This PDF file includes:

• Section I. Fabrication of the LGG membranes
• Section II. Tuning the average interlayer spacing through the capillary compression method
• Section III. Determination of the average interlayer spacing from membrane thickness
• Section IV. Small-angle neutron scattering of the compressed LGG membranes
• Section V. Time-lag diffusion and electrokinetic ion transport experiments
• Section VI. Continuum modeling of concentration-driven ion diffusion through the cascading nanoslits contained in the LGG membranes
• Section VII. Continuum modeling of electrokinetic ion transport through the cascading nanoslits contained in the LGG membranes
• Fig. S1. A schematic showing the fabrication of the LGG membranes and tuning of the interlayer spacing.
• Fig. S2. Isotropic SANS patterns of the compressed LGG membranes.
• Fig. S3. Concentration-driven ion transport through the LGG membranes.
• Fig. S4. Effect of circulation rate on ion permeation through the LGG membranes.
• Fig. S5. The continuum simulation model for steady-state diffusion across charge-neutral cascading nanoslits.
  Fig. S6. Determination of the geometrical variables L and δ through a reverse Monte Carlo method.
• Fig. S7. The continuum simulation model for steady-state diffusion across negatively charged cascading nanoslits.
• Fig. S8. Concentration and electric potential distribution profiles of the steady-state KCl diffusion across negatively charged cascading nanoslits.
• Fig. S9. An AFM image of CCG on mica substrates.
• Fig. S10. Continuum simulations of the electrokinetic ion flow across negatively charged cascading nanoslits.
• Fig. S11. Representative I-V curves of the electrokinetic ion transport measurements.
• Fig. S12. Typical I-V curves for the establishment of membrane selectivity.
• Fig. S13. The increase in channel concentration as a result of channel surface charge.
• Fig. S14. Scaling behaviors of the electrokinetic ion transport as a function of channel size across the range of sub–10 nm and of varied ionic concentrations.
• Fig. S15. The continuum simulation model for electroosmotic current across the negatively charged cascading nanoslits.
• Table S1. Geometries of the cascading nanoslits model.
• Table S2. Effect of surface charge status on ion diffusion coefficient across the cascading nanoslits.
• References (56–72)

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