Crystallization of gas-selective nanoporous graphene by competitive etching and growth: a modeling study

A robust synthesis methodology for crystallizing nanoporous single-layer graphene hosting a high density of size-selective nanopores is urgently needed to realize the true potential of two-dimensional membranes for gas separation. Currently, there are no controllable etching techniques for single-layer graphene that are self-limiting, and that can generate size-selective nanopores at a high pore-density. In this work, we simulate a unique chemical vapor deposition based crystallization of graphene on Cu(111), in the presence of an etchant, to generate a high density (>10¹³ cm^-2) of sub-nanometer-sized, elongated nanopores in graphene. An equilibrium between the growth rate and the etching rate is obtained, and beyond a critical time, the total number of the carbon atoms and the edge carbon atoms do not change. Using an optimal first-order etching chemistry, a log-mean pore-size of 5.0 ± 1.7 (number of missing carbon atoms), and a pore-density of 3 × 10¹³ cm^-2 was achieved. A high throughput calculation route for estimating gas selectivity from ensembles of thousands of nanopores was developed. The optimized result yielded H₂/CO₂, H₂/N₂ and H₂/CH₄ selectivities larger than 200, attributing to elongated pores generated by the competitive etching and growth. The approach of competitive etching during the crystal growth is quite generic and can be applied to a number of two-dimensional materials.