Decoupling Entrance and Inner Resistances in CNT Channels

Due to their high transport rates, a great deal of attention has been recently given to 2D materials and slippery 1-D nanochannels as promising building blocks for next generation membranes. While in 2-D materials high flux is expected because of the classical inverse scaling of the flow rate with the pore thickness, in smooth channels such as carbon nanotubes (CNT), orders of magnitude rate enhancements with respect to classical theories are attribute to a vanishing friction at the pore wall. Irrespectively of the high flux origin, in both atomically thin and thicker but slippery nanopores, the flow rates are largely dictated by the entrance/exit hydrodynamic resistance.<br/><br/>For CNT channels, experimental quantification of the magnitude of end and inner resistances is still lacking despite its importance for both practical applications and fundamental understanding. This has led to inaccuracy and disagreement in the calculation of slip lengths and flow rate enhancements from experimentally measured permeation rates, since often entrance/exit resistances are neglected altogether, or an arbitrary magnitude is assumed. Here, we quantified these resistances for both gases and liquids in CNT channels by fabricating membranes with controlled CNT length and known number of open pores. We found that the end resistance dominates the total resistance. For liquid water, measured viscous energy dissipation at the nanotube ends is quantitatively described by Sampson equation. For 2.4 nm wide single-walled CNTs, measured slip lengths approach several microns. A prevailing contribution of the end resistance was also found in pressure-driven gas transport, and recorded flow rate enhancements with respect to Knudsen theory appear to be independent of the gas type. These findings further advance the community understanding of the peculiar and often unusual CNT fluidic properties and may help reconciliating “conflicting” literature reports on the subject.