Assessing the Thickness–Permeation Paradigm in Nanoporous Membranes

Abstract

Driven by the need of maximizing performance, membrane nanofabrication strives for ever thinner materials aiming to increase permeation while evoking inherent challenges stemming from mechanical stability and defects. We investigate this thickness rationale by studying viscous transport mechanisms across nanopores when transitioning the membrane thickness from infinitely thin to finite values. We synthesize double-layer graphene membranes containing pores with diameters from ∼6 to 1000 nm to investigate liquid permeation over a wide range of viscosities and pressures. Nanoporous membranes with thicknesses up to 90 nm realized by atomic layer deposition demonstrate dominance of the entrance resistance for aspect ratios up to one. Liquid permeation across these atomically thin pores is limited by viscous dissipation at the pore entrance. Independent of thickness and universal for porous materials, this entrance resistance sets an upper bound to the viscous transport. Our results imply that membranes with near-ultimate permeation should feature rationally selected thicknesses based on the target solute size for applications ranging from osmosis to microfiltration and introduce a proper perspective to the pursuit of ever thinner membranes.

Revisiting Sampson's theory for hydrodynamic transport in ultrathin nanopores

“…As mentioned in the main part of the paper, our theory assumes circular pores. This assumption was also employed in previous studies [20,21] where the original Sampson theory was used to predict the flow rates in graphene pores. We plotted the largest and smallest pores (with a radius of 3.54 and 0.24 nm, respectively) considered in this work with an overlaid circle as shown in Fig.…”

“…In addition, in biological nanopores, such as aquaporins, water exhibits a unique single-file dynamical behavior [18,19] with a high flux of about 10 9 molecules per second due to the charge residues at the pore mouth causing water molecules to rotate and the conical structure of the pore minimizing the entrance/exit hydrodynamic resistance. In recent years, a great deal of attention has been given to two-dimensional (2D) materials (e.g., single-layer graphene, MoS 2 ) due to their high transport rates [10,15,20] as flux is expected (classically) to scale inversely with the thickness of the pore. For atomically thin pores, the flow rates are dictated by the entrance/exit hydrodynamic resistance governed by the viscous energy dissipation.…”

“…As the entrance/exit resistance dominates the total resistance in a CNT, a slight error in the estimation of the entrance/exit resistance could lead to a large error in the calculation of slip length. Therefore, the need for an accurate theory describing the entrance/exit resistance (defined as the ratio of the pressure drop to the volumetric flow rate, R = P Q ) in both ultrathin and thick pores has been recognized in the past few decades [18,20,23].…”

Architecture and mass transport properties of graphene-based membranes

“…Suk and Aluru pointed out that low ion partitioning is due to the large free energy penalty for dehydration [39], and is not consistent with the concept of dielectric exclusion of existing nanofiltration membranes [40]. In addition, it is known that the diffusion coefficient As the aspect ratio decreases below 1, transport deviates from the inverse relationship of thickness-permeation because entrance-dominated resistance becomes dominant [34] D p of ions in the graphene pore is lower than the diffusion coefficient D bulk in solution. Correlation between D p , D bulk and pore radius r is expressed by the following equation: 1 D p − 1∕D bulk ∝ 1∕r .…”

“…As the pore aspect ratio increases, possible by thickening the graphene layer via atomic layer deposition (ALD), the water flux deviates from that of effusion to that of channel flows (Fig. 3) [34].…”