Brownian clusters, thus expanding its domain. The video was recorded from the moment of the formation of the (quasi-)bicontinuous AgCl network, which was about 5 min after the beginning of the reaction. The playback is in real time. The arrows indicate the local velocities. The colour of the localized area visualizes the direction and intensity of the local vorticity, as indicated in the right colour bar.

Supplementary Video 4

Trapping of the nascent AgCl particles by the internal framework of the closed network. This video corresponds to Extended Data Fig. 8d,e. The left split screen shows a microscopic video that monitors the trapping process of the nascent AgCl particles produced inside the closed AgCl network. The time-course spatial distribution of these trapping locations is captured and recorded in the right split screen. These nascent particles born inside the closed network are immediately and randomly trapped by the wall of the AgCl framework. As a result, the areas of the holes are continuously diminished. The process was recorded from the moment of the formation of the closed AgCl network, which was about 15 min after the beginning of the reaction. The video was accelerated from real time by a factor of 3. The dots appearing in the right split screen mark the locations of these trapped nascent particles in the present moment. Their colours correspond to the actual time course in 36 s, as indicated in the right colour bar.

Supplementary Video 5

Simulation of the temporal evolution of the 2D particle system towards various GT phases. This video corresponds to Extended Data Fig. 10c–f. The video has four split screens, showing the independent simulations of the dynamic particle system towards the GT phases of node islands, clique islands, open network and closed network, respectively. The Brownian-motion random walk and the Cheerios-effect mathematical computations serve as the foundation for the simulations. As soon as the isolated particles are physically connected to other particles or particle clusters, their initial grey appearance is replaced by blue. Both the timescales and space scales were normalized for these four cases to highlight the visual comparability. The dynamic visualization was realized through a customized Python code.

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Zhang, C., Lu, W., Xu, Y. et al. Mechanistic formulation of inorganic membranes at the air–liquid interface. Nature 616, 293–299 (2023). https://doi.org/10.1038/s41586-023-05809-y

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