Vanadium Carbide (V₄C₃) MXene as an Efficient Anode for Li-Ion and Na-Ion Batteries

Abstract

Li-ion batteries (LIBs) and Na-ion batteries (SIBs) are deemed green and efficient electrochemical energy storage and generation devices; meanwhile, acquiring a competent anode remains a serious challenge. Herein, the density-functional theory (DFT) was employed to investigate the performance of V₄C₃ MXene as an anode for LIBs and SIBs. The results predict the outstanding electrical conductivity when Li/Na is loaded on V₄C₃. Both Li_2xV₄C₃ and Na_2xV₄C₃ (x = 0.125, 0.5, 1, 1.5, and 2) showed expected low-average open-circuit voltages of 0.38 V and 0.14 V, respectively, along with a good Li/Na storage capacity of (223 mAhg⁻¹) and a good cycling performance. Furthermore, there was a low diffusion barrier of 0.048 eV for Li_0.0625V₄C₃ and 0.023 eV for Na_0.0625V₄C₃, implying the prompt intercalation/extraction of Li/Na. Based on the findings of the current study, V₄C₃-based materials may be utilized as an anode for Li/Na-ion batteries in future applications.

1. Introduction

The everlasting consumption of fossil fuels leads to their depletion and greenhouse gas emissions, which are the primary cause of global warming [1,2,3]. A variety of endeavors are currently being dedicated to addressing these issues, including gas conversion reactions [4,5] and utilizing sustainable energy sources (i.e., solar power [6,7], hydrogen power [8], fuel cells [9,10], and energy storage devices [11,12,13,14,15]). Li-ion batteries (LIBs) and Na-ion batteries (SIBs), with their high energy, power density, and long cycle life, are among the most beneficial electrochemical energy conversion and storage technologies available for smart grids, mobile electronics, and electric vehicles [16,17,18]. The performance of LIBs and SIBs is primarily shaped by the electrochemical properties of the anode materials [16,17]. Graphitic carbon is the universally utilized commercial anode material, but its low Li/Na theoretical capacity (372/25 mAh/g) and low rate capability limit its widespread, practical use [19]. Despite the significant progress in LIBs and SIBs, the earth availability of Li/Na, charge time, durability, temperature tolerance, self-discharge, and recyclability of the decayed batteries are creating a significant challenge [16,17,18,19,20,21,22]. Therefore, developing novel anodes with high specific capacities, greater rate capabilities, and cycling longevity is imperative.

MXenes are a novel class of 2D transition metal carbide/carbonitride electrodes that have several advantages for LIBs, SIBs, and other applications, including hydrophilicity, high active surface areas, rich electron densities, and low costs [23,24,25]. Numerous MXenes such as Ti₂C, Ti₃C₂, V₂C, Nb₂C, and Mo₂C were utilized as anodes for LIBs, and SIBs with the Ti₃C₂ MXene phase has been studied most extensively [23,24,25,26,27,28]. Distinct from other MXenes, V₄C₃ MXene offers many advantages, including greater interlayer spacing, better structural durability, and high specific capacity, which are essential for the fabrication of high-performance anodes for LIBs and SIBs [29,30,31]. Besides its excellent mechanical properties and thermal stability, V₄C₃ MXene possesses excellent metallic properties due to its narrow band gap at the Fermi level [32,33]. Meanwhile, the vanadium metal (V) in V₄C₃ MXene has a prosperous valence state from +2 to +5, which may enhance the electrochemical performance of LIBs and SIBs [29,34,35]. For instance, the V₄C₃ MXene/MoS₂/C electrode significantly boosted LIB activity compared to MoS₂/C and MoS₂ electrodes, showing an outstanding reversible capability of 0.622 Ah/g at 1 A/g after 450 cycles and maintaining a superior rate capability of 0.5 Ah/g at 10 A/g [36]. That is due to the outstanding electrical conductivity, structural durability, and fast reaction kinetics promoted by V₄C₃. Likewise, V₄C₃T_x (T = O, OH, and F), which is formed by the ball milling (B.M.) of V₄AlC₃ followed by HF etching (V₄C₃T_x-BM-HF), enhanced the LIB performance over V₄C₃T_x-HF and yielded a specific capacity of 0.225 Ah/g after 300 cycles at 0.1 A/g and 0.125 Ah/g at 1/A g because of the superior interlayer spacing and specific surface area [37]. Despite the noted progress in V₄C₃ MXene, it is rarely reported on for applications in energy storage, and usually is exclusively with regard to LIBs; to the best of our knowledge, it has not been yet addressed theoretically for both LIBs and SIBs.

In pursuit of this aim, we employed the first principle, DFT simulation, to predict the performance of V₄C₃ MXene as an anode for LIBs and SIBs as a function of Li and Na loading. V₄C₃ MXene loaded with Li/Na was investigated for lithiation, sodiation, electrical conductivity, and surface energy. The surface energy is calculated by considering Li/Na loading on V₄C₃ with a diffusion barrier of 0.023 eV for Li and 0.048 eV for Na migration.

2. Methodology

To conduct the current DFT investigations, we employed VASP software (Vienna, Austria) known as the Vienna Ab Initio Simulation Package [38], whereas correlation potential and the electronic exchange were examined by utilizing a generalized gradient (GGA) combined with a Perdew–Burke–Ernzerhof (PBE) functional (GGA-PBE). This is because the GGA-PBE is a nonempirical functional with judicious accuracy for qualitative and quantitative prediction of the molecules interacting and being stored with metal surfaces over a wide range of systems [39]. In the present calculations, we restricted the force value to 1/100 eV/Å, and the energy was 1 × 10⁻⁶ eV. Based on the GGA-PBE level, we simulated the electronic structure of V₄C₃ and Li/Na loaded V₄C₃. For plane-wave expansion, cut-off energy of 500 eV was selected. The Monkhorst–Pack technique was employed to sample the k-points in the Brillouin zone, with a dense k-point grid of 17 × 17 × 1 [40]. Additionally, the DFT-D2 model [41] was applied in our calculations to acquire reliable binding strength between Li/Na and V₄C₃. In the structure of V₄C₃, we generated a vacuum space of 20 Å to prevent coupling between V₄C₃ layers.

Our simulations found that the materials under research are spin-polarized with Li/Na content loading. The voltage and energy profiles were computed with increasing Li/Na content, such that x = 0.125, 0.25. 0.5, 1.0, 1.5, and 2. The electronic structure calculations were carried out within the GGA-PBE to determine the electronic density of states (DOS). The AIMD simulations were used to investigate the change in the energy fluctuation of Li/Na-loaded V₄C₃ at 300 K within each time step of 1 fs for the total time duration of 5000 fs [42]. Several Li/Na concentrations were studied to procure the binding energies and voltage profile. The relationship of binding energy is shown in Equation (1) [43]:

$$E_b=(E_{Li-V_4{C}_3 }+n{E}_{Li}-E_{V_4{C}_3 })/n,$$

(1)

where $E_{Li-V_4{C}_3 }$ represents the Li-loaded V₄C₃ energy, $E_{V_4{C}_3 }$ denotes the bare V₄C₃ energy, $E_{Li}$ is the metallic Li energy, and n is the number of Li content loaded on the V₄C₃ sheet. Similarly, we adopt the above formula for Na adsorption by substituting Li with Na to estimate E_b. Next, we calculate the charge density difference based on the relation: $\Delta \rho \left(r\right)={\rho }_{Li-V_4{C}_3}\left(r\right)–{\rho }_{V_4{C}_3}\left(r\right)–{\rho }_{Li}\left(r\right)$). Here, ${\rho }_{Li-V_4{C}_3}$ specifies the charge density of Li-loaded V₄C₃, ${\rho }_{V_4{C}_3}$ denotes the charge density of bare V₄C₃, and ${\rho }_{Li}$ is the charge density of Li (isolated). For Na-loaded V₄C₃, a similar formulation is employed by substituting only Li with Na.

For each concentration of the Li_xV₄C₃ compound, the open-circuit voltage (OCV) is evaluated by Equation (2) [44]:

$$V\left(x1, x2\right)=\left[E_{L{i}_{x1}}-E_{L{i}_{x2}}+\left(x_2-x_1\right) E_{Li}\right]/\left(x_2-x_1\right)e$$

(2)

where $E_{L{i}_{x1}}$, $E_{L{i}_{x2}}$, and $E_{Li}$ are the energies of ${\mathrm{Li}}_{\mathrm{x}1}$ V₄C₃, ${\mathrm{Li}}_{\mathrm{x}2}$ V₄C₃, and bulk Li, respectively. A detailed discussion of the voltage profile is given in the supporting information.

The theoretical capacity (C) can be determined through Equation (3):

$$\mathrm{C} =n\mathrm{F}/{\mathrm{M}}_{{\mathrm{V}}_4{\mathrm{C}}_3 }$$

(3)

where n denotes the number of adsorbed Li/Na atoms, F defines the Faraday constant (26,801 mAh/mol), and ${\mathrm{M}}_{{\mathrm{V}}_4{\mathrm{C}}_3 }$ is the molar weight of V₄C₃.

The Bader charge technique was employed to calculate the amount of charge transferred from Li/Na to V₄C₃ (

Table 1. Structural parameters of pristine V₄C₃ MXene and Li/Na content-loaded V₄C₃ (2 × 2 × 1 supercell) at x = 0.0625, including binding energy and charge transfer.

Parameters	Simulated Values
Ead (eV) for Li	1-site	2-site	3-site	4-site
	0.90	0.884	0.828	0.897
Ead (eV) for Na	1.21	1.16	1.15	1.20
Charge q (|e|) for Li	0.84	0.83	0.83	0.883
Charge q (|e|) for Na	0.67	0.664	0.66	0.665
Height (hS-S)	6.96 Å
Lattice constants (a, b)	2.90 Å

). Finally, the charging and discharging processes were investigated by using the simulation of surface barriers and minimum energy paths (MEPs) of Li/Na migration in the V₄C₃ monolayer with the climbing nudged elastic band (CI-NEB) method. This technique approximately justifies metal-ion batteries’ lithiation/delithiation and sodiation/desodiation mechanisms [45].

3. Results and Discussion

3.1. Structure of V₄C₃ Monolayer

As a first step, we shall examine the structure of the V₄C₃ monolayer, which can be viewed in Figure 1a where the top and side views are shown. The structure portrays four layers of vanadium (V) and three layers of carbon (C) atoms. Each carbon layer is sandwiched between two V layers. In the relaxed structure, a unit-cell of V₄C₃ is composed of four V atoms and three C atoms with lattice parameters a = b = 2.90 Å and thickness d = 6.96 Å. These structural parameters are in line with the preceding results [46]. Currently, experimental data are available for the structure of V₄C₃ MXene; thus, it is interesting to investigate its anodic properties for LIBs and SIBs using DFT calculations. To determine the binding energies, the Li and Na are first adsorbed on V₄C₃ MXene. We selected four stable sites on the surface of V₄C₃ for Li/Na adsorption. The calculated E_b of the adsorbed four sites, site-1, site-2, site-3, and site-4 are 0.90 eV, 0.884 eV, 0.828 eV, and 0.897 eV, respectively, for Li (x = 0.0625). Similarly, for Na (x = 0.0625) adsorption, the binding energies are 1.21 (site-1) eV, 1.16 eV (site-2), 1.15 eV (site-3), and 1.20 eV (site-4) as depicted in Figure 1b. Comparatively, the adsorbed site-1 possesses greater binding energy for both Li/Na adsorptions. Thus, we picked site-1 for further adsorption of Li/Na loading. To avoid the repulsive interactions between Li⁺−Li⁺ and Na⁺−Na⁺, we consider that both surfaces (top/bottom) of V₄C₃ MXene acquire reliable binding strength and maximum Li/Na ion storage. Figure 1c depicts the decreasing binding energy curves with increasing Li/Na concentrations at x = 2. A decreasing trend in E_b curves is noticeable due to the Li⁺−Li⁺ and Na⁺−Na⁺ repulsive forces. A similar pattern was also discerned in other 2D materials upon Li/Na loading [47,48]. The various optimized Li/Na-loaded content structures with front and side views are shown in Figure 2 and Figure S1, respectively. Subsequently, we found the amount of charge transferred from Li/Na to V₄C₃ by employing the Bader charge analysis. The amount of charge transfer from Li to V₄C₃ and Na to V₄C₃ is given in Table 1 [47,48,49]. A large amount of charge transfer from Li/Na to V₄C₃ confirms the binding energy curve (Figure 1c). The decrease in binding energy means there is a repulsion of charge due to Coulomb forces. It could be deduced from these results that there is a charge transfer from Li/Na to the V₄C₃ surface [47,48,49]. This reveals that an electrochemical reaction may occur between Li/Na and V₄C₃.

3.2. Safety and Stability of Li/Na-Loaded V₄C₃

Volume alteration of the V₄C₃ monolayer was studied in the in-plane expansion of the V₄C₃ single-layer (Figure S2) upon Li/Na adsorption. The results reveal that the lattice parameters increased with Li/Na adsorption increments in both Li_2xV₄C₃ and Na_2xV₄C₃, whereas the highest expected lattice expansions were about ~4.31% and 6.20%, respectively. Noticeably, V₄C₃ revealed a lower volume alteration during adsorption/desorption of Li/Na than graphite [50,51]. The energy fluctuation was computed and compared to time duration at 300 K (25 °C) using AIMD simulations to estimate the change in the structure of Li_2xV₄C₃ and Na_2xV₄C₃ (x = 0.125, 0.5, 1, 1.5, and 2) (Figure 3).

The energy fluctuation reduced with increasing Li/Na loading in both Li_2xV₄C₃ and Na_2xV₄C₃. However, the energy remained stable without any significant change over time, as illustrated in the straight line (Figure 3). That serves as an indication of the insignificant change in the structures of Li_2xV₄C₃ and Na_2xV₄C₃ without any deformations during Li/Na intercalation on the time scale of 1 fs to 5000 fs, which is in line with other reports on 2D materials [52,53,54]. We executed our simulations up to 5 ps (5000 fs) at 300 K. These steps are enough as the structure is retained at the end of 5 ps. It is noticed that the total energy converges right after as the time duration increases. Furthermore, our results show a low energy fluctuation.

3.3. Voltage and Li/Na Storage Capacity

To further examine the electrochemical behavior of V₄C₃ as a Li/Na host for LIBs and SIBs, we calculated the open-circuit voltage (OCV). Here, we discuss the anodic behavior of V₄C₃ for both LIBs and SIBs. During the lithiation and delithiation processes, the anode reaction is indicated by V₄C₃ + xLi⁺ + xe⁻ $\rightleftarrows$ Li_xV₄C₃. In this reaction, the charges (positive) start the motion between electrolyte and electrodes while the electrons pursue their motion through the external circuit of the cell. Ignoring the impact of temperature, pressure, and entropy, the voltage profile for Li/Na-loaded V₄C₃ is plotted in Figure 4a. Since the voltage profile depends on the binding energy, it decreases with the increase in Li/Na loading. However, our average voltages are estimated at around 0.38 V and 0.14 V for LIBs and SIBs. The computed voltages are underneath the described voltages of monolayers with Li/Na adsorption, where Li_xSnC is 0.44 V, Li_xSi₂H₂ is 0.42 V, Na_xSi₂H₂ is 0.64 V, Na_xSnS₂ is 1.0 V, and Na_xSnSe₂ is 0.68 V [17,55,56]. Furthermore, our evaluated average voltages also satisfy the commercial anode materials (i.e., 0.11 V for graphite and 1.5–1.8 V for TiO₂) [57,58]. Therefore, the suitable OCV designates the monolayer V₄C₃ as the superior Li/Na host material for LIBs and SIBs. Additionally, the amount of charge transfer is confirmed by evaluating the charge density difference as shown in Figure 4b,c for Li and Na, respectively. The isosurface marked with yellow exhibits the electron deficit, whilst the blue isosurface indicates the accumulated electrons. The results showed the possible charge transfer from Li/Na to the V₄C₃ surface and subsequently probable electrochemical reaction may occur between Li/Na and V₄C₃ [47,48,49].

The Li/Na storage capacity of 2D V₄C₃ is computed by employing the formula [59], C = xF/${\mathrm{M}}_{{\mathrm{V}}_4{\mathrm{C}}_3}$. In this equation, the terms x, F, and ${\mathrm{M}}_{{\mathrm{V}}_4{\mathrm{C}}_3}$ define the Li/Na content loaded on V₄C₃, the Faraday constant possesses a noted value of 26,801 mAh mol⁻¹, and the molar mass is per formula unit V₄C₃, correspondingly. According to the above formula, the Li/Na storage capacity is 223.5 mAhg⁻¹ with a maximum loading of Li/Na content (x = 2).

3.4. Li/Na Activation Energy Barriers

In an electrochemical cell, the fast transportation of electrons and ions is desirable in a rechargeable battery to reduce the charging and discharging time. It is necessary to diffuse the metal ion at a rapid rate as it depends on the rate capability of the battery. To investigate the energy surface of V₄C₃ with Li/Na loading, we adopted a technique recognized as the climbing image nudged elastic band (CI-NEB) technique. This method is useful for finding the activation barriers and the corresponding paths. In the case of the monolayer V₄C₃ (2 × 2 × 1 supercell), we selected three minimum energy paths (MEPs), path-I (1-2-1), path-II (2-3-2), and path-III (1-4-1), for the migration of Li/Na content (x = 0.0625) as depicted in Figure 5. Five images are incorporated between the final and initial sites for each path. The simulated activation barriers for Li migration along the three pathways are 0.048 eV (path-I), 0.064 eV (path-II), and 0.073 eV (path-III). For Na migration, the computed diffusion energy barriers along the three paths are 0.048 (path-I), 0.023 eV (path-II), and 0.065 eV (path-III). The comparison of the results was made with the prior attempts, such as with Li_xMoN₂ (0.49 eV), Na_xMoN₂ (0.56 eV), Li_xVN₂ (0.237 eV), Na_xCP₃ (0.356 eV), and Li_xB₃S (0.32 eV). The MXene (V₄C₃) is dominant over other 2D materials due to its high Li/Na charging-discharging rates and low activation barriers. Moreover, we compared the diffusivity and voltages with some well-known anodes, as depicted in

Table 2. Comparison of voltages and energy barriers with Li_xV₄C₃ and Na_xV₄C₃.

Material	Voltage	Diffusion Barrier Energy		Reference
NaxMoS2	0.56 V	0.08 eV	Method	[62]
			NEB
NaxW2C	0.43 V	0.019 eV	NEB	[59]
NaxSiS	0.10 V	0.18 eV	CI-NEB	[63]
LixWSe2	0.67 V	0.24 eV	NEB	[64]
LixSiH	0.42 V	0.18	CI-NEB	[56]
2D KxPC	0.69 V	0.26 eV	NEB	[65]
2D KxSnC	0.41 V	0.17 eV	NEB	[66]
3D LixPBC2	0.48 V	0.29 eV	CI-NEB	[67]
3D LixSi2BN	0.27 V	0.44 eV	NEB	[68]
LixV4C3	0.38 V	0.048 eV	CI-NEB	This work
NaxV4C3	0.14 V	0.023 eV	CI-NEB	This work

. The simulated results predict low diffusion energy barriers for Li/Na on V₄C₃ compared to graphitic materials (0.277~0.47 eV) [60,61], illustrating an enhanced rate capability of the host (V₄C₃) for LIBs and SIBs.

3.5. Electronic Properties

Besides electronic conductivity, another essential attribute of anode materials is their superior performance. This can be assessed thoroughly to study the electronic structure, such as the density of states (DOS). Therefore, we performed the GGA-PBE calculations to establish the density of states (DOS) and partial density of states (PDOS) of pristine V₄C₃ MXene and Li/Na (x = 0.0625)-loaded V₄C₃ (Figure 6). Employing the GGA-PBE technique, the DOS of the monolayer V₄C₃ was expected to be of a possible metallic nature (Figure 6a). The metallic character of the bare V₄C₃ was further examined by PDOS. The main contributions occur due to the state of V_d and C_p in the conduction band. However, the other states show small contributions to electronic conductivity. The states, such as V_p and C_s, mainly contribute to the valence band. These results justify the initial efforts made on electronic structures of the V₄C₃ [46].

The PDOS is depicted in Figure 5b,c after loading the Li/Na content on the supercell of V₄C₃ at an insignificant amount (x = 0.0625). Furthermore, the electronic structures of Li/Na-loaded V₄C₃ are inspected at x = 0.0625. At low Li/Na loading, the metallicity of the material is still maintained (i.e., Li_s or Na_s). Thus, the charge carrier transfer to the conduction band is predicted to improve electronic conductivity. The enhanced electronic conductivity suggests the better performance of V₄C₃ as an outstanding host material for both LIBs and SIBs.

4. Conclusions

In summary, a first-principle DFT simulation was utilized to predict the performance of V₄C₃ MXene as an anode for LIBs and SIBs. To this end, the electronic properties, durability, voltage, storage capacity, and activation barriers of Li/Na-loaded V₄C₃ were assessed. The results displayed super performances of the Li_2xV₄C₃ and Na_2xV₄C₃ as anodes for LIBs and SIBs, with an average potential of 0.38 V (for Li) and 0.14 V (for Na), as well as a reasonable Li/Na storage capacity of 223 mAhg⁻¹ and good cycle performance. In addition, V₄C₃ reveals very low diffusion energy barriers of 0.048 eV (for LIBs) and 0.023 eV (for SIBs), indicating the possible fast lithiation/delithiation and sodiation/desodiation processes. As the Li/Na content increased, the voltage decreased from 0.8 to 0.1 V for Li V₄C₃ and from 0.5 to 0.05 V for NaV₄C₃. During Li and Na intercalation, the energy fluctuation vs. time duration revealed a straight line, implying structural stability without any apparent deformations. The process also stems from the prompt recovery of V₄C₃, structure stability during Li/Na, and ion intercalation/extraction. The presented findings may create the opportunity for further usage of V₄C₃ as an anode material for LIBs and SIBs.