Extended Data Fig. 5: Structural characterizations of the (quasi-)bicontinuous Ag membrane.
From: Mechanistic formulation of inorganic membranes at the air–liquid interface
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).
