Nitride MXenes as sulfur hosts for thermodynamic and kinetic suppression of polysulfide shuttling: a computational study

Abstract

The practical applications of lithium–sulfur (Li–S) batteries are greatly hindered by the poor conductivity of sulfur, the shuttling of lithium polysulfides (LiPSs), and the sluggish kinetics in the charge–discharge process. In order to solve these problems, here we propose the surface-functionalized V₂N MXenes as the host materials to improve the electrochemical performance of Li–S batteries. Based on the density functional theory (DFT) calculations, we found that both the bare and functionalized V₂NT₂ (T = O, F, OH, and S) exhibit metallicity, and three of them (V₂NO₂, V₂NF₂, and V₂NS₂) possess moderate LiPS adsorption strength, which thermodynamically benefits the suppression of the dissolution and shuttling of LiPSs. Besides, V₂NS₂ shows the lowest Gibbs free energy barrier for the sulfur reduction reaction (0.49 eV) during discharge, which kinetically suppresses the dissolution and shuttling of LiPSs by expediting the decomposition process from soluble LiPSs to insoluble ones. Moreover, surface functionalized V₂NT₂ also exhibits outstanding catalytic ability for Li₂S decomposition during charge, which decreases the energy barrier from 3.64 eV (bare V₂N) to 1.55 (V₂NO₂) and 1.19 eV (V₂NS₂), and increases the charging kinetics. Based on these results, V₂NS₂ monolayers are suggested as promising host materials for S cathodes due to the fast charge/discharge kinetics and effective suppression of LiPS shuttling. This theoretical study provides further insight into the application of nitride MXenes and other two-dimensional materials as conductive anchoring materials for Li–S batteries.

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1. Introduction

In recent years, battery technology has made considerable progress which greatly promotes the application of large-scale electrical energy storage in our daily life.^1–6 Lithium–sulfur (Li–S) batteries, because of their high theoretical specific capacity of 1675 mA h g⁻¹ and high theoretical specific energy of 2600 W h kg⁻¹, have received a great deal of attention.^7–11 Their practical energy density is expected to be 500–600 W h kg⁻¹, which is around twice that of traditional lithium-ion batteries. Moreover, Li–S batteries show an inherently low competitive cost because of the abundance of sulfur.

Despite these promising features, practical applications of Li–S batteries are hindered by several obstacles.^12–15 One of the major issues is the short cycle life stemming from the dissolution of lithium polysulfides (LiPSs) into liquid electrolytes and the migration of LiPSs between the anode and the cathode, which causes the so-called “shuttle effect” and would induce low discharge energy capacity and low coulombic efficiency. Besides, the relatively poor electrical conductivity of sulfur and the ∼80% volume expansion during the cycling of sulfur will lead to low utilization of active materials and rapid aging of electrodes. Last but not least, the large energy barriers of the sulfur reduction reaction (SRR) during discharge and Li₂S decomposition during charge lead to slow kinetics in Li–S batteries, which greatly affects their performance.^16,17 Therefore, the rational design of Li–S host materials should take into consideration not only the suppression of LiPS shuttling, but also the catalytic activity of the SRR and Li₂S decomposition, the latter being long overlooked.

Two-dimensional (2D) materials have been demonstrated to be effective sulfur hosts with improved electrochemical performance for Li–S batteries.^18–20 Among them, 2D transition metal carbides and nitrides, named MXenes, have attracted much attention due to their excellent electronic conductivity, high surface area, controllable hierarchical structures, and physical confinement for electrode volume changes.^21–26 For instance, Liang et al. demonstrated that 70 wt% S/Ti₂C composites exhibited long-term stability as cathodes and showed excellent cycling performance with a specific capacity close to 1200 mA h g⁻¹ at C/5 current rate;²⁷ Zhang et al. used a phase engineering strategy to fabricate Ti₃C₂ MXene/1T-2H MoS₂–C nanohybrids which greatly improved the capacity (1194.7 mA h g⁻¹ at 0.1C), rate ability (677.2 mA h g⁻¹ at 2C), and cycling stability (0.07% per cycle) in Li–S batteries.²⁸ Nevertheless, their bifunctional catalytic activities toward the SRR and Li₂S decomposition have not been investigated yet, and until now, the majority of studies about the application of MXenes in Li–S batteries are focused on the carbides; more than 20 types of carbide MXenes have been synthesized while only a few nitride MXenes with higher conductivity than corresponding carbides are reported.^21,29,30 Recently, the successful synthesis of 2D V₂N and Mo₂N further expanded the family of experimentally achievable 2D transition-metal nitrides.²⁹ Particularly, V₂N MXenes are worthy of attention because the VN/graphene composite has been experimentally proven to have a number of desirable properties as a Li–S host material in a pioneering report.³¹ For the vanadium element, its multiple-valence-state feature (from V²⁺ to V⁵⁺), stable crystalline framework when forming compounds, and rich distribution in the Earth's crust³² endow V₂N MXenes with great potential as sulfur hosts.

Except for the surface terminations (–O, –F, and –OH) which are commonly introduced during the MXene synthesis process,^33–35 non-native functional groups, such as –S, also inevitably exist on the surface of MXenes when they are used in Li–S batteries. It is also reported that S-functionalized MXenes may exhibit lower Li₂S decomposition barrier because of the trapping effect between Li atoms and the S-containing surface.¹⁶ Thus, the understanding of these surface groups, including the distribution and arrangement of surface terminations, is important in both theoretical studies and the interpretation of the resultant properties. In this work, we select the V₂N monolayer as a typical nitride MXene to systematically investigate its potential as a host material by means of DFT calculations. The electronic properties, anchoring strength, catalytic ability, and vacancy effect are comprehensively studied. Our calculations reveal that the anchoring strength and bifunctional catalytic ability of V₂N can be modulated by the surface terminating groups (T = O, F, and S). The computational scheme in this work can open up a new avenue for the rational design of other 2D materials as hosts for S cathodes.

2. Computational methods

First-principles calculations were performed in the framework of DFT using the Vienna ab initio simulation package (VASP).³⁶ The exchange-correlation energy was described by the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional.³⁷ For geometry optimization, the plane-wave cut-off energy was set as 500 eV. The Brillouin-zone integration was performed using a Monkhorst–Pack grid of k-point sampling, and the Γ-centered meshes of 15 × 15 × 1 and 3 × 3 × 1 were used for the unit cell and the 4 × 4 × 1 supercell, respectively. During geometric relaxation, the convergence criteria for energy and force were set at 10⁻⁵ eV and 0.01 eV Å⁻¹, respectively, while for self-consistent field calculations, an energy convergence criterion of 10⁻⁵ eV was also used.

The van der Waals (vdW) interaction between V₂N/V₂NT₂ and Li₂S_n (S₈) (n = 1, 2, 4, 6, and 8) was considered by using the semiempirical DFT-D2 (ref. 38) approach. A vacuum layer of 20 Å along the c-axis was added to the slabs to avoid the interlayer interaction. Furthermore, charge differential analysis was performed to estimate the charge redistribution and transfer. The climbing image nudged elastic band (CI-NEB) method³⁹ was applied to calculate the minimum diffusion energy barrier and decomposition barriers. To investigate the dynamical stability, the phonopy code was used to calculate the phonon dispersion spectra.⁴⁰ During all the calculations, all the atoms were fully relaxed.

In the discharge process of Li–S batteries, the overall reaction of the reduction of one S₈ molecule (SRR) to form eight Li₂S molecules is a 16-electron process:¹⁷

S₈ + 16(Li⁺ + e⁻) → 8Li₂S

and the elementary steps in the reaction pathway for generating one Li₂S molecule is:^41,42

*S₈ + 2(Li⁺ + e⁻) → *Li₂S₈

*Li₂S₈ → *Li₂S₆ + 1/4S₈

*Li₂S₆ → *Li₂S₄ + 1/4S₈

*Li₂S₄ → *Li₂S₂ + 1/4S₈

*Li₂S₂ → *Li₂S + 1/8S₈

where * denotes active sites on the catalyst surface. The Gibbs free energy change ΔG of each step was calculated using:

ΔG = ΔE + ΔZPE − TΔS

where ΔE, ΔZPE, and TΔS represent the changes of the DFT-calculated total energy, zero-point energy (ZPE), and entropic contribution, respectively. The ZPE and entropic contribution were calculated from the vibrational frequencies, and a temperature of 298 K was used.

3. Results and discussion

3.1 Structural and electronic properties of V₂N and V₂NT₂ monolayers

The V₂N monolayer is built up of a sandwich structure containing one N and two V layers in the sequence of V(1)–N–V(2) (Fig. 1a and b). The optimized V₂N monolayer has the lattice parameters of a = b = 2.89 Å and a thickness of c = 2.08 Å. In the phonon dispersion spectra, the absence of imaginary phonon modes in the first Brillouin zone indicates that the V₂N monolayer is dynamically stable (Fig. S1†).^40,43 For the V₂NT₂ monolayer, the most favorable sites for terminating groups T are determined by performing the total energy calculations. Three possible high-symmetry sites α, β, and γ are considered (Fig. 1b), and the total energies of all possible V₂NT₂ phases are listed in Table S1.† Based on the analysis, the α site is the most favorable adsorption site (Fig. 1c–f). With the terminal groups, both V(1)–N and V(2)-N bonds are elongated (Table S2†), implying that the terminal atoms strongly interact with the original V₂N monolayer. The thermal stability of V₂NT₂ was verified by ab initio molecular dynamics (AIMD) simulations (Fig. S2†). Moreover, we also obtain the lowest energy configuration of the isolated S₈ and Li₂S_n molecules by DFT calculations, as shown in Fig. 1g and S3.† The structural parameters and symmetries of our configurations are very close to those obtained by B3LYP/6-311G(3df)-level quantum chemistry calculations⁴⁴ and structure prediction using the particle-swarm optimization algorithm⁴⁵ with negligible differences.

Fig. 1 DFT-optimized structures. (a) Top view of V₂N; (b) side view of V₂N, (c) V₂NF₂, (d) V₂NO₂, (e) V₂N(OH)₂; (f) V₂NS₂; (g) S₈ and Li₂S_n (n = 1, 2, 4, 6 and 8) structures. V, N, O, F, H, S and Li atoms are represented in brown, grey, red, purple, pink, blue and orange colours respectively.

The metallicity of the sulfur host material is an important factor to consider for Li–S battery applications. Based on the calculated electronic density of states (DOS) of V₂N and V₂NT₂, both the bare and terminated (V₂N and V₂NT₂) phases exhibit excellent metallicity and the majority of electron states at the Fermi level originate from the V 4d orbitals (Fig. 2), with very little contribution from the non-metal atoms. As a result, the excellent metallic characters of V₂N and V₂NT₂ are expected to improve the electrochemical performance of Li–S cells. Since sulfur and short-chain LiPSs (Li₂S₂ and Li₂S) exhibit insulating behavior,⁴² the metallicity of V₂N and V₂NT₂ is particularly significant for the electron transfer in the bifunctional catalytic reaction (SRR and Li₂S decomposition).

Fig. 2 Total and partial density of states of 2D V₂N and V₂NT₂ (T = O, F, OH, and S). Fermi levels are set to be zero (denoted as black dotted lines).

3.2 Anchoring ability for S₈ and Li₂S_n

The anchoring effect of V₂N and V₂NT₂ monolayers is evaluated by calculating the adsorption energies. We have conducted a comprehensive search for the most energy favorable adsorption sites for each S₈ and Li₂S_n species. To be specific, we have tested three symmetry unique sites (α, β, and γ) and two different rotational orientations on the host surface (Fig. S4,† with a total number of 180 different structures) for each compound to obtain the most stable adsorption site and configuration. The results showed that the adsorption strength of S₈ and Li₂S_n on bare V₂N is extremely strong, as indicated by the large adsorption energy values in the range from −5 to −25 eV (Fig. 3a). However, with such a large adsorption strength, S₈ and Li₂S_n are easily decomposed into single S (and Li) atoms, which are then tightly captured by the outer V layer of V₂N monolayers (Fig. 3b–d). Thus, bare V₂N is not suitable for direct application in Li–S batteries, and it will automatically transform into S-functionalized V₂N upon S₈ adsorption, so it is not discussed in the following sections.

Fig. 3 (a) Adsorption energies of S₈ and Li₂S_n on V₂N; adsorption structures of (b) S₈, (c) Li₂S₈, and (d) Li₂S₆ on V₂N before (left) and after (right) optimization. The V, N, Li, and S atoms are distinguished by brown, gray, orange, and blue colors, respectively.

For all the functionalized V₂NT₂ structures, the adsorption strengths of S₈ and Li₂S_n on V₂N(OH)₂ are relatively stronger than those on V₂NO₂, V₂NF₂, and V₂NS₂ during the whole lithiation process (Fig. 4a). However, V₂N(OH)₂ becomes unstable after the adsorption of Li₂S_n species, where H atoms spontaneously migrate toward S atoms in Li₂S_n while the remaining O atoms interact with Li atoms, leading to the breakage of the Li₂S_n species eventually (Fig. 4d). For V₂NO₂, V₂NF₂, and V₂NS₂ monolayers, in contrast, the structures remain stable, which indicates the relatively mild adsorption strength (Fig. 4b, c, and e). We also identify the interactions between V₂NT₂ and S₈/Li₂S_n by comparing the adsorption energies with and without vdW corrections. From the results of the ratio of vdW (Fig. S5†), we can conclude that physical interactions (vdW) play a major role in the adsorption of S₈/Li₂S_n on V₂NS₂, exhibiting R_vdW values higher than 90%. V₂NF₂ and V₂NO₂, on the other hand, with relatively lower R_vdW values especially for S₈ and long-chain LiPSs, imply that chemical interactions also contribute a lot to the S₈/Li₂S_n adsorption. In short, the vdW interaction should be considered when studying the adsorption of LiPSs on V₂NT₂ monolayers.

Fig. 4 (a) Adsorption energies of S₈ and Li₂S_n on V₂NT₂ (T = O, F, OH, and S), and the corresponding optimized structures of S₈ and Li₂S_n on the surface of (b) V₂NO₂, (c) V₂NF₂, (d) V₂N(OH)₂, and (e) V₂NS₂. The adsorption energy values are marked under each structure. The V, N, O, F, H, Li, and S atoms are distinguished by brown, gray, red, purple, pink, orange, and blue colors, respectively.

In addition, since there are usually small amounts of vacancies on the surface of MXenes, we also investigate the vacancy effect based on the structure of V₂NO_2−x/V₂NF_2−x/V₂NS_2−x (x = 1/16). Similar to intact V₂NO₂/V₂NF₂/V₂NS₂, none of the adsorbed Li₂S_n structures exhibit a tendency of decomposition, and the adsorption of Li₂S_n (S₈) on V₂NO_2−x/V₂NF_2−x/V₂NS_2−x (x = 1/16) is energetically favorable (Fig. S6†). This can be attributed to the electron-rich regions with lone-pair electrons induced by the O/F/S vacancy, as indicated by the electron localization function (ELF) results (marked by red arrows in Fig. S7†),⁴⁶ and after Li₂S_n (S₈) species are adsorbed on the surface of V₂NT_2−x, they can form chemical bonds with the vacancy sites through those electrons, which leads to the easy bonding with S of Li₂S_n (S₈). Consequently, for nitride-based MXenes, the shuttle suppression ability would not be hampered by the small amounts of vacancies in Li–S batteries.

To verify the ability of surface terminations in suppressing the LiPS shuttling, it is necessary to evaluate the binding effects between polysulfides and 1,3-dioxolane (DOL)/1,2-dimethoxyethane (DME) electrolyte.^47,48 Through comparing the two different types of adsorption energies (E_{V2NT2+S8/Li2Sn} and E_{DOL/DME+S8/Li2Sn}), we found that S₈ and Li₂S_n prefer to be adsorbed on V₂NT₂ rather than DOL/DME molecules since the adsorption energies between LiPSs and DOL/DME molecules were between −1 and 0 eV (Fig. S8†), larger than those between LiPSs and V₂NT₂ monolayers (Fig. 4a). Based on the above discussion, V₂NO₂, V₂NF₂, and V₂NS₂ can not only fix S₈ and Li₂S_n on their surfaces but also maintain their own structures stably. Thus, they exhibit great potential in preventing polysulfide dissolution and shuttling in the electrolyte.

To assess the nature of the interaction between the host material and polysulfides, the charge density difference is also analyzed. Taking V₂NO₂ as an example (Fig. 5a), for S₈, obvious charge transfer occurs between S and V, indicating the formation of polar covalent bonds between V and S. For other Li₂S_n structures, electron accumulation regions (yellow) appear between the Li atoms and the outer O layer, while electron depletion (blue) happens around the Li–S and S–S bonds, explaining the binding behavior of Li₂S_n on V₂NO₂ with the formation of Li–O bonds. A similar phenomenon can be observed in V₂NF₂ and V₂NS₂ (Fig. 5b and c).

Fig. 5 Charge density difference of S₈ and Li₂S_n adsorbed on (a) V₂NO₂, (b) V₂NF₂, and (c) V₂NS₂. Yellow and blue regions indicate electron accumulation and depletion, respectively. The V, N, O, F, Li and S atoms are distinguished by brown, gray, red, purple, orange, and blue colors, respectively.

3.3 Bifunctional catalytic performance and Li⁺ diffusion kinetics for Li–S batteries

Apart from the anchoring ability, the diffusion properties and catalytic effect are also key indicators for Li–S batteries. In the discharge process, the fast kinetics of S₈ reduction to long-chain soluble LiPSs (Li₂S₈, Li₂S₆, and Li₂S₄), and finally short-chain insoluble LiPSs (Li₂S₂ and Li₂S) could shorten the LiPS accumulation time in the cathode and thus reduce the LiPS dissolution. The final discharge product, Li₂S, which suffers from low Li⁺ diffusivity and high decomposition energy barrier greatly affects the conversion between the polysulfides and will cause high overpotential and low-rate capability. Thus, the decomposition kinetics of LiPSs during discharge and that of Li₂S during charge processes, as well as Li⁺ diffusion on hosts, are all vital for the kinetic performance of Li–S batteries.

To analyze the decomposition kinetics of Li₂S on V₂NT₂, the CI-NEB method is used. The decomposition process can be described by the following equation: Li₂S → LiS + Li⁺ + e⁻. That is, a Li₂S molecule can be decomposed into a LiS cluster by releasing a single Li atom, which corresponds to the charging process. The natural decomposition barrier of Li₂S is calculated to be 3.64 eV, while the decomposition barriers on V₂NO₂, V₂NF₂, and V₂NS₂ are remarkably reduced to 1.55, 2.31, and 1.19 eV (Fig. S9†), respectively. Thus, surface functionalization can efficiently catalyze the Li₂S decomposition and reduce the overpotential of Li–S batteries, especially for V₂NO₂ and V₂NS₂ (Table 1). Besides, the diffusion barriers were studied to discuss the Li⁺ diffusion on host materials. The energy profiles along the Li⁺ diffusion coordinates show much smaller barriers than decomposition, where the minimum Li⁺ diffusion barriers on V₂NO₂, V₂NF₂, and V₂NS₂ were 0.21, 0.17, and 0.16 eV, respectively (Fig. S10†). These values are comparable to or smaller than those for other MXenes such as V₂CO₂ (0.26 eV), Ti₃CNO₂ (0.26 eV), and Ti₂NS₂ (0.17 eV) (Table S3†).^45,49–51 The low Li₂S decomposition and Li⁺ diffusion barriers imply the improved kinetics during Li₂S decomposition and Li⁺ diffusion, which can accelerate the whole charging process in the Li–S batteries.

Table 1 Calculated Li₂S decomposition barriers, Li⁺ diffusion barriers, and ΔG of the rate-limiting step during the SRR on V₂NO₂, V₂NF₂, and V₂NS₂

Substrate	Li2S decomposition barrier (eV)	Li^+ diffusion barrier (eV)	ΔG of the rate-limiting step during the SRR (eV)
V2NO2	1.55	0.21	1.88
V2NF2	2.31	0.17	2.14
V2NS2	1.19	0.16	0.49

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To gain a deeper understanding of the discharge reaction kinetics of polysulfides on the hosts (i.e. SRR), the overall reactions based on the reversible formation of Li₂S from S₈ and Li bulk were considered (Fig. 6). The Gibbs free energies for all the reaction steps in the SRR are calculated and the evolution profiles (from S₈ to Li₂S species) for V₂NO₂, V₂NF₂, and V₂NS₂ are exhibited.

Fig. 6 Gibbs free energy profiles for the sulfur reduction reaction on V₂NO₂, V₂NF₂, and V₂NS₂.

For V₂NO₂, it can be seen that the reduction steps from S₈ to the Li₂S₈ and from Li₂S₆ to the Li₂S₄ are exothermic, with the Gibbs free energy change (ΔG) values of −5.90 and −1.18 eV, respectively. The other three reduction steps, from Li₂S₈ to Li₂S₆, Li₂S₄ to Li₂S₂, and Li₂S₂ to Li₂S, are all endothermic, and among them, the step from Li₂S₈ to Li₂S₆ exhibits the largest ΔG value of 1.88 eV, which is determined as the rate-limiting step (RLS). For V₂NF₂, two exothermic reaction steps include those from S₈ to Li₂S₈ and from Li₂S₈ to Li₂S₆, while the other three steps are endothermic steps, and RLS is the last step (Li₂S₂ to Li₂S) with a ΔG of 2.14 eV. The significant differences in ΔG of step Li₂S₈ → Li₂S₆ and step Li₂S₂ → Li₂S for the three systems are related to the differences in their anchoring abilities of LiPSs: for V₂NO₂, the Li₂S₈ adsorption is the strongest among the three systems, and its Li₂S₆ anchoring ability is relatively weak (Fig. 4), leading to its high Li₂S₈ → Li₂S₆ barrier; for V₂NF₂, the adsorption strength of Li₂S is significantly decreased compared with that of Li₂S₂, while for V₂NO₂ and V₂NS₂, the Li₂S₂ and Li₂S adsorption energies are relatively close to each other (Fig. 4). Among all three structures, V₂NS₂ exhibits the smallest ΔG value for RLS in the SRR (0.49 eV, Li₂S₄ to Li₂S₂, see Table 1) due to moderate LiPS adsorption. Thus, its outstanding bifunctional catalytic activity during charge (Li₂S decomposition) and discharge (SRR) can be achieved simultaneously. In combination with its metallic behavior and moderate LiPS anchoring ability, V₂NS₂ can be an outstanding host material for Li–S batteries (Fig. 7).

Fig. 7 Schematics of 2D V₂NS₂ MXenes as promising sulfur hosts for Li–S battery applications.

4. Conclusions

In summary, we have explored the potential applications of 2D V₂N/V₂NT₂ monolayers as the S cathode host for Li–S batteries by means of DFT calculations. It was shown that both bare and functionalized V₂NT₂ monolayers exhibited excellent metallic character. However, bare V₂N cannot be directly used in Li–S batteries because of the extremely strong V–S or V–Li bond. Among the four functional groups (O/F/OH/S) studied, the V₂NS₂ monolayer is identified as the most promising candidate through a comprehensive examination of its metallicity, LiPS anchoring ability, Li₂S decomposition barrier, Li⁺ diffusion barrier, and SRR thermodynamics. This study gives insightful guidance for further experimental work on nitride MXenes and other novel 2D materials as promising host materials for Li–S batteries.

Author contributions

Ke Fan: conceptualization, data curation, investigation, software, methodology, writing – original draft; Yiran Ying: data curation, writing – review & editing; Xin Luo: supervision, writing – review & editing; Haitao Huang: funding acquisition, supervision, writing – review & editing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU152178/20E), the Hong Kong Polytechnic University (Project No. RHA3), and Science and Technology Program of Guangdong Province of China (Project No. 2019A050510012 and 2020A0505090001). X. L. acknowledges support from NSFC (No. 11804286, No. 12172386), the National Natural Science Foundation of Guangdong Province, China (Grant No. 2021B1515020021), and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University (Grant No. 2021qntd27).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1ta06759a

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