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# Functionalization of 2D materials for enhancing OER/ORR catalytic activity in Li–oxygen batteries

## Abstract

A major barrier toward the practical application of lithium-oxygen batteries is the high overpotential caused by the precipitation of oxygen-reduction products at the cathode, resulting in poor cyclability. By combining first-principle calculations and reactive molecular dynamics simulations, we show that surface functionalization of 2D MXene nanosheets offers a high degree of tunability of the catalytic activity for oxygen-reduction and oxygen-evolution reactions (ORR/OER). We show that the controlled creation of active vacancy sites on the MXene surface enhances ORR in excess of a factor of 60 compared to graphene-based cathode materials. Furthermore, we find that increasing the ratio of fluorine vs. oxygen termination of the functionalized Ti4N3-MXene catalyst reduces the charge overpotential by up to 70% and 80% compared with commercial platinum-on-carbon and graphene catalysts, respectively. These results provide direct guidance toward the rational design of functionalized 2D materials for modulating the catalytic activity for a wide range of electrocatalytic applications.

## Introduction

Lithium–oxygen (Li-O2) batteries1,2 have attracted significant interest as a promising candidate for rechargeable power sources due to their high theoretical specific energy (3458 Wh/kg) compared with state-of-the-art lithium-ion batteries (265 Wh/kg)3. However, their deployment has been hindered by fundamental challenges such as poor cyclability, large discharge overpotential1, degradation of the cathode material4, and slow oxygen reaction kinetics5.

The operation cycle of Li-O2 batteries involves the oxygen-reduction reaction (ORR) during the discharge and the oxygen-evolution reaction (OER) within the charging process. It is well understood that the kinetics of ORR is sluggish, resulting in a decrease in power density and higher discharge overpotential6. Furthermore, products of the reduction step precipitate on the surface of the cathode, leading to high charge overpotential and poor cyclability of the cell due to their insulating characteristics and sluggish kinetics decomposition7,8. Hence, selecting an appropriate catalyst as cathode material is of fundamental importance to promote ORR/OER.

Thus far, various types of carbonaceous materials, such as carbon nanofibers9,10, graphene11,12, functionalized graphene10, and porous carbon13, have been considered as cathodes in Li-O2 batteries. Among various proposed carbon-based cathode materials, porous carbon loaded with catalytic nanoparticles (either metal or metal oxide) is the most extensively studied material10. Employing catalytic particles reduces the overpotential, thus leading to enhanced cyclability. Nevertheless, noble metal catalyst particles (such as Au, Pt, and MnO2) that are typically used in these systems are quite expensive. Furthermore, their catalytic properties are mostly effective in enhancing ORR rather than OER, for which the high overpotential is more crucial14. In addition, the carbon substrate in these cathode systems is readily oxidized at higher voltage (above 3.0 V)15, thereby reacting with the discharge products in Li-O2 batteries to form lithium carbonate (Li2CO3)16,17. Therefore, identifying a suitable alternative catalyst cathode to carbonaceous material is one of the greatest challenges.

Carbonate-based electrolyte solvents that are used in Li-O2 batteries are known to decompose upon cell discharge, giving rise to deposition of Li2CO312, which acts an insulator by blocking the active sites of the catalyst18. To alleviate issues concerning the instability of organic carbon-based electrolytes, substantial efforts have been devoted to finding alternative solvents. Alkali metal nitrate molten salt electrolytes (e.g., LiNO3-KNO3 eutectic) together with porous carbon cathodes have demonstrated high energy efficiency of ORR through two-electron pathways. In this battery system, the discharge product, lithium peroxide (Li2O2), is stable and moderately soluble in the molten salt electrolyte19. Recently, Xia et al.20 reported a highly reversible four-electron redox Li-O2 cell that was demonstrated to operate for many cycles at high current rates without appreciable degradation in capacity.

Glyme-based material have been recognized as a promising electrolyte due to their good stability toward the oxidation potential of up to 4.0 V. The employment of glyme and ionic liquid-based electrolytes was found to lower the overpotential and enhance the cycle stability21,22. However, these materials suffer low ionic conductivity, and exhibit limited O2 solubility. In another effort, the addition of redox mediators (RMs)23 into the electrolyte solution was recognized to effectively reduce the capacity degradation due to Li2O2 precipitation on the cathode surface by transforming the heterogeneous ORR on the cathode surface to the homogeneous one in an electrolyte solution, resulting in improved discharge capacity. In the reverse reaction, they can decrease the lifetime of superoxide in the Li-O2 battery, leading to the reduction of the overpotential through the 2e pathway. The utilization of RM, such as ethyl viologen (EtV2+), was demonstrated to promote the ORR24 and direct electrochemical decomposition of lithium superoxide (LiO2) through the OER process25.

The emergence of two-dimensional (2D) materials over recent years has offered a number of promising candidates for improving the electrocatalysis of ORR/OER due to their high specific surface area and high surface density of active catalytic sites. Some materials of interest to Li-O2 batteries are nitrogen-doped graphene26, hexagonal boron nitride (h-BN) on Ni surfaces14,27, and molybdenum carbide (Mo2C)28. Layered transition metal-carbide and metal-nitrite MXenes with the general formula of Mn+1Xn, with M being a transition metal and X = {C, N}, are highly stable 2D materials containing 2n + 1 layers of atoms29 (see Supplementary Fig. 1, Supplementary Note 1). In the MXene structure, the X-atom that occupies the inner octahedral site covalently bonds with the three-folded transition metal atoms of the outer layers.

The synthesis of MXene involves selective etching of aluminum from the bulk MAX-phase in the presence of various solutions, such as hydrofluoric acid (HF), hydrochloric acid (HCl), sulfuric acid, and other acidic mixtures and fluoride salt. The chemically exfoliated layers are subsequently rinsed with water30. An example of the latter case is a LiF–HCl mixture, resulting in formation of HF during the etching process31,32,33. Increasing the concentration of LiF can lead to the formation of larger MXene flakes34. This process causes the bare surface of MXene to become functionalized with −O, −OH, and/or −F groups. The formation of functionalized MXene (f-MXene) whose formula is Mn+1NnT2, with T = {O, OH, F} denoting a functional group, makes the basal plane of MXene more stable35. The large specific surface area of MXene and the flexibility of its surface termination motivate the utilization of MXene as cathode catalyst to mediate ORR/OER in nonaqueous Li-O2 batteries. MXene offers the benefit of being considerably less expensive compared with precious metal catalysts and exhibits high chemical and mechanical stability while catalyzing ORR and OER36,37,38. The electric conductivity of MXene due to free electrons of the transition metal and its versatile surface-catalytic chemistry make it a unique material for energy storage, in metal (Li, Na, K, and Ca) ion batteries35,39,40, and for the electrocatalysis in hydrogen evolution reaction33.

In this study, we investigate the feasibility of modulating the overpotential and power density of nonaqueous Li-O2 batteries through the functionalization of titanium-based MXene nanosheets as highly tunable cathode catalysts. By combining first-principle calculations using density functional theory (DFT) and reactive molecular dynamics (rMD) simulations, we identify electrocatalytic pathways at the f-MXene surfaces. Specifically, we report that the surface functionalization of the MXene basal plane leads to significantly enhanced catalytic activities and reduced overpotential of ORR and OER. We show that reduced electronegativity difference between Ti and N, compared with that of Ti and C, along with an increased MXene-sheet thickness and fluorine-surface functionalization reduces the overpotential, ηtot, thereby enhancing the catalytic performance. We find Ti4N3F2 with ηtot ≈ 1.04 V to be the most promising candidate for ORR/OER in nonaqueous Li-O2 batteries. We demonstrate that the enhanced ORR catalytic activity of MXene, which is superior to existing Pt(111) and N-doped graphene catalysts, can be controlled by active vacancy sites on the surface. These results indicate that functionalization in 2D materials is a promising approach for modulating the catalytic activities, thereby enabling the tunability of the overpotential and enhancing the power density of cathode materials in Li-air batteries.

## Results

### Ab initio thermodynamic analysis of charge and discharge processes at low overpotential

In order to examine the electroctalytic performance of MXene surfaces within discharge and charge processes, we first calculate the ORR and OER overpotentials, utilizing the highest level of ab initio simulations based on the PBE/DFT-D241 potential in VASP42,43. We compute the adsorption energies of intermediate discharge lithium oxides (LipOq) products for bare and f-MXene (Tin+1Xn, and Tin+1XnTx, where n = {1, 2, 3}, X = {C, N}, and T = {O, F, V} with V denoting a vacant site) surfaces. These DFT simulations (Computational Details) are validated by calculating the structural properties and the stability of bare and f-MXene, and good agreement with previously reported results44,45 is obtained (see Supplementary Note 2, Supplementary Table 1). Following the approach used by Yun et al.46, the Gibbs free energy of intermediate adsorbate molecules is determined based on their optimized adsorption geometries and the ab initio thermodynamic formalism, which is further explained in the Computational Details.

### Role of surface vacancies to mediate catalytic activities of MXene during discharge

To gain a fundamental understanding about the role of the surface structure of MXene cathode catalysts on mediating the power density, a kinetic analysis is performed by employing rMD simulations using a ReaxFF force field50. We choose the ReaxFF force field because it is well suited to study the energetics of multiphase systems especially in catalytic reactions and because of its demonstrated capability in modeling the catalytic behavior of metal oxide nanoparticles for PdO251, CeO252, and TiO253. The ReaxFF force field parameters are trained to describe Ti/N/Li/O interactions, and the potential is based on an existing parameter set that was validated for studying the intercalation of cations on Ti-C MXene surfaces in aqueous environments54. The detailed description of the developed force field together with the training and validation procedures are provided in Supplementary Note 3.

We consider the abundant MXene surface to be terminated with different coverage ratios of O- and F-functional groups. In addition to studying the effect of the partial pressure of O2 on the ORR rates, we prepare the homogeneous mixture of Li and O2 in four different composition ratios of α = N(O2)/N(Li) = {0.125, 1.0, 2.0, 4.0}.

In these simulations, the formation rate of discharge products is analyzed assuming that the dissociation of O2 molecules gives rise to the formation of Li2O2 through the global reaction 2Li + O2 → Li2O2 (see Computational Details). This assumption was validated by studying the kinetic behavior of ORR in the bulk phase, consisting of a Li/O2 mixture. The ORR rate of the bulk-phase reaction predicted by this model was found to be in good agreement with experimental measurements (see Supplementary Fig. 7).

Snapshots of the rMD simulations at the end of the calculation for a temperature of 300 K are illustrated in Fig. 2. In these simulations, a free-standing single-layer Ti3N2Tx MXene sheet is placed in the center of the simulation box in contact with the Li/O2 mixture in the bulk phase. It is observed that throughout the simulation over 150 ps, O2 molecules react with Li atoms either in the bulk phase or at the MXene surface leading to the formation of LipOq compounds. It is worth noting that when the surface of MXene is not functionalized (see Fig. 2a) the number of unreacted O2 molecules in the bulk phase is markedly less than that covered by O- (Fig. 2b) and F-termination groups (Fig. 2c).

The principal surface reaction steps, observed from the rMD simulations, are shown below the final configurations of Fig. 2. For bare MXene (Fig. 2a), O2 dissociates at the surface (9.75 ps) upon which a chemisorbed O atom reacts with two Li atoms to form Li2O (10.5 ps). The Li2O-complex recombines with neighboring O atoms to form Li2O2 (17.35 ps), and proceeds with the agglomeration into larger Li2O2 clusters (132.5 ps). The Li2O2 formation on fully functionalized O-MXene surfaces (Fig. 2b) is initiated by the diffusion of Li toward the hollow sites and the chemisorption via the formation of three covalent bonds with neighboring O-termination groups (1.25 ps). This is followed by the reaction with an O atom in the gas phase (2.75 ps) to form Li2O; the Li2O combines with another Li atom to form Li2O2 (3.5 ps), leading to the formation of larger Li2O2 clusters (141 ps). In contrast to these chemisorption processes, our calculations show that O2 is physisorbed on the F-terminated MXene surface (Fig. 2c, 14.75 ps), which is followed by the formation of LipOq complexes through the reaction of Li with physisorbed O2 or O2 in the bulk (59.75 and 76.25 ps), and the separation from the surface (112.5 ps).

To examine the surface-mediated ORR kinetics, ternary diagrams for the Li/O2 electrochemical reaction on MXene surfaces are presented in Fig. 3. Every point on these plots represents a different MXene surface composition, which is either vacant (V) or terminated by oxygen (O), fluorine (F), or by a mixture of both. The coverage of each termination group is varied between 0 and 100%. Vertices of each triangle represent a fully covered MXene surface. As will be described later, the ORR reaction in contact with OH-terminated MXene will not be studied here, since it was found not to be a suitable cathode material due to the hydroxide dissociation and the subsequent formation of H2. From this viewpoint, OH-terminated MXene might be more suitable for the catalysis of Li-O2 batteries with aqueous electrolytes. The electrochemical ORRs in the presence of an aqueous electrolyte and OH-terminated MXenes can lead to the formation of LiOH and potentially compensate peeling the H-atom from the OH-terminated MXene surface as observed from the GCMC–rMD simulations in Supplementary Fig. 10 and Supplementary Note 5.

To demonstrate the superior catalytic performance of MXene surfaces in accelerating the reaction of Li and O2, we report ORR rates nearby MXene surface, kMXene; these rates are normalized by those obtained from ORR on pristine graphene catalyst surfaces, kGr, at otherwise identical conditions. Graphene is a prevalent cathode material due to its highly catalytic active surface and large specific surface area10,55. The homogeneous structure of pristine graphene, which only consists of carbon atoms in the sp2-hybridized state, facilitates a direct comparison between the reaction rates of various f-MXene materials. To facilitate a direct comparison, we determine the relative reaction rate constant, $$\overline k = k_{{\mathrm{MXene}}}/k_{{\mathrm{Gr}}}$$, by performing two simulations with identical Li/O2 mixture composition on MXene and graphene (see Computational Details for the procedure of evaluating the ORR rates). The influence of partial pressure on the kinetics of ORR is examined by changing the O2:Li ratio in Fig. 3a–c. The results show that, irrespective of the partial pressure of O2, Ti3N2T2–MXene surfaces exhibit at least a fivefold increase in the ORR rates (compared with the state-of-the-art graphene catalysts), indicating that the basal plane of Ti3N2T2–MXene is electrocatalytic active for ORR enhancement. As illustrated in Fig. 3a–c, among all studied surface-termination compositions, vacancies provide the most effective surface sites for enhancing ORR. Compared with bare and partially f-MXene, increasing the surface functionalization reduces the effective catalysis sites, which results in a reduction in the effective ORR rate (see Fig. 3f). The kinetic analysis of Fig. 3a–c further shows that unterminated MXene surfaces deliver a high exchange current density and therefore enhanced power density compared with fully O- and F-terminated MXene. These results also indicate that for partially terminated MXenes synergistic effects of vacancies with neighboring F- and O-termination groups provide active sites for the O2 dissociation. The enhanced ORR kinetics achieved by introducing vacancy sites on the surface of MXene (Supplementary Table 3) suggest that the basal plane of MXene, which is often functionalized by F- and O-termination groups, is highly tunable for achieving enhanced power density and ORR catalysis by controlling the population of vacancy defects on the surface.

Analysis of the temporal evolution of ORR (see Supplementary Fig. 10) shows that Li2O2 species are rapidly formed (within the first 40 ps). However, the initial Li2O2 formation through the dissociation of O2 slows down and reaches an equilibrium state after approximately t = 150 ps. It is worth noting that the trajectories of our rMD simulations and the species evolutions (Supplementary Fig. 9) show that the final ORR products contain a combination of Li2O and Li2O2. The coexistence of these compounds indicates that ORR involves the disproportionation reaction16,56,57 by which Li2O2 is converted to Li2O and O2. In particular, when the basal plane of MXene is fully functionalized with fluorine, we observe that small clusters of LiO2, which are formed near the surface, diffuse into the bulk phase and react with the remaining Li and O2. A portion of the Li2O2 that detaches from the catalyst surface participates in the chemical disproportionation reaction.

Examining the effect of partial pressure on the ORR rates (Fig. 3) shows that the efficiency of the electrochemical catalysis is significantly affected by the increase in partial pressure of oxygen. In particular, when the MXene surface is terminated by a particular functional group, the ORR rate increases with increasing O2:Li ratio, and is highest for α = 4. This trend is consistent with the experimentally reported ORR kinetic behavior over Pt catalyst surfaces58. However, near bare MXene, ORR is found to become slower at higher O2:Li ratio (see Supplementary Table 2).

The dependence of the ORR kinetic rates on temperature is examined by considering Arrhenius plots in Fig. 3d, e. It can be seen that for fully and partially f-MXenes, the ORR process is endothermic (Fig. 3f). The reduced rates in the presence of O/F-terminated MXenes are attributed to a less adsorptive dissociation of the O2-molecules near F- and O-termination groups compared with that near the bare MXene surface, leading to a higher Li/O2 reaction rate in the gas phase. Nevertheless, when the MXene surface is partially functionalized, even the presence of few vacancy sites on the basal plane significantly alters the ORR kinetics to an exothermic behavior. Due to higher dissociation rates of the reaction between the dissolved O2 molecules and the active vacancy sites, the ORR process over the vacancy-rich MXene surfaces becomes more exothermic. Consequently, fully f-MXenes are not a suitable materials for ORR catalysis. However, due to the low charge overpotential (Fig. 1), they are efficient catalysts for OER.

To assess the kinetic barriers, we compute the apparent electrochemical activation energies (ΔEa). As depicted in Fig. 3f, for the homogeneous Li-O2 mixture and fully f-MXene, the calculated activation energy is positive. In contrast, increasing the concentration of vacancy sites up to 25% may result in a reduction of the apparent activation energy from 450 meV to −50 meV (100 meV to 5 meV) over the partially oxygenated (fluorinated) MXenes. This indicates that the formation of vacancies in F-terminated MXenes leads to the more efficient promotion of ORR. A further increase in the concentration of vacancy sites only has a marginal effect on the reduction of the ORR activation barrier. The functionalization of MXene with F- and O-termination groups increases the ORR activation barrier. In particular, at fully functionalized surfaces, the activation energy is always positive, however, increasing the coverage ratio of F vs. O results in a slight reduction in ΔEa.

The results presented in Fig. 3 demonstrate that for practical applications, the ORR rate and with this the exchange current density and power density of the discharge process can be actively modulated by the surface coverage of the MXene catalyst. The increase in the surface area of electrochemically active vacancy sites results in a faster ORR. These significant advantages of the Ti-based MXene, including the low overpotential of its functionalized surfaces and the tunable catalytic activities due to the formation of surface vacancy sites, are superior to most cathode-catalyst materials that are commonly employed for Li-O2 batteries, such as doped graphene or Pt-based catalysts.

### Electrochemical reaction mechanisms during ORR near MXene catalyst surfaces

Based on the DFT and rMD results, we propose the following principal ORR mechanism at the MXene catalyst surfaces (Fig. 4). Depending on the surface terminations of MXene the peroxide-mediated pathways involve the following steps.

1. 1.

ORR on bare MXene (Fig. 4a):

• Step i—Adsorptive dissociation of oxygen: Upon discharge, both Li and O2 diffuse toward the active vacancy sites. Due to the higher adsorption energy, O2 chemisorbs on the surface: O2 → 2O*.

• Step ii—Lithiation: The adsorbed oxygen is electrochemically reduced and reacts with Li to form lithium oxide: 2O* + Li+ + e→(LiO2)*.

• Step iii—Lithium-peroxide nucleation: Small clusters of Li2O2 nucleate at the surface of bare MXene through an electrochemical reaction between adsorbed lithium superoxide and the MXene surface: (LiO2)* + e + Li + →(Li2O2)*. The overall Li2O2 nucleation reaction can be regarded as a combination of the two elementary reactions from step ii and step iii, through a two-electron transfer mechanism.

• Step iv—Precipitation: Larger clusters of Li2O2 are formed due to the agglomeration of small Li2O2 clusters that are anchored to the bare MXene surface.

1. 2.

ORR on O-terminated MXene (Fig. 4b):

• Step i—Lithiation: Li is first chemisorbed on the oxygenated surface due to its higher adsorption energy compared with that of O2: Li → Li*. The preferred adsorption site for Li is on top of the X-atom (see Supplementary Fig. 2, Supplementary Note 1).

• Step ii—Oxygen chemisorption: Oxygen is adsorbed on the lithiated surface to form lithium superoxide: Li* + O2 → (LiO2)*.

• Step iii—Lithiation: In the presence of an excess of Li+ through the reaction with the intermediate (LiO2)* complex, Li2O2 is formed: (LiO2)* + e + Li+ → (Li2O2)*. Compared with ORR on bare MXenes, the electron charge transfer between the LipOq-adsorbates and the O-terminated surface is weak.

• Step iv—Desorption: The large clusters of Li2O2 desorb from the surface into the bulk Li/O2 mixture.

1. 3.

ORR on F-terminated MXene (Fig. 4c):

• Step i—Oxygen physisorption: On the fluorinated MXene surface, O2 is physisorbed to the surface via weak van der Waals forces.

• Step ii—Lithium oxidation: Li reacts with O2 in the bulk phase to form LiO2: O2 + Li → LiO2. There is a small charge transfer between the F-terminated surface and the adsorbed O2-molecule.

• Step iii—Lithium-peroxide nucleation: The LiO2 molecules weakly bind to the surface, and charge transfer happens between Li and F from the surface: LiO2 → (LiO2)*.

• Step iv—Lithium-peroxide desorption: The LiO2 molecule that is loosely bonded to the surface reacts with another Li atom to form Li2O2: (LiO2)* + e + Li+ →Li2O2. Since Li2O2 detaches from the surface and diffuses into the bulk, ORR near the fluorinated MXene surface mainly proceeds within the gas phase rather than the surface-controlled reaction.

The bare surface of MXene provides active sites for the ORR process (Fig. 4a). By receiving electrons from the conductive MXene, the basal plane is capable of reducing O2 molecules faster than the O/F-terminated surfaces. As a result of the enhanced electron transfer, the rate of ORR, and thus the power and current density of the battery increases, which is confirmed by Fig. 3 and Supplementary Fig. 9). The rate limiting step for O-terminated MXenes is the lithiation step. In contrast, since the electron transfer between the F-terminated MXene surface and LipOq is reduced (Fig. 4c), the Li2O2 molecules that are weakly bonded to the surface diffuse into the bulk phase, reducing the effectiveness of the catalyst surface and reduced reaction rates.

### Effect of surface potential on the discharge process

In order to quantify the stability of the ORR product and to investigate the potential of utilizing MXene as a cathode for Li-O2 batteries, we construct a phase diagram in Fig. 5, showing that N-based MXene adsorbs intermediate discharge products through the thermodynamically favorable 2e pathway, leading to the formation of 2(Li2O2). In analogy to previous analysis on hydrogen electrodes in fuel cells59, the effect of voltage, U, is considered by shifting the chemical potential of electrons by −meU, i.e., ΔG = ΔG0meU, where m is the number of electrons and e is an electron charge. This technique has been successfully used for understanding catalysis activities of Pt(111) and Au(111) surfaces in ORR/OER60. Figure 5a shows that the first lithiation step of ORR on O-MXene, i.e., the formation of LiO2, occurs below 4.03 V. However, the second ORR step is not spontaneous. Rather, the Li2O2 nucleation is initiated when the electrode potential drops to 2.08 V. In contrast, on the F-terminated MXene surface, both LiO2 and Li2O2 nucleate nearly simultaneously below 2.16 V (see Fig. 5b). The third ORR step on O- and F-terminated MXenes, which is the formation of (Li2O2)* and 2(Li2O2), occurs below 1.87 and 1.89 V, respectively. This is represented by the lower stability of (Li2O2)* and (Li2O)* at U  > 1.87 V, which is close to the maximum discharge potential of noble metals, such as Pt and Cu(111) (≈1.99 V)46.

Contrary to the discharge process by which ORR proceeds through the intermediate adsorption of LipOq, the charging process takes place directly by the decomposition of Li2O2 at the interface of the electrolytes and Li2O2 within the OER process. According to the phase diagrams of Fig. 5, beyond 2.22 and 2.8 V, which are the intersections of 2(Li2O2)* and (Li2O2)* lines for O-terminated and F-terminated MXenes, respectively, 2(Li2O2) dissociates to Li2O2, 2Li, and O2. These threshold potentials can be regarded as the minimum charge potentials, which were calculated in Fig. 1. The lower charge potential of F-terminated MXene compared with that of O-terminated MXene strongly indicates that Li2O2 separates easier.

In summary, we have proposed MXene nanosheets as novel and highly tunable 2D materials for the cathode-catalyst of Li-O2 batteries. Through comprehensive mechanistic studies, employing first-principle calculations and reactive molecular dynamics simulations, the favorable reaction pathways for the adsorption of discharge and charge products have been identified. We found that ORR on both bare and f-MXenes proceeds by the 2e pathway. Our calculations demonstrate that functionalization of MXene significantly enhances the catalytic activities of MXene for OER, while the formation of vacancies on the already f-MXene surfaces improve the ORR kinetics by more than a factor of 60 compared with that of graphene-based cathode materials.

These results provide new understanding of the influence of surface functionalization of 2D electrodes to control the electrochemical activity in nonaqueous Li-O2 batteries, thereby paving the way toward the rational engineering of catalyst surfaces for ORR/OER processes.

## Methods

### Quantum mechanical calculations

Plane wave DFT calculations are conducted using the projector augmented-wave (PAW) method61. To examine the electronic exchange correlation function of electrons, the Perdew–Burke–Ernzerhof (PBE) exchange functional with generalized gradient approximation is used. In addition, the DFT-D2 approach is used to consider van der Waals interactions. The valence electrons from the 2 s orbital for Li, and 3d2 4s2, 2s2 2p3, 2s2 2p5, 2s2 2p4, and 1s1 for Ti, N, F, O, and H are expanded on a plane wave basis set. Kinetic energy cut off of 520 eV is used. It is iterated over self-consistent loops until the total energy difference between two adjacent steps is less than 10−4 eV. The structure is relaxed until forces are in the range of 0.02 eV/Å. The Brillouin zone is sampled using 8 × 8 × 1 k-points mesh generated based on the Γ-centered Monkhorst–Pack approach62. The simulations employ 3 × 3 super cells for investigating the adsorption mechanisms, corresponding to chemical stoichiometries of Ti18N9Tx, Ti27N18Tx, and Ti36N27Tx, where T = {O, F, OH} with Li, O2, LiO2, Li2O2, 2(Li2O2), and 2(Li2O) adsorbate species. The vacuum space for the DFT calculations is considered to be ~15 Å on each side.

### Ab initio thermodynamic analysis

Free energy diagrams are constructed based on the adsorption energies pertinent to the most stable configuration of the ORR intermediate products, i.e., (LiO2)*, (Li2O2)*, 2(Li2O2)*, and 2(Li2O)*. The Gibbs free energies of these molecules through the electrochemical adsorption reactions are calculated using the following expression:

$${\mathrm{\Delta }}G = {\mathrm{\Delta }}E_{{\mathrm{tot}}} + {\mathrm{\Delta }}E_{{\mathrm{ZPE}}} - T{\mathrm{\Delta }}S,$$
(1)

where ΔEtot denotes the change in total energy obtained from DFT, ΔEZPE, and ΔS are the changes of the zero-point energy and the entropy at standard conditions (T = 298 K and at potential of 0 V vs. Li/Li+ reference electrode for O2 reduction).

Following Lee et al.63, intermediate reaction steps can be categorized based on their preference for Li and O2 adsorption, such that

$${\mathrm{\Delta }}G_f^0 = G_{{\mathrm{Li}}_p{\mathrm{O}}_q}^0 - pG_{{\mathrm{Li}}_p}^0 - \frac{q}{2}G_{{\mathrm{O}}_2}^0.$$
(2)

The adsorption energies of LipOq intermediates, for a given site, are defined as

$$E_{{\mathrm{ads}}} = E_{{\mathrm{surf}} + Li_pO_q} - E_{{\mathrm{surf}}} - E_{Li_pO_q},$$
(3)

where Esurf is the energy of the surface, $$E_{{\mathrm{Li}}_p{\mathrm{O}}_q}$$ is the energy of molecular LipOq species, and $$E_{{\mathrm{surf}} + Li_pO_q}$$ is the total energy of the system.

It is worth noting that in this method, the lower adsorption energy values, Eads, implies stronger binding between adsorbate molecules and MXene surface. The equilibrium potential for bulk Li–bcc metal, Li2O2 (Föppl structure), and Li2O (antifluorite structure) are obtained from the standard free energies of formation with the following equation:

$$U_{{\mathrm{eq}}} = - \frac{1}{{ne}}\left[ {{\mathrm{\Delta }}G_f^0({\mathrm{Li}}_2{\mathrm{O}}_{2({\mathrm{s}})}\,{\mathrm{or}}\,{\mathrm{Li}}_2O_{({\mathrm{s}})})} \right].$$
(4)

Since volume and entropy changes are negligible for a solid-state reaction, the change in free energy is approximated by the internal energy change ΔE.

### rMD simulations

The rMD simulations are carried out on a mixture of Li and O2 nearby the surface of bare, and f-MXene sheets. MXene nanosheets contain 40 × 30 unit cells. In these calculations, Li and O2 molecules are homogeneously dispersed in a simulation box, with the lateral dimensions (96.7 Å × 83.4 Å × 100.0 Å), corresponding to the x−, y−, and z-direction, respectively. The number of Li atoms is set to be fixed with N(Li) = 2000. However, the ratio of O2 vs. Li is varied to study the influence of oxygen partial pressure.

Periodic boundary conditions are applied along all three directions. The system properties and concentration ratios are chosen to represent experimental operating conditions of Li-O2 batteries57. For each case, the atomic configuration is equilibrated at constant temperature, ranging from T = 200 to T = 1000 K, in increments of 100 K. Prior to performing rMD simulations, the potential energy of the system is minimized to avoid simulation artifacts that are usually caused by excessive close-range and high-energy interactions of atoms. All rMD simulations are performed using the LAMMPS package64,65 in conjunction with a newly developed ReaxFF force field (see Supplementary Note 2). A small time step of 0.25 fs is chosen to ensure that the total energy of the system is conserved within the simulation time frame. The temperature of all rMD simulations is controlled by employing a canonical (NVT) ensemble using Nos–Hoover thermostat with temperature damping constant of 25.0, and the velocity Verlet algorithm is used to integrate the phase space.

### Evaluation of the reaction rate constants

To determine the reaction rates, we consider the Li2O2 formation through the third-order reaction:

$$2{\mathrm{Li}} + {\mathrm{O}}_2 \to {\mathrm{Li}}_2{\mathrm{O}}_2,$$
(5)

with the law of mass action

$$\frac{1}{2}\frac{{d[{\mathrm{Li}}]}}{{dt}} = \frac{{d[{\mathrm{O}}_2]}}{{dt}} = - k[{\mathrm{Li}}]^2[{\mathrm{O}}_2].$$
(6)

By introducing the stoichiometric relations for O2 and Li consumption during ORR66

$$f_s = \frac{{[{\mathrm{Li}}]_0 - [{\mathrm{Li}}]}}{{[{\mathrm{O}}_2]_0 - [{\mathrm{O}}_2]}},$$
(7)

the reaction rate constant, k, can be determined as

$$\left( {1 - f_s\frac{{[{\mathrm{O}}_2]_0}}{{[{\mathrm{Li}}]_0}}} \right)\left( {1 - \frac{{[{\mathrm{Li}}]_0}}{{[{\mathrm{Li}}]}}} \right) + {\mathrm{ln}}\left( {\frac{{[{\mathrm{Li}}][{\mathrm{O}}_2]_0}}{{[{\mathrm{Li}}]_0[{\mathrm{O}}_2]}}} \right) = kt([{\mathrm{Li}}]_0 - f_s[{\mathrm{O}}_2]_0)^2$$
(8)

where the subscript ‘0' denotes the initial concentration.

### Grand canonical Monte Carlo (GCMC)

To further validate the ReaxFF potential description, the open circuit voltage (OCV) is calculated based on a combined GCMC and intermediate rMD simulations. For this purpose, a super cell, consisting of 2 × 2 × 1 unit cells of Ti3N2(OH)2 and Ti3N2(OH)2, is employed. As discussed in Supplementary Note 5, Li atoms from a fictitious reservoir, with chemical potential μLi = −1.62 eV (cohesive energy of Li in Li–bcc), are deposited on the O- and OH-MXene surfaces. During the GCMC simulation, the temperature, T = 300 K, and the chemical potential of the reservoir are maintained under a μ-P-T ensemble. This condition allows the cell dimensions to be relaxed along the basal-plane directions.

## Data availability

Kinetic Study of ORR in the bulk phase, validation of DFT simulations, potential adsorption site on f-MXenes, the ReaxFF force field and DFT calculated values for adsorption energy, binding energies and equation of states of bare and functionalized Ti-N MXenes, the configuration of Li intercalated MXene using GCMC, adsorption energies, and OCV of f-MXene surfaces. Activation energy associated with ORR near MXene with various termination groups and coverages, and the electron difference density of LipOq adsorbed on MXene surface.

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## Acknowledgements

The authors acknowledge the Center for Mechanistic Control of Water-Hydrocarbon-Rock Interactions in Unconventional and Tight Oil Formations, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, and the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. M.I. acknowledges support through the DFG Mercator Fellowship SPP1980 ‘SpraySyn: Nanopartikelsynthese in Sprayflammen'. We benefited from fruitful discussions with Y. Gogotsi and M. Lukatskaya. This research used 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.

## Author information

Authors

### Contributions

M.I. and A.O. designed the research. A.O. developed ReaxFF parameters, performed DFT and rMD simulations. A.O., J.G., and M.I. collaboratively analyzed the data. F.S. contributed to the interpretation of the results. A.O. and M.I. wrote the paper and prepared revisions.

### Corresponding author

Correspondence to Matthias Ihme.

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Ostadhossein, A., Guo, J., Simeski, F. et al. Functionalization of 2D materials for enhancing OER/ORR catalytic activity in Li–oxygen batteries. Commun Chem 2, 95 (2019). https://doi.org/10.1038/s42004-019-0196-2

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