Ab initio study of graphene-like monolayer molybdenum disulfide as a promising anode material for rechargeable sodium ion batteries

Abstract

Using first-principles study based on density functional theory (DFT), the adsorption sites, diffusion kinetics, theoretical capacity and average voltage of Na atoms in graphene-like monolayer MoS₂ are systematically investigated in comparison with bulk MoS₂. It is found that for the graphene-like monolayer MoS₂, a maximum theoretical capacity of 335 mA h g⁻¹ could be achieved by double-side Na adsorption. Upon sodiation process, the graphene-like monolayer MoS₂ can maintain a low voltage platform at about 1.0 V. A Na diffusion pathway on the graphene-like monolayer MoS₂ is identified as from two adjacent T-sites passing through the nearest-neighbor H site in a zigzag manner. The activation barrier of this process is only 0.11 eV, a considerable decrease compared to that of the bulk MoS₂ interlayer migration (0.70 eV), which indicates that Na can diffuse faster in the graphene-like monolayer MoS₂ than in bulk MoS₂. The present results suggest that the graphene-like monolayer MoS₂ can provide excellent battery performance as the anode material of a sodium ion battery.

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1. Introduction

Rechargeable sodium ion batteries as an alternative to lithium-ion batteries for large-scale energy storage have been undergoing rapid expansion due to the widespread abundance and low cost, and very suitable redox potential of sodium^1–3 ( versus standard hydrogen electrode, which is only 0.3 V above that of lithium). However, most of the scientific interest in Na-ion batteries has focused on cathode materials, few anode materials have been reported as viable. Interestingly, the reactivity of Li and Na with anode materials is quite different despite their close chemical properties. For instance, graphite, the most common anode material in Li-ion batteries, cannot be satisfactorily used as an insertion electrode in Na-ion batteries because Na atoms do not intercalate well between carbon sheets^4,5 Na metal is also not a good choice because of its high reactivity and low melting point of 97.7 °C compared to 180.5 °C for Li. Thus, the identification of a novel anode with a proper Na storage voltage platform, large reversible capacity and high structural stability is a critical issue for the successful development of Na-ion batteries.

Molybdenum disulfide (MoS₂), structurally similar to graphite, is constructed by three atom layers: a Mo layer sandwiched between two S layers. Similar to graphite, the MoS₂ trilayers are held together by weak van der Waals forces. The large surface areas and interlayer spaces of MoS₂ make it an attractive host for ion intercalation/deintercalation.^6,7 Experimentally, bulk MoS₂ has been investigated as electrode materials for lithium-ion batteries.^8,9 However, large voluminal expansion usually results in their structural instability during the ion intercalation process.¹⁰ Recently, the breakthroughs in preparing graphene-like MoS₂ nanostructures by mechanical or solvent-based exfoliation method^11,12 endow MoS₂ with high reversible lithium storage capacity, good cyclability, and superior rate performance.^13–15 It is suggested that the exfoliated nanosheets with loose stacking can accommodate volume variation and thus alleviate the structural instability confronted by bulk crystals during the charge–discharge processes; furthermore, the ion diffusion path could be significantly shortened. Recently, several groups reported the experimental studies of MoS₂ as a potential host for sodium ion intercalation/deintercalation,^16,17 which open a new ground for rechargeable Na ion batteries. In this work, first principles calculations were used to systematically study the comparison of adsorption and diffusion of Na atoms on bulk and graphene-like monolayer MoS₂. The theoretical capacity and average voltage for bulk and graphene-like monolayer MoS₂ were also computed. Based on our study, it can be found that the graphene-like monolayer MoS₂ may be a promising anode material for Na-ion batteries.

2. Computational details

2.1 Methodology

All the calculations were performed via the ab initio total energy and molecular-dynamics program VASP (Vienna ab initio-simulation program) developed at the Institute für Materialphysik of the Universität Wien.^18,19 The interactions between valence electrons and ions were described with the projector augmented wave (PAW) pseudo-potentials.¹⁹ The GGA/PBE method was used in all the calculations of properties. The convergence tests of the total energy with respect to the k-points sampling and cut-off energy have been carefully examined, which ensure that the total energy is converged to 10⁻⁵ eV per formula unit. It is well-known that the formation of solid electrolyte interface (SEI) can occur on the surface of electrode materials and the surface is solvated. However, in this study, the adsorption and diffusion of Na atoms into idealized MoS₂ systems were carried out. This method mainly calculated the behavior of metal atoms in idealized MoS₂ systems to avoid the complexity of solvent and the presence of SEI. The Brillouin zones of bulk and graphene-like monolayer MoS₂ were sampled with 5 × 5 × 5 and 5 × 5 × 1 k-points, respectively. Energy cut-off for the plane waves is chosen to be 400 eV. Prior to the calculation of the electronic structure, both the lattice parameters and the ionic position are fully relaxed, and the final forces on all the relaxed atoms are less than 0.01 eV Å⁻¹. Especially, to accurately account for van der Waals interactions which might play an important role in layered structure, the PBE + D approach with the vdW correction²⁰ was adopted for the calculation of bulk MoS₂.

To study the diffusion kinetics of Na ion, energy barriers were calculated using the nudged elastic band (NEB) method.^21,22 The NEB is an efficient method for determining the minimum energy path and saddle points between the given initial and final positions. It was performed with the linear interpolation of nine images between the initial and final configurations of the diffusion paths. The geometry and energy of the images were then relaxed until the largest norm of the force orthogonal to the path is less than 0.02 eV Å⁻¹. Each image searches for its potential lowest energy configuration along the reaction path while maintaining equal distance to nearby images.

2.2 Models

In the bulk phase of MoS₂, the MoS₂ layers can be stacked in three patterns: 1T-MoS₂ with the molybdenum atoms coordinated by the sulfur atoms and one Mo atom per unit cell (CdI₂ type),²³ 2H-MoS₂ with two-molecule layers per unit cell (P6₃/mmc)²⁴ and 3R-MoS₂ with trigonal prismatic coordination but with three S–Mo–S units in the c-axis direction.²⁵ However, the most stable form of bulk phase MoS₂ is 2H-MoS₂, which is a stable form up to 1000 °C.²⁶ Meanwhile, graphene-like monolayer MoS₂ presents the sandwich-like structure with the Mo layer sandwiched between two S layers. Two crystal phases of graphene-like monolayer MoS₂ have been reported: trigonal (1T) phase with trigonal prismatic coordination of Mo and hexagonal (1H) phase with octahedral coordination of Mo.^27,28 At room temperature, 1H-phase is more stable than 1T-phase. Therefore, 2H type bulk MoS₂ and 1H-phase structure graphene-like monolayer MoS₂ are considered in our calculations.

To study the effects of Na concentration on the adsorption and diffusion of Na, we construct the 4 × 4 × 1 supercell for bulk MoS₂, which contain 64 S atoms and 32 Mo atoms. For graphene-like monolayer MoS₂, the supercell with a 4 × 4 slab and a 15 Å vacuum space in the periodic directions used to avoid interactions between two neighboring images of the supercell is constructed, containing 32 S atoms and 16 Mo atoms.

3. Results and discussion

3.1 Crystal structures of bulk and graphene-like monolayer MoS₂

A full geometry optimization of both lattice parameters and atomic coordinates for 2H-type bulk MoS₂ and 1H-phase graphene-like monolayer MoS₂ structures was performed. The computed lattice constants are listed in Table 1 and compared with experimental data.²⁹ It can be seen that the a-lattice constants and bond length of Mo–S for both bulk and graphene-like monolayer MoS₂ calculated in GGA/PBE or PBE + vdW method are in good agreement with experimental data. For bulk MoS₂ the c-lattice constant calculated in the GGA method produce an overestimated value of 13.78 Å. In contrast, the PBE + vdW approach shows an optimal value of 12.40 Å, close to the experimental value of 12.29 Å.

Table 1 Lattice parameters and bond length from DFT calculations in comparison to experimental data

	Bulk		Monolayer	Experiment^29
	PBE	PBE + D	PBE
a/Å	3.18	3.19	3.18	3.16
c/Å	13.78	12.40	—	12.29
c/a	4.33	3.89	—	3.89
dS–Mo/Å	2.41	2.41	2.41	2.41

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3.2 Adsorption of Na atoms on bulk and graphene-like monolayer MoS₂

In the present study, different Na adsorption positions and amounts are given a comprehensive consideration. Binding energy (E_b) is used to represent the stability of the Na adsorbed system, which is defined as E_b = [E_MoS2 + nE_Na − E_Na@MoS2]/n, where E_Na@MoS2 denotes the total energy of Na-adsorbed MoS₂ (bulk or monolayer), E_MoS2 is the total energy of the pristine MoS₂ (bulk or monolayer), and E_Na is the energy of an isolated Na atom. According to this definition, a more positive binding energy indicates a more favorable exothermic sodiation reaction between MoS₂ and Na atoms.

First, single Na atom adsorption behavior of bulk and graphene-like monolayer MoS₂ is examined. In bulk MoS₂, there are two representative adsorption sites: one is the tetrahedral site (T_s) formed by one S atom from the upper triple layer and three S atoms from the lower triple layer (Fig. 1a) and the other is the octahedral site (O_s), in which Na can bind to three S atoms from each of the triple layers (Fig. 1b). The total energy calculation results reveal that the adsorption site O_s is energetically more stable than the T_s site in bulk MoS₂. For graphene-like monolayer MoS₂, there are also two stable adsorption sites: the hollow site (H) above the center of the hexagon and the top site (T) directly above one Mo atom, as shown in Fig. 1c and d. From the calculation results, the total energy of adsorption for site T is lower than site H in monolayer MoS₂. Therefore, a single sodium atom adsorbs at the octahedral site (O_s) in bulk MoS₂ and adsorbs at the T site on graphene-like monolayer MoS₂. The calculated binding energies of each site are shown in Table 2.

Fig. 1 Side views of a Na atom adsorbed at T_s (a) and O_s (b) sites in MoS₂ bulk. Top (c) and side (d) views of a Na atom adsorbed on the graphene-like monolayer MoS₂.

Table 2 Na bind energies and Bader charges in bulk and monolayer MoS₂

	Bulk		Monolayer
	Ts	Os	H	T
Eb (eV)	1.03	1.70	1.23	1.27
qNa (|e|)	+0.79	+0.77	+0.86	+0.86

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To quantitatively estimate chemical bonding and charge transfer between Na atoms and MoS₂, Bader charge analysis^30,31 is performed (Table 2). It can be seen that the bonding between the adsorbed Na and substrate MoS₂ is predominantly ionic with a small part of covalence, and the valence electrons from the adsorbed Na atoms are transferred to the MoS₂. The calculation results suggest Na atoms transfer 0.77|e| and 0.86|e| charge to bulk and graphene-like monolayer MoS₂, respectively. The adsorbed Na forms six Na–S bonds in bulk MoS₂, while in graphene-like monolayer MoS₂ there are only three Na–S bonds, which will slow Na diffusion in bulk MoS₂.

To further study the Na adsorption amount, the adsorption behavior of two Na atoms on the graphene-like monolayer MoS₂ is examined. Five typical cases are illustrated: (a) unifacial adsorption on the top of two Mo atoms, (b) bifacial adsorption up and downward to one hollow site (H-site), (c) bifacial adsorption up and downward to one Mo atom (T-site), (d) bifacial adsorption up and downward to the two nearest neighboring Mo atoms, (e) bifacial adsorption up and downward to two next nearest neighboring Mo atoms, the geometries with the binding energy of each case are displayed in Fig. 2. The calculation results indicate that model (c) has the strongest binding energy, and the binding energy of model (d) is 0.005 eV lower than model (e). It suggests that two sodium atoms energetically prefer to coordinate upward and downward to the same Mo atom on graphene-like monolayer MoS₂, and repulsive electrostatic interactions between Na⁺ cations lead to Na atoms coordinate decentralized. In this case, we construct the structures of more Na atoms adsorbed on the graphene-like monolayer MoS₂ in a manner similar to that discussed above. Meanwhile, the adsorption behavior of two Na atoms in bulk MoS₂ is studied based on the similar details and conditions as on graphene-like monolayer MoS₂. The calculation results indicate that Na atoms prefer to adsorb upward and downward to the same O_s site of bulk MoS₂. Further investigation on binding energies as a function of the number of Na atoms for both bulk and graphene-like monolayer MoS₂ is performed, as shown in Fig. 3. It can be seen that the Na binding energy of bulk MoS₂ increases gradually with the increase in the number of Na atoms n from one to eight, and then displays a flat trend and maintains about 2.2 eV from 8 to 32 Na adatoms. However, the binding energies of graphene-like monolayer MoS₂ are independent of sodium concentration. It displays a flat trend and maintains about 1.25 eV. The Na binding energy of graphene-like monolayer MoS₂ remains 1.21 eV even at n = 32, indicating that Na atoms can still be stably adsorbed at graphene-like monolayer MoS₂ and the phase separation problem can be safely avoided at such a high concentration.

Fig. 2 Different potential positions investigated of two sodium atoms adsorbed on the graphene-like MoS₂ monolayer. Binging energy (E_b) of each case is listed right below.

Fig. 3 Binding energies with increasing number of Na atoms for bulk () and the graphene-like monolayer MoS₂ ().

3.3 Electrochemical performance

The Na storage capacity and average voltage of bulk and graphene-like monolayer MoS₂ are further explored because it directly determines the potential applications of these kinds of materials. Because Na atoms can absorb on both the sides of the graphene-like monolayer MoS₂, Na₂MoS₂ represent the highest Na storage capacity of monolayer. It can be deduced that the graphene-like monolayer MoS₂ has a theoretical capacity of 335 mA h g⁻¹. As a comparison, bulk MoS₂ can only store Na atoms up to NaMoS₂, the theoretical capacity is only half of the graphene-like monolayer MoS₂. Therefore, the graphene-like monolayer MoS₂, with fully exposed additional active sites for the accommodation of Na atoms can provide a higher power density than bulk MoS₂.

Next, the average voltage for Na intercalation on graphene-like monolayer and bulk MoS₂ can be calculated. The charge–discharge processes of MoS₂ follow the common half-cell reaction vs. Na/Na⁺:

MoS₂ + xNa⁺ + xe⁻ ↔ Na_xMoS₂

The theoretical procedure to calculate the average voltage through first principles can be established from the energy difference based on the equation below:³²

where , are the total energies of Na_x1MoS₂ and Na_x2MoS₂, E_Na is the total energy of metallic sodium in a body-centered-cubic (bcc) phase, x₂ − x₁ refers to the number of sodium ions intercalated. According to this equation, the computed average voltage of the graphene-like monolayer MoS₂ display a flat platform at about 1.0 V, which provides significant feasibility to be applied as Na ion battery anodes. In contrast, the calculated average voltage of bulk MoS₂ is between 1.7–2.0 V, which is inapplicable for anode materials. Experimental data reported recently in literature on Na intercalation in MoS₂ are qualitatively consistent with the theoretical predictions mentioned above. Park et al. reported that bulk MoS₂ delivered a first discharge capacity of 190 mA h g⁻¹ at 0.4–2.6 V by intercalation/deintercalation reaction and maintained a capacity of 84 mA h g⁻¹ even after 100 cyles.⁸ In addition, an exfoliated MoS₂/C composite has been reported as an excellent anode material for sodium ion batteries. The graphene-like exfoliated MoS₂/C composite achieved a high capacity of ∼400 mA h g⁻¹ at an average working voltage of 1.0 V for 100 cycles.³³ Accordingly, it can be suggested that the graphene-like monolayer MoS₂ is more suitable as an anode for Na ion battery electrode material because of its lower electrode potential and higher capacity than bulk MoS₂.

3.4 Na diffusion

It is known that the rate performance of sodium ion battery electrode material is mainly determined by the electrical conductivity and sodium diffusion rate. Fast Na diffusion determines high charge–discharge rates of batteries. Thus, it is significant to study the diffusion of sodium atoms on MoS₂ in terms of its actual application as the anode material of Na ion batteries. Na migration in the interlayer of bulk MoS₂ is firstly considered. The diffusion path is investigated between two adjacent octahedral-sites (O_s1–O_s2). The diffusion pathway and energy barrier are shown in Fig. 4a–c. The computed diffusion barrier for this path is 0.70 eV. For comparison, Na migration in the graphene-like monolayer MoS₂ is also examined. In this case, Na migration between two adjacent T-sites (T₁–T₂) is investigated because of the energetic favorability to the H sites. It can be found that the specific path of sodium diffusion is from a T₁ site to an adjacent T₂ site passing through the nearest-neighbor H site in a zigzag manner, as is presented in Fig. 4d–f. The energy barrier of this process is only 0.11 eV, which is considerably lower than that of bulk MoS₂. According to the Arrhenius equation, the diffusion constant (D) is proportional to exp(−E_barrier/k_BT), where E_barrier and k_B are the activation energy and Boltzmann constant, respectively. Therefore, it can be concluded that at room temperature Na diffusion on the graphene-like monolayer MoS₂ is about 10⁹ faster than on bulk MoS₂. The significantly enhanced mobility of the graphene-like monolayer MoS₂ makes it more attractive for promising anode materials with fast charge–discharge rates.

Fig. 4 Na migration path in the interlayer of bulk MoS₂ and the corresponding energy profiles along the Na diffusion path: (a) side view (b) top view (c) diffusion path; Na diffusion path on the surface of the graphene-like monolayer MoS₂ and corresponding energy profiles along the Na diffusion path: (d) side view (e) top view (f) diffusion path.

4. Conclusion

In conclusion, based on density functional theory (DFT), the adsorption, diffusion properties, as well as the maximum capacity and average voltage of the graphene-like monolayer MoS₂ in comparison with bulk MoS₂ were systematically investigated by first principles calculations. The results demonstrated that the monolayer can stably adsorb Na up to Na₂MoS₂, which converts to a higher theoretical capacity (335 mA h g⁻¹). Upon sodiation processes, the graphene-like monolayer MoS₂ can maintain a lower and applicable voltage platform (1.0 V) compared to bulk MoS₂ (1.7–2.0 V). Although the bulk MoS₂ have higher Na binding energies, the lower Na mobilities do not make them ideal candidates for anode materials. Na mobility can be considerably enhanced by the dimensionality reduction, the diffusion barrier decreases from 0.70 eV to 0.11 eV because the MoS₂ changes from bulk to a monolayer structure. Therefore, because of high stability and low Na diffusion energy, high theoretical capacity, low average voltage, the graphene-like monolayer MoS₂ can be used as a promising anode material for high performance rechargeable Na-ion batteries.

Acknowledgements

This work is funded by the National Natural Science Foundation of China under project no. 51472211, Scientific and Technical Achievement Transformation Fund of Hunan Province under project no. 2012CK1006, Key Project of Strategic New Industry of Hunan Province under project no. 2013GK4018, and Science and Technology plan Foundation of Hunan Province under project no. 2013FJ4062. YP is supported by Natural Science Foundation of China (Grant no. 21103144) and Hunan Provincial Natural Science Foundation of China (12JJ7002, 12JJ1003).

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