Fig. 2: Analysis of activated gas permeation through graphene nanopores.

Temperature-dependent gas permeance through nanoporous graphene before (a) and after (b) pore creation, on PITEM(10) supports. The gas permeance through nanoporous graphene is calculated by normalizing the membrane permeance by support porosity and removing the flow resistance from the support. The error bars on the y-axis denote the standard deviation of permeance based on error propagation (Supplementary Note 2). c Activation energy, error bars represent the standard error of the activation energy derived from permeance fit to Equation (1) and (d) pre-factor derived by fitting the transport model equation (1) to the gas permeation data, plotted as a function of gas kinetic diameter. Inset depicts membrane surface with intrinsic nanopores and created nanopores. e Gas permeation behaviors align with a Knudsen diffusion model through leakage in nanoporous graphene, i.e., gas transport through large defects that are not in the activated regimes, obtained by subtracting the total permeance by that from the activated transport according to equation (1). Molecular weight \({M}_{i}\) is in kg mol^-1. Comparison of experimentally measured helium permeance across nanoporous graphene after pore creation against simulated helium permeance using the f, rigid pore model, g pore switching model, and h, edge flexible model (details in Supplementary Note 3). The minutes notation, i.e., 5, 13, 25, 60 and 120 min in the legend corresponds to various pore growth times. The numbers at the top left of (a−e) indicate the multiplication factor (e.g., 1e-6) applied to the y-axis values. Source data are provided as a Source Data file.