Models and Regulations of MXenes.

MXenes are prepared by selectively etching the layers of “A” element atoms from their layered MAX precursor phases, which are a large family of ternary carbides and nitrides with more than 70 experimentally reported examples thus far (36). The general formula of MAX is M_n+1AX_n, where M represents an early transition metal, A is an A-group element (mostly groups IIIA and IVA), X is carbon and/or nitrogen, and n = 1, 2, or 3 (i.e., M₂AX, M₃AX₂, or M₄AX₃). In MXenes, n + 1 M layers cover n layers of X in an [MX]_nM arrangement (37), such as Ti₂CT_x (38), Ti₃C₂T_x (39), and Nb₄C₃T_x (40), where T_x stands for the surface terminations (hydroxyl, oxygen, or fluorine) (41). Therefore, taking 2D TMCs as representative, we illustrate the four modification schemes in Fig. 1 by changing the transition metal species, layer thickness, surface functional group and mechanical strain. A structural optimization is performed for each 2D TMC (M₂C, M₃C₂, M₄C₃, and M₂CT₂), and the calculated equilibrium M–C bond lengths and lattice constants are listed in Table 1, which show good agreement with those in previous publications (23, 25, 41⇓⇓⇓–45).

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Fig. 1.

Four methods to modify 2D TMCs, namely, changing the transition metal species (A), strain (B), layer thickness (C), and surface functional group (D). Red circles marked in E and F show two different adsorption sites (i and ii) of surface functional groups in vertical views.

Mechanical Stability.

To predict the performances of 2D TMCs as flexible devices, investigating the mechanical properties, such as elastic stiffness, flexibility, and ideal strength, under various deformations is essential. In studying the intrinsic mechanical responses of 2D TMCs to tensile strain we considered three loading conditions (Fig. 1B): biaxial tension, uniaxial tension along x direction (the zigzag direction), and uniaxial tension along y direction (the armchair direction). Fig. 2 A and D present the calculated stress-strain curves for Ti₂C and Zr₂C under both biaxial and uniaxial load conditions. It is observed that Ti₂C (Zr₂C) can sustain large strains of 8 (12)%, 16 (16)%, and 18 (17)% under biaxial and uniaxial tensions along the x and y directions, respectively. Fig. S3 presents the stress-strain relationships for Ti₂C, Ti₃C₂, and Ti₄C₃, and an increase of layer thickness is shown to improve the critical strain. As reported in previous X-ray photoelectron spectroscopy and energy-dispersive X-ray spectroscopy analyses, MXenes are generally terminated with various functional groups, such as O, OH, and F (16, 17, 46), and consequently their electronic structures and electrochemical performances are strongly influenced by these functional groups (42, 47). Thus, an in-depth understanding of the effect of functional groups is critical to pursue an excellent performance. Experimentally, a high temperature induces the conversion from -OH to -O termination based on the reaction -OH + -OH → -O + H₂O (47). Therefore, here, we only focus on -F and -O terminations. As shown in Fig. 2C, Ti₂CO₂ can sustain large strains of 19%, 24%, and 29% under biaxial and uniaxial tensions along x and y direction, respectively, which are obviously larger than the corresponding strains of Ti₂C (8%, 16%, and 18%) and graphene (15%, 20%, and 24%) (48). Compared with Ti₂C (biaxial 8%), Ti₂CF₂ can sustain a larger biaxial strain of 20% (Fig. 2B). Similar to Ti₂CO₂ and Ti₂CF₂, the surface groups can also increase the critical strain of Zr₂C (Fig. 2 D–F). Surface groups (O and F) considerably slow down the collapse of the transition metal layers induced by strain and provide more mechanical flexibility to the 2D TMCs (23). In addition to pure tensile strain, we performed a global exploration of in-plane strains, including both tension and compression. Interestingly, as shown in Fig. S4, a compression strain induces a lattice instability at smaller critical strain in graphene, whereas Ti₂C and Ti₂CO₂ can tolerate higher compression strains up to 8%, suggesting that 2D TMCs may be more promising as flexible materials compared with graphene.

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Fig. 2.

Strain-stress relationships for (A) Ti₂C, (B) Ti₂CF₂, (C) Ti₂CO₂, (D) Zr₂C, (E) Zr₂CF₂, and (F) Zr₂CO₂ under both biaxial and uniaxial load conditions.

Ionic Mobility.

The rate capability is a crucial factor in the design of promising electrode materials. For example, in cell phones or electric vehicles the full charge time is critical for device usability, while the discharge rate dominates the amount of power that can be delivered in the battery. The rate capabilities of LIBs critically depend on the Li⁺ and electron diffusion rates. According to the reported transition state, Li hopping is regarded as the microscopic mechanism for Li diffusion. Each individual hopping pathway must overcome the Gibbs free energy of activation ΔG during diffusion. The diffusion rate k at which the hopping process occurs can be expressed as (49)k(T)=v∗(T)e−ΔGkBT,[1]where v∗ is the temperature-dependent effective attempt frequency, kB is the Boltzmann constant, and T is the temperature. Neglecting the entropy change during diffusion, ΔG can be approximated by the activation energy ΔE=Et−Ei, where Et and Ei are the energies of the transition and initial state, respectively. Typical values for the prefactor v∗ in Eq. 1 are 10¹¹ to 10¹³ s⁻¹ (50). When the hopping distance a is known, the ionic diffusivity can be approximately obtained from D(T)=a2k(T) (51). Since quantitative data and mechanistic information are hard to obtain in experiments, the theoretical calculations are powerful tools to provide elaborate information on Li diffusion (30). The climbing image nudged elastic band (CI-NEB) method (52) provides an efficient algorithm to compute transition state energies in a quantitative manner.

During the charging/discharging process, the electrode polarization inevitably occurs in LIBs and accordingly an exploration of the influence of polarization on the Li⁺ diffusion is much demanded. Therefore, we considered two cases: (i) the unpolarization state (i.e., if there is negligible electrical current, the electrode potential keeps a constant; it should be noted that the adsorbed Li atoms become partially ionized because of the sufficient charge transfer between Li and the anode when an Li atom intercalates into the anode) and (ii) the charge-transfer polarization state (i.e., if the electrical current passes through LIBs, the electrode potential deviates from the equilibrium value, and this phenomenon is called the electrode polarization) (31). When the polarization is generated by the charge transfer reaction it is termed charge transfer polarization. In addition, external charge, electric field, vacancy, and impurities generally disturb the charge distribution at the surface of an electrode (32⇓⇓–35).

As a proof of concept, an evaluation of the diffusion barrier, charge, and adsorption height on graphene was first performed under both cases and a similar trend was observed (Fig. S6). In our calculations of the adsorption energy, equilibrium voltage, and theoretical capacity, the unpolarization state is adopted to focus on the equilibrium state involving the surface-adsorbed Li with no electrical current passing through. In our calculations of the ionic mobility, the charge-transfer polarization state is assumed to simulate the dynamic process of Li⁺ diffusion while passing electrical current. Afterward, the Li⁺ diffusion barriers on the charged 2D materials are systematically investigated, and the corresponding energy profiles as a function of the diffusion coordinate are presented in Fig. 3 A–E and Fig. S5.

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Fig. 3.

Potential-energy profiles of Li⁺ diffusion on the charged surfaces of (A) pristine Ti₂C, Zr₂C, and Hf₂C; (B) pristine Ti₂C, Ta₂C, Mo₂C, s-Ta₂C, and s-Mo₂C; (C) pristine Ti₂C, Ti₃C₂, and Ti₄C₃; (D) pristine Ti₂C, Ti₂CF₂, and Ti₂CO₂; and (E) pristine Ti₂C, MoS₂, and graphene. Potential-energy profiles of Li⁺ diffusion on the charged surfaces of (F) Ti₂C, (G) Ti₂CF₂, and (H) Ti₂CO₂ under biaxial strain. Schematic representations of the diffusion paths are shown in the Insets. ΔE represents the corresponding diffusion barrier.

Influence of transition metal and thickness.

For bare 2D TMCs the minimum energy pathway (MEP) occurs from the site on top of the metal atom to the site on top of the C atom and then to another site on top of the metal atom. The calculated lattice constants vary distinctly among Ti₂C, Zr₂C, and Hf₂C, which allows a comparative study on the effect of lattice constants by neglecting the influence of the valence electron numbers (VENs). The barriers for Ti₂C, Zr₂C, and Hf₂C are calculated to be ∼16 meV, 29 meV, and 20 meV, respectively (Fig. 3A), and therefore, the Li⁺ diffuses exceptionally quickly on them. Notably, the M–C bond lengths in Ti₂C, Zr₂C, and Hf₂C are 2.102 Å, 2.278 Å, and 2.238 Å, respectively, which follows interestingly the order of the calculated diffusion barriers. A similar trend between the bond lengths and diffusion barriers is also found for pristine Mo₂C and W₂C, which possess the same VEN but different lattice constants (Fig. S5A), providing a general rule that a smaller M–C bond length corresponds to a lower Li⁺ diffusion barrier on the surface of the charged 2D TMCs. However, the energy barriers of W₂C and Mo₂C are larger than that of Ti₂C; simultaneously, the M–C bond lengths of these two species are smaller than that of Ti₂C. To explore the influence of VEN on the energy barrier, we forced the lattice constants of Ta₂C and Mo₂C to be equal to that of Ti₂C by applying strain to eliminate the influence of the bond length. As shown in Fig. 3B, the barriers of Ti₂C, Ta₂C under strain (s-Ta₂C), and Mo₂C under strain (s-Mo₂C) are calculated to be ∼16 meV, 22 meV, and 32 meV, respectively, indicating that a smaller VEN corresponds to a lower Li⁺ diffusion barrier on the surface of the charged TMCs. Interestingly, the energy barrier increases remarkably by 40% at a 3% strain for Mo₂C, indicating that the strain may greatly influence the energy barrier, as will be discussed in the next section. Although large differences exist in the layer thicknesses between pristine Ti₂C (4.828 Å), Ti₃C₂ (7.269 Å), and Ti₄C₃ (9.794 Å), their diffusion barriers are nearly identical [i.e., 16 meV (Ti₂C), 18 meV (Ti₃C₂), and 15 meV (Ti₄C₃), respectively], suggesting that the layer thickness has a negligible influence on the Li⁺ mobility on the charged 2D TMCs.

Before continuing our further investigation, the transport properties of 2D TMCs should be compared with those of graphene, a widely studied system for electrode materials. Clearly, the calculated energy barriers of Li⁺ diffusion for all of the bare 2D TMCs are one order lower than that of graphene (152 meV), supporting bare 2D TMCs as promising anode candidates for LIBs (53). To determine the physical origin for the energy barrier changes we further investigated the electronic interactions between the Li⁺ and 2D TMCs. Bader charge analysis is used to quantify the charge transfer between Li⁺ and the substrate. First, the Li⁺ charges at all points along the diffusion path on Ti₂C are calculated (Fig. 4A). The increasing energy barrier follows the same trend as the electron charge reduction, concluding that the charge difference (∆e = e_S − e_T) between the stable site (e_S) and transition site (e_T) can also be used to determine the Li⁺ transport barrier height. Second, to verify this conclusion, the Li⁺ charges at all of the points along the diffusion path on graphene are calculated, and a similar trend is observed (Fig. S6 A and B).

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Fig. 4.

(A) Relative energy, charge, and adsorption height of Li⁺ diffusion on the charged Ti₂C. Charge differences of Li Δe and barriers of (B) Ti₂C, Ti₂CF₂, Ti₂CO₂, Zr₂C, Zr₂CF₂, and Zr₂CO₂ and (C) Ti₂C, s-Ta₂C, s-Mo₂C, MoS₂, and graphene. TDOS and PDOS of Li on (D) Ti₂C, (E) Ti₂CF₂, and (F) Ti₂CO₂. The Fermi levels are set to zero and indicated by the dashed lines.

Uniaxial stress effect.

To explore the uniaxial loading effect we applied a uniaxial stress scheme by dynamically adjusting the in-plane strain components that are orthogonal to the stress component. Under a uniaxial stress state, tension/compression stress (not strain) exists in a certain direction, and, accordingly, the effects of uniaxial stress along the x axis and y axis are opposite (i.e., the effect of the x-axis in-plane tension is similar to that of the y-axis compression). Therefore, we took Ti₂C under x-axis stress as a representative to explore the uniaxial stress effect on the diffusion behavior of Li⁺. Fig. 5A shows the energy barriers along the two transport pathways (path I and path III) during tensile and compression loading along the x-axis direction, while Fig. 5B shows the energy barriers along path II and path III. Since path I is completely symmetrical with path III, path I is studied. Both the Ti–C bond length and energy barrier of path I (III) simultaneously increase (decreases) as the x-axis strain increases (Fig. S11), again demonstrating that the energy barrier increases with an increasing Ti–C bond length. To better clarify the energy barrier difference along the different paths, a relative factor is defined as δ=ΔEI/ΔEII, where ΔEI and ΔEII are the energy barriers along path I and path II, respectively. As shown in Fig. 5C, the δ value increases as the strain increases. At equilibrium, δ=1 indicates that the energy barrier along path I is equal to that along path II. These results reveal that the Li⁺ prefers to diffuse between all of the hollow sites. When a compressive strain is applied (i.e., δ<1), the Li⁺ is more likely to transport along path I and path III. A higher compressive stress results in a smaller δ and a greater tendency for transportation along path I and path III. When tensile stress is applied, δ>1, which favors Li⁺ transport along path II. Therefore, the uniaxial stress can efficiently modify the Li⁺ diffusion path. Nevertheless, the energy barrier along the preferred transport pathway will be reduced by either uniaxial tensile or compressive stress. Among all of the studied 2D TMCs, Ti₂C possesses the lowest energy barrier under either uniaxial or biaxial loading and therefore is an excellent candidate as a promising flexible LIB anode.

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Fig. 5.

Potential-energy profiles of Li⁺ diffusion on the charged surface of Ti₂C under uniaxial strains along (A) path I and path III and along (B) path I and path II. Schematic representations of the diffusion paths are shown in the Insets. (C) Relationship between δ and the uniaxial strain. Path I and path III are along the zigzag path, and path II is along armchair path.

Equilibrium Voltage and Theoretical Capacity.

The energy density is another crucial factor in designing promising battery materials. Increasing the cell voltage without exceeding the electrolyte stability window is a promising strategy to enhance the energy densities of LIBs. The equilibrium Li intercalation voltage can be expressed as (30)V=−μLicathode−μLianodezF,[2]where μLicathode and μLianode represent the Li chemical potentials of the cathode and anode, respectively, z is the transferred charge, and F is the Faraday constant. The average voltage as a function of the free energy change of the combined anode/cathode reaction is calculated using the following equation (30):V¯=−ΔGrzF.[3]At 0 K, the reaction free energy can be approximated by the internal energy, that is, ΔGr=ΔEr. Therefore, the charging/discharging processes of 2D TMCs follow the common half-cell reaction:(x2−x1)Li++(x2−x1)e−+Mn+1CnLix1↔Mn+1CnLix2.[4]Considering the above reaction, the average voltage of M_n+1C_nLi_x in the concentration range of x1≪x≪x2 is obtained byV¯(x1, x2)≈E(Mn+1CnLix1)−E(Mn+1CnLix2)+(x2−x1)E(Li)(x2−x1)F,[5]where E(Mn+1CnLix1),E(Mn+1CnLix2),and E(Li) represent the internal energies of Mn+1CnLix1,Mn+1CnLix2 and body-centered cubic Li, respectively. The equilibrium voltage between the intermediate phases can be calculated using Eq. 5 after all structures of intermediate phases are determined. Courtney et al. (59) calculated the 0-K voltage profile of the Li-Sn alloy, demonstrating excellent agreement with the experimental voltage curves. However, the intermediate phases cannot always be experimentally obtained, yet first-principles computations provide a suitable pathway for the prediction of stable phases (60). Since the formation energy with respect to stable reference materials quantifies the relative stability of different phases, the following equation is thus used to calculate the formation energy of Mn+1CnLix with an intermediate Li content:Ef(Mn+1CnLix)=E(Mn+1CnLix)−x2E(Mn+1CnLi2)−(1−x2)E(Mn+1Cn),[6]where E(Mn+1CnLi2) and E(Mn+1Cn) are the internal energies of the fully lithiated Mn+1CnLi2 and delithiated Mn+1Cn, respectively (61, 62).

Fig. 6A shows the calculated formation energies and the resulting 0-K voltage profiles for Li adsorption on Ti₂C. The formation energy of Ti₂C reaches the lowest value at the Li concentration of 0.88, and the subsequent 0-K voltage profile simulates the first charging/discharging process of the corresponding LIB. As the Li concentration increases the voltage of Ti₂C remains at ∼0.4 V, whereas for Ti₂CO₂ the voltage gradually declines from 2 to 0.8 V and remains stable at 0.8 V (Fig. 6D). To determine the stability of the voltage variation in the charging/discharging process, the voltage of the first Li adsorption is defined as the initial voltage, and a smaller difference between the initial and average voltage indicates a more stable voltage in the charging/discharging process. The initial and average voltages of other bare 2D TMCs (M₂C, M = Ti, Zr, Hf, Ta, Mo, and W) are also calculated and compared in Fig. 6C. It is found that the voltage is primarily dominated by the VEN, that is, the initial and average voltages increase as the VEN increases, except for W₂C. Fig. S13C shows that the initial and average voltages of Ti₂C, Ti₃C₂, and Ti₄C₃ are nearly identical, indicating that the layer thickness has a negligible effect on the voltage. A desirable potential ranges from 0.1 to 1 V for anode materials, suggesting that all of the bare 2D TMCs are good candidates for low-voltage battery applications. Moreover, the strain effect on the voltage is also considered. Under biaxial strain, the initial and average voltages of Ti₂C are maintained at ∼0.4 V, while the initial voltage of Ti₂CO₂ dramatically changes (Fig. 6 B and E). Therefore, compared with Ti₂CO₂, Ti₂C is more suitable as an anode because of its lower and more stable equilibrium voltage, which is more immune to strain. In addition, for Ti₂CF₂, a critical composition is observed at x = 0.22, above which the voltage becomes negative (Fig. S13A). Note that the maximum number of Li⁺ in a 3 × 3 supercell of Ti₂CF₂ is four, corresponding to a chemical stoichiometry of Ti₂CF₂Li_0.444. The lower Li capacity in Ti₂CF₂ is mainly attributed to the steric effect of F, which impedes the spatial occupancy of more Li; otherwise, the surface F groups would be repulsed, leading to the formation of LiF by-products.

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Fig. 6.

Calculated formation energies and resulting voltage profiles of (A) Ti₂C and (D) Ti₂CO₂ obtained along the energy structures. Initial voltages and average voltages of Ti₂C (B) and Ti₂CO₂ (E) under biaxial strains. (C) Initial voltages and average voltages of M₂C. (F) Theoretical gravimetric capacities of the studied 2D TMCs.

The theoretical capacity, a key parameter in evaluating the electrode performance for LIBs, can be estimated from the following equation (18):CA=nAZAFMMXene+nMA,[7]where nA is the number of adsorbed metal adatoms, ZA is the valence state of the metal adatoms, F is the Faraday constant (26,801 mAh⋅mol⁻¹), MMXene is the molecular weight of the MXene nanosheet, and MA is the molecular weight of the metal adatoms. The weight of the adsorbed metal atom is not considered in most calculated capacities presented in the literature. Fig. 6F shows the calculated theoretical capacities of the studied 2D TMCs. The theoretical capacities of many 2D TMCs are much higher than that of a commercial TiO₂ anode material (167.5 mAh⋅g⁻¹). In general, Ti₂C has the greatest theoretical capacity among all of the bare 2D TMCs, while Ti₂CO₂ is the best among all of the O-terminated 2D TMCs.

Overall, several key factors, including the bond length, VEN, strain, surface functional group, and layer thickness, can influence the properties of 2D TMCs as anode materials in LIBs. The ionic mobility has a strong dependence on the atomic configuration of the three surface layers. First, the outermost atoms have a dominant effect on the energy barriers, and materials with nonmetallic surface atoms have larger barriers than those with metallic surface atoms due to bonding between Li and the nonmetal, explaining the much more rapid Li diffusion on bare 2D TMCs compared with that on other 2D materials. Second, the energy barrier increases as the bond length and VEN increase. Third, the strain plays a critical role in determining the energy barrier. In general, on one hand the energy barrier increases as the biaxial strain increases within the critical strain. Compared with graphene, the barriers of 2D TMCs increase more dramatically as the biaxial strain increases, which can be primarily attributed to the changes of the bond angle and layer thickness when the 2D TMCs are under applied strain. On the other hand, the uniaxial loading increases the ionic mobility, efficiently modifying the corresponding Li⁺ diffusion pathway. Moreover, the Li concentration is another crucial factor that influences the ionic mobility owing to the interactions between Li⁺ at higher Li coverage, impeding the Li⁺ diffusion. Therefore, increasing the bond length, VEN, biaxial strain, and Li concentration and introducing surface functional group negatively affect the ionic mobility. Similarly, increasing the VEN and introducing surface functional group decrease the cell voltage and capacity. In contrast, introducing surface functional group and increasing the layer thickness have positive effects on the stiffness, mechanical flexibility, and strength.

Suggestions for Fabricating a Promising Anode.

Several critical factors may influence the properties of 2D TMCs as anode materials in LIBs and accordingly can provide strategies for optimizing the performance of 2D TMCs for application in LIBs. For instance,

• i) Due to the negative effect of the bond length and VEN on the ionic mobility, Ti₂C can be utilized to ensure the highest ionic mobility.

• ii) Increasing the layer thickness may improve mechanical flexibility; this, however, slightly reduces the ionic mobility and voltage. As a result, M₃C₂ and M₄C₃ are better candidates for applications under relatively large strains.

• iii) Strain is a key parameter that affects the energy barrier for Li⁺ diffusion, while uniaxial stress can efficiently modify the Li⁺ diffusion path. Interestingly, an appropriate control over the compression strain may increase the ionic mobility by decreasing the energy barrier. Therefore, the diffusion performance on 2D TMCs can be efficiently tuned by strain.

• iv) Introducing surface functional groups decreases the ionic mobility, cell voltage, and theoretical capacity. Therefore, the electrochemical properties can be improved by removing surface functional groups. Since the bare 2D TMCs have not been prepared thus far, we propose Ti₂CO₂ as the best anode material among all of the presented functionalized 2D TMCs for the following reasons. First, first-principles calculations suggest that Ti₂CO₂ possesses thermodynamic, mechanical, and dynamic stability, indicating that Ti₂CO₂ can be experimentally realized (44, 63). Second, several experiments provide strong evidence for the possible synthesis of optimal Ti₂CO₂ (38, 47, 64). Third, compared with TiO₂ anode materials, Ti₂CO₂ possesses enhanced electronic conductivity, faster Li transport, higher charging/discharging rates, decreased equilibrium voltage, and improved Li storage capacity. Compared with graphene, the better mechanical properties and increased theoretical capacity make Ti₂CO₂ more suitable for flexible anode materials in high-performance LIBs.