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Abstract Monolayer graphene growth on liquid copper (Cu) has attracted attention due to advantages of a flat/smooth catalytic growth surface, high synthesis temperature (>1080 °C) as well as the possibility of forming graphene domains that are mobile on the liquid Cu with potential to minimize grain boundary defects and self-assemble into a continuous monolayer film. However, the quality of monolayer graphene grown on liquid copper and its suitability for size-selective ionic/molecular membrane separations has not been evaluated/studied. Here, we probe the quality of monolayer graphene grown on liquid Cu (via a metallurgical process, HSMG^®) using Scanning Electron Microscope (SEM), High-resolution transmission electron microscope (HR-TEM), Raman spectroscopy and report on a facile approach to assess intrinsic sub-nanometer to nanometer-scale defects over centimeter-scale areas. We demonstrate high transfer yields of monolayer graphene (>93% coverage) from the growth substrate to polyimide track etched membrane (PITEM, pore diameter ∼200 nm) supports to form centimeter-scale atomically thin membranes. Next, we use pressure-driven transport of ethanol to probe defects > 60 nm and diffusion-driven transport of analytes (KCl ∼0.66 nm, L-Tryptophan ∼0.7–0.9 nm, Vitamin B12 ∼1–1.5 nm and Lysozyme ∼3.8–4 nm) to probe nanoscale and sub-nanometer scale defects. Diffusive transport confirms the presence of intrinsic sub-nanometer to nanometer scale defects in monolayer graphene grown on liquid Cu are no less than that in high-quality graphene synthesized via chemical vapor deposition (CVD) on solid Cu. Our work not only benchmarks quality of graphene grown on liquid copper for membrane applications but also provides fundamental insights into the origin of intrinsic defects in large-area graphene synthesized via bottom-up processes for membrane applications.