Fig. 1

Sub-nanopores sputtered through silicon nitride membranes. (a, b; top) HAADF-STEM images of two sub-nanopores with mean-diameters at the waist of 0.28 nm and 0.40 nm, respectively, acquired with an aberration-corrected Themis Z. (a, b; 2nd from top) Line-plots associated with the white dashed lines in (a, b top). The shot-noise between the red dashed lines indicates the pore diameter. (a, b; 2nd from bottom) 2D-projections from the top through models of the sub-nanopores in (a, b; top) that indicate the atomic distribution near the pore waist. The atoms are depicted by space-filling models in which each Si is represented by a blue sphere and each N is a pink sphere. (a, b; bottom) 3D-perspectives of the space-filled models (a, b; 2nd from bottom). (c, d; top) TEM images of two sub-nanopores with mean-diameters at the waist of 0.42 nm and 0.70 nm, respectively, acquired with the Titan. The dashed circles delineate the shot noise that defines the pore waist. (c, d; 2nd from top) The corresponding multi-slice simulations of the TEM images (c, d; top) that were consistent with the imaging conditions. (c, d; 2nd from bottom) 2D-projections from the top through the models used in (c, d; 2nd from top) that indicate the atomic distribution near the pore waist. (c, d; bottom) 3D-perspectives of space-filled models of (c, d; 2nd from bottom). (e; top) HAADF-STEM images acquired from a pore with a mean-diameter of 0.89 nm at 0° (top, left) and 26° (top, right) tilt angles relative to the optic axis of the microscope. (e; bottom, left) The corresponding line-plot associated with the white dashed line (e; top) that indicates the mass-density under the beam. (e; bottom, right) An idealized model that illustrates the effect of the tilt angle on the image. f A snapshot extracted from MD of an idealized, negatively charged (−3e) 0.30 nm diameter sub-nanopore immersed in 1 M NaCl, illustrating the distortion of the hydration shell surrounding a Na⁺ (green) as it permeates through the (ghost) pore. The Cl⁻ (purple) are excluded from the pore because of de-hydration and electrostatic repulsion. Only the silicon (blue) and nitrogen (pink) atoms in the membrane at the pore surface are represented in the model, and even they are ghosted