Monte Carlo Simulations of Framework Defects in Layered Two-Dimensional Nanomaterial Desalination Membranes: Implications for Permeability and Selectivity

Two-dimensional nanomaterial (2-D NM) frameworks, especially those comprising graphene oxide, have received extensive research interest for membrane-based separation processes and desalination. However, the impact of horizontal defects in 2-D NM frameworks, which stem from nonuniform deposition of 2-D NM flakes during layer build-up, has been almost entirely overlooked. In this work, we apply Monte Carlo simulations, under idealized conditions wherein the vertical interlayer spacing allows for water permeation while perfectly excluding salt, on both the formation of the laminate structure and molecular transport through the laminate. Our simulations show that 2-D NM frameworks are extremely tortuous (tortuosity ≈103), with water permeability decreasing from 20 to <1 L m–2 h–1 bar–1 as thickness increased from 8 to 167 nm. Additionally, we find that framework defects allow salt to percolate through the framework, hindering water–salt selectivity. 2-D NM frameworks with a packing density of 75%, representative of most 2-D NM membranes, are projected to achieve <92% NaCl rejection at a water permeability of <1 L m–2 h–1 bar–1, even with ideal interlayer spacing. A high packing density of 90%, which to our knowledge has yet to be achieved, could yield comparable performance to current desalination membranes. Maximizing packing density is therefore a critical technical challenge, in addition to the already daunting challenge of optimizing interlayer spacing, for the development of 2-D NM membranes.