Ions play a crucial role in many biological and technological processes, and their selective transport through membranes is of great interest for various applications such as energy harvesting, fuel cell membranes, and ion sieving. 

Ions in aqueous solutions acquire hydration shells due to the electric field of a charged ion, which forces dipolar molecules of water to rearrange around them.  The hydrated diameter and  the charge of ions primarily determine their permeation through nanoporous materials. However, biological channels can distinguish even between ions of similar hydrated sizes. A well-known example is potassium protein channel which has a selectivity of up to ~10⁴ between similar-sized ions K⁺ and Na⁺. Mimicking this feat of nature and creating artificial solid-state channels capable of specific ion selectivity is of significant interest but remains a challenge. To design artificial channels that can differentiate same-charge ions of similar size, we require an understanding of why and how such selectivity can occur.

In 2016, some of us (Radha, Geim and co-workers) reported angstrom (Å)-scale channels constructed out of 2D materials¹ with their height tunable with a precision of one graphene layer thickness . These channel walls made from mechanically exfoliated 2D materials bear negligible surface charge, are chemically inert and are atomically smooth. An initial observation with the Å-channels was the ultra-fast flow¹ of water molecules with velocities of up to 1 metre per second. Following this study, we investigated the influence of ion’s hydrated diameter (D_H) on the ion selectivity², with the same system of Å-channels. In the 2017 paper by Esfandiar et al., the tested ions had a range of D_H varying from smaller to larger than the channel height (~6.8 Å), and the ion mobility decreased with increasing D_H. The reduction of the ion mobility was due to steric hindrance where an ion larger than the channel cannot enter the channel without shedding most of its hydration layer². In 2019 manuscript by Gopinadhan et al.3, we further thinned down the channels down to about one graphene layer thickness (~3.4 Å) and observed complete rejection of ions by steric exclusion,  with only protons being able to permeate through water in channels. However, the complete story puzzle was still incomplete, with several missing pieces and several questions remaining unanswered. For example,  what factors govern the ion passage when D_H is not the key factor? How do ions behave in confinement and how is the water arrangement around the ions inside the channel? Is there any effect of the ionic charge sign?

Our current study addresses the above questions by choosing ions with similar hydrated diameter but different ionic diameter. Indeed, these ions were able to enter the angstrom channels (height, 6.8 Å) without much entry resistance, thus excluding steric effects. The main factors influencing selectivity under these conditions were found to be the ionic core diameter (D_I) and the ionic charge. From our experiments, we observed that the ions with a larger D_I showed reduced mobility compared to the ions with smaller D_I (Figure 1). With the help of molecular dynamics and density functional theory simulations, we realized that the ion-core size defines the position of ions inside the Å-channels. Ions with larger D_I which are more likely to be near the wall were slower than the ions with smaller D_I that are positioned in the channel’s centre (Figure 2). This showed a new mechanism for ion selectivity that has certain parallels with ion transport through protein channels where selectivity also depends on how snugly ions fit inside channels⁴.

We also studied the effect of ion charge by examining several anions of salts with the same cation. Despite the same D_H and D_I, we observed selectivity between two oppositely charged ions (Cl^- & Cs⁺) which was attributed to the arrangement of water molecules around each ion (Fig.1b). In addition, we have found that cations and anions can affect transport of each other in confined channels (see Fig.1c). This is a big surprise because ions diffuse independently in bulk solutions, whereas in such atomic-scale confinement the ion diffusion can be altered by the counter ions.

These findings demonstrate that strong geometrical confinement of the ions of similar D_H can lead to notable selectivity between them. This selectivity depends on difference in ions’ positions inside Å-scale channels which has resemblance to the way ion selectivity is governed in biological channels, where snugly fitting of ions between the walls plays a crucial role. 2D channels with functionalized walls should allow higher selectivities and may offer a venue towards development of designer sieves to filter out specific ions.

For more details, please check out our paper “Beyond steric selectivity of ions using angstrom-scale capillaries” in Nature Nanotechnology (Link: https://www.nature.com/articles/s41565-023-01337-y).

References:

1. Radha B, Esfandiar A, Wang FC, Rooney AP, Gopinadhan K, Keerthi A, et al. Molecular transport through capillaries made with atomic-scale precision. Nature 538, 222-225 (2016). 

2. Esfandiar A, Radha B, Wang FC, Yang Q, Hu S, Garaj S, et al. Size effect in ion transport through angstrom-scale slits. Science 358, 511-513 (2017). 

3. Gopinadhan K, Hu S, Esfandiar A, Lozada-Hidalgo M, Wang FC, Yang Q, et al. Complete steric exclusion of ions and proton transport through confined monolayer water. Science 363, 145-148 (2019). 

4. Epsztein R, DuChanois RM, Ritt CL, Noy A, Elimelech M. Towards single-species selectivity of membranes with subnanometre pores. Nat. Nanotechnol. 15, 426-436 (2020). 

5. Tansel B. Significance of thermodynamic and physical characteristics on permeation of ions during membrane separation: Hydrated radius, hydration free energy and viscous effects. Sep. Purif. Technol. 86, 119-126 (2012). 

6. Nightingale ER. Phenomenological Theory of Ion Solvation. Effective Radii of Hydrated Ions. J. Phys. Chem. 63, 1381-1387 (1959).