Tuneable ion selectivity in vermiculite membranes intercalated with unexchangeable ions

Domain: physics
Published: 2025-12-02
Editorial outcome: major_revision

Abstract
Membranes selective to ions of the same charge are increasingly sought for water waste processing and valuable element recovery. However, while narrow channels are known to be essential, other membrane parameters remain difficult to identify and control. Here we show that Zr⁴⁺, Sn⁴⁺, Ir⁴⁺, and La³⁺ ions intercalated into vermiculite laminate membranes become effectively unexchangeable, creating stable channels, one to two water layers wide, that exhibit robust and tuneable ion selectivity. Ion permeability in these membranes spans five orders of magnitude, following a trend dictated by the ions’ Gibbs free energy of hydration. Unexpectedly, different intercalated ions lead to two distinct monovalent ion selectivity sequences, despite producing channels of identical width. The selectivity instead correlates with the membranes’ stiffness and the entropy of hydration of the intercalated ions. These results introduce an ion selectivity mechanism driven by entropic and mechanical effects, beyond classical size and charge exclusion.

Introduction
Evidence from biological channels and artificial systems, such as nanopores has shown that achieving selectivity between ions of the same charge requires membranes with precisely controlled pore size, typically in the subnanometre range. This has attracted attention to laminate membranes made with 2D materials like graphene oxide (GO), MoS or MXenes as systems that could enable such selectivity with scalable technologies. In these membranes, the stacked 2D crystals form narrow channels that can in principle provide such selectivity. However, these membranes swell in water, which increases the interlayer space beyond the hydrated diameters of ions in common salts, making them non-selective to these ions. This led to the design of mechanically confined GO membranes, and more recently, to cation control of the interlayer spacing in GO and MXenes. In this latter strategy, ions such as Al3+ or K+ are pre-intercalated into the nanotubes, nanochannels, and two-dimensional (2D) membranes, and because of their strong binding to the 2D material, prevent the membrane from swelling.

In this context, clays merit attention. This abundant material can be exfoliated into 2D layers, which enables fabricating laminate membranes similar to GO or MXene. The material consists of negatively charged aluminosilicate layers with native cations such as Mg2+ adsorbed in the interlayer spaces that hold the layers together. Crucially, these native ions can be easily substituted for others via ion exchange, which enables tuning the interlayer separation. This versatility, however, is also the biggest hindrance to using vermiculite membranes in ion sieving applications. Exposing the membranes to electrolyte solutions exchanges the interlayer ions for those in the solution within hours making their properties unstable and sometimes even leading to complete membrane disintegration. One strategy to tackle this problem is to chemically bond the layers with organic or oxide linkers, which preserves membrane stability and enables ion-selective membranes. In this work, we adopt a different strategy. We show that a group of high valence ions, namely zirconium, iridium, tin and lanthanum intercalated in vermiculite clay laminates, is effectively impossible to exchange at ambient conditions yielding robust and tuneable ion selective membranes.

Results
Vermiculite laminate membranes were fabricated from aqueous dispersions prepared from thermally expanded vermiculite crystals via a two-step Na+ and Li+ ion exchange process, as reported previously. This yielded stable aqueous colloid solutions of high-quality vermiculite nanosheets ~1 nm thick and ~10 μm in lateral size. Membranes with a well-ordered lamellar structure, typically ≈2 µm thick, were fabricated from the dispersions via vacuum filtration. This as-fabricated vermiculite membrane, saturated with Li+ ions (Li-Ver), was then immersed in different electrolyte solutions to exchange the Li+ cations for those in the electrolyte. We tested various cations, such as K+, Na+ or Cs+, all of which were successfully inserted into the membrane, yielding K-Ver, Na-Ver, etc. However, while this makes vermiculite membranes highly tuneable, it also makes them unstable as ion separation membranes. This can be clearly appreciated for Li+ electrolytes, for which the problem is particularly severe. We found that the sharp XRD signal of these membranes (e.g. K-Ver) is lost within ~24 h of continuous exposure to LiCl electrolyte and visual examination revealed that these membranes had disintegrated. For other electrolytes (e.g. K-Ver in NaCl), the membranes did not disintegrate in the electrolyte, but their composition changed rapidly. Inductively coupled plasma optical emission spectrometry (ICP-OES) of the membranes revealed that within 24 h of exposure to different electrolyte solutions, the mass loss of interlayer ions was >95%; that is, practically all the initial intercalated ions were exchanged.

We found that Zr4+, Ir4+, Sn4+ and La3+ inserted in vermiculite membranes are effectively impossible to remove by immersing the membranes in common electrolytes at ambient conditions and that this makes these membranes robust in ion transport experiments. To fabricate the membranes, the Li-Ver membranes described above were immersed in electrolyte solutions of these ions (e.g. 1.0 M ZrCl for about 1 h) and then rinsed with deionised (DI) water. We then tested the stability of the exchanged membranes by immersing them in various aqueous electrolyte solutions, including LiCl, between 1 to 180 days. XRD characterisation showed that the interlayer separation of the membranes remained stable for as long as we decided to test them, up to 180 days. Additional ICP-OES characterisation revealed only a minor ~5% loss of intercalated ions, which remained stable over the whole testing period. We therefore call these strongly bonded ions ‘unexchangeable ions’, to differentiate them from those that can be readily exchanged (e.g. K+ or Ba2+). Microscopic insights into the distribution of the unchangeable ions were obtained with aberration-corrected scanning transmission electron microscopy (AC-STEM). This revealed that the ions tended to form domains with quasi-hexagonal symmetry separated by large Zr⁴⁺-free regions. In fact, only a small fraction of the flake surface is occupied by Zr⁴⁺, leaving extensive areas without coverage. This low coverage is expected, as the 4+ valence of each Zr⁴⁺ ion balances multiple adsorption sites in vermiculite (each with −1 valence).

These robust laminates could be used as ion sieving membranes. We measured the permeability of 14 common inorganic cations focusing on Zr-Ver membranes, which is used as a model system. In the experiments, the membrane was used as a separator between two reservoirs, one containing a solution of a common chloride salt and the other filled with deionised (DI) water. The concentration of ions in this latter reservoir was then measured as a function of time using ICP-OES and atomic absorption spectroscopy (AAS). Figure 2a shows that such concentration increased linearly with time and decreased linearly with membrane thickness, l. This allowed extracting the ions’ flux through the membrane, J, and the membrane permeability P as: P = J l ΔC⁻¹, with ΔC the difference in electrolyte concentration between feed and permeate chambers. These experiments revealed that the permeability of different monovalent cations extended over an order of magnitude, with Cs+ the most permeable (P~10⁻¹¹ m² s⁻¹) and Li+ the least (P~10⁻¹² m² s⁻¹); whereas multivalent cations all displayed lower permeability of P~10⁻¹²–10⁻¹³ m² s⁻¹. Reference experiments with nitrate salts yielded the same cation selectivity sequence, indicating that the selectivity is intrinsic to the membranes, and not dependent on the specific salt used. We also measured the permeability of the counterions in solutions with various salts, which revealed that all anions permeated through the membrane at a similar rate than their associated cation. This was expected. The unexchangeable Zr⁴⁺ ions already maintain the membrane’s electroneutrality and remain adsorbed during permeation experiments. Hence, anions must accompany cation permeation to preserve charge balance. No appreciable osmotic flow was observed during the measurements, and vapour transport measurements revealed low water flux, consistent with the narrow channels in the membranes and the small slip length of water in clays.

To understand the membrane’s selectivity, we started by plotting the cation permeability versus their Gibbs energy of hydration. This revealed that the cations’ permeability was strongly correlated with their Gibbs energy of hydration, with lower hydration energy associated with larger P. On the other hand, XRD measurements of the membranes immersed in the different electrolytes revealed that for most electrolytes, the interlayer spacing in Zr-Ver membranes was d ≈ 14.8 Å. Given the vermiculite aluminosilicate monolayer thickness (≈10 Å), this d accommodates ≈2 water layers, revealing that the membrane’s interlayer spacing is comparable to or smaller than the hydrated diameters of common cations. The only exceptions to d ≈ 14.8 Å were Cs+ and K+ electrolytes, which led to even narrower d ≈ 12.2 Å, just one water layer thick (XRD measurements in Methods). This well-known phenomenon, so-called ‘collapse’ of the interlayer space, arises because Cs+ and K+ are easily dehydrated, and are stabilised as adsorbed inner sphere complexes on the lattice, forming polar bonds with the structural oxygen atoms in the vermiculite layers. During interlayer collapse, the areas of the flake covered with Zr⁴⁺ retain a fixed ≈14.8 Å interlayer distance. However, since areas without Zr⁴⁺ dominate the surface, their collapse governs the overall XRD response. This results in spectra centred at ≈12.2 Å, albeit with a broad distribution due to the less uniform interlayer spacing.

The collapse of the interlayer space with Cs+ electrolyte provides a way to study ion diffusion in channels just one water molecule thick, offering further insight into the membranes’ selectivity. To test this, we added 1 M of CsCl into all our 1 M chloride solutions and measured ion transport as discussed above. XRD characterisation confirmed interlayer spacing of d ≈ 12.2 Å, corresponding to a single water layer inside the channels. Figure 2e shows that ion flux in these narrower channels remained correlated with their Gibbs energy of hydration, but with a much sharper dependence. Monovalent ion flux remained similar, but divalent ions now displayed P about 100 times smaller than in the absence of Cs+ and trivalent and tetravalent ions displayed P about 1000 times smaller, rendering them effectively impermeable within our measurement’s sensitivity. As a result, ion flux now spanned five orders of magnitude. This pronounced selectivity stems from the increased energy cost associated with ion transport through a space confined to a single water layer. Taken together, the selective ion transport phenomenon can be understood as arising from the difference in the ions’ Gibbs energy inside and outside the channels (ΔG). Weakly hydrated monovalent ions are stabilised by the channel walls and permeate easily even in the narrowest channels. This is particularly evident for Cs+, which is more strongly attracted to the channel walls than to water, leading to interlayer collapse and high flux. In contrast, strongly hydrated multivalent ions experience a much larger ΔG, interact weakly with the walls, and display low flux.

We then studied the transport of monovalent ions through membranes intercalated with different unexchangeable ions, namely Zr4+, La3+, Ir4+ and Sn4+. As shown in Fig. 3a, La-Ver and Zr-Ver membranes followed the same selectivity sequence shown above, Cs⁺ > K⁺ > Na⁺ ≳ Li⁺, whereas Ir-Ver and Sn-Ver displayed a different sequence: Li⁺ > Na⁺ ≈ Cs⁺ ≈ K⁺. As a result, P for Li⁺ in Ir-Ver and Sn-Ver was about 60 times higher than in Zr-Ver and La-Ver. This behaviour remained stable for as long as we decided to test these membranes, typically >100 h. To understand this finding, and given that ion permeability depends on both the ions’ equilibrium concentration and diffusion constant within the membrane, we measured the composition of the membranes with ICP-OES after the transport measurements. This revealed that differences in concentration of the permeating ion in the membranes explained nearly all permeability variations. This was confirmed with electrochemical impedance spectroscopy measurements, which showed that the ions’ diffusion constants varied negligibly across different membranes. For example, the concentration of Li+ was ≈50 times higher in Sn-Ver and Ir-Ver than in Zr-Ver and La-Ver, but the diffusion constant changed by less than 20%. To understand why the concentration of the ions changed so strongly across the four different membranes, we first measured the XRD spectra of the membranes immersed in the different electrolytes. Intriguingly, this revealed that the interlayer spacing of the four membranes was the same for a given electrolyte: d ≈ 14.8 Å, for LiCl and NaCl and d ≈ 12.2 Å for CsCl and KCl, thus ruling out channel width differences as the cause of these different selectivity sequences.

At first glance, these results seem puzzling, since the selectivity cannot be explained by differences in channel width, nor does it correlate with the charge of the unexchangeable ions. For example, despite the different charges of Zr⁴⁺ and La³⁺, both Zr-Ver and La-Ver exhibit similar selectivity. To solve this puzzle, we draw insights from biological channels, in which ion selectivity is thought to be primarily determined by three parameters: hydration free energy of the permeating ion, electrostatic interaction between ion and channel and, finally, channel elasticity. Since the first two parameters do not account for our observations, we turned our attention to channel elasticity. This parameter affects ion selectivity in biological porins because it changes the Gibbs energy of ions inside the channel due to thermal fluctuations of channel width. In a first approximation, this elastic component is modelled as Gₑ(x) = (1/2)k(x)[d(x) – dₒ(x)]², where k(x) is the elastic constant as a function of position in the channel, x, and dₒ(x) is the equilibrium channel width. Similar ionic-mechanical coupling effects have been observed in clays, with time-resolved X-ray scattering revealing that ion exchange is accompanied by dynamic fluctuations of the basal plane spacing. Motivated by this, we measured the Young’s moduli of the membranes, which determines the elasticity of the channels. As shown in Fig. 3a (inset) and Supplementary Fig. 13, the moduli of Zr-Ver and La-Ver (0.55 GPa and 0.3 GPa, respectively) were an order of magnitude larger than for Sn-Ver (0.01 GPa) and Ir-Ver (0.03 GPa), suggesting a link between selectivity and membrane stiffness. Hence, understanding why different unexchangeable ions lead to different membrane stiffness should provide insights into the selectivity phenomena.

With this insight, we recall that water exhibits an unusually high resistance to local deformation due to its hydrogen-bond network. This can be quantified by several thermodynamic parameters, such as cohesive energy density, isothermal compressibility, heat capacity density, and dipole orientational correlation. Collectively, these quantities capture the energetic cost of disrupting its structured environment and can be used to define a quantity known as water ‘stiffness’, which is the work required to create a cavity for an additional water molecule. Ions with highly ordered hydration shells—and thus with more negative hydration entropy, ΔS—are known to lead to a more ordered water network, thus increasing water’s stiffness. Since confined water in clays is more structured than bulk, the influence of solvated ions on its stiffness, and thus the mechanical properties of the membrane, can be expected to be even larger. This is consistent with our observations. Of the unexchangeable ions tested, Zr⁴⁺ (−763 J mol⁻¹ K⁻¹) and La³⁺ (−454 J mol⁻¹ K⁻¹) have the most negative ΔS and also yield the stiffest membranes. On this basis, we propose that the unexchangeable ions modulate the stiffness of water in the membrane, thereby controlling the channels’ elasticity, and thus modulating ion selectivity, similar to the role of elasticity in biological channels. This explains why Li+ displays the largest variations in permeation: having the largest hydrated diameter amongst monovalent ions, it displays the largest changes in Gₑ.

Methods
Materials
Vermiculite clay was sourced from Sigma Aldrich (CAS No 1318-00-9). To characterise its elemental composition, bulk crystals with grain-size of 2–3 mm were initially subjected to thermal expansion and subsequently ground into powders, dried at 80 °C for 24 h and then dissolved using dilute HF. Inductively coupled plasma atomic emission spectroscopy (ICP-AES) was used to determine the elemental composition. The detected interlayer metal cation mass fractions were 3.20% K+ (K O: 3.86%), 14.99% Mg²⁺ (MgO: 24.98%), 7.77% Al³⁺ (Al O : 14.35%), 7.77% Fe³⁺ (Fe O : 11.08%), and 18.95% Si (SiO: 40.60%).

Vermiculite suspension preparation
Vermiculite crystals were exfoliated in a two-step ion exchange process, as depicted in Supplementary Fig. 1. In the process, 100 mg of vermiculite granules 2–3 mm in size were immersed in 200 mL of saturated NaCl solution (36 wt%) and refluxed for 24 h. The treated vermiculite flakes were filtered and washed extensively with water and ethanol to remove residual salts. Next, 200 mL of a 2 M LiCl solution was used to disperse the sodium-exchanged vermiculite, followed by a 24-h reflux to facilitate Li+ ion exchange. The resultant lithium vermiculite flakes were filtered and subjected to thorough washing with 1 L of hot water and 0.5 L of acetone. Then, the lithium-exchanged vermiculite flakes were dispersed in water and underwent three cycles of centrifugation at 1076 × g. This dispersion was subsequently sonicated for 20 min at 100 W to exfoliate the material into monolayer vermiculite flakes. Further centrifugation at 1076 × g was employed to eliminate multilayers and bulk residues. The resulting final dispersions exhibit a pronounced Tyndall effect (Supplementary Fig. 1b), evidencing high quality dispersions.

To determine the concentration of vermiculite in the suspensions, 1 mL of the suspension was dropped onto an Anodic Aluminium Oxide (AAO) membrane with a diameter of 2.5 cm and dried. After drying, the thin film was peeled off the AAO membrane and weighed to calculate the dispersion concentration. Alternatively, the difference in mass before and after coating the AAO membrane with vermiculite suspension was also used to calibrate the dispersion concentration. Three thin film samples were typically used for concentration calibration.

We characterised the vermiculite flakes using optical microscopy, transmission electron microscopy (TEM) and atomic force microscopy (AFM). For optical microscopy observations, the vermiculite stock solution was diluted to a concentration of 10⁻⁴ mg/mL, and the diluted suspension was dropped onto a silica substrate. The sample was dried at 80 °C, followed by heating at 200 °C for 2 h. We found that most of the flakes had dimensions ranging from 10 to 20 µm (Supplementary Fig. 1c). TEM images revealed that the large vermiculite flakes exhibited no noticeable defects (Supplementary Fig. 1d).

Membrane preparation
Vermiculite laminate membranes were prepared by vacuum filtration and ion exchange. The dispersion of exfoliated vermiculite nanosheets underwent vacuum filtration using polyether sulphone (PES) membranes (Millipore) or AAO membranes (Whatman) as filters. The PES membranes with pore size of 0.22 μm and diameter of 2.5 cm or 4.7 cm were purchased from Millipore. The AAO membranes (pore size of 0.2 μm and diameter of 2.5 cm) were purchased from Whatman. Generally, the filtration process to form the vermiculite membrane takes 1–3 days to complete. Once finished, the substrate with the vermiculite membrane is removed from the filtration apparatus and transferred to an oven for drying for 12 h. The vermiculite membranes can then be easily peeled off the substrate, resulting in intact and complete pristine vermiculite membranes.

The interlayer ions in the resulting membranes are Li+ due to the exfoliation procedure. To replace them for ‘unexchangeable’ ions, the membranes were immersed in solutions of either 1 M of ZrCl , IrCl, SnCl or 0.1 M for IrCl. The concentration of the ion (e.g. Zr⁴+) within the membranes was measured by dissolving the membranes in a 2.0 mL solution of 1 wt% dilute HF and then measuring the solution with ICP-OES. We found that the exchange process equilibrated within 1 h for 1 M solutions and over 24 h for 0.1 M solutions. Using this method, vermiculite membranes were immersed in various ion solutions to prepare the various membranes for the study (e.g. K-Ver, Sr-Ver, Ir-Ver, etc). In all cases, including SnCl , the solutions used were well-dispersed and did not display obvious precipitation. TEM characterisation of the resulting membranes revealed that the ions, including Sn4+, were incorporated as single atoms.

Stability of membranes immersed in electrolyte solutions
We employed three criteria to evaluate the stability of the membranes immersed in electrolyte solutions: the membrane’s visual appearance, the interlayer spacing characterised by XRD and the mass loss of the inserted ion characterised by ICP mass spectrometry.

For optical tests, 1 cm² membranes were soaked in both pure water and various salt solutions, such as 1.0 M LiCl. Membranes exchanged with unexchangeable ions (Zr4+, Ir4+, Sr4+ and La3+) exhibited robust mechanical integrity. The membranes remained intact even under vigorous agitation after weeks of immersion in the electrolyte solution. In contrast, membranes intercalated with ions such as K+, Ba2+ and Sr2+ (Supplementary Fig. 3) disintegrated after 24 h.

To test the compositional stability of the membranes, a 1 cm² membrane was cut in six squares, dried at 80 °C for 24 h and weighed with an electronic balance (Mettler Toledo, XPE26; accuracy: 0.001 mg). Each membrane was then soaked in 2 mL of different electrolyte solutions. We tested 1 M LiCl, 1 M NaCl, 1 M KCl, 1 M CsCl, 1 M SrCl , 1 M MgCl, 1 M CaCl, 1 M LaCl, 0.1 M IrCl , as well as acidic (HCl, pH ≈ 3) and basic (NaOH, pH ≈ 12) solutions or pure water for 24 h. After soaking, the membranes were rinsed with deionised water, degraded with dilute HF, and analysed with ICP-OES to determine the content of the unexchangeable ion in the membrane. The membranes soaked in pure water served as a reference for total unexchangeable ion content in the original membrane. The results for ion mass loss are presented in Fig. 1e and Supplementary Fig. 5, revealing mass loss typically below 5% and always below 10%. In contrast, the mass loss in reference membranes exchanged with K+, Ba+ and Sr+ was nearly 100% after the exposure to the electrolytes for the same period (Supplementary Fig. 3).

The interlayer spacing in the membranes in aqueous environments was characterised via X-ray diffraction (XRD) analysis (Rigaku MiniFlex600-C with Cu Kα radiation). 1 cm² membranes were soaked in 5 mL of the chloride solutions studied in this work (1 M concentration, except for Fe³+, and Sn4+, which were 0.1 M) for 24 h. After soaking, the membranes were thoroughly rinsed with deionised water. The wet membranes were mounted on a silicon wafer for XRD measurements, with excess water removed using filter paper. Scans were performed at 10°/minute with a step size of 0.01°. For membranes soaked in 1 M LiCl for 180 days, the most aggressive test for vermiculite membranes, no significant shift or disappearance of XRD peaks was observed. We also performed this experiment with all the electrolytes used in this study. Supplementary Figs. 4, 5 show that the XRD was stable for all these electrolytes. It also shows that for most electrolytes the main peak position was at ~6.1°. The exception to this were K+ and Cs+ solutions as well as mixtures of other electrolytes with Cs electrolyte. In this case, the peaks were around 7.2°.

Measurements of ion flux
For permeation measurements, the membranes were affixed over a 0.5 cm diameter hole in a polymethyl methacrylate (PMMA) plate. The plate was then mounted in a polytetrafluoroethylene (PTFE) cell that consisted of two compartments. One compartment (the feed) was filled with 12 mL of salt solution with concentration of 1.0 M for monovalent/divalent cations or 0.1 M for trivalent and tetravalent cations, whereas the other (permeate) contained 12 mL of deionized water. The ion concentration in the permeate solution was monitored periodically using ICP-OES and AAS. Each ion flux experiment was repeated with at least 10 different membranes. The flux, J, was calculated using the expression: J = C V A⁻¹ t⁻¹, where C is the ion concentration in the permeate water, V the volume of the solution in the permeate (12 mL), A the membrane area and t the testing time. From the flux, we estimated the permeability for each ion from the equation: J = P l⁻¹ ΔC, where D is the diffusion constant, ΔC = C - C is the difference in concentration between feed and permeate chambers and l is the membrane thickness. The diffusion constant D is extracted from the expression: P = D K, where K is the sorption coefficient, which satisfies K C(m) = ½(C + C), with C the average ion concentration in the membrane.

We measured concentration of ions inside the membrane with ICP-OES. We then estimated the ion concentration as a function of channel volume (Supplementary Fig. 11). To that end we converted ion content from millimoles per gram of membrane obtained by ICP-OES in C[mmol/g] to millimoles per cubic centimetre of channel volume C[mmol/cm³] using: C[mmol/cm³] = C[mmol/g] × ρ × d/(d–θ ), where the density of vermiculite is taken as ρ ≈ 2.5 g cm⁻³, the interlayer spacing d is obtained from XRD, and the monolayer thickness of vermiculite is approximated as θ ≈ 1 nm.

Electrochemical impedance measurements
Electrochemical impedance measurements of the membranes were performed following the methods reported in ref. 51. Zr-Ver and Ir-Ver membranes were cut into four equal pieces and then stacked on top of each other to form stacks with thickness from 1 to 4 layers of the original membrane. The stacks were soaked with different electrolyte solutions and then clamped in between two stainless steel plates in a custom-made cell (Supplementary Fig. 12a). Reference experiments were performed using the same methods but using polyethersulfone (PES) membranes instead of vermiculite membranes. Supplementary Fig. 12 shows that the resistance scales linearly with thickness for all membranes, which allows extracting the resistance per layer from the slope of this dependence. We then estimated the diffusion coefficient (D) using the expression: D = L R T (R A z² F² C)⁻¹, where L is the membrane thickness, R is the universal gas constant, T is the absolute temperature, A is the membrane area, z is the charge number of the ions, F is Faraday’s constant, and C is the ion concentration within the membrane. This analysis yields D of about 2 × 10⁻¹² m² s⁻¹. These values are consistent with the D estimated from our flux measurements and the independently measured ion concentrations. Reference experiments with PES membranes yielded D about ~100 times larger, consistent with literature values.

Osmotic flow measurements
Water vapour flux was quantified gravimetrically using a 1 cm² Zr-Ver membrane under a nitrogen atmosphere in a glove box. Supplementary Fig. 9 shows that the water permeation is low, approximately ≈100 g m⁻² h⁻¹, confirming that osmotic effects are minimal under the experimental conditions.

Mixed salt experiments
We measured ion flux through Zr-Ver and Sn-Ver membranes in equimolar (1 M total) mixtures of two different monovalent salts. For all mixtures containing Cs⁺ or K⁺, the interlayer spacing collapses (Supplementary Fig. 10). Under these conditions, both membranes yield the same selectivity based on Gibbs hydration energy, as expected given that the channels are now one water layer thick. The only mixture that retains the original interlayer spacing in Sn-Ver is the Na⁺/Li⁺ mixture (Supplementary Fig. 10c, d). In this case, Sn-Ver exhibits a much larger Li⁺ flux than Zr-Ver, consistent with its permeability in single-salt experiments. However, Na⁺ permeates approximately twice as fast as Li⁺ in Sn-Ver. This represents an intermediate behaviour between the selectivity of Sn-Ver in single-salt experiments, where Li⁺ permeated about six times faster than Na⁺, and that of Zr-Ver membranes, where Na⁺ permeated roughly ten times faster than Li⁺. This difference likely arises from competition for adsorption sites between ions within the confined channels. Less strongly hydrated Na⁺ ions may preferentially interact with the channel walls, enhancing their local concentration and flux. Similar competitive adsorption effects are well documented in mineral–water interfaces, where the presence of one ion alters the binding and transport of others.

Elastic modulus of vermiculite membranes
Membranes with an area of 1 cm² and 2 μm in thickness were glued onto silicon wafers using Stycast 1266. The mechanical properties of the membrane were characterised in liquid environment (DI water) using atomic force microscopy (AFM) in mapping mode. The scanning process included 200 scan lines, with 200 data points per line, and a map scan rate of 0.31 Hz. The AFM experiments were conducted using Bruker Instruments (Multi-Mode 8 SPM), equipped with a Bruker’s SCM-PIT-V2 probe whose spring constant was calibrated via the thermal noise method. During imaging, a set point force of 100 nN was applied, and the Fast Force Mapping mode was used to measure the mechanical properties of the sample. The indentation depth was determined from the difference between the displacement of the sample and the deformation of the AFM probe, which was measured via a detector in the instrument that enables observing the probe’s deformation. These curves were then calibrated to establish the indentation depth’s zero point.

Supplementary Fig. 13 shows the representative force curves for different vermiculite membranes. To extract the modulus from the force curves, we modelled the tip as a sphere in the Hertz model. This yields the relation: F = 4/3 E* R δ³/², where F is the applied force, δ is the indentation depth, R is the probe radius, and E* is the effective modulus. The effective modulus accounts for both the sample and probe material properties. However, a posteriori, we find that our membranes, which are rather thick, have moduli of ~0.1 GPa, whereas that of the probe is much stiffer, ~170 GPa. We can therefore neglect the effect of probe on the membranes’ moduli. The sample’s Young’s modulus E is then calculated from the formula E = E*(1-v²), where v ≈ 0.28 is the Poisson ratio for vermiculite.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this manuscript, the authors present a study of vermiculite-based membranes intercalated with high-valence, unexchangeable cations, yielding mechanically stable and tunable nanochannels one to two water layers thick with good ion selectivity. The authors demonstrate that ion permeability across these membranes spans five orders of magnitude and correlates strongly with the Gibbs free energy of hydration, offering a route to size- and energy-based ion discrimination. Most strikingly, despite identical interlayer spacing, membranes intercalated with different ions show distinct monovalent ion selectivity sequences, attributed to variations in membrane stiffness and the entropy of hydration of the intercalated ions. This introduces an entropically mediated selectivity mechanism, reminiscent of biological ion channels, that extends beyond traditional charge and size exclusion models. The study offers a conceptual advance by linking hydration entropy, membrane elasticity, and ion transport within nanoscale confinement, providing a new framework for understanding and designing selective membranes. This work is likely to be of interest to the fields of nanofluidics, membrane science, and bioinspired materials, particularly in applications related to water purification, critical ion recovery, and ionic separations. Publication would be recommended, pending revision to address the following issues:\n- While the authors argue that the observed selectivity differences arise from differences in ion concentrations within the membrane rather than diffusion coefficients, the latter are not directly measured. The use of time-resolved spectroscopy or electrochemical impedance techniques to extract independent diffusion constants could strengthen this claim.\n- The manuscript attributes the ~5% mass loss of unexchangeable ions to surface-bound species, but this assumption is not experimentally verified. Techniques like depth-profiling XPS or STEM-EDS mapping could more rigorously differentiate between surface and interlayer ion distributions, especially given the potential for surface-mediated exchange.\n- The introduction omits most of the relevant reports in the literature on ion separation with vermiculite membranes. Monovalent ion separations with vermiculite membranes: Adv. Mater. 37 (2025) 2417994. In that work, ions of like charge are effectively separated, counter to the impression from the introduction that this has not been achieved. Also, the first report of stable vermiculite membranes for ion separations can be found here: ACS Nano 16 (2022) 18266. Other phyllosilicate membrane ion separations: ACS Appl. Mater. Interfac. 15 (2023) 57144.\n- The study relies heavily on the interpretation that Gibbs hydration energy dominates selectivity, but does not address possible ion pairing or specific ion-ion interactions within the membrane environment, especially in mixed salt experiments. Including control experiments with non-coordinating counterions (e.g., nitrate instead of chloride) could help rule out pairing effects as a contributor to observed permeability trends.\n- Although the authors state that Cl- accompanies cation transport to preserve electroneutrality, a direct analysis of anion-specific permeability (e.g., with differing anions at constant cation) would enrich the understanding of ion transport mechanisms and test the robustness of the hydration-driven selectivity model.", "reviewer_2": "In this paper, the authors show that Zr4+, Sn4+, Ir4+, and La3+ ions, once intercalated into vermiculite membranes, become effectively unexchangeable, thus creating stable channels that can be used to regulate ion transport and selectivity. Moreover, despite having similar interlayer spacing, vermiculite membranes intercalated with different types of intercalated ions show distinct monovalent ion selectivity sequences due to the membranes’ stiffness and the hydration entropy of the intercalated ions. The reported results are very interesting and highly important. I would like to recommend the publication of this paper in Nature Communications after a minor revision.\n1. The manuscript states that the bright spots correspond to Zr4+ ions adsorbed on vermiculite nanosheets (Fig. 1b). However, this identification appears to be based solely on image contrast, without supporting evidence such as EDX to confirm the elemental composition of these regions. Moreover, the characteristic structure of the vermiculite nanosheet can not be distinguished well in the micrograph, making it difficult to verify the presence of the host aluminosilicate layers. More evidence is suggested to given to support the claim “the ions formed domains with quasi-hexagonal symmetry in the vermiculite layer separated by cation-vacancy regions”.\n2. In Fig. 1d and Fig. 1e, the authors state that \"unexchangeable ions\" such as Zr4+ remain stably intercalated within the vermiculite nanochannels and can’t be replaced by outside ions such as Li+, Na+, K+, Cs+, and Sr2+ ions. This conclusion is supported by the unchanged XRD patterns of Zr-Ver membranes after 180 days of immersion in 1 M LiCl. However, in Fig. 2a, the XRD spectra show a reduction in interlayer spacing when the membrane is immersed in Cs+ and K+ electrolytes. The change is attributed to the so-called ‘collapse’ of the interlayer space, caused by the easy dehydration of Cs+ and K+, which then adsorb as inner sphere complexes and form polar bonds with the structural oxygen atoms in the vermiculite layers. Similarly, in Fig. 2d, interlayer spacing varies across different salt solutions. These observations appear inconsistent with the earlier claim that Zr4+ ions are unexchangeable. If K⁺ and Cs⁺ cannot replace Zr4+ in the interlayer, it is unclear how they could induce a collapse in interlayer spacing. These points should be clarified.\n3. The authors mentioned that Sn4+ ions are unexchangeable ions in the vermiculite nanochannels and ion exchange process is performed by immersing the Li-Ver membrane in various chloride solutions. However, SnCl4 is highly hydrolytically unstable in water. Upon contact with water, SnCl4 readily hydrolyzes to form insoluble hydroxides or hydrated oxides such as Sn(OH)4 or SnO2·xH2O, along with the release of HCl. This raises concerns about whether Sn4+ can exist as free ions in aqueous solution long enough to effectively intercalate into the vermiculite layers via ion exchange. More details should be provided about the conditions used to prepare the Sn-Ver membranes and supporting evidence that Sn4+ ions were successfully and stably incorporated into the interlayer structure.\n4. There are discrepancies between Fig. 1b-e and the corresponding descriptions in the text.\n5. The results presented in Fig. 2a-e should be introduced in a logical and sequential order consistent with their labeling. The current text introduces Fig. 2b, 2d, and 2e before 2a and 2c, which may confuse readers. It is recommended to either revise the text or restructure the figure layout to improve clarity and coherence of the paper.", "reviewer_3": "This study presents the development of vermiculite laminate membranes with tunable interlayer widths through the incorporation of non-exchangeable cations. The fabricated membranes, particularly those intercalated with Zr⁴⁺, demonstrated exceptional performance in separating ions of different valences, especially in the presence of Cs⁺. Notably, the authors observed varying trends in the selectivity of monovalent ions depending on the specific cation incorporated. For instance, Li⁺ ions permeated most rapidly through membranes containing Ir⁴⁺ and Sn⁴⁺, whereas their transport was the slowest in membranes with Zr⁴⁺ and La³⁺. These differences were attributed to variations in membrane stiffness and the hydration entropy of the intercalated cations.\nIn my opinion, while the observed transport phenomena are potentially of interest to the research community, the mechanistic interpretation remains relatively weak. Therefore, I believe the current version requires substantial revision and is not yet suitable for publication.\n1. The reviewer is surprised that the laminate membranes retained their structural integrity during the ion exchange process, for example, during the exchange of Li⁺ with Zr⁴⁺. Given the dynamic nature of this process, it is possible that membrane delamination occurred. What mechanisms maintain the structural stability of the membranes during ion exchange?\n2. The observed change in interlayer spacing in the presence of monovalent ions is intriguing, but the underlying mechanism remains unclear. The authors suggest that dehydrated K⁺ or Cs⁺ ions form polar bonds with structural oxygen atoms in the vermiculite layers. However, two concerns arise: (1) On Page 3, the manuscript states that all adsorption sites in the vermiculite lattice are occupied by high-valence cations (e.g., Zr⁴⁺) for charge neutrality. Then, how can additional monovalent cations (e.g., Cs⁺) bond with oxygen atoms in the vermiculite layers? (2) For interlayer spacing to decrease, Cs⁺ ions would need to bridge oxygen atoms across adjacent layers. It is unclear whether these interactions are strong enough to draw layers closer, especially in the presence of tightly bound Zr⁴⁺ ions.\n3. According to Fig. 2e, monovalent ion permeation rates appear largely unaffected by channel width. However, the presence of Cs⁺ reduces the interlayer spacing from 5.8 Å to 3.2 Å, a substantial change. One would expect a significant decline in permeation under such confinement. Could the authors explain this apparent inconsistency?\n4. Extended Data Fig. 7: Rather than expressing ion concentration in the membranes as mmol ions/ g membranes, it would be more accurate and informative to report ion concentrations within the nanochannels (ions/ channel volume). This is particularly important given that channel widths vary depending on the monovalent ion, which directly impacts ion transport behavior.\n5. According to Fig. 2a, the interlayer spacing of Zr-Ver membranes in the presence of KCl is 12.2 Å. However, the discussion at the bottom of Page 5 states that the interlayer spacing of all four membranes is the same under KCl (d ≈ 14.8 Å). Please clarify which value is correct and reconcile this inconsistency.\n6. On Page 6, the authors discuss the potential impact of unexchangeable ion hydration Gibbs energy on ion selectivity, concluding that it does not influence selectivity. However, could the authors elaborate on the mechanisms by which this property might be expected to affect selectivity?\n7. In Fig. 3a (inset), the authors present the Young’s modulus of the membranes. It is unclear how this macroscopic mechanical property directly relates to the nanoscale channel elasticity that would influence ion selectivity. Could the authors clarify this connection?\n8. Following the previous point, the manuscript introduces a separate concept water stiffness, defined as the energy required to disrupt water’s hydrogen-bonding network. The authors suggest that ions with highly ordered hydration shells increase water stiffness and that this is consistent with their observations. However, this work does not appear to include any direct characterization of water stiffness, and the relationship between water stiffness, membrane stiffness, and channel elasticity is not clearly established. The proposed consistency, therefore, appears speculative. Further clarification is needed.\n9. The core mechanism proposed is very vague: “On this basis, we attribute the correlation between membrane stiffness and selectivity to entropy-driven effects. These effects likely stem from a complex interplay of factors, including variations in water viscosity and interactions between unexchangeable and permeating ions, all occurring within the nanoscale confinement of the membrane channels.” The authors need to clarify the following questions: how does membrane stiffness affect ion selectivity? How does variation in water viscosity impact ion selectivity? How does interactions between unexchangeable and permeating ions affect selectivity? And how does nanoscale confinement amplify these effects? Ideally, these points should be addressed with more quantitative or simulation-based support.\n10. The authors should carefully check figure citations throughout the manuscript. For instance, on Page 3, the disappearance of the XRD signal in K-Ver should refer to inset Fig. 1d, not inset Fig. 1c. The retention of the XRD signal in Zr-Ver should be cited as Fig. 1d and Extended Data Fig. 5, not Fig. 1c and Extended Data Fig. 4. The STEM image should be cited as Fig. 1b, not Fig. 1d and e.", "reviewer_4": "This manuscript reports on the novel finding that certain ions can strongly intercalate with vermiculite, leading to stable membranes with ion selectivity. The stability of the membranes, interlayer spacing, and ion selectivity is characterized, revealing intriguing selectivity trends. In particular, Cs ions are found to decrease spacing leading to large selectivity. Even more intriguingly, La and Zr intercalated vermiculite is found to have much lower permeability to Li compared to other monovalent ions, than Sn and Ir intercalated vermiculite. The difference is traced to the partitioning of Li and correlates with the entropy of hydration of the intercalating ions and the membrane stiffness. This result constitutes clear evidence of effects beyond ion size and charge in ion transport. Overall, the work is thorough and presents intriguing new phenomena related to ion transport in nanoscale channels that is relevant to ion-ion separations. The reviewer recommends publication after addressing the comments below.\nThe membrane stability is reported in salts of monovalent ions, and in SrCL2. The claims of stability will be strengthened by including exposure to CaCl2 and MgCl2, which are ubiquitous in many practical applications. Furthermore, it will be helpful to address whether the membranes are stable in solutions of cations with +3 or +4 charges, as well as in acidic and basic solutions.\nSome of the data relevant to the study are not provided. For example, a consolidated table of interlayer spacings should be added. Similarly, it would be very useful to add a table of permeabilities, along with the ion concentration in the membrane and associated interlayer spacing. Another example, the methods section states that 10 mM or 1 M solutions were used for permeation tests, but it is not clear which concentration is used in which experiment.\nWas osmosis of water observed during any of the ion permeation experiments? If yes, it would be very interesting to report the measured water fluxes. Was stirring employed to ensure good mixing, or was it not found to be necessary?\nWas the permeability observed to be independent of the membrane thickness? If not, it would suggest percolation effects, defects, or variation in the membrane structure.\nThe manuscript largely reports ion permeation experiments with a single cation at a time. To ascertain selectivity, it is necessary to perform mixed ion experiments to assess whether the selectivity observed in single salt experiments also carries over to mixed salt experiments.\nWas the effect of salt concentration and pH on permeation investigated? In particular, measuring the partitioning of ions, interlayer spacing, and permeability, along with estimating the diffusivity as a function of salt concentration will reveal whether the salt concentration affects the interlayer spacing and ion transport, what kind of adsorption isotherms describe ion uptake into intercalated vermiculite, and whether transport in the dilute limit can explain transport at higher salt concentrations.\nThe hypothesis of entropic effects in the hydration of the intercalating ion on the differences in Li ion transport is very intriguing. However, the reason for the behavior is not pursued apart from correlation to entropy of hydration and mechanical stiffness of the membrane. Does the interlayer spacing change in the presence of Li ions, especially in the case of Sn and Ir intercalation where the membranes are more flexible? Do the observations correlate with the thermodynamic behavior of mixed salt solutions of the intercalating ion and lithium indicating that it may be a bulk effect, or is nanoconfinement essential? What explains the order of magnitude difference in ion partitioning for Sn and Ir intercalated membranes – can it be attributed to interlayer spacing, or are other effects essential? Similarly, does Li partition more favorably than the other monovalent ions in the Sn and Ir intercalated membranes and why (and if not, it must diffuse faster given the data in Fig. 3)? Similarly, temperature dependence to extract the free energy change of partitioning of ions will likely provide additional insights."}, "author_response": "Response to comments from Reviewer #1\nIn this manuscript, the authors present a study of vermiculite-based membranes intercalated\nwith high-valence, unexchangeable cations, yielding mechanically stable and tunable\nnanochannels one to two water layers thick with good ion selectivity. The authors demonstrate\nthat ion permeability across these membranes spans five orders of magnitude and correlates\nstrongly with the Gibbs free energy of hydration, offering a route to size- and energy-based ion\ndiscrimination. Most strikingly, despite identical interlayer spacing, membranes intercalated with\ndifferent ions show distinct monovalent ion selectivity sequences, attributed to variations in\nmembrane stiffness and the entropy of hydration of the intercalated ions. This introduces an\nentropically mediated selectivity mechanism, reminiscent of biological ion channels, that\nextends beyond traditional charge and size exclusion models. The study offers a conceptual\nadvance by linking hydration entropy, membrane elasticity, and ion transport within nanoscale\nconfinement, providing a new framework for understanding and designing selective membranes.\nThis work is likely to be of interest to the fields of nanofluidics, membrane science, and\nbioinspired materials, particularly in applications related to water purification, critical ion\nrecovery, and ionic separations. Publication would be recommended, pending revision to\naddress the following issues:\nWe thank the reviewer for this positive assessment of our work and for the focused and\nconstructive critique of the manuscript. We have done our best to address the points raised.\n- While the authors argue that the observed selectivity differences arise from differences in ion\nconcentrations within the membrane rather than diffusion coefficients, the latter are not directly\nmeasured. The use of time-resolved spectroscopy or electrochemical impedance techniques to\nextract independent diffusion constants could strengthen this claim.\n30\n25\n)Ω\n(\ne\n20\nc\nn a ts\nis15\ne\nR\n5\n1 2 3 4\nNumber of membranes\nFigure R1.1. (a) Experimental setup. (b) Resistance of typical membrane stack (Zr-Ver) soaked in\nelectrolyte solution (LiCl) as a function of number of stacked membranes. The membrane\nresistance was extracted from the slope of the linear fit of the resistance vs. the numbers of\nmembranes stacked layer-by-layer. Inset, Nyquist plot of membrane stacks from which\nresistance in main panel is extracted. (c) Diffusion coefficients for different ions in Zr-Ver,\nIr-Ver\nand PES-membrane (bulk) membranes extracted from resistance data.\nFollowing the reviewer’s suggestion, we have performed electrochemical impedance\nspectroscopy measurements of monovalent ion permeation in Zr-Ver and Ir-Ver, and for\nreference, also in polyethersulfone (PES) membranes. To obtain accurate measurements of the\nsamples, we followed the method described in Dai, Q. et al. Nat. Comms. 2020, 11, 13. In brief,\nwe cut the membranes into four equal pieces that are stacked on top of each other to form stacks\nwith thickness from 1 to 4 layers of the original membrane. The stacks are soaked in the\n1\n)Ω(\n''Z-\n3\n2\n1\n0\n0\n1\n1\n2\n0\n3 4\n2 0 Z ' (Ω ) 3 0 4 0\na b c\n1 2 3 4 Stainless steel\nplates\nMembrane\n)1-s\n2m(\ntneiciffeoC\nnoisuffiD\n-9 1 0\n-10 1 0\n-11 1 0\n-12 1 0\nC s +\nZ r-V e r\nIr-V e r\nB u lk s o\n+ K\nS o lu tio\nlu tio\nn e n\nn\nv\n+ N a\niro m e n t\nL +i\nelectrolyte solution and clamped in between two stainless steel plates. Fig. R1-1 shows that the\nmembrane resistance scales linearly with thickness for all membranes, which allows extracting\nthe resistance per layer of membrane from the slope of this dependence. We then estimate the\ndiffusion coefficient (D) using the expression: D = LRT(R Az2F2C)-1, where L is the membrane\nΩ\nthickness, R is the universal gas constant, T is the absolute temperature, A is the membrane area,\nz is the charge number of ions, F is Faraday’s constant, and C is the ion concentration within the\nmembrane.\nThis analysis yields D of about 2 × 10⁻¹² m²/s, for the different monovalent ions in our membranes,\nconsistent with the D estimated from our flux measurements and the independently measured\nion concentration inside the membrane. This confirms that the observed differences in ion flux\nare fully explained by concentration differences within the membranes, rather than differences\nin diffusion coefficients. For the reference samples, we found about ~100 times larger D,\nconsistent with literature values (Ref. 48). We have included these data as Supplementary Fig. 12\nand this discussion in page 6 in the revised manuscript.\n- The manuscript attributes the ~5% mass loss of unexchangeable ions to surface-bound species,\nbut this assumption is not experimentally verified. Techniques like depth-profiling XPS or STEM-\nEDS mapping could more rigorously differentiate between surface and interlayer ion\ndistributions, especially given the potential for surface-mediated exchange.\nTo address this comment, we examined the depth profile of unexchangeable Zr ions using XPS\n(Fig. R1-2). No significant change in Zr concentration was observed after immersion in different\nelectrolytes. With hindsight, this was expected, as Zr constitutes only ~1% of the membrane\nmass, and detecting a 5% change\nof such a small fraction exceeds\nthe technique’s sensitivity. The\nlack of a measurable change in\nthe Zr signal after electrolyte\ntreatment indicates that Zr⁴⁺ loss\nis indeed minimal, confirming\nthat the ions are effectively\nunexchangeable.\nFollowing the Reviewer\ncomment, we have removed the\nstatement about the origin of the\nloss of the ions.\nFigure R1-2. a, The XPS spectrum\nof the Zr-Ver membrane with\ndifferent depth after different\nsolution immersion. b, Zoom in of\narea in dashed box in panel a.\n- The introduction omits most of the relevant reports in the literature on ion separation with\nvermiculite membranes. Monovalent ion separations with vermiculite membranes: Adv. Mater.\n37 (2025) 2417994. In that work, ions of like charge are effectively separated, counter to the\nimpression from the introduction that this has not been achieved. Also, the first report of stable\nvermiculite membranes for ion separations can be found here: ACS Nano 16 (2022) 18266. Other\nphyllosilicate membrane ion separations: ACS Appl. Mater. Interfac. 15 (2023) 57144.\n2\n).u.a(\nytisnetnI\n1 0 0 0\n+ C s -im m ersion\n+ Li-im m ersion\nD I H O -im m ersion 2\n8 0 0 6 0 0\nB in d in g e n e\n4 0 0\nrg y (e V )\nZr 3ddepth\n10 nm\n5-6 nm\n1-2 nm\n10 nm\n5-6 nm\n1-2 nm\n10 nm\n5-6 nm\n1-2 nm\n2 0 0 0\na b\nCs+-immersion Zr 3d\ndepth\n10 nm\n55--66 nnmm\n11--22 nnmm\nLi+-immersion\n).u\n.a (\ny\n10 nm\ntis\n5-6 nm\ne tn\nI 1-2 nm\nDI HO-immersion\n2\n10 nm\n5-6 nm\n1-2 nm\n190 185 180 175\nBinding energy (eV)\nThese are indeed very relevant references. We now discuss them in the introduction of the revised\nmanuscript (page 2) as Refs. 32-34. Apologies for the oversight.\n- The study relies heavily on the interpretation that Gibbs hydration energy dominates selectivity,\nbut does not address possible ion pairing or specific ion-ion interactions within the membrane\nenvironment, especially in mixed salt experiments. Including control experiments with non-\ncoordinating counterions (e.g., nitrate instead of chloride) could help rule out pairing effects as a\ncontributor to observed permeability\ntrends.\nFollowing the Reviewer comment we\nfixed NO₃⁻ as the counterion and\nmeasured permeation of various\ncations. Fig. R1-3 shows that the\nselectivity sequence remained the\nsame, with only some cations\ndisplaying flux differences of a factor ~\n2 between different salts. These\nresults indicate that ion pairing does\nnot significantly influence membrane\nselectivity. The data are included as\nSupplementary Fig. 7 in the revised\nmanuscript.\nFigure R1-3. Nitrate salt ion flux of the\nZr-Ver membrane\n- Although the authors state that Cl- accompanies cation transport to preserve electroneutrality,\na direct analysis of anion-specific permeability (e.g., with differing anions at constant cation)\nwould enrich the understanding of ion transport mechanisms and test the robustness of the\nhydration-driven selectivity model.\nFollowing the Reviewer comment, we\ninvestigated anion permeability with Li⁺ as the\nfixed cation (Figure R1-4). Chloride and nitrite\nsalts give similar results, whereas SO₄²⁻,\nbeing more strongly hydrated, permeates\nmore slowly than Cl⁻, and Li⁺ transport is\ncorrespondingly reduced to preserve\nelectroneutrality. These data have been\nadded as Supplementary Fig. 8b in the revised\nmanuscript.\nFigure R1-4. Flux of lithium salts with\ndifferent anions through Zr-Ver membranes.\n3\n)1-h\n2-m\nlomm(\nxulF\n1\n)1-h\n2-m\nlomm(\nxulF\n1\n1\n1 0\n0 0\n− 1\n0\n1 1 0\n0 1 0\n-1 1 0\n+ s\n+ K\nN aL +\n+i\n2 + S r\n2 + M g\n− 2 0 0 0\nG ib b s e n\n+ L i\nA n io n\nL iN O\n3 + L a\n− 4 0 0\ne rg y o f h\nL i S O\n2\ne rm e a te\n0\ny d ra\n4d\ns a\ntio\nlt\n- N O s a lt\n3\n- C l s a lt\n4 + Z r\n− 6 0 0 0 −\n-1 n (k J m o l )\nZ r-V e r\nL iC l\n8 0 0 0\nResponse to comments from Reviewer #2\nIn this paper, the authors show that Zr4+, Sn4+, Ir4+, and La3+ ions, once intercalated into\nvermiculite membranes, become effectively unexchangeable, thus creating stable channels that\ncan be used to regulate ion transport and selectivity. Moreover, despite having similar interlayer\nspacing, vermiculite membranes intercalated with different types of intercalated ions show\ndistinct monovalent ion selectivity sequences due to the membranes’ stiffness and the hydration\nentropy of the intercalated ions. The reported results are very interesting and highly important. I\nwould like to recommend the publication of this paper in Nature Communications after a minor\nrevision.\nWe are very grateful to the Reviewer for this encouraging assessment of our work. We have\ncarefully addressed all the comments.\n1. The manuscript states that the bright spots correspond to Zr4+ ions adsorbed on vermiculite\nnanosheets (Fig. 1b). However, this identification appears to be based solely on image contrast,\nwithout supporting evidence such as EDX to confirm the elemental composition of these regions.\nMoreover, the characteristic structure of the vermiculite nanosheet can not be distinguished well\nin the micrograph, making it difficult to verify the presence of the host aluminosilicate layers.\nMore evidence is suggested to given to support the claim “the ions formed domains with quasi-\nhexagonal symmetry in the vermiculite layer separated by cation-vacancy regions”.\nFollowing the Reviewer comment, we have now included EDX measurements (Figure R2-1), which\nconfirm the presence of Zr in the regions corresponding to the bright spots in the image. All the\npeaks, except Zr (and Cu from the holder), arise from native vermiculite, which contains O(Z = 8),\nO\nMg(Z = 12), Al(Z = 13), Si (Z = 14), with trace elements of Ca (Z = 20), Ti (Z = 22), Cr (Z = 24),\nMg Al Si Ca Ti Cr\nFe(Z = 26). Moreover, no bright spot can be observed when imaging pristine vermiculite under\nFe\nADF mode (collection angle 40-200 mrad). Since Zr (Z = 40) is the only heavy element in the\nZr\nsample, the bright atom columns can be unambiguously attributed to Zr. We thank the Reviewer\nfor pointing this out to us, we agree that this is an important characterisation. We have added this\nto the revised Supplementary Fig. 1.\na b c\n- -\n110\n-\n110\n020\n1 µm 1 nm -1\nFigure R2-1. Extended TEM data taken from the sample shown in Fig. 1 in the manuscript. (a) ADF-\nSTEM image showing the over-view image of Zr-Ver nanosheets on TEM grids. (b) The selected-\narea electron diffraction taken from the sample. (c) Corresponding EDS spectrum, where the Cu\npeaks are from the TEM holder and the supporting grids.\nRegarding the imaging of the aluminosilicate layers, we found that these cannot be resolved in\nplan-view images due to their beam sensitivity and complex [001*] projection. A low electron\ndose allows clear imaging of the heavy Zr columns without damaging the crystal, but imaging the\naluminosilicate layers requires a higher dose. This causes rapid damage and therefore\n4\ndistinguishing the aluminosilicate layer is not possible. In this work, we applied a low electron\ndose to image Zr atoms and SAED collected after imaging (Fig. R2-1b) confirms that the\naluminosilicate layers preserve a high crystal quality, indicating that our imaging reflects the real\narrangement of Zr atoms.\n2. In Fig. 1d and Fig. 1e, the authors state that \"unexchangeable ions\" such as Zr4+ remain stably\nintercalated within the vermiculite nanochannels and can’t be replaced by outside ions such as\nLi+, Na+, K+, Cs+, and Sr2+ ions. This conclusion is supported by the unchanged XRD patterns of\nZr-Ver membranes after 180 days of immersion in 1 M LiCl. However, in Fig. 2a, the XRD spectra\nshow a reduction in interlayer spacing when the membrane is immersed in Cs+ and K+\nelectrolytes. The change is attributed to the so-called ‘collapse’ of the interlayer space, caused\nby the easy dehydration of Cs+ and K+, which then adsorb as inner sphere complexes and form\npolar bonds with the structural oxygen atoms in the vermiculite layers. Similarly, in Fig. 2d,\ninterlayer spacing varies across different salt solutions. These observations appear inconsistent\nwith the earlier claim that Zr4+ ions are unexchangeable. If K⁺ and Cs⁺ cannot replace Zr4+ in the\ninterlayer, it is unclear how they could induce a collapse in interlayer spacing. These points\nshould be clarified.\nWe clarify that K⁺ and Cs⁺ ions do not replace Zr⁴⁺ in the interlayer during permeation\nexperiments. The concentration of Zr⁴⁺ is relatively low because, due to its +4 valence, each Zr⁴⁺\nion compensates multiple exchange sites in the vermiculite (each with valence -1). As a result, a\nlarge number of cation vacancies remain even after Zr⁴⁺ intercalation, leaving many sites\navailable for additional adsorption—more than those occupied by Zr⁴⁺ ions. This can be\nappreciated more clearly in zoom-out STEM images of Zr-Ver membranes (Fig. R2-2).\nFig. R2-2. STEM image of Zr-Ver over larger areas. Bright spots, Zr-atoms.\nScale bar, 1 nm.\nThe observed reduction in interlayer spacing in Cs⁺ and K⁺ electrolytes is\ntherefore not due to ion exchange with Zr⁴⁺, but rather to the adsorption of\nCs⁺ and K⁺ at these vacant sites (see also Fig. R3-1, page 8 below). During\ninterlayer collapse, the areas of the flake covered with Zr⁴⁺ retain a fixed ≈14.8 Å interlayer\ndistance, whereas those with adsorbed Cs⁺, collapse. Since Zr⁴⁺-free areas occupy a larger\nsurface area, their collapse governs the overall XRD response. This can be observed in the XRD\nspectra in Fig. 2c,d and Supplementary Fig. 4. The XRD spectra yield a peak centred at ≈12.2 Å,\nhowever, the distribution is broader due to larger interlayer distance in the areas with adsorbed\nZr⁴⁺. Following the Reviewer comment, we have clarified this point in the manuscript on page 5,\nlast sentences in the first paragraph.\n3. The authors mentioned that Sn4+ ions are unexchangeable ions in the vermiculite\nnanochannels and ion exchange process is performed by immersing the Li-Ver membrane in\nvarious chloride solutions. However, SnCl4 is highly hydrolytically unstable in water. Upon\ncontact with water, SnCl4 readily hydrolyzes to form insoluble hydroxides or hydrated oxides such\nas Sn(OH)4 or SnO2·xH2O, along with the release of HCl. This raises concerns about whether\nSn4+ can exist as free ions in aqueous solution long enough to effectively intercalate into the\nvermiculite layers via ion exchange. More details should be provided about the conditions used\nto prepare the Sn-Ver membranes and supporting evidence that Sn4+ ions were successfully and\nstably incorporated into the interlayer structure.\nSn(OH)₄ or hydrated SnO₂. However, we find that our carefully dispersed 1 M SnCl₄ aqueous\nsolutions do not display obvious precipitation. As shown in Figure R2-3, our 1 M SnCl₄ solution\nremains visibly clear after half a year (Fig. R2-3a), indicating that hydrolysis is either suppressed\nor proceeded very slowly. Moreover, both XRD (Fig. R2-3b) and TEM (Fig. R2-3c) of the Sn-Ver\nmembranes show no evidence of Sn(OH)₄ or SnO₂·xH₂O phases. Our TEM images show that the\nSn⁴⁺ ions are incorporated into the crystals as single ions, which can be seen as bright spots from\nexperimental atomic-resolution ADF-STEM images (see Fig. R2-3c below). This discussion has\nbeen added in page 8, paragraph 4 in the revised manuscript.\n10 20 30 40 50 60\nFigure R2-3 (a) Digital photo of a 1 M SnCl₄ aqueous solution taken 6 months after its preparation,\n(b) XRD pattern of Sn-Ver membrane (blue spectrum) against pure vermiculite PDF (black lines\nbelow), (c) ADF-STEM image showing well-dispersed Sn ions as those bright spots from Sn-Ver\nmembranes.\n4. There are discrepancies between Fig. 1b-e and the corresponding descriptions in the text.\nWe have corrected these discrepancies in the text. Much appreciated.\n5. The results presented in Fig. 2a-e should be introduced in a logical and sequential order\nconsistent with their labeling. The current text introduces Fig. 2b, 2d, and 2e before 2a and 2c,\nwhich may confuse readers. It is recommended to either revise the text or restructure the figure\nlayout to improve clarity and coherence of the paper.\nWe agree with this suggestion. Fig. 2 has been reordered to follow the logical sequence of the\ndraft. Much appreciated.\n6\n).u.a(\nytisnetnI\nVermiculite PDF#16-0613\n2q (°)\n)200(\n)400( )600(\n)800( )0100(\n)4100(\n)922(\na b c\n1 nm\nResponse to comments from Reviewer #3\nThis study presents the development of vermiculite laminate membranes with tunable interlayer\nwidths through the incorporation of non-exchangeable cations. The fabricated membranes,\nparticularly those intercalated with Zr⁴⁺, demonstrated exceptional performance in separating\nions of different valences, especially in the presence of Cs⁺. Notably, the authors observed\nvarying trends in the selectivity of monovalent ions depending on the specific cation\nincorporated. For instance, Li⁺ ions permeated most rapidly through membranes containing Ir⁴⁺\nand Sn⁴⁺, whereas their transport was the slowest in membranes with Zr⁴⁺ and La³⁺. These\ndifferences were attributed to variations in membrane stiffness and the hydration entropy of the\nintercalated cations.\nIn my opinion, while the observed transport phenomena are potentially of interest to the research\ncommunity, the mechanistic interpretation remains relatively weak. Therefore, I believe the\ncurrent version requires substantial revision and is not yet suitable for publication.\nFollowing the Reviewer comment, we have revised the manuscript to strengthen the discussion\nof the transport mechanism. We believe the updated version provides a clearer interpretation.\n1. The reviewer is surprised that the laminate membranes retained their structural integrity during\nthe ion exchange process, for example, during the exchange of Li⁺ with Zr⁴⁺. Given the dynamic\nnature of this process, it is possible that membrane delamination occurred. What mechanisms\nmaintain the structural stability of the membranes during ion exchange?\nWe agree that it is surprising that the membranes retained their structural integrity during ion\nexchange. However, we are confident about this result. Regarding the mechanism, we studied ion\nexchange in 2D clays in detail, including STEM images during intermediate stages of the\nexchange, in our previous work Y.-C. Zou et al., Nat. Mater. 2021, 20, 1677-1682 (Ref. 28). The\nstability arises for two reasons. First, ion exchange occurs gradually within the interlayer galleries,\nwithout disrupting the layered structure, which is bound both by short range electrostatic forces\nand long-range van der Waals interactions. Second, ion exchange in 2D vermiculite is orders of\nmagnitude faster than in bulk crystals, avoiding the accumulation of local strain that could\notherwise delaminate the membrane. This fast but gentle dynamics allows cations to be replaced\nefficiently while preserving the structural integrity of the laminate.\n2. The observed change in interlayer spacing in the presence of monovalent ions is intriguing, but\nthe underlying mechanism remains unclear. The authors suggest that dehydrated K⁺ or Cs⁺ ions\nform polar bonds with structural oxygen atoms in the vermiculite layers. However, two concerns\narise: (1) On Page 3, the manuscript states that all adsorption sites in the vermiculite lattice are\noccupied by high-valence cations (e.g., Zr⁴⁺) for charge neutrality. Then, how can additional\nmonovalent cations (e.g., Cs⁺) bond with oxygen atoms in the vermiculite layers? (2) For interlayer\nspacing to decrease, Cs⁺ ions would need to bridge oxygen atoms across adjacent layers. It is\nunclear whether these interactions are strong enough to draw layers closer, especially in the\npresence of tightly bound Zr⁴⁺ ions.\n(1) Following the comment from the Reviewer and also from Reviewer #2, we now see that this\npoint was not clear. The manuscript states the opposite. It is not possible for all adsorption sites\nto be occupied by Zr4+ because the ion’s 4+ valence compensates the charge of multiple lattice\nsites (each site has a -1 valence). As a result, many more sites remain empty than occupied by\nZr⁴⁺ (e.g. Fig. R2-2, page 5 above). Cs⁺ ions adsorb on these empty sites.\n(2) The reduction in interlayer spacing arises from the dehydration of Cs⁺ ions, a well-established\nphenomenon in clays (refs. 31, 38–41 in the manuscript). Because water molecules are weakly\n7\nbound to Cs⁺, the electrostatic attraction between the negatively charged vermiculite layers and\nthe ions strips part of the hydration shell, leading to a collapse of the interlayer space. In our\nmembranes, regions with fixed Zr⁴⁺ retain their spacing, while Cs⁺-exposed areas collapse, as\nillustrated schematically in Fig. R3-1. We can see this in the XRD spectra of these samples (e.g.\nFig. 2c and Supplementary Fig. 4). The main peak in the presence of Cs⁺ is centred around 12.2\nÅ, but it is broader than for ions that do not induce layer collapse, indicating less uniform\nthickness, as expected.\nFollowing the Reviewer comment, we now see that these two important points were not clear in\nthe paper. We have clarified them in\nthe revised manuscript in page 3\nlast paragraph and page 5 first\nparagraph.\nFigure R3-1. Schematic diagram of Cs+-induced collapse of the interlayer space of Zr-Ver\nmembrane.\n3. According to Fig. 2e, monovalent ion permeation rates appear largely unaffected by channel\nwidth. However, the presence of Cs⁺ reduces the interlayer spacing from 5.8 Å to 3.2 Å, a\nsubstantial change. One would expect a significant decline in permeation under such\nconfinement. Could the authors explain this apparent inconsistency?\nThis observation may appear inconsistent with expectations based on steric exclusion. However,\nin charged, hydrophilic systems like vermiculite membranes, ion permeability is not governed\nsolely by steric exclusion but by the thermodynamics of ion partitioning—that is, by the\nequilibrium concentration of ions inside the membrane. This is shown in Supplementary Fig. 11\nand the new Supplementary Fig. 12, which show that the concentration of ions inside the\nchannels, rather their diffusion, determine the permeability of the membrane. In turn, this\nequilibrium concentration is determined by the difference in the ions’ Gibbs energy between the\nexternal solution and the membrane (ΔG).\nFor monovalent ions, which are relatively weakly hydrated compared to higher valence ions, the\nelectrostatic attraction to the negatively charged clay surfaces can be stronger than to water\nmolecules, as discussed above. Cs⁺ provides the clearest example. Its strong affinity for the walls\ndrives interlayer collapse and the same attraction results in a high concentration of Cs⁺ within\nthe channel, leading to high permeability. Hence, channels of different width can lead to similar\npermeability if ΔG is similar. This has now been explained in paragraph 2, page 5 of the main text.\n4. Extended Data Fig. 7: Rather than expressing ion concentration in the membranes as mmol\nions/ g membranes, it would be more accurate and informative to report ion concentrations\nwithin the nanochannels (ions/ channel volume). This is\n3) particularly important given that channel widths vary\n-m\nc100 depending on the monovalent ion, which directly impacts\nn i\nn\nlo\nm\nmm\nion transport behavior.\no ita\nrtn\ne\n( s\nle\nn n\nK\ns\n+\n+\nFig. R3-2. Estimation of ion concentration inside the\nc a\nn o h c channels.\nc n\no I\ne n\na rb 1\nNa+\nmem\nLi+\nThe conversion from ion content expressed as millimoles\nm\nSn4+ Ir4+ La3+ Zr4+\nper gram of membrane (C\nmmol/g\n) to millimoles per cubic\nUnexchangeable ion in membrane centimetre of channel volume (C ) was calculated\nmmol/cm3\n8\nusing the formula: C = C  d/(d-q ). The density of vermiculite is taken as  = 2.5\nmmol/cm3 mmol/g ver ver ver\ng/cm3, the spacing height d with different ions is taken from the XRD results. The thickness of the\nvermiculate layer q of the monolayer vermiculite is estimated as ≈1 nm. Fig. R3-2 shows these\nver\nestimates. The concentrations range from 1-100 mmol cm-3 for the different membranes.\n5. According to Fig. 2a, the interlayer spacing of Zr-Ver membranes in the presence of KCl is 12.2\nÅ. However, the discussion at the bottom of Page 5 states that the interlayer spacing of all four\nmembranes is the same under KCl (d ≈ 14.8 Å). Please clarify which value is correct and reconcile\nthis inconsistency.\nIt should say 12.2 Å for KCl. Much appreciated.\n6. On Page 6, the authors discuss the potential impact of unexchangeable ion hydration Gibbs\nenergy on ion selectivity, concluding that it does not influence selectivity. However, could the\nauthors elaborate on the mechanisms by which this property might be expected to affect\nselectivity?\nThat sentence in the original manuscript (page 6) aimed to emphasise that conventional\ndescriptors fail to explain our results. To avoid confusion, we have removed the reference to\nhydration Gibbs energy from this paragraph.\n7. In Fig. 3a (inset), the authors present the Young’s modulus of the membranes. It is unclear how\nthis macroscopic mechanical property directly relates to the nanoscale channel elasticity that\nwould influence ion selectivity. Could the authors clarify this connection?\nThe bending modulus of a clay layer in the direction i, κ, is related to the Young’s modulus in the\ni\ni direction, E, by the equation: κ = Eh3/(12(1-ν2)), with h the clay thickness and ν its Poisson ratio\ni i i\n(e.g., J. L. Suter, et al. J. Phys. Chem. C 2007, 111, 8249-8259). We explain how channel elasticity\nis related to selectivity in point #9.\n8. Following the previous point, the manuscript introduces a separate concept water stiffness,\ndefined as the energy required to disrupt water’s hydrogen-bonding network. The authors suggest\nthat ions with highly ordered hydration shells increase water stiffness and that this is consistent\nwith their observations. However, this work does not appear to include any direct\ncharacterization of water stiffness, and the relationship between water stiffness, membrane\nstiffness, and channel elasticity is not clearly established. The proposed consistency, therefore,\nappears speculative. Further clarification is needed.\nMeasuring water stiffness, even in bulk water, requires specialised techniques, and extending\nthem to our system would constitute a major independent study. Nonetheless, we argue that\nusing this concept is both justified and informative, based on established thermodynamic\ndescriptors for water and prior experiments of water confined between clay layers.\nWater exhibits an unusually high resistance to local deformation due to its extended hydrogen-\nbond network. This resistance can be quantified by several thermodynamic parameters,\nincluding cohesive energy density, isothermal compressibility, heat capacity density, and\norientational correlation of its dipoles. Collectively, these quantities capture the energetic cost\nof disrupting its structured environment or “stiffness”. Marcus and others have shown that ions\nwith high solvation entropy form highly ordered hydration shells and induce long-range\nstructuring of surrounding water, increasing water’s stiffness (Ref. 46).\nUnder confinement, and specifically between clay layers, water becomes even more structured.\nDirect imaging studies using high-resolution AFM (Fukuma et al., Phys. Rev. Lett. 2010, 104,\n016101) have demonstrated clear layering and orientational order of water at clay surfaces.\nAcademic Press 2011, Ch. 15) show that confined water strongly resists compression over\nnanometre-scale distances with forces that exceed expectations from bulk. Hence, these highly\nordered water layers are expected to display even more pronounced stiffness changes than bulk\nwater when ions with highly ordered solvation shells are introduced.\nAlthough we do not directly probe water structure in our membranes due to the complexity of\nsuch measurements, our data show that membranes intercalated with ions forming strongly\nordered hydration shells consistently display higher Young’s moduli. This supports the view that\nstructured interlayer water contributes directly to membrane stiffness and that ions solvated in\nthese water layers significantly affect their stiffness. We therefore propose that the mechanical\nresponse of our membranes reflects both the intrinsic elasticity of the clay layers and, crucially,\nthe resistance to deformation provided by the structured water phase. As water stiffness\nincreases with the hydration entropy of the intercalated ions, these thermodynamic properties\noffer a consistent framework for interpreting the observed mechanical trends.\n9. The core mechanism proposed is very vague: “On this basis, we attribute the correlation\nbetween membrane stiffness and selectivity to entropy-driven effects. These effects likely stem\nfrom a complex interplay of factors, including variations in water viscosity and interactions\nbetween unexchangeable and permeating ions, all occurring within the nanoscale confinement\nof the membrane channels.” The authors need to clarify the following questions: how does\nmembrane stiffness affect ion selectivity? How does variation in water viscosity impact ion\nselectivity? How does interactions between unexchangeable and permeating ions affect\nselectivity? And how does nanoscale confinement amplify these effects? Ideally, these points\nshould be addressed with more quantitative or simulation-based support.\nWe agree with the Reviewer that the mechanism could be clearer and have done our best to\nclarify the proposed mechanism in the revised manuscript. Specifically, regarding the questions\nfrom the Reviewer.\nStiffness vs selectivity. The link between membrane stiffness and ion selectivity was first\nobserved in biological porins, where channels of similar size exhibit different monovalent ion\nselectivity sequences. This behaviour is captured by analytical models that describe the system’s\nHamiltonian with three key components: ion hydration free energy, ion–channel electrostatic\ninteraction, and channel elasticity (A. Laio & V. Torre, Biophhysical Journal 1999, 76, 129-148).\nElasticity is critical because thermal fluctuations cause the channel radius to fluctuate around\nits equilibrium value, which changes the ion’s Gibbs energy as: Hₑ(x) = (1/2) k(x) [R(x) – R₀(x)]²,\nwhere k(x) is the stiffness as a function of position in the channel, x, and R₀(x) is the equilibrium\nradius. All else being equal, this can lead to different monovalent ion selectivity sequences, as\nshown in Fig. 4&5 in Laio et al (Ref. 43).\nAnalogous effects have been reported in clay systems. For example, M. L. Whittaker, et al. (PNAS\n2019, 116, 22052-22057) reported time-resolved X-ray scattering experiments that showed that\nion exchange in clays is coupled to the dynamic fluctuation of the average basal plane spacing.\nThis has been modelled, for example using simulation boxes with over 10⁵ atoms and timescales\nof the order of hundreds of picoseconds (Suter et al. J. Phys. Chem. C, 2007, 111, 8249–8259). To\nmodel our system, in addition to this, we would need to incorporate the many different ions\n(permeating and unexchangeable) and let the sheet relax. We believe that a comprehensive\ntheoretical treatment of this system warrants a dedicated follow up study.\nWater stiffness vs selectivity and confinement. Water stiffness affects Young’s modulus (point\n#8), which affects channel elasticity, and thus selectivity, as described above.\npermeating ions should be affected by the presence of highly charged unexchangeable ions, as\npredicted by Debye-Huckel theory. However, this effect is not central to our findings, since\nmembranes’ properties differ even when intercalated with ions of the same charge (e.g. Zr-Ver\nand Ir-Ver). To avoid confusion, we have removed this statement from the manuscript.\nConfinement. Water becomes more ordered under confinement. Entropic effects from ions with\nlarge hydration entropy should be more evident in these ordered films, as discussed above.\nFollowing the Reviewer comment, we have extended the discussion of the mechanism in the\nrevised manuscript, page 7.\n10. The authors should carefully check figure citations throughout the manuscript. For instance,\non Page 3, the disappearance of the XRD signal in K-Ver should refer to inset Fig. 1d, not inset Fig.\n1c. The retention of the XRD signal in Zr-Ver should be cited as Fig. 1d and Extended Data Fig. 5,\nnot Fig. 1c and Extended Data Fig. 4. The STEM image should be cited as Fig. 1b, not Fig. 1d and\ne.\nWe thank the Reviewer for noticing this. We have carefully checked and corrected all figure\nreferences throughout the manuscript.\nThis manuscript reports on the novel finding that certain ions can strongly intercalate with\nvermiculite, leading to stable membranes with ion selectivity. The stability of the membranes,\ninterlayer spacing, and ion selectivity is characterized, revealing intriguing selectivity trends. In\nparticular, Cs ions are found to decrease spacing leading to large selectivity. Even more\nintriguingly, La and Zr intercalated vermiculite is found to have much lower permeability to Li\ncompared to other monovalent ions, than Sn and Ir intercalated vermiculite. The difference is\ntraced to the partitioning of Li and correlates with the entropy of hydration of the intercalating ions\nand the membrane stiffness. This result constitutes clear evidence of effects beyond ion size and\ncharge in ion transport. Overall, the work is thorough and presents intriguing new phenomena\nrelated to ion transport in nanoscale channels that is relevant to ion-ion separations. The reviewer\nrecommends publication after addressing the comments below.\nWe sincerely thank the Reviewer for their encouraging assessment of our work. We have carefully\naddressed all the comments and have revised the manuscript accordingly. Detailed responses\nto each point are provided below.\nThe membrane stability is reported in salts of monovalent ions, and in SrCL2. The claims of\nstability will be strengthened by including exposure to CaCl2 and MgCl2, which are ubiquitous in\nmany practical applications. Furthermore, it will be helpful to address whether the membranes\nare stable in solutions of cations with +3 or +4 charges, as well as in acidic and basic solutions.\nFollowing the Reviewer’s comment, we investigated the stability of Zr-Ver membranes upon\nexposure to 1 M CaCl₂, 1 M MgCl₂, 1 M LaCl₃, 0.1 M\nIrCl₄, as well as acidic (HCl, pH ≈ 3) and basic (NaOH,\npH ≈ 12) solutions. We quantified Zr⁴⁺ loss using mass\nspectrometry and found it to be below ~5% in all\ncases (Fig. R4-1, now revised Fig. 1e). We also\nmonitored the membranes visually over 30 days and\nconfirmed that they remained intact, with no signs of\nswelling, delamination.\nFigure R4-1. Zr4+ mass loss after immersing the ionic\nsolutions for 24h.\nSome of the data relevant to the study are not provided. For example, a consolidated table of\ninterlayer spacings should be added. Similarly, it would be very useful to add a table of\npermeabilities, along with the ion concentration in the membrane and associated interlayer\nspacing. Another example, the methods section states that 10 mM or 1 M solutions were used for\npermeation tests, but it is not clear which concentration is used in which experiment.\nFollowing the Reviewer comment, we have added a table (See Supplementary Table 1)\nsummarising ion permeabilities, membrane ion concentrations, and associated interlayer\nspacings.\nThe statement that some experiments used 10 mM solutions was an error. Experiments were\nperformed with 1M solutions in all cases, except for salts with +3 and +4 valence cations, in which\nwe used 0.1 M to avoid making the solutions acidic—although with hindsight, we now know it\ndoesn’t matter (see Fig. R4-6 below). We have clarified this in the Methods section.\nWas osmosis of water observed during any of the ion permeation experiments? If yes, it would be\n12\nssol\nssam\n+4rZ\n)%(\nreV-rZ\nni\n7\n6\n5\n4\n3\n2\n1\nvery interesting to report the measured water fluxes. Was stirring employed to ensure good\nmixing, or was it not found to be necessary?\nWe did explore this possibility, but did not observe osmotic flux, most likely because it was too\nsmall. Following the Reviewer comment, we now tested\nwater vapour flux gravimetrically, using a 1 cm2 Zr-Ver\nmembrane. Fig. R4-2 shows that the water permeation\nwas low, at about 100 g m-2 h-1. Following the Reviewer\ncomment we have included this figure as\nSupplementary Fig. 9 in the revised manuscript.\nRegarding the second question, we did test both with\nand without stirring and did not observe any significant\ndifferences.\nFigure R4-2. Gravimetry measurements of water\nvapour permeation through Zr-Ver membranes.\nWas the permeability observed to be independent of the membrane thickness? If not, it would\nsuggest percolation effects, defects, or variation in the\nmembrane structure.\nThe ion permeability scales linearly with membrane\nthickness in the range of 0.5–2 μm, indicating that\ntransport is governed by through-plane diffusion and not\ndominated by percolation effects, defects, or structural\nvariations (Fig. R4-3). We have included this important\npoint as Supplementary Fig. 6 in the revised manuscript.\nFigure R4-3. the ion flux dependent on the thickness of\nZr-Ver membrane.\nThe manuscript largely reports ion permeation\nexperiments with a single cation at a time. To ascertain\nselectivity, it is necessary to perform mixed ion\nexperiments to assess whether the selectivity observed in single salt experiments also carries\nover to mixed salt experiments.\nIn response to the Reviewer’s comment, Fig. R4-4 below shows ion transport measurements\nusing equimolar (1 M total) mixtures of different monovalent ion salts for Zr-Ver and Sn-Ver\nmembranes.\nFor mixtures containing Cs⁺ or K⁺, the interlayer spacing in both membranes collapsed, as\nexpected. Under these conditions, both membranes showed the same selectivity observed with\nCs-cation mixtures in the original Fig. 2 (red data points). With hindsight, this was expected. In\nthis case, the one-water-layer-thick channel is expected to display selectivity based only Gibbs\nhydration energy due to its narrow d.\nThe only mixture that does not contain K⁺ or Cs⁺—and thus does not induce interlayer collapse—\nis the Na⁺/Li⁺ mixture. In this case, Sn-Ver membranes exhibit a much larger Li⁺ flux than Zr-Ver,\nreminiscent of the single-salt results, but the Na⁺ flux is about twice that of Li⁺. This represents\nan intermediate behaviour between the selectivity of Sn-Ver in single-salt experiments, where Li⁺\npermeated about six times faster than Na⁺, and that of Zr-Ver membranes, where Na⁺ permeated\nroughly ten times faster than Li⁺.\n13\n)gm(\nssol\nretaW\n0\n0\n0\n.0\n.0\n.0\n2\n1\n0\n0\n)1-h\n2-m\ng(\nxulf\nretaW\n120\n90\n60\n30\n0\n2 0 0\nT im e (m\nZ\nZ\nZ\nr-V e r 1\nr-V e r 2\nr-V e r 3\n4 0 0\n)\n6 0 0\nZr-Ver 1 Zr-Ver 2 Zr-Ver 3\n)1-h\n2-m\nlomm(\nxulF\n80\n60\n40\n20\n0\n0.0\n+ Li+\nC s\n0.5 1.0\n1 /l (μ m -1)\n1.5 2.0\nWe suggest that this latter finding may arise from competition between ions for space within the\nchannels. Na+ ions are less strongly hydrated than Li+, which may lead to a slightly higher affinity\nto the walls that enhances their concentration in the membrane. Similar competitive effects are\ncommonly reported at mineral–water interfaces, where one ion’s adsorption is altered by the\npresence of others with different hydration and binding strengths (e.g. S. Yang, et al. J. Phys.\nChem. C 2019, 124, 1500-1510 and S. Lee, et al. Geochimica et Cosmo. Acta 2013, 123, 416-\n426).\n40\n30\n20\n10\nthe (b),(c), Corresponding XRD of membranes in the feed solution.\nWas the effect of salt concentration and pH on permeation investigated? In particular, measuring\nthe partitioning of ions, interlayer spacing, and permeability, along with estimating the diffusivity\nas a function of salt concentration will reveal whether the salt concentration affects the interlayer\nspacing and ion transport, what kind of adsorption isotherms describe ion uptake into\nintercalated vermiculite, and\nwhether transport in the\ndilute limit can explain\ntransport at higher salt\nconcentrations.\nFigure R4-5. The effect of salt\nconcentration (a) on the Li ion\nflux through Zr-Ver\nmembranes. (b),\nCorresponding XRD of\nmembranes.\n14\n)1-h\n2-m\nlomm(\nxulF\nZr-Ver\nCs+/Li+Cs+/Na+Cs+/K+K+/Na+K+/Li+Na+/Li+\nPermeated ions\n)1-h\n2-m\nlomm(\nxulF\n4\n3\n2\n1\n0\n0\n0\n0\nP e\n+s /K\nrm e\n+ + + K /N a\na te\n+ + + K /Li\n+ + N a /Li\nKs\nS n-V\n+ + /Li N\ner\n+ + a /Li\na b\n).u.a(\nytisnetnI\n4 5 6\n2\n7\n( ) q °\n+ + C s /Li\n+ + C s /N a\n+ + C s /K\n+ + K /N a\n+ + K /Li\n+ + N a /Li\n9 1 0\n).u.a(\nytisnetnI\n4 5 6\n2\n7\n( ) q °\n+ + C s /Li\n+ + C s /N a\n+ + C s /K\n+ + K /N a\n+ + K /Li\n+ + N a /Li\n9 1 0\nc d\na 2.0 b\nLi+\n1.5\n1-\n2-m\nh\nlom\nm\n)\n1.0\n).u\n.a\n(\ny tis\nn\n1\n5\n0\n0\n0\n0\n0\nm\nm\nM\nM\nL\nL\ni\ni\n+\n+\nx\nu lF\n(\n0.5\ne tn\nI\n1\n5\n0\n0\n0\nm\nm\nM\nM\nL\nL\ni\ni\n+\n+\n10 mM Li+\n0.0\n101 102 103 4 6 8 10\nPermeated ions concentration (mmol L-1) 2q (°)\nFollowing the Reviewer comment, we investigated the effect\nof Li concentration on permeation through Zr-Ver\nmembranes. As shown in Fig. R4-5, the Li⁺ flux increased by\nonly by a factor of 2 over the salt concentration range 1mM to\n1M, with no detectable change in interlayer spacing.\nWe also studied the role of pH on ion flux through Zr-Ver. The\ncase of Cs+ is particularly relevant because it is the ion with\nthe strongest adhesion to the membrane. Fig. R4-6 shows\nthat the flux is largely insensitive to pH, with a drop in\npermeability of only a factor of ~2 when the pH changes from\n3.5-9.6.\nFig. R4-6. Cs+ flux through Zr-Ver as a function of pH. Feed reservoir electrolyte, 1M CsCl.\nThe hypothesis of entropic effects in the hydration of the intercalating ion on the differences in Li\nion transport is very intriguing. However, the reason for the behavior is not pursued apart from\ncorrelation to entropy of hydration and mechanical stiffness of the membrane. Does the\ninterlayer spacing change in the presence of Li ions, especially in the case of Sn and Ir\nintercalation where the membranes are more flexible? Do the observations correlate with the\nthermodynamic behavior of mixed salt solutions of the intercalating ion and lithium indicating\nthat it may be a bulk effect, or is nanoconfinement essential? What explains the order of\nmagnitude difference in ion partitioning for Sn and Ir intercalated membranes – can it be\nattributed to interlayer spacing, or are other effects essential? Similarly, does Li partition more\nfavorably than the other monovalent ions in the Sn and Ir intercalated membranes and why (and\nif not, it must diffuse faster given the data in Fig. 3)? Similarly, temperature dependence to extract\nthe free energy change of partitioning of ions will likely provide additional insights.\nThe proposed entropic effects explanation was prompted by both our findings and prior literature,\nas more conventional explanations such as interlayer spacing or bulk thermodynamics did not\nexplain the observed trends. Below we expand on these points.\n(1) Interlayer spacing: This was the first possibility we explored. Fig. 3b in the original manuscript\nshows that all four membranes immersed in Li⁺ electrolyte exhibit the same interlayer spacing\n(≈14.8 Å), ruling out channel height differences as the source of the selectivity.\n(2) Partitioning vs. diffusion: To unpick this unexpected finding, we measured Li⁺ concentration in\nthe membranes after permeation measurements using mass spectrometry (Supplementary Fig.\n11). The data showed that Li⁺ concentration in Ir-Ver and Sn-Ver is an order of magnitude higher\nthan in Zr-Ver and La-Ver (Supplementary Fig. 11). This revealed that partitioning, rather than\ndiffusion, was the dominant factor. Beyond this, and\nfollowing a comment from Reviewer #1, we have now directly\n1-g ) probed the diffusion in the membranes using\nlo\nm\n1.5\nelectrochemical impedance spectroscopy. This revealed\nm\ne n\n(\nthat the diffusion constants of Li changes by only about ~20%\na\nrb\nm1.0 Ir-Ver for the different membranes (Fig. R1-1, page 1 in this file and\ne m Zr-Ver\nn i n Supplementary Fig. 12 in revised manuscript). This confirms\no\nita rtn 0.5 that partitioning, rather than diffusion, explain the\ne\ncn differences in permeability.\no\n+\nc\niL\n0.0\n10 20 30 40 50\ntemperature (oC) Figure R4-7. temperature-dependent measurements of ion\npartitioning in the Zr-Ver membrane\n15\n)1-h\n2-m\nlomm(\nxulF\n4\n3\n2\n1\n0\n0\n0\n0\n0\n3 .5 4 .6 5 .6\np H\n6 .6 8 .6 9\n+ C s\n.6\nFollowing the Reviewer comment, we now include new temperature-dependent measurements\nof Li+ ion partitioning. As shown in Figure R4-7, the temperature dependence is very weak.\n(3) Thermodynamics of bulk solutions: Following the Reviewer comment, we also considered\nthermodynamic behaviour of bulk solutions. From Debye-Hickel theory, the presence of highly\ncharged intercalated ions, such as Ir⁴⁺ and Zr⁴⁺, should result in reduced ion activity coefficients\nfor the permeating ions. However, since both Ir⁴⁺ and Zr⁴⁺ have the same charge, this cannot\nexplain our observations.\n(4) Proposed explanation: Having ruled out channel height and ion activity as explanations, we\nturned to the biological literature, where channel elasticity is known to influence ion selectivity\nby altering the Gibbs energy of ions inside elastic versus rigid channels (Laio & Torre, Biophys. J.\n1999). Similar coupling between mechanics and ion exchange has also been observed in clays\n(Whittaker et al., PNAS 2019). Motivated by this, we measured the Young’s modulus of our\nmembranes and found two distinct groups: stiff (Zr-Ver, La-Ver) and soft (Ir-Ver, Sn-Ver), with\nmoduli differing by an order of magnitude. The stiff membranes showed classical selectivity (Cs⁺\n> K⁺ > Na⁺ ≳ Li⁺), while the soft ones showed the reverse (Li⁺ > Na⁺ ≈ Cs⁺ ≈ K⁺). Because the only\ndifference between the two groups is the intercalated ion, we attributed the changes in stiffness\nand selectivity to these ions. Marcus’ seminal work explains this link: ions with low hydration\nentropy (e.g. Zr⁴⁺) lead to more ordered and thus stiffer water, while those with higher entropy (e.g.\nSn⁴⁺) lead to more disordered water. Such effects, demonstrated in bulk, should be amplified\nunder confinement, where water is more structured and resistant to deformation (as shown in\nAFM and surface force studies, Refs. 47, 49). This amplification should make confined water\nespecially sensitive to the influence of intercalated ions, providing a natural explanation for the\nstiffness–selectivity correlation we observe.\n16"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have satisfactorily addressed the issues raised during the initial review. This work is now suitable for publication.", "reviewer_2": "The authors have addressed my comments properly, and I would like to recommend the publication of this manuscript in Nature Communications.", "reviewer_3": "The authors have addressed most of my concerns. I have two minor comments that I would like the authors to further clarify before this work is published:\n1. Monovalent ion permeation with varying channel widths\nReferring to my previous Comment 3, I remain surprised by the relatively unaffected permeation of monovalent ions with different channel widths (Fig. 2e). I understand that ion permeation is governed by the thermodynamic partitioning step, which depends on ion dehydration and ion–pore interactions. A smaller pore is typically expected to impose a higher dehydration penalty. At the same time, ions with fewer surrounding water molecules should interact more strongly with the pore walls, partially compensating for this penalty. The authors suggest that the observed unaffected monovalent permeation arises from a balance: the additional dehydration penalty is approximately offset by stronger ion–pore interactions, resulting in a similar overall free energy change for both channel sizes. My question is: is this balance merely coincidental in this case, or does it represent a more universal principle?\n2. Relation between elasticity and selectivity\nReferring to my previous Comment 9, I appreciate the improved discussion of the mechanism, but I still find the link between membrane elasticity and ion selectivity insufficiently explicit. The current revision convincingly shows that pore elasticity influences ion selectivity, and that incorporating different non-exchangeable ions alters the elasticity of the membrane. However, it remains unclear, at least to me, and potentially to readers, why Li⁺ permeates most slowly through membranes with higher Young’s modulus (Zr-Ver and La-Ver) and most rapidly through those with lower Young’s modulus (Sn-Ver and Ir-Ver). A clearer mechanistic explanation of this trend would strengthen the interpretation.", "reviewer_4": "The authors have addressed all the reviewer comments satisfactorily and the reviewer recommends publication without further revision."}, "author_response": "Response to comments from Reviewer #1\nThe authors have satisfactorily addressed the issues raised during the initial review.\nThis work is now suitable for publication.\nWe are grateful to the Reviewer for this recommendation.\nResponse to comments from Reviewer #2\nThe authors have addressed my comments properly, and I would like to recommend\nthe publication of this manuscript in Nature Communications.\nWe thank the Reviewer for this assessment of our work.\nResponse to comments from Reviewer #3\nThe authors have addressed most of my concerns. I have two minor comments that I\nwould like the authors to further clarify before this work is published:\nWe thank the Reviewer for this assessment of our revised manuscript. We have done our\nbest to clarify the points below.\n1. Monovalent ion permeation with varying channel widths\nReferring to my previous Comment 3, I remain surprised by the relatively unaffected\npermeation of monovalent ions with different channel widths (Fig. 2e). I understand that\nion permeation is governed by the thermodynamic partitioning step, which depends on ion\ndehydration and ion–pore interactions. A smaller pore is typically expected to impose a\nhigher dehydration penalty. At the same time, ions with fewer surrounding water molecules\nshould interact more strongly with the pore walls, partially compensating for this penalty.\nThe authors suggest that the observed unaffected monovalent permeation arises from a\nbalance: the additional dehydration penalty is approximately offset by stronger ion–pore\ninteractions, resulting in a similar overall free energy change for both channel sizes. My\nquestion is: is this balance merely coincidental in this case, or does it represent a more\nuniversal principle?\nOur understanding is that this balance is coincidental. We observe it only for monovalent\nions, which are relatively weakly hydrated. For multivalent ions, which are more strongly\nhydrated, we observe much sharper rejection as function of hydration energy in narrow\nchannels (Fig. 2, red dots). Thus, since this balance is not expected in general, we regard\nit as coincidental—although perhaps not entirely unexpected with hindsight, given these\nminerals’ well-documented affinity for monovalent ions.\nIn search for a more universal principle behind this observation, perhaps it may be helpful\nto note that a key principle of statistical mechanics is that distinct microscopic\nconfigurations of a system can yield the same ΔG. Since ΔG determines ion concentration\nand permeability in these membranes, different configurations of the system can yield the\nsame permeability.\n2. Relation between elasticity and selectivity\nReferring to my previous Comment 9, I appreciate the improved discussion of the\nmechanism, but I still find the link between membrane elasticity and ion selectivity\ninsufficiently explicit. The current revision convincingly shows that pore elasticity\ninfluences ion selectivity, and that incorporating different non-exchangeable ions alters the\nelasticity of the membrane. However, it remains unclear, at least to me, and potentially to\nreaders, why Li⁺ permeates most slowly through membranes with higher Young’s modulus\n(Zr-Ver and La-Ver) and most rapidly through those with lower Young’s modulus (Sn-Ver\nand Ir-Ver). A clearer mechanistic explanation of this trend would strengthen the\ninterpretation.\nOur mass spectrometry data show that Li⁺ permeates more slowly in membranes with\nhigher stiffness because its equilibrium concentration inside the membrane is lower. This\ndifference reflects the Gibbs energy of Li⁺ in the membrane, which includes an elastic\ncontribution. In the simplest approximation, this energy is given by Hₑ(𝑥̅) = (1/2) k(𝑥̅) [d(𝑥̅)\n– d (𝑥̅)]², where k(𝑥̅) is the stiffness as a function of position in the channel, 𝑥̅, and d\no o\n(𝑥̅) is the equilibrium channel width. Li⁺ has the largest hydration shell amongst the\nmonovalent ions. As a result, its associated term d(𝑥̅) – d (𝑥̅) in H (𝑥̅) should display\no e\nlarger differences than other ions and should thus be more strongly affected by a\nchange in k. Following the Reviewer comment, we have expanded on this point in the\nrevised manuscript, in the first and second paragraphs in page 7.\nResponse to comments from Reviewer #4\nThe authors have addressed all the reviewer comments satisfactorily and the reviewer\nrecommends publication without further revision.\nWe thank the Reviewer for their support of our work."}, {"round": 3, "reviewer_comments": {"reviewer_3": "The authors have addressed all my comments, and I recommend this manuscript for publication."}, "author_response": ""}]

Decision letter