Fig. 2: Water transport through cation intercalated GOMs.

a Variation of water flux of cation intercalated GOMs against hydrated diameter of cations. The red scatters correspond to the GOMs prepared by membrane intercalation method (X-M-GO) and blue scatters correspond to solution intercalation method (X-S-GO). The unit of water flux is L m⁻² h⁻¹ bar⁻¹ (LMH/bar). The black dashed line represents the flux of pure GOM. b Interlayer space of cation intercalated GOMs against hydrated diameters. The hydrated diameters of cations are listed in Table 1. c Variation of water flux of X-S-GO with controlled moles of cation, where H⁺ corresponds to the case of water flux of pure GOM. d Variation of slip length with hydrated diameter of cations; slip length is calculated using experimentally observed water flux and interlayer space. The dotted black line displays an exponential decay fit with a coefficient of determination (R²) of 0.998. For each data point shown in (a–d), three separate membranes were tested. Error bars indicate the standard deviation from these three membranes. e, f Schematic diagrams of water transport through pure GOM (e) and cation intercalated GOM (f). v(H₂O) corresponds to the velocity of water molecules. The dimension of water molecules, GO sheets and hydrated cations are chosen for illustration and are not intended to represent the realistic scale. Without the influence of cations or hydrogen ion (H⁺), the water flux through graphitic domains is illustrated as unimpeded². Source data are provided as a Source Data file.