Proton dynamics in water confined at the interface of the graphene–MXene heterostructure

MXenes, two-dimensional (2D) transition metal carbides and nitrides, first discovered in 2011,^1,2 have emerged as a versatile material for various applications, including energy storage,^3–7 membranes,^8,9 electronics,^10–12 sensors,^13–18 and catalysts.^19–22 The high electrical conductivity and high volumetric capacitance make MXenes a promising electrode material for energy storage.²³ Previous experimental studies reported that proton-involved reversible surface redox reaction was the key to the pseudocapacitive behavior of MXene electrodes in the aqueous H₂SO₄ electrolyte,^24,25 while a recent computational study showed that the thickness of the water layer impacts the rates of the surface redox reaction and the proton transport in the MXene-confined water.²⁶ 

Hybridizing MXenes with carbon-based materials (graphene nano-flakes, carbon nanotubes, etc.), metal oxides, or polymers^27–33 has been found to further enhance the performance of energy storage. For example, graphene/Ti₂CT_x@polyaniline composite³⁴ and MXene/reduced-graphene-oxide electrodes⁶ exhibit higher capacitances and excellent cycling stability in the H₂SO₄ electrolyte. However, how the interface of MXene/graphene impacts proton surface redox and proton transport in the electrolyte is still unclear. Recent computational studies have shed light on different heterostructures and their dissimilar interfaces, focusing on the electronic structure of the electrode itself.^35–37 

The experimental studies of MXene/graphene composites and the computational studies of various heterostructures prompted us to seek the fundamental understanding of the capacitive energy-storage mechanism of electrolytes at the dissimilar interface, especially proton redox and transport. To this end, here we explore the effects of the interfacial properties and configurations on proton redox and dynamics in a water layer confined between graphene and MXene layers via ab initio molecular dynamics (AIMD). The proton was chosen because of its fast surface redox reaction and transport in water during the pseudocapacitive energy-storage process in MXenes that is accessible to the timescale of AIMD.³⁸ We chose Ti₃C₂O₂ as a representative MXene, whose –O termination will be partially converted to –OH in an acid electrolyte after binding with a proton. Below we first elaborate on our computational methods.

The Vienna ab initio simulation package (VASP^39,40) was used for both structure optimization and AIMD simulations based on density-functional theory (DFT) with periodic boundary conditions. The electron–ion interactions were described by the projector augmented-wave method,^41,42 while electron exchange–correlation by the Perdew–Burke–Ernzerhof (PBE⁴³) functional form of the generalized-gradient approximation (GGA). The kinetic energy cutoff of 500 eV was used for the plane-wave basis set. Grimme’s DFT-D3 method with the Becke–Jonson damping⁴⁴ was used for the van der Waals (vdW) interactions.^45,46

To model the dissimilar interface, we used a monoclinic supercell for both graphene–MXene (a 4 × 4 supercell of Ti₃C₂O₂ matched to a 5 × 5 supercell of graphene with a lattice mismatch of ∼1.3%). For comparison, we also examined the MXene–MXene interface (a 4 × 4 supercell of Ti₃C₂O₂). To avoid dipoles along the c direction, symmetric cells are used to model water/proton confined in graphene–MXene and MXene–MXene interfaces (Fig. 1). For convenience, MO_MO and G_MO_G denote Ti₃C₂O₂–Ti₃C₂O₂ and graphene–Ti₃C₂O₂–graphene systems, respectively. Each interface contains a single water layer of 12 water molecules and 0–3 protons; the whole simulation cell is charge neutral. We use “np” to denote the number of protons being intercalated, e.g., G_1p_MO_1p_G means one proton per interface of graphene–Ti₃C₂O₂.

The supercells were structurally optimized with convergence criteria of 0.02 eV/Å in force and 10⁻⁵ eV in energy; the Brillouin zone was sampled by the 3 × 3 × 1 Monkhorst–Pack grid.⁴⁷ Coordinates for the optimized structures are provided in the supplementary material, and the optimized c-lattice parameters, corresponding to the supercells in Fig. 1, are presented in Table I. With the optimized structures as input, AIMD simulations were performed via the canonical ensemble (NVT) with the Nosé–Hoover thermostat at 300 K for 20 ps at 1 fs timestep^48–50 with Γ-point only for the k-point sampling. The last 15 ps of trajectories were used for the analysis. Proton movement was tracked by monitoring the hydronium O atoms; the diffusion coefficient was calculated from the Einstein relation and the time-dependent mean square displacement. See the supplementary material for details.

The goal of the present work is to reveal how the dissimilar interface of Ti₃C₂O₂–graphene impacts proton redox chemistry and transport. To simplify the problem, we used a monolayer of water but varying proton concentrations. Both in-water proton transfer and reversible surface redox processes of the proton can take place at the Ti₃C₂O₂–graphene interface where protons in hydronium ions (H₃O⁺) transfer to O atoms on Ti₃C₂O₂ surface to form hydroxyl groups (–OH), which, after a certain time interval, can release protons back to water molecules. Graphene, on the other hand, is inert, with respect to proton redox chemistry. From the AIMD trajectories, we tracked the events of in-water proton transfer vs surface redox reaction. As shown in Fig. 2(a) for the Ti₃C₂O₂–graphene interface, in-water proton transfer is much more frequent than the surface redox reactions, which as the concentration of proton increases become more frequent. Compared with the Ti₃C₂O₂–Ti₃C₂O₂ interface [Fig. 2(b)], surface redox reactions are much more frequent at the Ti₃C₂O₂–graphene interface. In the case of three protons, the estimated surface redox rate is 634 m/s at the Ti₃C₂O₂–graphene interface (G_3p_MO_3p_G), about nine times than that at the Ti₃C₂O₂–Ti₃C₂O₂ interface (MO_3p_MO). Therefore, both interfacial proton concentration and interface compositions can impact the proton surface-redox behavior. Below we analyze the proton mobility in detail.

By tracking the O atoms with an extra hydrogen atom such as O in the hydronium ion (H₃O⁺) or the hydroxyl O on Ti₃C₂O₂ surfaces (Fig. S1) and evaluating their root-mean-square displacements (Fig. S2), we determined the proton diffusion coefficients at the Ti₃C₂O₂–graphene and Ti₃C₂O₂–Ti₃C₂O₂ interfaces. As one can see from Fig. 3, proton diffusivity decreases with the increasing proton concentration at the Ti₃C₂O₂–Ti₃C₂O₂ interface but shows a maximum at two protons per water layer at the Ti₃C₂O₂–graphene interface. Although it is about the same at one proton per water layer for both interfaces, proton diffusivity in Ti₃C₂O₂–graphene is more than twice that in Ti₃C₂O₂–Ti₃C₂O₂ at two or three protons per water layer. In other words, at higher proton concentrations, proton diffusivity is much higher at the dissimilar interface than at the similar interface. Below we analyze the proton diffusivity in detail in order to understand the two different trends in Fig. 3.

Since the proton can be either in H₃O⁺ or in –OH group on Ti₃C₂O₂, we have estimated the probabilities of the proton in the two states from the AIMD trajectories. As shown in Table II, the proton remains in the water layer almost all the time in the case of one or two protons in the Ti₃C₂O₂–graphene interface. We further tracked the hydronium ions in these two cases (Fig. 4): one can see that the motion of the one hydronium ion is restricted in one region and half of the space is rarely explored [Fig. 4(a)] in the 1p case, but the two hydronium ions now explore almost all the interfacial space [Fig. 4(b)] in the 2p case. In the case of 3p, they roughly split the time equally in water or on the Ti₃C₂O₂ surface (Table II). This can explain the decrease in the overall proton diffusivity because the proton in –OH group on the Ti₃C₂O₂ surface is much less mobile than in water, as evidenced by the localized proton sites and more unexplored space at the interface [Fig. 4(c)].

Next, we analyzed proton mobility at the Ti₃C₂O₂–Ti₃C₂O₂ interface for comparison. In all three proton concentrations, we found that proton prefers to stay in water 99% of the time, so proton diffusion is dominated by the in-water proton transfer. From the trajectories of hydronium ions (Fig. 5), we found apparent gaps between different hydronium trajectories; in other words, proton motion is localized, and the more the protons, the more localized, leading to the decreasing trend of proton diffusivity in the Ti₃C₂O₂–Ti₃C₂O₂ interface.

Comparing proton diffusivity (Fig. 3) and trajectories at the dissimilar Ti₃C₂O₂–graphene interface (Fig. 4) and the similar Ti₃C₂O₂–Ti₃C₂O₂ interface (Fig. 5), the most striking feature is the opposite trend from one to two protons in the water layer. Two factors may contribute to this different trend in proton mobility in water: (i) water mobility itself and (ii) water structure. We found that water diffusivity in the dissimilar Ti₃C₂O₂–graphene interface decreases sharply with proton concentration (Fig. S3), so we can rule out water mobility in accelerating proton mobility at the Ti₃C₂O₂–graphene interface.

We next turn our attention to the water structure at the interface. The radial distribution function (RDF) and coordination number of the O_water–O_water and O_water–H are plotted in Fig. 6. When changing from G_1p_MO_1p_MO to G_2p_MO_2p_MO, both the O_water–O_water peak [Fig. 6(a), from 2.8 to 2.4 Å] and H-bond peak [Fig. 6(b), from 1.8 to 1.6 Å] shifted left, indicating shortened distances and denser hydrogen-bond networks within the interface. We also investigated the water dipole orientation and OH bond orientation (Fig. 7). One can see that as proton concentration increases, the orientation of the water dipole [Fig. 7(b)] shifts to the region at ∼52°, and the O–H bonds [Fig. 7(c)] are aligned toward two regions (10°<β < 30° and 80°<β < 110°). Because the H–O–H angle in water is about 105°, the results in Fig. 7 suggest the formation of more directional water structures with one OH bond from water molecules pointing directly toward the Ti₃C₂O₂ surface, leading to the denser hydrogen-bond network (Fig. 6). This is the reason for enhanced proton mobility in G_2p_MO_2p_MO, as further supported by the analysis below.

We think that the interfacial charge transfer and the resulting polarization are the reasons behind the denser and more oriented water structure at the Ti₃C₂O₂–graphene interface. In the case of MXene/graphene heterostructures without the electrolyte, the charge transfer has already been shown to be from graphene to Ti₃C₂O₂.³⁷ We further confirmed that this is also the case when water/hydronium molecules are presented in the Ti₃C₂O₂–graphene interface from a detailed Bader charge analysis (Fig. S4). In other words, an interfacial electric field directed from graphene to Ti₃C₂O₂ across the water/hydronium layer will always be there [Fig. 8(a)], which aligns water molecules. Such field is missing in the similar Ti₃C₂O₂–Ti₃C₂O₂ interface [Fig. 8(b)]. As more protons are intercalated into the Ti₃C₂O₂–graphene interfaces, the greater interfacial electric field across the water/hydronium layer causes stronger interfacial interactions and shorter O_water–O_MXene distances (Fig. S5). This closer interaction together with the aligned O–H bonds pointing toward surface O atoms on Ti₃C₂O₂ surfaces enhances proton transfer both in water and across the Ti₃C₂O₂–graphene interface. We note that, as done previously, plotting the average electrostatic potential^51,52 and the charge-density variation⁵³ is a more accurate approach to describe the interfacial polarization, instead of using the partial atomic charges such as the Bader charges due to the certain arbitrariness in partitioning the electrons to atoms; nevertheless, the Bader charges have been shown to correlate well with the interfacial polarization across the heterostructure interface.^37,54 In addition, the interfacial polarization as shown in Fig. 8(a) is not a result of the symmetric cell that we have used, because a similar amount of charge transfer in the same direction was also found at the interface in the asymmetric cell that we tested.

Nuclear quantum effects (NQEs) have been shown to be important in describing proton diffusion in confined water^55,56 but they tend to be very computationally expensive to include. The present AIMD shows a picture of proton diffusion in a monolayer of water confined in the Ti₃C₂O₂–graphene interface by treating the proton as a classical particle with the forces derived from DFT within the Born–Oppenheimer approximation. Looking ahead, it would be more desirable to include NQEs for a more accurate description of proton motion in confined water, with efficient approaches such as machine learning.⁵⁵ 

Reorganization of the hydrogen-bond work has been shown to be important in proton transport in bulk water⁵⁷ and auto-protolysis of water.⁵⁸ In our systems, the water molecules being just one-monolayer thick are very different from the bulk in that they are interacting very strongly with both graphene and the MXene surface. So the reorganization of the hydrogen bond network is slow by our AIMD timescale. We have previously found that, once there are three water layers in the interface, the proton and water dynamics begin to resemble the bulk.²⁶ Further simulations on these thicker confined water/proton systems in the Ti₃C₂O₂–graphene interface, together with the analysis of the associated reorganization of the hydrogen bond network, are warranted to shed light on how the Grotthuss mechanism⁵⁹ might be modulated by the interfacial polarization.

In our Ti₃C₂O₂–graphene interface, we have used both an ideal termination for Ti₃C₂O₂ and a perfect graphene layer. In real experiments, there will be defects and functional groups due to the chemical processing of the building blocks. For example, –OH and –F groups are often present on the Ti₃C₂-based MXenes,⁶⁰ while graphene oxides are most used to produce solvent-processable graphene flakes via various reduction pathways, inevitably leaving O-containing functionals and defects on the graphene sheet.⁶¹ Hence, it is highly desirable for future simulations to incorporate those functional groups and defects in their models of the interfaces for confined proton transport, to better guide the experimental efforts.

Using ab initio molecular dynamics, we have examined proton transfer and surface redox chemistry as water-solvated hydronium ions confined in the graphene–Ti₃C₂O₂ heterostructure. In comparison with the similar interface of water confined between Ti₃C₂O₂ layers, we found that the proton redox rate is much higher in the graphene–Ti₃C₂O₂ interface due to the formation of a denser hydrogen-bond network with a preferred orientation of water molecules as a result of the interfacial charge transfer and the resulting electric field. This denser and more directional hydrogen-bond network also leads to an optimal proton concentration where in-water proton mobility reaches the maximum in the graphene–Ti₃C₂O₂ interface. Our work shows that the dissimilar interface offers greater opportunities in tuning interfacial structure and properties to achieve faster proton transfer and redox in the confined water.

See the supplementary material for details of diffusivity calculations, Bader charges across the interfaces, the analysis of water–MXene interaction, and coordinates for the simulated systems.

This research was sponsored by the Fluid Interface Reactions, Structures, and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy. This research used the resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

The authors have no conflicts of interest to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.