A Matthew MXene (Ti3C2Tx) Lamellar Membrane as a Potassium-Sieving Amplifier

Zong Lu , Haoyu Wu , Yanying Wei , Haihui Wang

Engineering ›› 2024, Vol. 42 ›› Issue (11) : 223 -232.

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Engineering ›› 2024, Vol. 42 ›› Issue (11) :223 -232. DOI: 10.1016/j.eng.2023.11.025
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A Matthew MXene (Ti3C2Tx) Lamellar Membrane as a Potassium-Sieving Amplifier

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Abstract

Transport channels with ultrahigh K+ selectivity over other ions play a crucial role for living beings, but constructing ionic channels with promising K+ selectivity and permeability remains a challenge. Here, an asymmetric bilayer membrane based on MXene (Ti3C2Tx) lamellar channels consisting of a recognition layer (RL) on top of an enhancement layer (EL) exhibits an amazing Matthew effect: amplification of the preferred transport of K+, resulting in an excellent K+-separation performance. The K+ ion is selected by the 1-aza-18-crown-6 ether-modified RL, owing to preferential affinity energy, and then rapidly transported as a hydrated ion through the EL, based on the confinement effect. Other undesired ions such as Na+ are hindered from entering the RL by the preferred K+ occupation of the crown ether. The MXene (Ti3C2Tx)-based Matthew membrane presents high K+-permeation rates of 0.1-0.2 mol∙m−2∙h−1, with a significant K+/Na+ selectivity of 5-9. The molecular separation mechanism of the Matthew membrane is investigated deeply to explore the nature of the Matthew amplification effect on K+ sieving, where the precise matching of the RL and EL within the membrane governs the fast K+ permeation with good selectivity. The asymmetric structure of our Matthew membrane is the key to understanding the biological function of ion channels for precise and fast ion transport, which will guide us in the creation of artificial ion channels or membranes.

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Keywords

MXene (Ti3C2Tx) membrane / Membrane separation / Ion sieving / K+ selectivity

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Zong Lu, Haoyu Wu, Yanying Wei, Haihui Wang. A Matthew MXene (Ti3C2Tx) Lamellar Membrane as a Potassium-Sieving Amplifier. Engineering, 2024, 42(11): 223-232 DOI:10.1016/j.eng.2023.11.025

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1. Introduction

Selective permeation of the potassium ion, K+, is regarded as an essential process in natural cellular environments [1], [2]. Artificial ion channels are considered to be an exciting option for biomimetic energy conversion [3], [4], [5], [6], molecule transport [7], [8], and high-value metal recovery [9]. However, constructing artificial ion channels with exact recognition of target ions and fast transport is still an arduous task in the field of future ionic interfaces, ionic processors, and ionic sensors.

Biomimetic channels (e.g., biomimetic protein and organic channels) have been widely studied and can currently achieve an effective selectivity of K+ over Na+ [10], [11], [12], [13], [14], [15]. However, their complex preparation processes, the instability of their protein structure originating from non-covalent interactions, their notorious toxicity, and their occupation of only a few square microns of the organic structure may cause such devices to be fragile and useless in practice-relevant separation processes, hindering the large-scale application of these K+-selective channels [16], [17], [18], [19]. Compared with the aforementioned sophisticated artificial ionic channels, ion-selective separation membranes with good scalability in the preparation of relatively large effective areas, high efficiency, and low energy consumption have become one of the most promising targets in monovalent-ion separation, especially for the ion pair K+/Na+ [20]. Cation transport is usually rate limiting, since common anions (e.g., Cl−), with their smaller hydrated size and weaker dehydration energy barrier, can more easily pass through a porous membrane, along with cations to maintain electroneutrality. For example, highly porous organic cage (POC) membranes, covalent organic framework (COF) membranes, and metal-organic framework (MOF) membranes with numerous transfer channels exhibit excellent K+-permeation rates but fail to select K+ against Na+ due to their unsuitable pore size [21] and the lack of capability to mimic the key functions of biological recognition [22], [23], [24], [25], [26]. A few two-dimensional (2D) material-based membranes with confinement channels have also been used for K+ selective separation [27], [28], [29], [30], [31], [32]. However, the one-pot modification method endows the membrane with K+ selectivity but decreases the permeability [30]. Therefore, selective K+ separation is still a bottleneck issue in the field of monovalent ion separation, and the development of a membrane with both amplified K+ selectivity and promising permeability for precise ion sieving remains challenging.

Herein, we design a kind of Matthew membrane with an asymmetric structure as an amplifier of K+ separation to address the above issue. The term “Matthew effect” is commonly used by sociologists and economists to reflect a state of polarization in society, which can be simplified as “the rich get richer and the poor get poorer”; it was coined by the sociologist Robert K. Merton in 1968 [33] and is derived from the biblical Gospel of Matthew. In our case of ionic transport through a membrane, the preferred transport of K+ is amplified by the Matthew effect. A Matthew membrane is a bilayer membrane composed of an ion-selective recognition layer (RL) and an ion-permeable enhancement layer (EL).

It is well known that crown ether molecules with biological binding sites have adjustable rings that can bind target ions, laying a foundation for specific ion selectivity [34]. For example, 15-crown-5 ether [35] and 12-crown-4 ether [36] derivatives have attracted much attention in the field of biological ion channels because of their special binding properties with Na+ and Li+, respectively. Interestingly, 18-crown-6 ether has been proven via simulation [37] and experiment [38] to bind K+ strongly. Therefore, inspired by biological ionic protein channels containing a recognition structure, we modify a lamellar stack of MXene (Ti3C2Tx) [39], [40], [41], [42], [43], [44], [45] nanosheets—a new type of 2D nanomaterial with polyatomic layers that have excellent features (hydrophilicity, exceptional flexibility, superior thermal stability, high electrical conductivity, and large surface area)—through the incorporation of 1-aza-18-crown-6 ether (CE) to construct a K+-selective permeation amplifier as the RL (Fig. 1(a) [33]; see Fig. S1 in Appendix A for the detailed process). The EL, consisting of pure MXene (Ti3C2Tx) nanosheets without any CE modification, is intended to promote fast transport of the K+ ions previously selected by the RL. In this way, the whole asymmetric Matthew membrane acts as an amplifier to amplify the selective transport of the target ion K+ over Na+, thereby achieving excellent K+ permeation and selectivity.

In practice, a stack of CE-modified MXene (Ti3C2Tx) nanosheets does indeed act as an RL and can effectively recognize and incorporate the target ion K+ via preferential K+-CE interaction energy, while the EL, as an unmodified MXene (Ti3C2Tx) layer, permits faster transport of hydrated K+ than hydrated Na+ through confinement molecular sieving (Fig. 1(b)). When comparing the CE-modified MXene membrane (i.e., with MXene-CE as the RL) with the pristine MXene (Ti3C2Tx) membrane (i.e., an EL without an RL), faster permeation of hydrated K+ in comparison with Na+ ion transport is found and a good K+/Na+ selectivity is achieved for the Matthew membrane [46] (Fig. 1(c)). Thus, selective transport of the targeted K+ enriched in the RL by specific interaction with a crown ether can be significantly enhanced through the EL, with the confined and amplified transport of hydrated K+ ions. This interplay of K+ enrichment by the RL and fast selective transport by the EL is the key point of the Matthew amplification effect.

2. Materials and methods

2.1. Materials

The bulk material, MAX (Ti3AlC2) (200 mesh), was purchased from Laizhou Kai Kai Ceramic Materials Co., Ltd. (China). Lithium fluoride (LiF; > 99%) was purchased from Aladdin (China), and hydrochloric acid (HCl; 12 mol∙L−1) was purchased from Guangzhou Chemical Reagent (China). The details of other materials are provided in Appendix A.

2.2. Preparation of MXene (Ti3C2Tx) nanosheets

MAX (Ti3AlC2) powder with a large lateral size was obtained through the gravity sedimentation method. Large MXene (Ti3C2Tx) nanosheets were obtained via the minimally intensive layer delamination (MILD) method. The details of other processes are provided in Appendix A.

2.3. Preparation of pristine and asymmetric MXene (Ti3C2Tx) membranes

A pristine MXene (Ti3C2Tx) membrane was obtained by depositing MXene (Ti3C2Tx) nanosheets on a nylon-66 substrate by means of vacuum-assisted filtration. Asymmetric MXene membranes were obtained via CE infiltration into a stack of deposited MXene (Ti3C2Tx) nanosheets through the concentration-diffusion method. Details on the other processes are provided in Appendix A.

2.4. Monovalent metal-ion permeation test

The monovalent metal-ion permeation test was based on the concentration-diffusion method. Details are provided in Appendix A.

2.5. Characterization

The MXene (Ti3C2Tx) nanosheet and membrane were characterized through scanning electron microscopy (SEM), transmission electron microscopy (TEM), atomic force microscopy (AFM), Fourier-transform infrared (FTIR) spectroscopy, X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), thermogravimetry-mass spectroscopy (TG-MS), and inductively coupled plasma-mass spectroscopy (ICP-MS). Details are provided in Appendix A.

2.6. Theoretical simulation

A simulation of the interaction between the CE and the ions was obtained using density functional theory (DFT) based on the large-scale atomic/molecular massively parallel simulator (LAMMPS). A mass-transport simulation of ions through the MXene (Ti3C2Tx) channel was obtained using molecular dynamic (MD) simulation based on LAMMPS. Details are provided in Appendix A.

3. Results and discussion

3.1. Characterization of the Matthew membrane

In order to achieve a highly ordered lamellar structure for an excellent separation performance, relatively large MXene (Ti3C2Tx) nanosheets were required as building blocks. The size of the starting material MAX (Ti3AlC2), which was collected from the bottom of a vessel by means of gravity sedimentation, was three times greater than the size before sedimentation (Fig. S2 in Appendix A). SEM showed that the aluminum (Al)-etching conditions (i.e., the ratio of MAX to the etching chemicals, temperature, and reaction time) were optimal. The size of the as-synthesized MXene (Ti3C2Tx) nanosheets was increased to 4-6 µm compared with the size in our previous work (0.3-0.8 µm) [42] (Fig. 2(a); Fig. S3 in Appendix A), which was beneficial for building a highly ordered MXene (Ti3C2Tx) stacking membrane for the precise separation of monovalent ions. The results of AFM (Fig. S4 in Appendix A) and TEM (Figs. 2(b) and (c)) showed that the MXene (Ti3C2Tx) nanosheets were ultrathin and had a lateral extension of several microns, which was conducive to the subsequent preparation of 2D lamellar membranes with precise ion-sieving channels. A cross-section SEM image (Fig. 2(d)) showed that the Matthew membrane had an obvious and regular 2D-nanosheet stacking structure. Energy-dispersive X-ray (EDX) spectroscopy and elemental mapping from TEM (Figs. S5 and S6 in Appendix A) indicated that the Al layer in the bulk phase of the MAX had been completely removed, and Al was not found in the MXene (Ti3C2Tx). All the elements (titanium (Ti), carbon (C), oxygen (O), and fluorine (F)) were uniformly distributed, which was advantageous for membrane construction [43]. Subsequently, CE was introduced into the RL to endow K+ selectivity, since the CE molecule exhibits special recognition for K+ [37], [47] (Figs. S7 and S8 in Appendix A), in complete accordance with our computational simulation (Section 3.3). Thus, the RL was obtained using the concentration-diffusion method and was expected to exhibit effective K+ recognition due to the different affinity energies between K+ and CE, with K+ transport occurring through activated jumps along the CE sites.

The modification of the MXene (Ti3C2Tx) nanosheet stack through the incorporation of CE reduced the surface roughness of the RL membrane (Fig. S9 in Appendix A), which was beneficial for precise ion sieving [48]. An EDX line-scan elemental distribution of the cross-section of the Matthew membrane showed that the thickness of the RL was around 220-300 nm. After this distance, the intensity of the element nitrogen (N), representing the CE molecules, attenuated sharply (Figs. 2(d) and (e)).

In order to study the structure-property relationship of the bilayer Matthew membrane with the RL and EL, pristine MXene (Ti3C2Tx) membranes without an asymmetrical structure and without CE modification were prepared for comparison. The chemical compositions in cross-sections of the pristine MXene (Ti3C2Tx) membrane and the Matthew membrane were certified by means of etching XPS (Figs. S10 and S11 in Appendix A) [49]. Etching XPS was carried out to further study the thickness of each layer (Fig. 2(f); Fig. S12 in Appendix A). The elemental ratio of Ti (a tracer for MXene (Ti3C2Tx)) and N (a tracer for CE in the RL) changed dramatically at a depth of 220-300 nm within the bilayer Matthew construct. This finding is in complete accordance with the EDX line-scan elemental distribution of the cross-section of the Matthew membrane (Fig. 2(e)). Compared with the N 1s XPS signal of the membrane surface, strong Ti-N characteristic binding peaks (456.9 and 397.1 eV) were found at an etching depth of 200 nm inside the RL of the Matthew membrane. This experimental finding was attributed to the bond formation between the CE molecules and the -OH functional groups of the MXene (Ti3C2Tx) nanosheets (Fig. 2(g); Fig. S13 in Appendix A) [50]. As shown in Figs. 2(h) and (i), the shift in the (002) diffraction in the XRD illustrates that the introduction of CE enlarges the interlayer spacing from 3.4 Å (the EL of the Matthew membrane in the dry state) and 6.3 Å (the EL of the Matthew membrane in the wet state) to 7.1 Å (the RL of the Matthew membrane in the dry state) and 7.6 Å (the RL of Matthew membrane in the wet state) with a good anti-swelling ability, which is beneficial for sharp molecular sieving. It is worth mentioning that the degree of structural order (a narrow half-width and high peak intensity) is still maintained after the introduction of CE, which differs from a previous report [30] in which decreased structural order always resulted from the incorporation of a modifier.

Moreover, the SEM and corresponding EDX results (Figs. S14 and S15 in Appendix A) showed a uniform elemental distribution of Ti, C, O, and F. As expected, the intensity of the EDX signal of N on the top surface of the RL in the Matthew membrane was significantly higher than that at the bottom surface of the EL, verifying the asymmetric structure, with the N-containing CE as a guest in the RL and the CE-free EL lacking an N signal (Fig. S16 in Appendix A). As shown in Fig. S17 in Appendix A, because the RL was modified by CE molecules with high hydrophilia due to their cyclic ether-oxygen skeleton, the RL had a water contact angle much lower than that of the non-modified MXene (Ti3C2Tx) layer (the EL). The different water contact angles on the top and bottom surfaces of the Matthew membrane confirm the asymmetric membrane structure. The increased surface hydrophilicity of the Matthew membrane on the RL side further facilitates the transport of hydrated K+ ions [51].

The attenuated total reflection Fourier-transform infrared (ATR-FTIR) spectroscopy results for the Matthew membrane showed a stretching vibration peak of C-O-C at 840, 983, and 1117 cm−1. Characteristic peaks near 1248, 1347, and 3760 cm−1 were attributed to the stretching vibrations of the C-N-C and N-H of CE, demonstrating the existence of CE inside the RL of the Matthew membrane (Fig. S18(a) in Appendix A). The redshift of the -OH peak near 3480 cm−1 was attributed to the interaction between CE and the terminal groups of the MXene (Ti3C2Tx) nanosheets in the RL of the Matthew membrane [52]. The Raman spectroscopy results (Fig. S18(b) in Appendix A) further confirmed the presence of CE in the RL, due to the peaks belonging to C-O-C [53].

In addition, the TG-MS result (Figs. S19(a) and (b) in Appendix A) showed that, with increasing modification time ranging from 10 to 120 min, the losing weight ratio increased from 5.60 to 17.46 wt% with increasing CE loading in the RL. As expected, the characteristic peak intensity of N increased with increasing modification time, as shown in Fig. S19(c) in Appendix A.

3.2. K+/Na+-sieving performance

3.2.1. K+ selectivity as the function of modification time

The permeation of K+ and Na+ ions through the membranes was studied using a home-made U-shaped permeation device (Fig. S20 in Appendix A). First, the K+-sieving performances of a series of membranes with different CE modifications made via the concentration-diffusion method were studied to identify the optimum preparation. Different concentrations of CE changed the modification rate of the RL or simultaneously resulted in different thicknesses of the RL, but did not change the actual loading amount of CE retained in the RL. The CE penetration profiles as a function of the modification time are exhibited in Fig. 3(a). For a CE modification time of 60 min, an MXene (Ti3C2Tx) membrane with an asymmetric structure consisting of an RL and an EL was obtained, as derived from the signal intensity of the element N in the etching XPS profile. When the CE modification time was prolonged to 120 min, a symmetric MXene-CE membrane was formed—that is, the whole membrane consisted of only the RL. In addition, the effective interlayer spacing of the 120 min MXene membranes was similar to that of the Matthew membrane in its dry and wet states, suggesting that the modification time only affected the thickness of the RL (Fig. S21 in Appendix A). A comparison of the K+/Na+ sieving performances through the asymmetric Matthew membranes with different CE modification times (Fig. 3(b); Fig. S22 in Appendix A) suggested that the optimal CE modification time was 60 min. Therefore, an asymmetric MXene (Ti3C2Tx) membrane modified with CE for 60 min, named “the Matthew membrane,” was chosen for subsequent monovalent metal-ion permeation testing. It is worth mentioning that excessive CE modification led to increased thickness of the RL and decreased EL thickness. In the latter case, the membrane could not effectively exploit the K+ enriched in the thick RL, resulting in a decrease in the experimental K+/Na+ selectivity.

3.2.2. Structural engineering of the Matthew membrane

To explore the nature of the Matthew amplification effect, membranes with different structures—referred to herein as M1, M2, M3, and M4—were prepared and their structure-performance relationship was studied (Fig. 3(c)). Compared with the MXene-CE membrane, which had a thickness of 250 nm (M1), an MXene-CE membrane with a thickness of 500 nm (M2) showed higher K+/Na+ selectivity but a lower K+-permeation rate; this was because the MXene-CE membrane only provides K+ recognition function and lacks the subsequent condition for fast hydrated K+ ion transport. When comparing the Matthew membrane (M4) with an MXene-CE membrane with the same thickness in the forward direction (i.e., ion-transport direction going from the RL to the EL), the Matthew membrane exhibited a higher K+/Na+ selectivity and K+-permeation rate. In the optimized Matthew membrane, the RL has an optimal thickness for proper K+ recognition, and the EL has the necessary thickness with confinement nanochannels to accelerate K+ transport. Finally, when the Matthew membrane was measured in the backward direction (M3; i.e., with the ions moving from the EL to the RL), the K+-separation performance dropped to a level comparable with that of M1, showing a huge difference in comparison with the Matthew membrane measured in a forward direction (M4). These findings demonstrate that the amplifying effect of K+ separation through the Matthew membrane exhibits unipolarity. In other words, it is only when the ions pass through the Matthew membrane from the RL to the EL that the K+-separation performance is amplified. It can be seen in Fig. 3(c) that M1 and M3 exhibit a similarly poor performance, indicating that the EL has no influence if the ions are moving from the EL to the RL, and only the proper function of the RL occurs. It can be concluded that the promising K+-separation performance of the membrane is related not only to the optimal asymmetric structure but also to the direction of K+ ions passing through. The targeted K+ ions must be recognized and enriched by the RL before they are removed through the EL in order to exhibit an amplified K+-separation performance.

Fig. S23 in Appendix A shows the surprising ion-permeation performance through the pristine MXene (Ti3C2Tx) membrane and the Matthew membrane, with the linear dependence between ion conductivity and testing time demonstrating the negligible effect of K+ adsorption. Here, the permeation rate of K+ through the pristine MXene (Ti3C2Tx) membrane and the Matthew membrane increases from about 0.106 mol∙m−2∙h−1 to about 0.160 mol∙m−2∙h−1, a rise of about 50%, while that of Na+ decreases from approximately 0.0852 mol∙m−2∙h−1 to approximately 0.0208 mol∙m−2∙h−1, a reduction of about 75%. Furthermore, the transport performance of the tested ions through the Matthew membrane showed the following order, in line with their hydrated radius: K+ > Na+ > Li+ > Ca2+ > Mg2+ > Al3+ (Fig. 3(d)). The obvious cut-off between K+ and Na+ suggests preferential K+ permeation against other metal ions through the Matthew membrane.

3.2.3. Binary K+ selectivity

ICP-MS was used to study the permeation behavior of K+ and Na+ in mixed salt solutions (Figs. S24 and S25 in Appendix A). At the very beginning, Na+ exhibited a slightly higher permeation rate than K+ due to its lower affinity toward the CE in the RL. The higher affinity interaction between K+ and CE efficiently selects K+ [37]. In the initial stage (< 100 min) before the ion permeation rates reach a steady state, the K+-permeation rate increases due to its gradual enrichment in the CE-containing RL, which continues until the equilibrium state is attained; in contrast, the Na+-permeation rate decreases due to the gradually increased steric hindrance caused by the enrichment of K+. Compared with state-of-the-art monovalent-ion selective membranes, the Matthew membrane exhibits a promising K+-selective performance (Fig. 3(e); Table S3 in Appendix A).

3.2.4. K+/Na+ selectivity at different pHs

In order to verify the effective K+-sieving performance of the Matthew membrane under various pH conditions, the K+/Na+-separation performance of the pristine MXene (Ti3C2Tx) membrane and that of the Matthew membrane were evaluated at various pHs ranging from 2 to 11. Due to poor K+ recognition, the K+-separation performance of the pristine MXene (Ti3C2Tx) membrane without the RL exhibited only a slight dependence on pH when the pH was varied (Fig. S26(a) in Appendix A). In contrast, the K+-sieving performance of the Matthew membrane varied significantly with pH (Fig. S26(b) in Appendix A). At high pH, deprotonation of CE enhances its affinity toward K+, and more K+ becomes incorporated into the RL, increasing the K+/Na+ selectivity [24]. With decreasing pH, the protonation of CE weakens the interaction energy between CE and the monovalent ions, resulting in decreased K+/Na+ selectivity. It should be noted that, at a pH of 2, the high proton concentration supports the exiting of K+ from CE via H+/K+ exchange, which promotes the permeation of K+ and improves the K+ selectivity [54]. The immersive testing also showed the excellent stability of the Matthew membrane in acid and alkali environments (Fig. S27 in Appendix A).

3.3. Simulation of the ion-sieving mechanism

Simulations were carried out to understand the structure and amplification effect of the Matthew membrane from a theoretical perspective. Detailed simulation procedures are provided in Appendix A. Simulations employing DFT were used to study the affinity between K+ or Na+ ions and CE (Fig. 4(a)), as well as the structure stability. First, the ion-CE affinity energy was simulated by subtracting the energy of the ion-H2O and CE from the CE-ion-H2O complex (Table S4 in Appendix A).

The higher the ion-CE affinity energy is, the easier it is for CE to capture the ion. The affinity energy between Na+ and CE is much lower than that between K+ and CE, resulting in a preferential affinity of CE for K+. This is consistent with the EDX characterization, in which the Matthew membrane was analyzed after being soaked in mixed K+/Na+ salt solution (equimolar 0.1 mol∙L−1 KCl + NaCl) for 24 h (Fig. S28 in Appendix A). Secondly, in order to confirm the stability of the slit-shaped nanochannels of the RL after the incorporation of CE, the average reduced density gradients (aRDGs) were calculated to analyze the short-range interaction between the ions and CE. The short-range interactions between the ion-CE complex and the MXene (Ti3C2Tx) surface were also calculated for various channel surfaces. The interactions between the ion-CE complexes and the wall surface of the different MXenes (Ti3C2Tx) were calculated according to four models: Ti3C2 (without terminal groups), Ti3C2O2, Ti3C2(OH)2, and Ti3C2F2. For the interaction energy of the ion-CE, we obtained the following order: Ti3C2 > Ti3C2O2 > Ti2C2(OH)2 > Ti3C2F2. In Fig. 4, the color bar below the maps represents different types of short-range interactions, where strong attraction and repulsion originate from hydrogen bonds and steric hindrance effects. It was found that the model surface Ti3C2O2 exhibited the best structural stability due to relatively strong van der Waals interactions between the ion-CE complex and the Ti3C2O2 surface (Fig. 4(b)), which was consistent with the findings from our previous experimental work [55]. In other words, the interactions between the ion-CE complex and the MXene (Ti3C2Tx) interface effectively stabilized the membrane structure.

In addition, the ion permeation and ion-CE interactions were simulated using the classical MD method. Firstly, the interaction energy between the ions and the oxygen atoms of the CE in water was computed. When ions are moving in the slits between neighboring MXene (Ti3C2Tx) nanosheets and are approaching a CE, the total attraction energy between K+ and CE is higher than that between Na+ and CE due to an add-on effect of two attractive kinds of interaction energies: the van der Waals forces and the electrostatic interaction energy of the K+-O interplay. When ions move close to the CE, the attraction forces between the ion and the CE draw K+ faster than Na+. Afterward, K+ also leaves faster than Na+ through the EL. These results provide another demonstration of the preferential transport of K+ in the RL channel. (Figs. S29 and S30 in Appendix A). Secondly, MD-simulated ion-migration results showed that the presence of CE significantly promotes the transport of K+ over Na+ in the RL (Fig. S31 in Appendix A).

The simulation results (Fig. 5(a)) showed that inserting CE between two layers of the pristine MXene (Ti3C2Tx) structure (case (ii)) inhibited the transport of both ions but allowed K+ to permeate faster than Na+ through the MXene-CE membrane. It was inferred that the ion selectivity could be further increased by having multiple RLs, with a simultaneous decrease in ion permeability. Interestingly, adding an additional EL to the RL and thus creating a Matthew membrane (case (iii)) improved the ion selectivity without sacrificing much of the ion permeability. This additional EL appeared to magnify the difference between the ion transport of the two ions (Fig. S32(a) in Appendix A).

The energy barriers of the ions passing around the CE were also calculated (Figs. S32(b) and (c)). The high energy barrier of hydrated ions approaching CE explains the low permeation rate of K+ and Na+ in the RL. The energy barrier of K+ is 32% higher than that of Na+, indicating a sieving effect based on the sizes of the hydrated ion when they are close to the CE molecule. Afterward, when the ions leave the CE, the energy barrier of K+ becomes negative, resulting in a relatively easy detachment of K+. These results are consistent with the ion transport time in Fig. S31 and help to explain the K+-selective property of the RL.

These findings show that the CE does not only effectively select K+ by preferential affinity interaction; in combination with an EL, the effective release of K+ from CE through the EL-confined structure also becomes possible. To verify this function of the EL, the local movements of water molecules were calculated. To our surprise, the mean squared displacement (MSD) results of water in between layers (both region 1, the intersection of two RLs in MXene-CE membranes, or the intersection of RL and EL in Matthew membranes, and region 2, the interface of free bulk water in contact with the RL for the MXene-CE membranes, or the interface between RL and EL for the Matthew membranes) showed that the movement of water molecules increased after an EL was added (Figs. 5(b) and (c)), such that the permeation of the hydrated ions was enhanced in the presence of water molecules. This finding further illustrates that the EL in the Matthew membrane plays an important role in the fast diffusion of K+ via water movement from the RL to the EL. Based on a comparison between the average release rate of K+ from the CE centers in the Matthew membrane and that in the MXene-CE membrane (Fig. 5(d); Fig. S33 in Appendix A), we inferred that the fast-moving water pushes the ions and promotes their release from the CE centers, thereby creating empty CE sites for subsequent K+ ions coming from the upstream side. The Matthew structure increases ion selectivity without sacrificing ion permeability.

In order to further verify the Matthew effect’s amplification of our asymmetric membrane with an RL and EL for K+/Na+ separation, in addition to the analysis of the RL function as discussed above, the transport behavior of metal ions and water molecules in the bulk solution and the confined surrounding of the EL was simulated via MSD (Fig. 5(e); Fig. S34 in Appendix A). It was clearly observed that the transport of water molecules and ions in a confined channel of the EL was several times higher than that in the aqueous bulk solution, which indicated that the EL can be regarded as an amplifier that promotes the permeation of the K+ previously selected by the RL and thus increases the K+/Na+ selectivity. In comparison, the MXene-CE consists of only an RL but lacks an inducible transport layer EL that can quickly detach the K+ from the affinity site through a steep K+ concentration gradient; thus, the MXene-CE exhibited a poor permeation rate and average selectivity. To sum up, the Matthew membrane consisting of both an RL and an EL exhibits an ultra-fast K+-permeation rate and high selectivity of K+ over Na+.

4. Conclusions

In summary, an MXene-based Matthew membrane was designed and exhibited an outstanding K+-sieving performance with a K+/Na+ selectivity of up to about 9. Experiments and simulations revealed that the excellent performance could be attributed to the following reasons: ① Crown ether incorporation into the RL provides a strong affinity for K+ in comparison with Na+, leading to K+ recognition and selection; and ② the reasonable design of the EL permits faster transport of the K+ enriched in the RL via the confinement effect of the EL, in comparison with the transport of Na+. This smart design of a suitably matching RL and EL endows the asymmetric MXene (Ti3C2Tx) membrane with a Matthew K+-transport amplification effect. The resulting membrane exhibits high K+/Na+ selectivity with fast K+ permeability, based on a combination of a specific K+-recognition effect in the RL and fast transport of the hydrated K+ through the slit-shaped nanochannels between the MXene (Ti3C2Tx) nanosheets of the EL. Considering the remarkable monovalent ion-sieving performance of our Matthew membrane, this work provides new insight into the ion sieving of 2D materials-based membranes. Exploitation of the Matthew effect can be widely used in the fields of efficient high-value ion extraction, sustainable energy utilization, artificial bionic ion channels, brain-computer interfaces, and healthcare.

Acknowledgments

We gratefully acknowledge the support from the National Key Research and Development Program (2021YFB3802500) and the National Natural Science Foundation of China (22022805 and 22078107). This work was supported by State Key Laboratory of Pulp and Paper Engineering (2022PY04) and Fundamental Research Funds for the Central Universities (2022ZYGXZR010).

Compliance with ethics guidelines

Zong Lu, Haoyu Wu, Yanying Wei, and Haihui Wang declare that they have no conflict of interest or financial conflicts to disclose.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.eng.2023.11.025.

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