Article pubs.acs.org/JPCC
First-Principles Investigation of Transition Metal Dichalcogenide Nanotubes for Li and Mg Ion Battery Applications Aline O. Pereira* and Caetano R. Miranda* Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André, Brazil
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S Supporting Information *
ABSTRACT: First-principles calculations are employed to explore and rationalize the potentialities of MoS2 and WS2 armchair nanotubes for Li and Mg ion battery applications. A comparison with the reported values for Li insertion in TiS2 and MoS2 nanotubes shows that WS2 and MoS2 nanotubes presented enhanced ion mobility. Especially for MoS2, the Li mobility is 4 times faster than in TiS2 nanotubes. On the other hand, analysis of the Mg diffusion properties suggests that WS2 nanotubes would be a better option, with ion mobility 3 times faster in relation to MoS2 nanotubes. In terms of mobility, the Mg intercalation in WS2 and MoS2 nanotubes shows remarkable properties in comparison with Li insertion. Although it seems that Li and Mg insertion in WS2 and MoS2 nanotubes will be thermodynamically unstable, it is expected that the combination of nanotubes and high voltage electrode materials will increase the ion stability while keeping the faster ion mobility. Therefore, our results suggest high ion mobility at the surface of MoS2 and WS2 and support the potential application of the use of such systems as additive electrode materials for high-rate battery applications.
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a capacity of 800 mA h g−1, and maintains a capacity of 750 mA h g−1 after 20 charge/discharge cycles. Also, hydrothermally prepared MoS2 nanoflakes exhibit a capacity of about 1000 mA h g−1.28 MoS2 nanoflowers and nanoplates show a capacity of 900 and 1062 mA h g−1, respectively.29,30 A remarkable specific capacity of more than 1100 mA h g−1 is obtained for MoS2 coated carbon nanotubes.31 When considering WS2, an electrochemical study of Julien32 demonstrates the ability to intercalate 0.6 mol of Li ions per mol of WS2. Nanorods of Codoped WS2 are capable of reversibly store lithium at a capacity of 568 mA h g−1.33 Storage capacities higher than 700 mA h g−1 were reported for WS2 nanoflakes and mesoporous WS2 structures.34,35 A graphene−WS2 composite shows a capacity of 905 mA h g−1.26 For magnesium batteries, experimental studies have shown a capacity of 213 mA h g−1 for sandwich-structured graphene-like MoS2/C microspheres.36 In addition, the adsorption of Mg in MoS2 nanoribbon is able to deliver a capacity of about 223 mA h g−1.37 However, a limiting factor for Mg based batteries is related to the ion mobility, since the Mg2+ insertion into ion transfer hosts proceeds slowly because of the strong polarization effect of small and divalent Mg2+ ions.38,39 The incorporation of nanotubes to electrode materials may considerably reduce the activation energy and consequently improve the ion mobility.40−43 The combination of the layered structure of TMD and the open-ended tubular topology of nanotubes is expected to have a considerable effect on ion
INTRODUCTION The search for efficient energy storage and conversion technologies has received a significant amount of attention in the past few years.1−3 The interest in progressively smaller scale and larger capacity devices for a wide range of portable, automotive, and stationary systems continues to be a strong driving force for the development of advanced rechargeable batteries.4 Although important achievements were obtained, the development of batteries with the ability to retain their capacity over thousands of cycles and progressively higher energy storage densities is still required. In addition, the improvement of the charging time is also an essential issue.5−7 The recent advances in nanostructured materials have opened a wide range of new multifunctional materials with promising potential for battery applications.8−11 Nanostructured materials of transition metal dichalcogenide (TMD) have shown the ability to efficiently intercalate/deintercalate foreign ions or molecules, which is a consequence of its high surface area and shorter diffusion path for transport.12−15 These features are strongly correlated to the layered structure of TMD, which provides more room for storage. In bulk form, each layer is composed of a metal atom sandwiched between chalcogen atoms in a trigonal prismatic or octahedral coordination.16 These basic triple layer structures are held together by weak van der Waals interactions, which allow the production of nanostructured materials such as, monolayers, nanotubes, nanoflakes, nanorods, and nanoflowers.17−20 In particular, the use of MoS2 and WS2 based materials as electrodes can substantially improve the cycle stability and rate capabilities.21−26 For lithium batteries, Du et al.27 have shown that a MoS2 structure with enlarged c-lattice parameter presents © 2015 American Chemical Society
Received: October 8, 2014 Revised: February 6, 2015 Published: February 9, 2015 4302
DOI: 10.1021/jp510182u J. Phys. Chem. C 2015, 119, 4302−4311
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The Journal of Physical Chemistry C mobility and capacity of an electrode, since it would provide a fast pathway for ion diffusion and more room for storage. In this sense, a complete understanding of the size effect on ion mobility and voltage profile is essential. It can provide a useful guide to the development of new electrode materials with improved capacity and charging/discharging time. In view of this, we explore and rationalize the potentialities of MoS2 and WS2 armchair nanotubes for Li and Mg batteries applications. To this end, first-principles calculations, based on the density functional theory (DFT),44,45 and the curved surface method46 were employed to investigate how the diffusion properties, voltage profile, and binding energy change for the different sizes and chemical compositions. Electronic structure calculations were also performed.
Figure 1. (a) Schematic representation of a trigonal prismatic transition metal dichalcogenide (MS2; M = Mo, W) monolayer. The red box defines the armchair structure. (b) Comparison between an armchair nanotube and its associated curved surface.
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COMPUTATIONAL DETAILS First-principles calculations were carried out using the Vienna ab initio simulation package (VASP).47,48 The exchange and correlation terms were treated in the generalized gradient approximation (GGA) of Perdew−Burke−Ernzerhof (PBE),49 and projector-augmented wave pseudopotentials50,51 were used. Convergence was tested for supercell size effects, Brillouin sampling, and energy cutoff. Plane waves with kinetic energy cutoff of 600 eV are used and atomic positions were relaxed until all forces are less than 0.03 eV/Å. Tests with dipole moment and spin polarization corrections were performed with no significant observed change. MoS2 and WS2 share the same topological structure; both are composed of a layered structure of S−M−S, with the metal atom M in a trigonal prismatic coordination (2H phase). The monolayer structure was determined using a three-atom unit cell, with a 15 Å vacuum layer. Atomic positions, unit cell shape, and volume were relaxed using a 13 × 13 × 13 Monkhorst− Pack k-point mesh. The calculated lattice parameter for both MoS2 and WS2 monolayers is 3.19 Å, which is slightly higher than the computed bulk value (approximately 3.16 Å), in agreement with previous reported values.52 The computational modeling of inorganic nanotubes with realistic size requires the use of hundreds or even thousands of atoms, which is far too large for typical DFT calculations. In order to reduce the required computational power and allow the investigation of radii observed experimentally, the nanotube structure was modeled using the curved surface method.46 This method proposes that a curved surface, with constant curvature radius, is able to reproduce the surface environment of a complete nanotube. Figure 1 shows a schematic representation of a trigonal prismatic TMD monolayer (MS2; M = Mo, W), a full nanotube, and the equivalent curved surface. The armchair structure is defined in red and a comparison between a full nanotube and a curved surface is presented. The curved surface (Figure 1b) is a modulated surface that can have any radius of curvature without increasing the number of atoms. It has a constant curvature everywhere with the exception of a series of inflection points, where an inversion in curvature is seen. Local properties, such as ion voltage and activation barrier for diffusion, can be accurately estimated when analyzed far from the inflection points. In fact, by comparison of the full nanotube and the curved surface calculations, accuracies of 1% and 3% were obtained for voltage and activation barrier calculations, respectively.46 This is the case when the nanotube’s diameter is lager enough, so there is no interaction between the internal insertion sites and the far
side of the nanotube. Therefore, a constant curvature was applied to the relaxed monolayer of MoS2 and WS2. For voltage and electronic structure calculations, the curved surface is represented by a computational cell containing a vacuum layer of 15 Å along the direction perpendicular to the surface (y-direction). The nanotube axis is oriented in the zdirection and contains one metal atom (c ≈ 3.19 Å), and the curved surface contains two inflection points at the x-direction. To simulate nanotubes with a curvature radius of 10 Å, this computational cell contains 36 atoms, while for nanotubes with radius size larger than 25 Å, 60 atoms were required. In order to investigate the ion migration along the nanotube axis, a computational cell twice as long in the z-direction was used for activation barrier calculations. When relaxing the curved surfaces, the metal atoms located at inflection points were kept fixed in order to maintain the curvature. Energy convergence was achieved using a 1 × 1 × 9 Monkhorst− Pack k-point mesh. For the electronic structure calculations, i.e., projected density of states, a denser Monkhorst−Pack k-point mesh of 1 × 1 × 25 was used. Experimental studies of Lukowski et al.54 and Wang et al.55 have shown that MoS2 undergoes a structural transition from the 2H phase to the 1T phase under lithiation. Wang et al.55 have also shown that this transition depends on the Li concentration and occurs for ion concentration greater than 28%. Therefore, since in our calculations we consider an ion concentration of 25%, it is expected that structural changes do not present a significant role and we only consider the 2H phase. The trigonal prismatic MS2 bulk structure (2H phase) presents two possible sites for ion insertion, as represented in Figure 2a. In both cases, the insertion ion is located at the existent van der Waals gap between two consecutive S−M−S triple layers. In the first case (site A), the insertion ion sits at the center of a tetrahedra formed by three sulfur atoms from the bottom layer (yellow) and one atom from the top layer (brown). Another possibility is when the ion occupies an octahedral site (site B), in which three sulfur atoms from the bottom layer and three from the top layer coordinate the ion. The two possible sites for ion insertion on the surface of a monolayer or nanotube can be related to the bulk insertion sites. In both cases the insertion ion is coordinated by three S atoms of the surface. As shown in Figure 2b, in site A the ion sits above a metal atom. On the other hand, in site B the insertion ion sits at the center of a hollow site (without a 4303
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Figure 2. Schematic representations of the (a) insertion sites in the bulk structure, (b) insertion sites in the monolayer structure, (c) site A insertion at the inside and outside surfaces of a nanotube, and (d) site B insertion at the inside and outside surfaces of a nanotube. At the nanotube’s surface, the insertion ion is coordinated by three sulfur atoms, which defines a LiS3 pyramid (highlight in gray). Gray spheres represent the metal, while yellow and brown stand for sulfur atoms. The insertion ion is represented by green spheres.
Figure 3. (a) Voltage and (b) binding energy profiles for Li insertion at the inside and outside surfaces of WS2 nanotubes. The horizontal lines stand for the plain monolayer. Li insertion at the WS2 bulk structure leads to a voltage of approximately 1 V and a binding energy of about 4 eV.
central metal atom). Figure 2c,d shows the similar insertion sites at the inside and outside surface of a nanotube. At the nanotube’s surface, the insertion ion is coordinated by three sulfur atoms, which defines a LiS3 pyramid (highlight in gray), as shown in Figure 2c,d. Voltages were calculated for a single ion insertion at the inside and outside surface of the nanotube at sites A and B. Following the procedure proposed in ref 53, the theoretical average voltage of a Y ion inserted in a MS2 structure is defined as V=−
The energetic stability of a Y ion at the surface of a MS2 structure can also be analyzed with respect to the binding energy Y E bind = −(E YMS2 − E MS2 − E Yiso)
in which Eiso Y is the total energy of the isolated Y ion. Activation energy barriers for ion migration at the surface of a nanotube, monolayer and inside the bulk structure were calculated using the nudged elastic band (NEB) method.56−58 NEB is an efficient method to determine the minimum energy pathway between initial and final states. Convergence tests have shown that nine intermediate images are enough to accurately describe the activation energy barriers. It is also possible to estimate the changes in ion mobility by means of the Arrhenius’ formula, in which the diffusion coefficient D of a chemical reaction or physical process at a temperature T is related to the activation energy barrier EA through an exponential formula:
(E YMS2 − E MS2 − E Y ) zF
(2)
(1)
where F is the Faraday constant, Y is the intercalation ion (Li or Mg), z is the charge (in electrons) available for transport (z = 1 for Y = Li and z = 2 for Y= Mg), and EYMS2, EMS2, and EY are the total energies of the MS2 system with one adsorbed Y ion, the MS2 pristine surface, and the metallic Y as calculated in the bulk bcc (Y = Li) or hcp (Y = Mg). The ion concentration was estimated by comparing the voltage of a monolayer with various homogeneous ion distributions to those with a short ion−ion distance. This comparison indicates that the computed voltage for a single insertion ion in our supercell probably reflects a nanotube with an ion concentration of approximately 25%.46
⎡ E ⎤ D = K 0 exp⎢ − A ⎥ ⎣ kBT ⎦
(3)
where kB is the Boltzmann constant and K0 is a prefactor often assumed to be independent of the temperature. In our analysis we are interested in quantifying the improvements in ion mobility; therefore, only differences in activation energy are calculated. These differences will result in variations in the 4304
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Figure 4. Schematic representation of the minimum energy pathway for Li migration at the outside surface of a WS2 nanotube: (a) top view and (b) side view. For nanotubes and monolayer, the minimum energy pathway between two consecutive sites A is through a site B. In the case of bulk, it is between two consecutive sites B and passes through a site A. Gray, yellow, and green spheres stand for W, S, and Li atoms, respectively. (c) Energy diagram for Li migration.
unstable site. On the other hand, for outside insertion (Figure 2c), the strain leads to an expansion of the pyramid’s base and reduce its height in comparison to larger nanotubes, which provides more space for the Li−W interaction. Different from what is found for armchair nanotubes, the Li insertion in bulk WS2 is more stable at the octahedral site B (Figure 2b) and leads to a voltage of approximately 1 V and a binding energy of about 4 eV. The negative voltages and small binding energies shown in Figure 3 indicate that Li will not be stable at the surface of armchair nanotubes. Although these results correspond to a Li concentration of approximately 25%, it is expected that at lower concentration the voltage and binding energies will be higher, leading to positive voltages at some radii of curvature.59 In fact, it has been experimentally shown that an electrode composed of WS2 open ended multiwalled nanotubes presents charge/ discharge plateaus between 0.6 and 2.0 V.42 Activation energy barrier calculations for Li migration in WS2 structures were computed using the NEB method. Because high voltage and binding energy values are desirable in order to increase the energy density of a battery, we explore the energy pathway for Li migration at the outside surface of the nanotube. The reaction pathway for nanotubes and monolayer is between two consecutive sites A, since the highest voltage and binding energy are for Li insertion at site A. Exceptionally for the bulk structure, since the B site is more stable, the reaction pathway is between two consecutive B sites. Schematic representation of the minimum energy pathway for Li migration in a WS2 nanotube is presented in Figure 4a,b. The top view shows that at the outside surface the Li migration between two consecutive sites A is through a site B. For a WS2 monolayer the same pathway is seen. In the case of bulk, since the B site is the most stable for Li insertion, the reaction pathway starts at B, pass through A, and ends in an equivalent B site. The energy diagram for Li migration is presented in Figure 4c. These results show that the minimum energy pathway displays a mirror symmetry at the intermediary site for all sizes of nanotubes, monolayer, and bulk. The intermediary site represents an energy local minimum in the reaction pathway.
diffusion coefficient, which can be estimated without defining the K0 factor.
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RESULTS AND DISCUSSION Lithium. In order to explore and rationalize the use of TMD nanotubes for Li battery applications, we investigate the Li adsorption and diffusion properties for MoS2, WS2, and TiS2 armchair nanotubes. For this end, we reproduce the results presented by Tibbetts et al.46,59 for MoS2 and TiS2 and complement them with the evaluation of the adsorption and diffusion properties for Li insertion in WS2 nanotubes. Electronic structure calculations were also performed. The voltage and binding energy profiles for Li insertion at the inside and outside surfaces of WS2 nanotubes are shown in Figure 3. As a general trend, the monolayer voltage and binding energy values are recovered for large nanotubes. For all radii, lithium insertion at the outside surface of the nanotube has been shown to be the most stable, especially for insertion at site A. The highest voltage (−0.1 V) and binding energy (1.64 eV) are seen for a nanotube with 10 Å of radius. Voltage and binding energy values for inside insertion are usually smaller, which is a consequence of an increase in Li−W distance. As the radius increases, the voltage and binding energy are reduced for outside insertion, while the opposite behavior is found for inside insertion. The only exception is for inside insertion at site B of a 10 Å nanotube, where the voltage and binding energy values are slightly higher than the values found for nanotubes of 25 and 50 Å. This unexpected behavior may be explained by the fact that in the 10 Å nanotube the B site at the inner surface is an unstable insertion site; i.e., when considering the B site as the starting geometry, after relaxation the Li ion slides off to an intermediate site between sites A and B. For narrow nanotubes, the Li−W distances for outside and inside insertions are approximately 2.9 and 3.47 Å, respectively. The compression strain introduced at the inner surface of the nanotube changes the size of the LiS3 pyramid (Figure 2d). The base of the pyramid is reduced and the height increases in comparison to larger nanotubes (Li−W distance). This structural change reduces the interaction between Li and W at this specific insertion site and in some cases turns it into an 4305
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way to WS2 nanotubes, the fastest Li mobility in MoS2 nanotubes occurs at narrow systems (10 Å). Therefore, the incorporation of MoS2 and WS2 armchair nanotubes in electrode materials may delivery a higher voltage with improved ion mobility. In order to explore the differences between TiS2, MoS2, and WS2 nanotubes, a projected density of states (PDOS) analysis were performed. Figure 5 shows the electronic structure of each system before and after Li insertion at site A of the outside surface of a 10 Å nanotube. Results for the d state of the metal atom in pristine surfaces, Figure 5a, show that TiS2 nanotubes are metallic systems. Similar to what is found for bulk structures, MoS2 and WS2 nanotubes have a semiconductorlike behavior with a band gap of approximately 1.5 and 1.8 eV, respectively. As a consequence of its metallic properties, the electronic structures of TiS2 nanotubes are considerably affected by Li insertion. Figure 5b suggests a reduction in peak intensity at the valence band (VB) and a broadening of peaks at the conduction band (CB) for the d state of Ti. In relation to S atom, a reduction in peak intensity is seen for the whole p state. Regarding semiconductor-like nanotubes, it is not possible to identify any considerable change at the VB of the metal atom. However, a reduction in peak intensity at the conduction band is seen and the band gap values are increased to 1.84 and 1.86 eV for MoS2 and WS2, respectively. For S atom, there is no considerable change after Li insertion. A comparison of the s state of Li for the different nanotubes, Figure 5b, shows that in TiS2 nanotubes Li strongly interact with the VB. On the other hand, an opposite behavior is seen for MoS2 and WS2 nanotubes, where the most significant interaction happens at the CB. In addition, for these semiconductor-like nanotubes, the peak intensity of the CB of Li increases with the band gap value of the pristine nanotube. Another way to evaluate the interaction between Li and the nanotube surface is to compare the PDOS of the metal and S atoms closest to Li insertion site, far from Li insertion site and in systems without Li insertion (pristine nanotubes). Since Li insertion is a local phenomena, we do not expect any considerable interaction between Li and atoms far from the insertion site. These results are presented in Figure 6. For both MoS2 and WS2, our results indicate that this condition is indeed satisfied and Li insertion has a minor effect in the electronic structure of atoms far from the insertion site, whereas for TiS2 nanotubes a slight change of the electronic structure is seen for atoms far from the insertion site. The metallic character of this system allows the interaction with Li to be spread for the whole system.
The lowest activation energy barrier is 198 meV for Li migration for nanotubes with 10 Å of radii. As the curvature radius increases, the activation energy tends to the monolayer value, which is approximately 288 meV. These values are considerably lower in comparison to the WS2 bulk structure, where an activation energy of about 630 meV is found. Therefore, Li migration in narrow WS2 armchair nanotubes is considerably faster when compared with larger nanotubes, monolayer, and bulk structure. By considering the Arrhenius’ formula defined in eq 3, it is possible to estimate the size and composition effects in Li mobility. The use of an armchair nanotube of 10 Å instead of its bulk counterpart will reduce the activation energy by 400 meV. At room temperature, this reduction in energy can lead to an improvement in Li mobility by a factor of 106. A summary of the most relevant results for adsorption and diffusion properties of Li insertion in TiS2, MoS2 and WS2 nanotubes is shown in Table 1. Results for TiS2 and MoS2 were Table 1. Summary of the Most Relevant Results for Li Adsorption and Diffusion Properties in TiS2, MoS2, and WS2 Armchair Nanotubes with Curvature Radius of 10 and 100 Åa R = 10 Å TiS2 MoS2 WS2
R = 100 Å
voltage (V)
EA (meV)
voltage (V)
EA (meV)
1.30 0.10 −0.15
270 146 198
1.53 −0.11 −0.37
180 225 287
a
Results for TiS2 and MoS2 were reported by Tibbetts et al.46,59 EA stands for activation energy barrier.
previously reported by Tibbetts et al.46,59 The voltage and binding energy for Li insertion in TiS2 nanotubes increase with the radius of curvature, while the activation energy decreases. An opposite behavior is found for Li insertion in MoS2 and WS2, where the highest voltages/binding energies and lowest activation energies are observed for narrow nanotubes. The similarities between MoS2 and WS2 nanotubes are probably a consequence of the structural similarity of these systems. Although Li insertion in large TiS2 nanotubes delivers the highest voltage and binding energy values, the activation energies in small MoS2 and WS2 are the lowest. The highest difference is for MoS2 nanotubes, where the activation energy for the system with the highest voltage (10 Å nanotube) is 34 meV lower than that of the TiS2 nanotube with the highest voltage (100 Å nanotube). At room temperature, this change in energy may improve the Li mobility by a factor of 4. In a similar
Figure 5. Computed projected density of states (PDOS) for MoS2, WS2, and TiS2 nanotubes: (a) without Li insertion and (b) Li outside insertion at site A. EF stands for Fermi level energy. 4306
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Figure 6. Comparison between near, far, and no insertion projected density of states (PDOS) for MoS2, WS2, and TiS2 nanotubes: (a) d state of metal atom and (b) p state of S atom. EF stands for Fermi level energy.
Figure 7. Computed voltages and binding energies for Mg insertion at site A of the outside surface of MoS2 and WS2 nanotubes. Values for monolayer are also shown. The bulk MoS2 voltage and binding energy are 0.63 V and 2.75 eV, respectively. In the case of bulk WS2 these values are 0.15 V and 1.50 eV, respectively.
Giving these similarities, a complete description of the voltage and binding energy profiles are shown in the Supporting Information and only the highest voltage and binding energy values obtained for outside insertion at site A of MoS2 and WS2 are shown in Figure 7. In the same way as for Li insertion, the computed voltages and binding energies are higher for MoS2 nanotubes. Again, the negative voltages and small binding energies indicate that at an ion concentration of 25%, Li adsorption will be unstable. Higher values are expected when reducing the ion concentration. Actually, experimental results show that nanostructured MoS2 based materials display charge/discharge voltage plateaus between 0.6 and 2 V.36,39 In contrast to the results found for armchair nanotubes, Mg insertion in bulk MoS2 and WS2 is more stable at site B. The bulk MoS2 voltage and binding energy are 0.63 V and 2.75 eV, respectively. In the case of bulk WS2 these values are 0.15 V and 1.50 eV, respectively. The minimum energy pathway for Mg migration at the outside surface of MoS2 and WS2 nanotubes is very similar to that for Li migration in WS2 nanotubes. As schematically represented in Figure 4a,b, Mg migration between two consecutive sites A is through a site B, where, in the energy diagram, sites A are global minima and site B is a local minimum. For bulk structures, Mg migration is between two consecutive sites B. Because of these similarities, these energy diagrams are presented in the Supporting Information and a comparison of the activation energy barriers for Mg migration in MoS2 and WS2 is shown in Figure 8. Our results suggest that for both systems a considerable improvement in Mg mobility is observed in comparison to their bulk counterparts. Again, the activation energy increases with
In semiconductor-like nanotubes, the electronic structure for metal atoms near the Li insertion site indicates a reduction of peak intensity and peak broadening at the CB. Considerable changes in peak intensity and width are not observed for the p state of S atoms, and only a slightly negative shift in energy of the whole state is noticed. These results indicate that for MoS2 and WS2 nanotubes, Li strongly interacts with the CB of metal atoms. The metallic nature of TiS2 nanotubes allows the Li insertion to considerable change the electronic structure of near and far atoms, although only a positive shift in energy of the whole state for both Ti and S atoms far from Li is seen. In relation to near sites, a considerable reduction of peak intensity at the VB and a broadening of peak at the CB are observed for Ti atoms. For S atoms, a reduction in peak intensity and width is found. Results presented in Figure 6b indicate that these changes are more accentuated at the valence band of S atoms and suggest that the interaction between Li and S atoms in TiS2 nanotubes is larger than that observed in MoS2 and WS2 nanotubes. Magnesium. Since the use of semiconductor-like nanotubes seems to improve the Li mobility in relation to TiS2 nanotubes, we also investigate the Mg adsorption and diffusion properties in MoS2 and WS2 nanotubes. The computed voltage and binding energy profiles are very similar to those shown in Figure 3 for Li insertion in WS2 nanotubes: (i) the monolayer values are recovered for large nanotubes; (ii) for all sizes, Mg insertion at the outside surface of the nanotubes has been shown to be the most stable, especially for insertion at site A; (iii) the voltage values for inside insertion are usually smaller because of an increase in Mg−W distance. 4307
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intensity of these two peaks is small, and the Mg interaction is similar for both the VB and CB of WS2 nanotubes. In a similar way to Li insertion, an increase in band gap values is observed. After Mg insertion the band gap values are approximately 1.87 and 2.0 eV for MoS2 and WS2, respectively. In order to obtain a better understanding of the induced changes in the electronic structure due to Mg insertion, we also compare the PDOS of the metal and S atoms closest to the Mg insertion site, far from Mg insertion site, and in pristine surfaces. These results are presented in Figure 9b. As expected, the Mg insertion is a local phenomenon and no considerable changes are observed for atoms far from the insertion site. A larger peak in the s state of Mg is seen at the valence band. In similar way to Li insertion, Mg insertion locally changes the electronic structure, and electronic states for far and no insertion atoms are quite similar. For metal atoms, after insertion, a broadening of the CB is noticed without significative change in peak intensity. This result suggests a large interaction between Mg and S atoms. Results for S atoms show that Mg interaction introduces a small peak in the gap region, which is more pronounced for MoS2. For both systems, the electronic states of metal and S atoms are slightly reduced in energy. A peak broadening at the CB is seen for the d state of the metal atom, and there is an appearance of a new peak at the CB. In relation to the p state of S, near the VB maximum is also seen an appearance of a new peak in the VB, which is more pronounced for MoS2 nanotubes and may explain the higher activation energies seen in such systems. These results suggest that, different from what is seen for Li insertion, there is a considerable interaction between Mg and S atoms. A summary of the most important results are shown in Figure 10. This voltage−activation energy map offers an intuitive way to compare and analyze the adsorption and diffusion properties of Li and Mg insertion in TMD inorganic nanotubes. Owing to the similarity between larger nanotubes and the monolayer structure, we keep only the most significative results. The purple region in the map highlight the Li insertion data. These results indicate that MoS2 present an improved ion mobility: 4 times faster than in TiS2 nanotubes. In addition, narrow (
