Mechanistic insights into confinement-optimized through-plane water transport in multilayer r-N-graphdiyne...

Nanoscale confinement plays a pivotal role in dictating the transport behavior of water, with profound implications for the design of next-generation membrane technologies. Here, molecular dynamics simulations reveal that water permeation through multilayer r-N-graphdiyne membranes, where transport occurs through subnanometer pores along the direction normal to the membrane plane (through-plane), depends strongly and nonmonotonically on the interlayer spacing (d). Water permeance reaches a maximum at an intermediate spacing of d = 5.0 Å, whereas smaller spacings suppress permeation via steric exclusion and large transmembrane free-energy barriers. At this optimal spacing, confinement stabilizes ordered, undercoordinated, chain-like water structures that support fast, collective through-plane transport. Free-energy analyses indicate a highly anisotropic landscape, where moderate interlayer wells combined with large lateral barriers are consistent with enhanced water motion along the through-plane direction. In contrast, larger spacings (e.g., d = 6.0 Å) are associated with less ordered confined-water structuring, enhanced lateral diffusion and interlayer trapping, which together suppress through-plane flow. The same nonmonotonic regulation and optimal-spacing behavior is reproduced in a pseudo through-plane model with AAA stacking of the r-N-graphdiyne membrane, suggesting that this transport behavior is robust across different stacking geometries and may arise from the competition between confinement, through-plane ordering, and lateral mobility. These results suggest that interlayer spacing is an important design parameter for through-plane nanofluidics and offer mechanistic insight that can inform the engineering of high-performance two-dimensional membranes with optimized water transport.