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Multi-functional membranes with high permeance and selectivity that can mimic nature's designs have tremendous industrial and bio-medical applications. Here, we report a novel concept of a 3D nanometer (nm)-thin membrane that can overcome the shortcomings of conventional membrane structures. Our 3D membrane is composed of two three-dimensionally interwoven channels that are separated by a continuous nm-thin amorphous TiO 2 layer. This 3D architecture dramatically increases the surface area by 6000 times, coupled with an ultra-short diffusion distance through the 2 – 4 nm-thin selective layer that allows for ultrafast gas and water transport, ∼900 l m −2 h −1 bar −1 . The 3D membrane also exhibits a very high ion rejection ( R ∼ 100% for potassium ferricyanide) due to the combined size- and charge-based exclusion mechanisms. The combination of high ion rejection and ultrafast permeation makes our 3DM superior to the state-of-the-art high-flux membranes whose performances are limited by the flux-rejection tradeoff. Furthermore, its ultimate Li + selectivity over polysulfide or gas can potentially solve major technical challenges in energy storage applications, such as lithium – sulfur or lithium – O 2 batteries. 

Graphene is one of the stiffest materials ever measured, and yet foams of this material experience such massive degradation in mechanical properties at low densities that they are worse than polymer foams. (Z. Qin, G. S. Jung, M. J. Kang and M. J. Buehler, Sci. Adv., 2017, 3, e1601536). 3D printed mechanical metamaterials have shown the unprecedented ability to alleviate such degradation, but all current 3D printing techniques capable of printing graphene foam are unable to reproduce the complex metamaterial architectures (e.g. insufficient resolution, toolpath limitations, etc.). Here we demonstrate high-resolution graphene foams incorporating hierarchical architecture which reduces mechanical degradation of graphene foams with decreasing density. Our technique achieves an order-of-magnitude finer resolution and far more intricate structures than any previous method. This technique opens new possibilities not only to enhance graphene foam mechanical properties, but to explore complex architectures and mesoscale effects for other graphene applications including energy storage and conversion, separations, and catalysis.