Quantum water desalination: Water generation through separate pathways for protons and hydroxide ions in membranes

Ultrathin 2D materials such as graphene and MoS₂ have been shown to have a high water permeation rate.¹ In the area of water desalination, 2D materials have served as attractive alternatives to conventional membranes like zeolites,² which offer lower water fluxes and require higher energy costs. In addition to sieving ions and unwanted particles out of water, pores can be created in the 2D membranes that are selective toward certain ions. For instance, graphene-based membranes have been used to demonstrate cation selectivity with a high selectivity ratio.^3–5 OH⁻ ion selective membranes are also being explored, where recently, it was found that layered double OH⁻ (LDH) based-membranes can conduct OH⁻ ions and water through 2D nanochannels, while excluding other ions.⁶ OH⁻ ions have also been shown to play an important role in anion exchange membranes,^7,8 where it was shown that the local water structure can enhance or suppress the diffusion of OH⁻ and hydronium ions in water. In addition, OH⁻ ions were shown to diffuse through a vehicular mechanism, whereas protons preferred diffusing through a structural mechanism like the Grotthuss mechanism.⁹ Ultrathin materials like graphene and hexagonal boron nitride (hBN) have further been shown experimentally to conduct thermal protons at ambient conditions via quantum tunneling.^10,11 Protons, due to their small size, can also travel through the interstitials and vacancies available in materials like perovskite oxides¹² and MXenes.¹³ 

MXenes (M_n+1X_n) are a class of 2D materials that have a unique combination of properties like the ease of functionalization and hydrophilicity and, therefore, have found numerous potential applications in electronics, catalysis, energy storage, and optics.^14–18 For instance, spontaneous intercalation of ions has been observed between layers of trititanium dicarbide (Ti₃C₂), which then act as capacitors, enabling them to be used as energy storage devices.¹⁹ Due to their charge transfer kinetics and abundance of catalytic sites, they have also garnered attention as potential alternative electrocatalysts for water-splitting. The activation energy for water dissociation on transition metal carbides ranges from 0.05 to 0.4 eV,²⁰ which makes water dissociation practically spontaneous once it gets adsorbed on the surface. 2D nanoporous membranes can also be created by drilling pores of required size through the 2D materials.

In this paper, we demonstrate quantum desalination of water by using the catalytic properties of defective MXenes. Water molecules first get adsorbed on the surface and dissociate, forming protons and OH⁻ ions in the vicinity of the membrane. We show that the dissociated protons and OH⁻ ions follow two separate paths to translocate through the membrane. Protons translocate through the membrane by hopping from interstitial-to-interstitial and OH⁻ ions translocate through a positively charged, OH⁻ selective pore. The ions then recombine on the other side of the membrane after translocating to generate water. The dynamics of the OH⁻ ion transport are also studied and the barrier for OH⁻ translocation through the membrane is estimated. Alternative quantum water desalination strategies can include separate pathways for proton and OH⁻ transport and subsequent recombination to form water using ultrathin membranes like graphene and hBN where protons would translocate through the membrane by quantum tunneling¹⁰ and OH⁻ ions would translocate through OH⁻ selective pores. The movement of protons, either through interstitials or quantum tunneling, and the dissociation of water on the Ti₂C surface are dominated by electron correlations in the material and, thereby, require the inclusion of electronic contribution to describe their dynamics—signifying the importance of quantum processes. Since the proton transport process is dominated by quantum phenomena, we refer to this approach as quantum water desalination. By combining quantum water desalination techniques with traditional techniques that separate water from ions, water transport through membranes can be significantly enhanced.

To demonstrate quantum water desalination, we design the system as described in Fig. 1(a), where two water reservoirs are separated by the 2D cubic Ti₂C membrane. This membrane is a representative defective MXene and has atoms occupying a cubic lattice (Fd3m space group; materials project identifier mp-10721). For the system under consideration, water first adsorbs on the Ti₂C surface and is catalyzed by the membrane to dissociate into protons and OH⁻ ions. The presence of interstitials in the membrane allows the dissociated protons to travel through the membrane via a hopping mechanism. Furthermore, the dissociated protons and OH⁻ ions can create an induced electric field across the membrane as they move through the membrane, further affecting the transport of protons through the interstitials.¹³ It has to be noted that the interstitials in the membrane are not large enough to allow the OH⁻ ion to pass through. So, in order to translocate OH⁻ ions to the other side, a pore is created in the membrane with the dimensions shown in Fig. 1(b). Sizes of a water molecule and OH⁻ ion are also shown for comparison. Experimentally, it has been shown that Angstrom-sized defects can be created in 2D membranes, examples of which are illustrated in the papers by Ryu et al.²¹ and Thiruraman et al.,²² where ion irradiation was used to create Angstrom-sized pores of diameters between 0.5 and 1 nm.

Due to the negative charge on the OH⁻ ion, it can be expected that positive charges at the pore would increase the Coulombic attraction between the pore and the ion and aid in reducing the barrier for the ion to pass through the pore. In experiments, this can be controlled by adding positively charged functional groups at pore terminations. In Fig. 2(a), we show that when a positive charge is added to the system (see methods for details regarding the design of a positively charged pore), the excess charge localizes around the pore, thereby creating positively charged electron clouds (red contours in the figure). The additional positive charge at the pore increases the barrier for the proton to go through the pore, thereby reducing the total number of protons going through the pore. This is illustrated in the blue curve in Fig. 2(b), which plots the total number of protons going through the pore and is the sum of the number of protons moving in either direction. In contrast, when there is no added charge to the system, the total number of protons translocating through the pore increases with respect to time as observed from the black curve in Fig. 2(b). The selectivity of protons going through the interstitials over protons going through the pore is defined as the ratio of the total number of protons going through the interstitials and those going through the pore. This selectivity is calculated to be 6.33 and 2.47 for the systems with +1 charge and with no charge added, respectively, thereby demonstrating that adding a positive charge reduces the number of protons going through the pore.

To show quantum water transport across the membrane, we track the number of OH⁻ ions translocating across the pore with time in the form of the quantity $OHtrans(L→R)−−OHtrans(R→L)−$⁠, which is the difference between the number of OH⁻ ions translocating from the left-to-right reservoir and from the right-to-left reservoir. We see that the translocation of an OH⁻ ion occurs in jumps, with periods of rest, followed by translocation. In addition, as we do not apply any bias to the system, OH⁻ ions do not have a preferred direction of translocation and are observed to translocate bidirectionally. Following OH⁻ ion translocation, it can combine with a proton to form water. The times at which a water molecule is formed after OH⁻ ion translocation are tracked and shown as red dots in Fig. 3(a). We observe that the time for a proton to combine with a translocated OH⁻ ion ranges from 22.5 to 278 fs, with an average of 91 fs. It was observed from our ab initio molecular dynamics (AIMD) simulations that this proton can either be a proton that has translocated across the membrane or from a neighboring water molecule, facilitated by the Grotthuss mechanism.

In Fig. 3(b), we plot the same quantity as in Fig. 3(a) for water molecules and protons, along with the OH⁻ ions. Upon decomposing the type of protons translocating through the pore, we observe that protons prefer to go through the pore in the form of aqueous protons (H₃O⁺ or H₅O₂⁺). This is in contrast to the protons going through interstitials, which remain as H⁺ ions. The total number of water molecules, OH⁻ ions, and protons going through the pore in the 6 ps of simulation time are counted as 38, 22, and 6, respectively. Water is driven through the pore due to thermal transport, and as the number of water molecules in the system is larger than the number of OH⁻ ions and protons generated due to water splitting on the membrane, higher permeability is observed for water compared to OH⁻ ions and protons. The selectivity of OH⁻ ions over aqueous protons going through the pore is defined as the ratio of the total number of OH⁻ translocations to the aqueous protons and is found to be 3.66. In addition, the size of the pore permits a maximum of two molecules to go through at the same time, and it can be deduced that hydrogen bonding between the molecules plays a role in this. For instance, at around 1700 and 3850 fs, we see a H₃O⁺ ion going through the pore, tagging along with a water molecule. Similarly, OH⁻ ions can also take part in concurrent translocations when hydrogen bonded with water, like those observed at 800 and 3800 fs.

A simple representative mechanism for the driving force for OH⁻ translocation and the strategy for achieving desalination is described in Fig. 3(c). To achieve translocation in a preferred direction, an external bias needs to be applied. An example of such a bias would be a pH gradient, which can be maintained across the membrane, with the right reservoir being maintained at a higher pH than sea water. As sea water has more protons due to lower pH, it will initially be driven to the right reservoir, creating an induced electric field across the membrane toward the left. This electric field will drive the OH⁻ through the pore, which then combines with a proton. The excess protons translocated eventually will move into the bulk in the right reservoir, enabling the quantum transport of water. Comparing the total number of protons translocating through the membrane shown in Fig. 2(b) and the total number of OH⁻ ions translocating through the pore, we can observe that the limiting step in the quantum transport of water is the translocation of OH⁻ ion. Furthermore, a 3 ps AIMD simulation of the system in the presence of 1 Na⁺ and 1 Cl⁻ ion showed that the pore illustrated in Fig. 1(b) excludes these ions, and the behavior of protons and OH⁻ ions is similar to that when the ions are absent from the system.

The ratio of the total number of OH⁻ ions to water molecules translocating through the pore in either direction is 0.58 for a simulation of 6 ps. In addition, extrapolating the number of water molecules transporting across the membrane to a per nanosecond scale, we observe that water generated from the quantum transport of water comes out to around 3000 molecules/ns, compared to 6000 molecules/ns for the conventional transport of water. This indicates that water molecules generated via separate pathways for protons and OH⁻ ions (quantum transport of water) contribute to a significant part of the total number of water molecules translocated across the membrane. The additional water flux generated can potentially be used to improve the effectiveness of 2D membranes used to desalinate water. To further increase the efficiency of quantum water transport, the size of the pore created in the defective MXene can be controlled in a way that only allows OH⁻ ions and excludes water, aqueous protons, and ions in seawater.

To understand the dynamics of the OH⁻ ion as it goes through the pore, we estimate the potential of mean force barriers required for OH⁻ to translocate through the pore using molecular dynamics (MD) simulations. We observe that the OH⁻ ion faces a barrier of 0.12 eV when going through the pore as shown in Fig. 4(a). Assuming Maxwell–Boltzmann statistics²³ and calculating the energy distribution of molecules at 300 K, we estimate that 2.6% of the OH⁻ ions in bulk have the energy required to overcome the barrier. We observe that although MD can capture the dynamics of ions through 2D pores well enough, the dissociation of water molecules on the Ti₂C surface and the induction of the electric field due to translocation of protons through interstitials are not captured in the classical MD simulations used. The actual PMF barriers are, therefore, expected to be lower than the calculated value of 0.12 eV, which, in turn, would increase the fraction of OH⁻ ions having energy greater than the PMF barrier. In Fig. 4(b), the charge density difference map is shown when OH⁻ is in the process of translocating through the pore. We observe that compared to the positively charged electron clouds in Fig. 2(b), the map shows that the magnitude and extent of the positive charge reduce during OH⁻ ion translocation, along with the emergence of pockets of small negative and positive charge clouds (blue and red, respectively) created on the surface of the membrane while OH⁻ is translocating.

To interpret the structural dynamics of the OH⁻ ion, we calculate the number of hydrogen bonds an OH⁻ ion takes part in while it is translocating. We identify a hydrogen bond through the geometry criteria; the distance between oxygen atoms needs to be less than 3 Å and the O–O–H angle is less than 30° for it to be hydrogen bonded. From our simulations, we observe that after water dissociates into its constituents, the protons that go through interstitials in the MXene membrane do not take part in hydrogen bonding when they are inside the membrane. The OH⁻ ions formed diffuse along the surface until they reach the pore due to the interaction with titanium atoms at the interface. The interaction of OH⁻ ions with the membrane prevents them from forming four hydrogen bonds as they would in bulk. For each OH⁻ ion translocation, the number of hydrogen bonds it has is plotted in Fig. 4(c). We observe that the number of hydrogen bonds ranges from 0 to 2. This value is lower than the number of hydrogen bonds observed for OH⁻ ions in bulk, which have 3 or 4 hydrogen bonds.²⁴ The lower number of hydrogen bonds for a OH⁻ ion around the pore can be explained by the reduction in the number of neighboring molecules available for hydrogen bonding around the pore. Snapshots of OH⁻ ions translocating through the pore having 2, 1, and 0 hydrogen bonds are shown in Fig. 4(d), showing the reduced number of hydrogen bonds.

In summary, we demonstrate a mechanism to desalinate water by combining the catalytic prowess of MXenes to dissociate water on the membrane, the availability of interstitials in the membrane to allow protons to translocate through, a positively charged selective pore to allow OH⁻ ions to pass through but suppresses protons with a selectivity of 3.66 toward the OH⁻ ions, and an eventual recombination of the proton and OH⁻ ions to form water. We show from AIMD simulations that water can be desalinated using this mechanism and that the rate of formation of water is limited by the number of OH⁻ ions translocating through the membrane. We also study the dynamics of a OH⁻ ion translocating from MD simulations and estimate a barrier of 0.12 eV for the OH⁻ ion to translocate through the pore. Using the mechanism described in the paper, we show that water molecules generated via quantum processes can significantly enhance the overall transport of water across the membrane.

The analysis of proton transport through a 2D cubic Ti₂C has been carried out using ab initio molecular dynamics (AIMD) with the Vienna Ab initio Simulation Package (VASP).^25,26 The Perdew–Burke–Ernzerhof (PBE)²⁷ exchange-correlation functional, which comes under generalized gradient approximation (GGA), was used, and projected augmented wave (PAW) pseudopotentials²⁸ with an energy cutoff of 450 eV and a gamma-point-centered k-point grid of 2 × 2 × 2 were used. The system used to demonstrate the desalination consists of 60 titanium, 30 carbon atoms, and 160 water molecules, and is shown in the inset of Fig. 3(a). The simulation box has the dimensions of 17.278 × 17.278 × 28 ų and a canonical ensemble (NVT) is used at 300 K, with a timestep of 0.5 fs. At each time step, we track the number of OH⁻ ions, protons, and water molecules with respect to time. We also perform a separate AIMD simulation with 1 Na⁺ and 1 Cl⁻ added to the left reservoir and observe that pore excludes these ions. For the calculation of charge density maps in Figs. 2(a) and 4(b) and to design a OH⁻ selective pore, an excess positive charge is added to the system. In AIMD, the electronic charge density is calculated from density functional theory (DFT),²⁹ which restricts the ability to define charges on individual atoms in the system. However, the total number of electrons in the system can be controlled and removing an electron from the system will give it a charge of +1. In order to maintain charge neutrality in the system, a homogeneous background charge is added by VASP.

MD simulations were performed to estimate the p of mean force (PMF) barriers of OH⁻ ions translocating through the pore in the Ti₂C membrane. These simulations were performed using the large-scale atomic/molecular massively parallel simulator (LAMMPS)³⁰ MD toolkit. Water molecules in the system were modeled using TIP3P potential.³¹ Titanium and carbon atoms in the membrane were frozen and non-bonded interactions between them and water are modeled using the Lennard-Jones potential.³² The interaction parameters between titanium and carbon are taken from Ref. 33. The simulation box has the dimensions of 17.278 × 17.278 × 28 ų, with 160 water molecules and 2 OH⁻ ions. In addition, the system also contains 1 proton with frozen coordinates far away from the pore and a charge of 1 e⁻ is distributed equally among the atoms at the pore. A canonical ensemble (NVT) is used at 300 K, with a timestep of 0.5 fs. The simulations are equilibrated for 5 ns using the isothermal-isobaric (NPT) ensemble. The damping parameters used in LAMMPS for the thermostat and barostat are 2.5 and 25 fs, respectively, under the NPT ensemble during equilibration. For the production run using NVT, the damping parameter used for the thermostat is 2.5 fs. Simulation data of 20 ns are used to obtain the statistics required to ensure a smooth PMF distribution. Potential of mean force (PMF) calculations in Fig. 4(a) are performed on the trajectories obtained from these MD simulations by estimating the average force as a function of the z-coordinate (normal to the membrane) and finally integrating the average force with z.

This work was supported by the Center for Enhanced Nanofluidic Transport (CENT), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0019112. We also acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing the computing resources on Stampede2, Frontera, and Lonestar6 under Allocation Nos. TG-CDA100010, DMR20002, and DMR22008, respectively.

The authors have no conflicts of interest to disclose.

A.R performed simulations, analysis, and wrote the manuscript under the guidance of N.R.A.

Archith Rayabharam: Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). N. R. Aluru: Funding acquisition (equal); Investigation (equal); Methodology (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.