Molecule transport behaviors in ultrathin and porous membranes: The role of pore size

Abstract

Ultrathin (<100 nm) and porous membranes exhibit rapid molecule transport due to the high porosity and short transport path. However, molecule transport behaviors in terms of pore size (r) remain unclear. Herein, four kinds of porous MOF membranes with ultrathin thickness (∼20 nm) are prepared on the support layers. The pore sizes of MOF membranes are subtly adjusted (0.66, 0.81, 1.12, and 1.90 nm) by selecting carboxyl ligands with varied benzene-ring numbers. Based on these platforms, we demonstrate that the transport of both polar and non-polar molecules obeys the typical Hagen-Poiseuille model for ultrathin membrane with pore size larger than 1.0 nm. The permeance of solvents obeys $P=k_1\frac{r^4}{\mu }$ (μ, viscosity; k_1,1.90 = 126.84 and k_1,1.12 = 580.64). In contrast, for the pore size smaller than 1.0 nm, other factors such as molecule polarity and diameter count. Specifically, for the membrane with pore size of 0.81 nm, the transport of polar and non-polar molecules follows the Hagen-Poiseuille model, but with distinct slopes: $P=k_2\frac{r^4}{\mu }$ and $P=k_3\frac{r^4}{\mu }$, respectively. While for the membrane with pore size of 0.66 nm, new phenomenal equations are respectively proposed to describe the transport of polar and non-polar molecules. The permeance of polar and non-polar solvents obeys $P=k_4\frac{r^4}{R^{2}D\mu }$ and $P=k_5\frac{r^4}{R^2\mu }$, respectively (R and D represent molecule diameter and dipole moment, respectively). These findings should shed light on the molecule transport mechanism in porous and ultrathin membranes with confined nanochannels.