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Xing et al. Microstructures 2023;3:2023031 https://dx.doi.org/10.20517/microstructures.2023.11 Page 3 of 35

Table 1. Key characteristics of macrochannel, microchannel, and nanochannel membranes
Channel
Membrane size Key features Applications
type (typical
range)
Macrochannel > 100 µm Large channel size, low surface-to-volume ratio, Pre-treatment processes in chemical, environmental,
turbulent flow regime, and reduced resistance to flow pharmaceutical, mining, and other industries
Microchannel 1-100 µm Intermediate channel size, moderate surface-to- Microfluidics, lab-on-a-chip devices, chemical synthesis,
volume ratio, laminar flow regime, and diffusion and separation processes
dominates
Nanochannel < 100 nm Very small channel size, high surface-to-volume ratio, Water treatment, ion selectivity, gas separation, DNA
molecular selectivity, and electrostatic interactions sequencing, single-molecule analysis, nanofluidics, and
dominate biosensors

nanochannels, which improves permeation efficiency. Overall, the combination of these factors allows 2D-
material-based nanochannel membranes to achieve selective separations by exploiting the size, charge, and
interaction-based properties of the target species.

To comprehensively assess the performance of the membranes, several formulas can be utilized, including
the rejection coefficient, separation factor, permeability, flux, rejection, fouling index, and interlayer
spacing. By quantifying these parameters, researchers can better understand the potential benefits of using
2D materials with densely packed nanochannels for nanoscale separation applications.

The rejection coefficient (R) is determined by equation (1), where C is the solute concentration in the
feed
feed, and C permeate is the solute concentration in the permeate.

The separation factor (α) is defined as the ratio of the rejection coefficients of two different solutes, A and B,
which is determined by equation (2).

Permeability (P) measures the ease with which a solvent flow through a porous material and is calculated
using the formula (3), where Q is the permeate volume, A is the effective membrane area, and ΔP is the
transmembrane pressure.

Flux (J) represents the volume of permeate that passes through the membrane per unit area per unit of time
and is calculated using the formula (4), where Δt is the time.

Rejection (Rej) is defined as the ratio of the solute concentration in the feed to the solute concentration in
the permeate and is calculated using the formula (5).