Two-dimensional porous transition metal organic framework materials withstrongly anchoring ability as lithium-sulfur cathode
Tongtong Li a, Cheng He a,*, Wenxue Zhang b,**
a State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi’an Jiaotong University, Xi’an, 710049, Chinab School of Materials Science and Engineering, Chang’an University, Xi’an, 710064, China
A R T I C L E I N F O
Keywords:Lithium-sulfur batteryvdW interactionMetal organic frameworkShuttle effectDensity functional theory
Lithium-sulfur (Li-S) batteries are regarded as promising candidates for energy storage devices due to their hightheoretical energy density. An ideal Li-S batteries cathode should effectively prevent polysulfide dissolution inorder to achieve longer cycle life and higher rate performance. Herein, a new 2D transition metal organicframework material, hexaaminobenzene-based coordination polymers (HAB-CPs), has been systematicallyinvestigated as cathode candidate materials for Li-S batteries. First principles calculations combined with the vdWinteraction and solvent model reveal that V-HAB-CP has the best ability to hinder the shuttle effect of lithiumpolysulfides among the three polymers (V, Cr and Fe-HAB-CPs). Quantum conduction (G) and density of states(DOS) calculations indicate that HAB-CPs maintain excellent conductivity during the whole charging process.Moreover, a very small volume change (about 3.06%) of V-HAB-CP before and after the electrode reaction canwell deal with the volume expansion problem of Li-S batteries. Meanwhile, the energy density reaches808.465Wh kg-1 when the electrode reaction product is Li16S8/V-HAB-CP. Attributed to these benefits, V-HAB-CPis a suitable cathode material, which is expected to be used in future Li-S battery systems. The computationalmethod adopted in this paper can provide a guidance for considering the influence of electrolytes on the Li-Sbatteries in the future and be widely used in other simulation calculations involving the solution effect.
1. Introduction
Batteries, especially lithium ion batteries, have existed in every aspectof our daily life, and have been an indispensable part of modern scienceand technology society in the past few decade [1,2]. The lithium ionbatteries are composed of graphite and phosphate embedded withlithium ions. However, due to the intercalation and stabilities of thesecathodes, the energy density of lithium ion batteries is limited [1,2].Based on this situation, scientists try to explore different battery systemsto improve battery capacity and have achieved many incredible results,such as lithium-air [3], sodium-air [4], and lithium-sulfur (Li-S) batteries[5–7]. Owing to the high theoretical capacity of sulfur (around1675mAh g-1), Li-S batteries have been emerged as a prospective elec-trochemical energy-storage device [8]. In addition, elemental sulfur notonly possesses the advantage of abundant earth resources, but also hasthe characteristics of low cost and environmental friendliness. Never-theless, the commercial application of Li-S batteries still face many
challenges [9–11]. The first challenge is that the shuttling effect oflithium polysulfides (LiPSs) leads to the corrosion of lithium electrodes,serious loss of electrode materials, rapid capacity attenuation and so on;the second challenge is that as a non-conductive material, the conduc-tivity of S8 cluster and its discharge products Li2S and Li2S2 is very poor,which is not conducive to maintain the high rate performance of batte-ries; and the third challenge is about 80% volume expansion in the dis-charging process, which will damage the structure of material andstability of batteries. Recently, the scholars have done lots of researchesand found that porous conductive carbon materials are one of the po-tential materials to tackle these challenges [12,13]. These materials cansolve the poor conductivity of sulfur electrode and decrease the impactsof volume expansion because of their unique porous structure andexcellent physical and chemical properties. But this poses a new problem:the weak interaction between carbon materials and LiPSs leads to strongshuttle effect, which makes porous conductive carbon materials difficultto be used as the cathode materials [14–16]. To resolve this problem,
T. Li et al. Energy Storage Materials 25 (2020) 866–875
some scholars modify the electrode structure to encapsulate sulfur. Forexample, Liu et al. have built a mechanically stable network adhesive byweaving dual biopolymers via the intermolecular binding effect ofextensive functional groups. This network binder was effectively pre-venting LiPSs within the electrode from shuttling [17]. Moreover, Zhouet al. have designed the three-dimensional graphene cage structures,which can effectively hinder the shuttle effect of LiPSs [18].
However, it is difficult to stabilize elemental sulfur by solely relyingon improving the electrode structure. Meanwhile, another solution,making use of the strong interaction between LiPSs and metal oxide, hasbeen proposed by many researchers. Because their surface/volume ratioare larger than bulk materials, two-dimensional (2D) materials orframeworks could meet the requirement of high energy density for bat-teries. These materials generally have provided excellent electric con-ductivity. On the other hand, due to the unique electronic structure oftransition metals (TMs), they can be used as anchoring points for sulfuratom and LiPSs. Recently, metal-organic framework (MOF) materialshave attracted more attention of researchers because they can effectivelyhinder the volume expansion and shuttling effect [19–21]. MOFs are anew class of crystalline materials, which consist of metal centers con-nected by organic ligand through coordination bonding [22,23]. A hugenumber of MOFs with different composition, crystal structure,morphology and porosity have been evolved depending on the coordi-nation mode of the different ligands and metal centers [24]. These ma-terials have ultra-high porosity (� 90% free volume) and high internalsurface area, which are widely used in many fields [25]. Most recently, anew type of MOFs named 2D hexaaminobenzene-based coordinationpolymers (HAB-CPs) has been synthesized [26,27]. It can be obtained onreaction of the HAB linker and metal salts in a base and air environment.In general, MOFs for Li-S batteries need to add some other electricbinders to improve their poor electric conductivity before being used aselectrode materials [18]. Fortunately, as a result of in-plane chargedelocalization and extended p-conjugation in the 2D sheets, 2D HAB-CPis mediated by electronic communication through the metal nodes andelectrically conductive unlike common MOFs [28,29]. Hence, 2DHAB-CPs combine the advantages of porous carbon and metal-organicframework materials, which have potential as excellent electrode mate-rials for Li-S batteries.
Although Li-S battery has good potential for energy applications, thetheoretical studies of batteries are slightly insufficient. This is mainlybecause that the electrode reaction of Li-S battery is complex. Comparedwith the relatively single product of electrode reaction in common Libatteries, there are more intermediates products in Li-S batteries.Therefore, it is difficult to simulate the whole reaction process by con-ventional simulation methods. Moreover, Li ions in LiPSs are polarizableions and they have strong solvent interaction. So, how to introduce theinfluence of electrolyte into simulation is also a problem. These situationsmake it difficult to research the adsorption energies of the soluble LiPSs.In this work, a theoretical calculation based on DFT is used to study thepossibility of TM-HAB-CP as cathode material for Li-S batteries. Based onexperimental and theoretical data for the LiPSs in the Li-S battery [30,31], the static dielectric constant is determined for solvent model. Thenthe reaction of LiPSs adsorbed on TM-HAB-CPs are studied. It can befound that TM-HAB-CP can significantly reduce the dissolution of LiPSsand the anchoring ability of V-HAB-CP to sulfur atom is better thanCr-HAB-CP and Fe-HAB-CP. The global minimum configurations for LixS8(1�x�16) adsorbed on V-HAB-CP are searched by particle swarm opti-mization (CALYPSO) code. It can be found that TMs can effectively bind Satom during the electrode reaction process. Through the analysis ofelectronic properties, TM-HAB-CP can maintain excellent electric con-ductivity in the whole process of electrode reaction. As for the thirdchallenge mentioned before, we have built a structure which sandwichesthe S8 cluster and Li2S layer with two layers of V-HAB-CP. Preliminaryexperiment demonstrates that its volume change before and after reac-tion is about 3.06%, which is similar to common Li batteries and muchsmaller than existing Li-S batteries [32].
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2. Theoretical approach
The calculations were carried out by using DFT coded in the Viennaab initio simulation package (VASP) [33] code. The exchange correlationinteractions were solved by the generalized gradient approximation(GGA) of the Perdew - Burke - Ernzerhof (PBE) [34]. A vacuum distanceof 25 Å was used to avoid interaction between adjacent layers. The spinpolarization was used in calculating structural electronic properties andadsorption energy. A dispersion correction of the total energy (DFT-D3method) [35] was used to incorporate the long-range van der Waals in-teractions. The cut - off energy was set to 560 eV. The convergencetolerance and energy on each atom were set to 0.001 eV/Å and 10-5 eV,respectively. Numerical integrations over the first Brillouin zone weredone on a k-mesh of 8 � 8 � 1. The DFT þ U was used on the transitionmetal and the value for V, Cr and Fe were set to 3.1, 3.5 and 4.9 eV,respectively [36]. To further explore the stability of three TM-HAB-CPs,the classical Molecular Dynamics (MD) simulations were performed inthe NVT [37] statistical ensemble with the Universal [38]. V and T areconstants andN is the number of atom. To keep temperature constant, theAndersen [39] thermostat was applied. To further investigate the elec-trode reaction process, we performed the structure search of LixS8(1�x�16) adsorbed on V-HAB-CP by employing a particle swarm opti-mization algorithm by particle swarm optimization (CALYPSO) code[40]. Its validity has been confirmed by the application oftwo-dimensional materials [41–43].
In the vacuum, the adsorption energy (Eads) of polysulfide is definedby the following equation:
Eads ¼ETM�HAB�CP=X � ETM�HAB�CP � EX (1)
where ETM�HAB�CP=X, ETM�HAB�CP and EX denote the total energies of TM-HAB-CP (TM¼ V, Cr and Fe) monolayer bonded with different inter-mediate products (S8, Li2S and Li2S2n, n¼ 1, 2, 3, 4), a primitive TM-HAB-CP monolayer and one isolated intermediate product, respec-tively. The ratio for vdW interaction (RvdW) is defined by the followingequation [44,45].
Rvdw ¼EvdWads � Eno vdW
ads
EvdWads
� 100% (2)
where EvdWads and Eno vdW
ads are the adsorption energies computed with andwithout vdW function respectively [44].
The solvent effects were simulated by using the solvation model forthe plane wave DFT code VASP (VASP-sol) [46,47]. In this solvent model,no explicit solvent molecules are present. The solvent dielectric constantwas set to be 7.17 to simulate the effects of DME/DOL [48]. In the sol-vent, the adsorption energy of LiPSs on TM-HAB-CPs (Esol
Because the high conductivity of HAB-CPs mainly depends on TMs,how to select the appropriate TMs is particularly important. The selectionof transition metals mainly follow the following principles: on the onehand, the closer the d - band center is to the Fermi level, the stronger thestructural adsorption performance is [49]. The d - band center is defined
as [50]: Cd ¼R þ∞
�∞E�PDOSdðEÞdER þ∞
�∞PDOSdðEÞdE
. On another hand, as a cathode material
for lithium-sulfur batteries, it is necessary to have a high structural sta-bility to cope with large deformation in electrode reactions. So we dis-cussed the ashby plot of d - band center vs. cohesion energy to assist in thetransition metals selection, as shown in Fig. 1(a). In order to prove the
Fig. 1. (a) An ashby plot of d-band center vs. cohesion energy. The brown-yellow area in the figure represents the selected area. The geometric structures of (b) TM-HAB-CPs monolayers, (c) S8 cluster and LiPSs. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version ofthis article.)
T. Li et al. Energy Storage Materials 25 (2020) 866–875
accuracy of our calculation results, we have compared with some re-ported values of d - band center [51]. It can be found that the differencebetween the value of previously reported and our calculation value isvery small, which proves that our calculation method is suitable. Thebrown-yellow area in ashby plot show that Sc, V, Cr and Fe-HAB-CPs canachieve the balance of d-band center and cohesion energy: both suitabled-band center values and larger cohesion energy can ensure that the fourmaterials not only have high stability, but also have good adsorptionproperties. Moreover, the special properties of HAB-CPs depend on d-p-πconjugation in its electronic structure. Therefore, the right number ofd-electrons is necessary. Too much or too little electrons are not appro-priate to form a stable conjugate. Therefore, Sc element is not suitable forforming HAB-CP because of its few d-electrons. Through the aboveanalysis, V, Cr and Fe elements are chosen to test the excellentTM-HAB-CPs for the Li-S batteries application. Fig. 1(b) shows thestructure of TM-HAB-CP (TM¼ V, Cr or Fe). An organic small molecule isformed by substituting hydrogen atoms with amino groups in benzenerings. The structure of TM-HAB-CP is composed of these organic smallmolecules linked by transition metals. The three HAB-CPs are allbelonging to monoclinic system, but the lattice constants are different.For V-HAB-CP, lattice constants of a and b are 14.36 Å and 14.14 Å,respectively; For Cr-HAB-CP, lattice constants are a¼ 14.20 andb¼ 13.98 Å, respectively; For Fe-HAB-CP, lattice constants are a¼ 13.68and b¼ 13.44 Å, respectively. Next, the interlayer space of V-HAB-CP,Cr-HAB-CP and Fe-HAB-CP are also calculated, which are 3.314, 3.297and 3.365 Å, respectively. The results are shown in Fig. S1 (in the Sup-porting Information). Considering that HAB-CPs is completely preparedat room temperature, the stability of these materials is verified by MDsimulation at 300 K with 1000 ps. A relative large 4� 4 supercell is usedin the simulations and the results are shown in Fig. S2 (in the SupportingInformation). As indicated by the snapshots within 1000 ps, it can befound that the overall structures are intact. Moreover, thetime-dependent evolutions of total energies show very small fluctuation,which further proves that the structures are stable at room temperature.These results can also prove that the experimental synthesis of thesematerials are feasible. The electronic properties of cathode materialsstrongly correlate with the cyclability and rate performance of batteries.
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Therefore, the band structures at PBE level are calculated, as show inFig. 2(a). The metallic nature of TM-HAB-CP is confirmed by the no-gapband structure. This is caused by the special structures: the p and π or-bitals on the radical anionic HAB interact strongly with the d orbitals ofTM atoms, which enable a fully conjugated system and call d-p-πconjugation. The density of states (DOS) lines in Fig. 2(b) are also provedthis point. Moreover, the band structure of V-HAB-CP like Mn-HAB-CPhas a relatively large dispersion at the Fermi energy, which indicatesband-like charge transport instead of localized state hopping [30].Considering the existence of transition metals, we also calculate the bandstructure with SOC [52] effect and the results are shown in Fig. S3 (in theSupporting Information). It can be found that SOC has little influence onits electronic structure.
In order to fabricate the 2D layer structures from their bulk crystalswith weak vdW interaction, the common used methods are mechanicalcleavage and liquid exfoliation [53,54]. Therefore, the exfoliation en-ergies of three TM-HAB-CPs are calculated and the results are shown inFig. 3. Here, the n-layer exfoliation energy per unit area Eexf (n) is definedby the following formula [55].
Eexf ðnÞ¼Eiso ðnÞ � Ebulk n=mA
(4)
where Eiso (n) is the unit cell energy of an isolated n-layer slab in thevacuum, Ebulk is the unit cell energy of a bulk material with m layers, andA is the in-plane area of the bulk unit cell [55]. Taking graphite as abenchmark, the calculated n-layer exfoliation energy is 21.07 - 23.62meV/Å2, which is in excellent agreement with the previous theoreticalvalue [55]. Eexf (n) of TM-HAB-CPs are generally smaller than that ofgraphite, indicating that TM-HAB-CPs can be easily prepared from theirbulk forms using similar experimental approaches as graphene. Espe-cially, it is worth noting that Eexf (n) of V-HAB-CP is around 4.11 - 8.25meV/Å2, which is only about one-fourth of graphite. Consequently,V-HAB-CP monolayer has better experimental feasibility.
One of the key problems restricting the application of Li-S batteries isshuttle effect, which is caused by the dissolution of lithium ions in theelectrolyte of batteries. Therefore, a qualified cathode material needs to
Fig. 2. (a) Spin band structures and (b) density of states of V, Cr and Fe-HAB-CPmonolayer. The bands are plotted along the path Γ-M-K-Γ. The Fermi levelshave been shifted to zero.
Fig. 3. N-layer exfoliation energies per area of V, Cr and Fe-HAB-CP as wellas graphite.
T. Li et al. Energy Storage Materials 25 (2020) 866–875
have a good anchoring ability. To accurately describe the interactionbetween LiPSs and TM-HAB-CPs, the most stable structures of S8 cluster,Li2S and Li2S2n (n¼ 1, 2, 3, 4) adsorbed on TM-HAB-CPs are simulatedwith or without vdW function firstly, which are shown in Fig. 4(a) and(b). It is clear that the vdW interaction can greatly change the adsorptionform of LiPSs on TM-HAB-CPs. Specifically, LiPSs are more likely to beadsorbed on TM-HAB-CPs at a relatively distant location if only chemicaladsorption is considered, but the adsorption distance reduces andchemical bonds can be formed between LiPSs and TM-HAB-CPs whenvdW interaction is considered. It implies that both chemical and physicalinteractions exist between LiPSs and TM-HAB-CPs at the same time.
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Moreover, a structure change happens simultaneously: when LiPSs areadsorbed on TM-HAB-CPs, the structure of TM-HAB-CPs changes fromhorizontal surface structure to curved surface structure. Although thestructure is relatively deformed, the bonds of TM-HAB-CPs are notbroken during the whole electrode reaction process, which approves thatit has great stability. Moreover, S8 cluster and LiPSs are more likely to beadsorbed on transition metal atoms of TM-HAB-CPs, suggesting that d-orbital electrons in transition metals will affect the electronic distributionof the whole structure and act as the active adsorption sites for clusters.This situation has also occurred in other 2D materials, such as metalcarbides and nitrides (MXene) [56] and transition metal disulphides[57]. In addition, LiPSs tend to be adsorbed on TM-HAB-CPs through alithium atom rather than a sulfur atom, because of the active outerelectrons and low electronegativity (0.98) of lithium [58]. These factscan lead to a larger number of transferred electrons between Li andTM-HAB-CPs, and thus larger adsorption energies. As mentioned earlier,LiPSs are dissoluble in organic electrolyte solvents inducing batteryperformance degradation. To describe the underlying anchoring abilitiesof different substrates, we also calculate the Eads of different LiPSs clus-ters on three TM-HAB-CPs with or without vdW function shown inFig. 4(c). Specific data are listed in Table 1 and Table S1 (in the Sup-porting Information). It can be found that TM-HAB-CPs present a highadsorbent ability towards all the LiPSs, largely attributed to its uniqued-p-π conjugation. More importantly, compared with the other twostructures, V-HAB-CP shows an ultra-high adsorbent ability towardsLiPSs. The adsorption energies of S8, Li2S8, Li2S6, Li2S4, Li2S2 and Li2Sclusters on V-HAB-CP are -0.048 eV, -0.999 eV, -0.407 eV, -0.993 eV,-1.797 eV and -2.722 eV, respectively, and increase to -0.707 eV,-1.607 eV, -1.171 eV, -1.391 eV, -3.033 eV and -3.919 eV when the vdWinteraction is involved. Owing to that a mixed solvent of DOL and DME isoften used as the liquid organic electrolyte for Li-S batteries, the inter-action between LiPSs and two typical solvent molecules are considered toevaluate the competition between LiPSs-solvent and LiPSs substrate. Theadsorption energies of LiPSs in DOL and DME are calculated and shownin Table S2 (in the Supporting Information), which are smaller than withV-HAB-CP. Based on these investigations, we expect that V-HAB-CP canbe a promising cathode material for Li-S batteries.
Another interesting finding is that the vdW interaction showsdifferent weights towards different TM-HAB-CPs. Therefore, the ratio forvdW (RvdW) is calculated by Eq. (2) and shown in Fig. 4(d). According toRvdW, the contributions of vdW interactions in different lithiation stagescan be addressed and the bonding nature can be qualitatively known. Itcan be observed that the vdW interaction dominates the adsorptionprocess with the ratio RvdW exceeding 93.22% when S8 cluster adsorbedon V-HAB-CP, which means that the physical interaction between V-HAB-CP and S8 cluster is very strong. In detail, physical interaction withthe 65.26% RvdW plays a major role in the cases of Li2S6. However, forLi2S8, Li2S4, Li2S2 and Li2S, physical interaction becomes less influentialand RvdW decreases within the range 28.59 ~ 40.75%. Similar to V-HAB-CP, the vdW interaction dominates the adsorption process with the ratioRvdW exceeding 94.05% when S8 cluster adsorbed on Cr-HAB-CP, whichalso means that the physical interaction between Cr-HAB-CP and S8cluster is very strong. In addition, RvdW between LiPSs and TM-HAB-CPsare all enhanced within the range 38.97 ~ 63.00%. However, there is anunusual phenomenon on Fe-HAB-CP. The vdW interaction plays a rela-tively weak role in the adsorption processes with RvdW 59.21% when S8cluster is adsorbed on Fe-HAB-CP, which means that the physical inter-action between Fe-HAB-CP and S8 cluster is weaker than the other twoHAB-CPs. Moreover, in the whole process of electrode reaction, RvdW issmaller than the other two HAB-CPs too. Through observation theadsorption configuration, it can be found that the structural deformationof TM-HAB-CPs are relatively large in the process of adsorption, whichimplies the strong chemical interaction. This difference may be caused byd electrons. Fe (3d64s2) has more d-layer electrons than V (3d34s2) and Cr(3d54s1) and thus it is easier to form chemical bonds with S8 cluster andLiPSs to decrease the RvdW.
Fig. 4. The geometric structures of S8 cluster, Li2S and Li2S2n (n¼ 1, 2, 3, 4) adsorption on TM-HAB-CPs surface (a) without and (b) with vdW corrections. (c) Theadsorption energies of S8 cluster, Li2S and Li2S2n (n¼ 1, 2, 3, 4) on TM-HAB-CPs without (dotted line) and with (solid line) vdW corrections. (d) Ratio for vdWinteraction of S8 cluster, Li2S and Li2S2n (n¼ 1, 2, 3, 4) on TM-HAB-CPs.
Table 1The calculated Eads (eV) and the shortest distance Δd (Å) between S8 cluster, Li2Sand Li2S2n (n¼ 1, 2, 3, 4) on TM-HAB-CPs monolayer when vdW interaction isinvolved.
T. Li et al. Energy Storage Materials 25 (2020) 866–875
Even though tremendous achievements have been made experimen-tally in the performance of Li-S battery, theoretical studies in this area arelagging behind due to the complexity of the Li-S systems and the effects ofsolvent. In this process, dielectric constant is a critical parameter todetermine the solvation energy. Unfortunately, the default parameter forthe solvation model is not providing accurate solvation energy becausethe common electrolyte used in Li-S batteries is a mixture of DME andDOL. The solvent dielectric constants of DME and DOL are 7.20 and 7.13,respectively [48]. According to the law of mixing, the solvent dielectricconstant is fixed and set to be 7.17 to simulate the solvent effects. Oncedetermining the solvent model, the adsorption energies of LiPSs onTM-HAB-CPs are estimated in the solvent and shown in Fig. 5. It can befound that Eads of Li2S, Li2S2 and S8 clusters on TM-HAB-CPs have nochange in the solvent and vacuum environments, while Eads of Li2S2n(n¼ 2, 3 and 4) adsorbed on TM-HAB-CPs have a major change in thesolvent and vacuum environments. For V-HAB-CP, Eads of Li2S4, Li2S6 andLi2S8 in the vacuum are -1.391, -1.171 and -1.607 eV, respectively.However, in the solvent, Eads reduce to -1.114, -0.898 and -0.638 eV forLi2S4, Li2S6 and Li2S8, respectively. Similar situations also appear inCr-HAB-CP and Fe-HAB-CP structures. These negative adsorption en-ergies indicate that LiPSs are more easily adsorbed on the surface ofTM-HAB-CPs rather than being extricated in solvents. Therefore,
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TM-HAB-CPs have strong ability to capture LiPSs. Moreover, V-HAB-CPperforms better performance than the other two structures, which ismore likely to be a candidate for cathode materials. For a morecomprehensive discussion of the ability of V, Cr and Fe-HAB-CP to hindershuttle effects, we select seven common electrolytes, which are DOL,DME, Dimethyl sulfoxide (DMSO), Ethylene carbonate (EC), Tetra-methylene sulfone (SL), Propylene carbonate (PC) and Dimethyl car-bonate (DMC), respectively. The adsorption energies of soluble LiPSs onthree HAB-CPs in other solvents are given in Table 2. For comparison, theadsorption energies of different solvents for LiPSs are given in Table S2(in the Supporting Information). It can be found that V-HAB-CP exhibitsgood anchoring properties in other solvents except in solvents EC and PC,which implies that the two solvents should be avoided as electrolytesolution in the experiment. However, Cr-HAB-CP can hinder the shuttleeffect in solvents DOL, DME and DMC. Fe-HAB-CP can only hinder theshuttle effect in solvents DOL and DME. These results indicate that theability of V-HAB-CP to hinder shuttle effect can be applied to manyelectrolyte solutions, while the application range of Cr and Fe-HAB-CP isrelatively narrow.
To get an in-depth knowledge of the bonding process in adsorptionreaction, we have calculated the charge transfer between LiPSs and V-HAB-CP. The charge density difference of LiPSs adsorbed systems isshown in Fig. S4 (in the Supporting Information), which is made bysubtracting electron density of LiPSs and V-HAB-CP in standalone statefrom the whole system. The formula can be expressed as:
Δρ¼ ρV�HAB�CP=X � ρV�HAB�CP � ρX (5)
where ρV-HAB-CP/X, ρV-HAB-CP and ρX are the charge distribution of thewhole system, V-HAB-CP, and S8/LiPSs, respectively. The yellow andblue iso-surfaces represent the region of electron density accumulationand depletion after S8 cluster and LiPSs adsorbed on V-HAB-CP, respec-tively. For S8 cluster adsorbed on V-HAB-CP, because physical adsorptionis a leading factor in adsorption reaction, few charge transfer could beobserved between S8 cluster and V-HAB-CP. Besides, when LiPSs areabsorbed on V-HAB-CP, there are charge accumulation between LiPSs
Fig. 5. The adsorption energies of S8 cluster, Li2S and Li2S2n (n¼ 1, 2, 3, 4) on(a) V, (b) Cr and (c) Fe-HAB-CP in the vacuum (bars with net patterns) andsolvent (bars without pattern).
T. Li et al. Energy Storage Materials 25 (2020) 866–875
and V-HAB-CP. The charge accumulation increases with the increase ofadsorption energy because it indicates the formation of strong chemicalbonds. Then we quantitatively study the charge transfer by calculatingthe Bader charge of the adsorption system [59]. We plot the amount oftransferred charges on V-HAB-CP during the lithium process in Fig. S5 (inthe Supporting Information) to explore the relationship between theelectron transfer and chemical interaction strength. There are 0.095,0.064, 0.058, 0.145, 0.501 and 0.680 electron transferred from S8, Li2S8,Li2S6, Li2S4, Li2S2 and Li2S cluster to V-HAB-CP, leading to strongchemical interaction and enhancing the anchoring effect. The amount oftransferred charges on graphene is also calculated as a contrast [16]. Itcan be found that the charge transfer number between LiPSs and
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V-HAB-CP monolayer is larger during the whole process, while for pris-tine graphene, there is hardly electron transferred between clusters andgraphene. The reason can be ascribed to the localized polarization ofV-HAB-CP, which induces extra electrostatic interaction.
The whole charge-discharge reaction of lithium-sulfur batteries is avery complex oxidation process, which involves the occurrence of multi-step disproportionation reaction. The total reaction equation can beexpressed simply by the following equation: S8 þ 16Liþ þ 16e� ⇔8Li2S.From the ideal charge-discharge profile, it can be clearly seen that thereaction is divided into two parts: when the voltage is about 2.3 V, thefirst discharge platform appears. In this part, the S8 cluster first breaks theS-S bond, and it gradually combined with lithium ion to form a variety oflong-chain polysulfide lithium (Li2Sn, n> 4). After that, long-chainlithium polysulfide was further reduced to short-chain lithium poly-sulfide (Li2Sn, l< n< 4), corresponding to another low-voltage platform(< 2.1 V). In order to further investigate the electrode reaction process,one S8 molecule r is adsorbed on V-HAB-CP and then gradually add Liatoms one by one to LiPSs until forming Li16S8 (Li2S). For each inter-mediate product, we search for 50 structures to get the lowest possibleenergy configuration through the CALYPSO code. The most stable con-figurations for LixS8 (1�x�16) are shown in Fig. 6 (a)-(p). At first, one S8cluster adsorbed on the V-HAB-CP, which is shown in Fig. 4(b). Then, onelithium atom is added to form LiS8 by opening the S ring in Fig. 6(a). WithLi atoms added, LixS8 tend to form three layers structure: two layers oflithium atoms and one layer of sulfur atoms. The formation energies (Ef)of LixS8 on V-HAB-CP in the solvent are calculated. Ef is calculated byusing the following formula and shown in Fig. 6(q):
Ef ¼ELixS8=V�HAB�CPðsolÞ � ES8=V�HAB�CPðsolÞ � xELi (6)
where ELixS8=V�HAB�CPðsolÞ and ES8=V�HAB�CPðsolÞ are the adsorption en-ergies of LixS8 on V-HAB-CP and S8 cluster on V-HAB-CP calculated in thesolvent, respectively. ELi is the energy per Li atom. x is the number of Liatoms in LixS8. From Fig. 6(q), it can be found that the battery dischargeprocess is divided into two stages: insoluble polysulfides (1�x�4) andsoluble polysulfides (5�x�16). Moreover, there is a certain functionalrelationship between Ef of LixS8 and the number of lithium atoms. Theslope denotes the charge/discharge voltage. For insoluble polysulfides,the charge/discharge voltage is 1.011 V. For soluble polysulfides, as thenumber of lithium atoms increases, Ef also increases. Specifically, theslope of the fitting line changes from -1.011 to -0.362. The linear rela-tionship between the formation energy and the number of lithium atomsindicates a great advantage compared to other 2D cathode materials forLi-S batteries. Furthermore, the energy densities at different stages arealso calculated. When four lithium atoms add in the system (Li4S8), theenergy density is 381.368W h kg-1. With sixteen lithium atoms add(Li16S8), the energy density increase to 808.465W h kg-1, which is higherthan that of Li-S batteries value (589Wh kg-1) obtained in experimentusing 2D MoS2 as the electrode material [60].
In addition to the moderate adsorption energies towards LiPSs, po-tential cathode materials should have excellent electrical conductivity,otherwise LiPSs would accumulate on the anchoring materials and aredifficult to recharged leading to an enlarged battery polarization andreducing capacity retention. We have shown in Fig. 2 that pristine TM-HAB-CPs are all metallic in the vacuum. It is not clear whether theelectronic properties will change after it absorbs LiPSs. Therefore, it isnecessary to calculate the transport and electronic properties afteradsorption. For evaluating quantum transport, the formula for quantumconduction (G) function is as follows [61].
G¼G0
XM
M¼1
Ti (7)
where Ti is the transmission probability of the ith channel, G0¼ 2e2/h, edenotes the electronic amount, h is the Planck constant, and M is thenumber of propagating modes crossing the Fermi energy [61]. According
Table 2Adsorption energy of soluble LiPSs on V, Cr and Fe-HAB-CP in different solvents.
Sub. LiPSs Adsorption energy in different solvents (eV)
Fig. 6. (a)-(p) The optimized stable structure and (q) the formation energy of LixS8 (1�x�16) adsorbed on V-HAB-CP surface in the solvent. The functional re-lationships are plotted in dash-dot lines.
T. Li et al. Energy Storage Materials 25 (2020) 866–875
to the formula, the more bands passing through Fermi energy, the betterthe conduction effect. G of S8 cluster, Li2S and Li2S2n (n¼ 1, 2, 3, 4)adsorbed on V-HAB-CP are shown in Fig. 7(a) and (b). It can be seen thatthe value of G is not zero after adsorption. The conduction channelsappeared near the Fermi energy, which means the electrical conductivityof the adsorption system is improved. Moreover, the spin DOS of S8cluster and LiPSs adsorbed on V-HAB-CP are calculated and shown inFig. 7(c)–(h), respectively. During the whole process of electrode reac-tion, V-p and S-s orbitals have little effect on DOS of the whole adsorption
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system. The strong adsorption energies mainly come from the interactionbetween V-d and S-p orbitals. In addition, DOS of S8 cluster and LiPSsadsorbed on Cr-HAB-CP and Fe-HAB-CP are also calculated and shown inFigs. S6–S7 (in the Supporting Information), respectively. It is concludedthat these adsorption systems can maintain their metallic states duringeach step of electrode reaction, ensuring LiPSs adsorbed on V-HAB-CPcan be easily recharged in the charge process. Therefore, V-HAB-CP hasan excellent electrical conductivity during the whole process of electrodereaction, which will significantly improve the performance. The same
Fig. 7. G for six different adsorption systems (a) and (b). The spin density of states of S8 cluster, Li2S and Li2S2n (n¼ 1, 2, 3, 4) adsorbed on V-HAB-CP (c) - (h). TheFermi levels have been shifted to zero. The star represents V-HAB-CP.
T. Li et al. Energy Storage Materials 25 (2020) 866–875
situations occur in the adsorption systems of Cr and Fe-HAB-CP.Based on the above analysis, it can be predicted that TM-HAB-CPs can
effectively solve two-thirds of the challenges facing Li-S battery. The finalchallenge is the volume change. HAB-CPs are typical 2D layered mate-rials, so their volumetric capacity are relatively small. One approach tosolve this problem is to build a new system, which sandwiches the Li-Slayer with two layers of TM-HAB-CPs. As a matter of fact, this is equiv-alent to building a three-dimensional periodic layer structure artificially.Such a design not only increases the volumetric capacity, but also has apotential to prevent the volume expansion problem discussed above.Because V-HAB-CP behaves better than the other HAB-CP materials.Moreover, the product of complete reaction of S8 is Li2S in the idealsituation. Therefore, the situations of S8 cluster and Li2S inserted be-tween V-HAB-CP are studied. As shown in Fig. S8 (in the SupportingInformation), it can be found that when S8 cluster is inserted between V-HAB-CP layers, the interlayer distance of V-HAB-CP/V-HAB-CP is6.688 Å. When S8 cluster is inserted between V-HAB-CP layers, theinterlayer distance of V-HAB-CP/V-HAB-CP only increases to 6.893 Å.Thus, there is 3.06% lattice constant increase in the z-direction. Thisresult indicates that the volume change of V-HAB-CP before and after theelectrode reaction is lower than that of the common cathode materials ofLi-S batteries [32].
4. Conclusions
In summary, the three transition metal hexaaminobenzene-basedcoordination polymers (TM-HAB-CPs) have been systematically investi-gated as Li-S battery cathode via DFT calculation in combination with thevdW interaction and solvent model. Meanwhile, a particle swarm opti-mization algorithm is applied to obtain the structures of all possible in-termediate products of battery reaction on V-HAB-CP. The calculationresults show that the vdW interaction and solvent effect are the important
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factors in calculating the adsorption energies of LiPSs on TM-HAB-CPs. Inparticular, V-HAB-CP has the most negative adsorption energy for LiPSsamong TM-HAB-CPs, and thus V-HAB-CP has better ability to hinder theshuttle effect of Li-S batteries than Cr and Fe-HAB-CP. In addition, V-HAB-CP keeps metallic during the whole process of electrode reactionand its volume expansion rate predicted by a sandwiched structurebefore and after electrode reaction is only 3.06%. Moreover, the theo-retical energy density can reach up to 808.465W h kg-1 when the elec-trode reaction product is Li16S8/V-HAB-CP. All these results suggest thatV-HAB-CP can effectively deal with the critical challenges for the cathodeof Li-S batteries (shuttle effect, poor conductivity and volume expansion),and thus V-HAB-CP has an outstanding potential to be a good cathodematerial for Li-S batteries in the future. At the same time, the proposedcalculation method can also be used to deal with other problems, whichneed to consider the influence of solvents.
Data availability
The raw data required to reproduce these findings are available fromthe corresponding author upon reasonable request. The processed datarequired to reproduce these findings are available from the correspond-ing author upon reasonable request.
Conflicts of interest
The authors declare no conflict of interest.
Acknowledgments
The authors acknowledge supports by National Natural ScienceFoundation of China (NSFC, Grant No. 51471124), Natural ScienceFoundation of Shaanxi Province, China (2019JM-189), and the
T. Li et al. Energy Storage Materials 25 (2020) 866–875
Fundamental Research Funds for the Central Universities (No.xjj2016018).
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.org/10.1016/j.ensm.2019.09.003.
References
[1] J.B. Goodenough, K. Park, The Li-ion rechargeable battery: a perspective, J. Am.Chem. Soc. 135 (2013) 1167–1176.
[2] G. Assat, J. Tarascon, Fundamental understanding and practical challenges ofanionic redox activity in Li-ion batteries, Nature Energy (2018) 1.
[3] H. Jung, J. Hassoun, J. Park, Y. Sun, B. Scrosati, An improved high-performancelithium-air battery, Nat. Chem. 4 (2012) 579.
[4] W. Liu, Q. Sun, Y. Yang, J.Y. Xie, Z.W. Fu, An enhanced electrochemicalperformance of a sodium-air battery with graphene nanosheets as air electrodecatalysts, Chem. Commun. 49 (2013) 1951–1953.
[5] C. Wang, K. Su, W. Wan, H. Guo, H.H. Zhou, J.T. Chen, X.X. Zhang, Y.H. Huang,High sulfur loading composite wrapped by 3D nitrogen-doped graphene as acathode material for lithium-sulfur batteries, J. Mater. Chem. 2 (2014) 5018–5023.
[6] H.Q. Yuan, W.K. Zhang, J.G. Wang, G.M. Zhou, Z.Z. Zhuang, J.M. Luo, H. Huang,Y.P. Gan, C. Liang, Y. Xia, Facilitation of sulfur evolution reaction by pyridinicnitrogen doped carbon nanoflakes for highly-stable lithium-sulfur batteries, Energy.Storage. Mater. 10 (2018) 1–9.
[7] M. Rana, S.A. Ahad, M. Li, B. Luo, L.Z. Wang, I. Gentle, R. Knibbe, Review on arealcapacities and long-term cycling performances of lithium sulfur battery at highsulfur loading, Energy. Storage. Mater. 18 (2019) 289–310.
[8] S. Evers, L.F. Nazar, New approaches for high energy density lithium-sulfur batterycathodes, Acc. Chem. Res. 46 (2012) 1135–1143.
[9] Z.H. Sun, J.Q. Zhang, L.C. Yin, G.J. Hu, R.P. Fang, H.M. Cheng, F. Li, Conductiveporous vanadium nitride/graphene composite as chemical anchor of polysulfidesfor lithium-sulfur batteries, Nat. Commun. 8 (2017) 14627.
[10] L. Zhang, D. Sun, J. Feng, E.J. Cairns, J.H. Guo, Revealing the electrochemicalcharging mechanism of nanosized Li2S by in situ and operando X-ray absorptionspectroscopy, Nano Lett. 17 (2017) 5084–5091.
[11] Y. Lu, S. Gu, X.H. Hong, K. Rui, X. Huang, J. Jin, C.H. Chen, J.H. Yang, Z.Y. Wen,Pre-modified Li3PS4 based interphase for lithium anode towards high-performanceLi-S battery, Energy, Storage. Mater. 11 (2018) 16–23.
[12] Z. Chang, B. Ding, H. Dou, J. Wang, G.Y. Xu, X.G. Zhang, Hierarchically porousmultilayered carbon barriers for high-performance Li-S batteries, Chem. Eur J. 24(2018) 3768–3775.
[13] S. Rehman, S. Guo, Y. Hou, Rational design of Si/SiO2@Hierarchical porous carbonspheres as efficient polysulfide reservoirs for high-performance Li-S battery, Adv.Mater. 28 (2016) 3167–3172.
[14] B. Wang, S.M. Alhassan, S.T. Pantelides, Formation of large polysulfide complexesduring the lithium-sulfur battery discharge, Phys. Rev. Appl. 2 (2014) 034004.
[15] Y.P. Zheng, H.H. Li, H.Y. Yuan, H.H. Fan, W.L. Li, J.P. Zhang, Understanding theanchoring effect of Graphene, BN, C2N and C3N4 monolayers for lithium-polysulfides in Li-S batteries, Appl. Surf. Sci. 434 (2018) 596–603.
[16] Y. Qie, J.Y. Liu, S. Wang, S. Gong, Q. Sun, C3B monolayer as an anchoring materialfor lithium-sulfur batteries, Carbon 129 (2018) 38–44.
[17] J. Liu, D.G. Galpaya, L.J. Yan, M.H. Sun, Z. Lin, C. Yan, C.D. Liang, S.Q. Zhang,Exploiting a robust biopolymer network binder for an ultrahigh-areal-capacity Li-Sbattery, Energy Environ. Sci. 10 (2017) 750–755.
[18] G.M. Zhou, J. Sun, Y. Jin, W. Chen, C.X. Zu, R.F. Zhang, Y.C. Qiu, J. Zhao, D. Zhuo,Y.Y. Liu, Sulfiphilic nickel phosphosulfide enabled Li2S impregnation in 3Dgraphene cages for Li-S batteries, Adv. Mater. 29 (2017) 1603366.
[19] R. Demir-Cakan, M. Morcrette, F. Nouar, C. Davoisne, T. Devic, D. Gonbeau,R. Dominko, C. Serre, G. F�erey, J.-M. Tarascon, Cathode composites for Li-Sbatteries via the use of oxygenated porous architectures, J. Am. Chem. Soc. 133(2011) 16154–16160.
[20] X.J. Hong, X.Y. Tang, Q. Wei, C.L. Song, S.Y. Wang, R.F. Dong, Y.P. Cai, L.P. Si,Efficient encapsulation of small S2-4 molecules in MOF-derived flowerlike nitrogen-doped microporous carbon nanosheets for high-performance Li-S batteries, ACSAppl. Mater. Interfaces 10 (2018) 9435–9443.
[21] G. Su, S. Yang, S. Li, C.J. Butch, S.N. Filimonov, J.-C. Ren, W. Liu, SwitchableSchottky contacts: simultaneously enhanced output current and reduced leakagecurrent, J. Am. Chem. Soc. 141 (2019) 1628–1635.
[22] J. Lee, G. Ali, D.H. Kim, K.Y. Chung, Metal-organic framework cathodes based on avanadium hexacyanoferrate prussian blue analogue for high-performance aqueousrechargeable batteries, Adv. Energy Mater. 7 (2017) 1601491.
[24] W.G. Lu, Z.W. Wei, Z.Y. Gu, T.F. Liu, J. Park, J. Park, J. Tian, M.W. Zhang, Q. Zhang,T. Gentle III, Tuning the structure and function of metal-organic frameworks vialinker design, Chem. Soc. Rev. 43 (2014) 5561–5593.
874
[25] K.K. Gangu, S. Maddila, S.B. Mukkamala, S.B. Jonnalagadda, A review oncontemporary metal–organic framework materials, Inorg. Chim. Acta 446 (2016)61–74.
[26] D.W. Feng, T. Lei, M.R. Lukatskaya, J. Park, Z.H. Huang, M. Lee, L. Shaw, S.C. Chen,A.A. Yakovenko, A. Kulkarni, Robust and conductive two-dimensional metal-organic frameworks with exceptionally high volumetric and areal capacitance,Nature Energy 3 (2018) 30.
[27] N. Lahiri, N. Lotfizadeh, R. Tsuchikawa, V.V. Deshpande, J. Louie,Hexaaminobenzene as a building block for a family of 2D coordination polymers,J. Am. Chem. Soc. 139 (2016) 19–22.
[28] M.G. Campbell, D. Sheberla, S.F. Liu, T.M. Swager, M. Dinca,Cu3(hexaiminotriphenylene)2: an electrically conductive 2D metal-organicframework for chemiresistive sensing, Angew. Chem. Int. Ed. 54 (2015)4349–4352.
[29] G.P. Gao, E.R. Waclawik, A.J. Du, Computational screening of two-dimensionalcoordination polymers as efficient catalysts for oxygen evolution and reductionreaction, J. Catal. 352 (2017) 579–585.
[30] G.P. Gao, F. Zheng, F. Pan, L.W. Wang, Theoretical investigation of 2D conductivemicroporous coordination polymers as Li-S battery cathode with ultrahigh energydensity, Adv. Energy Mater. 8 (2018) 1801823.
[31] C. Barchasz, F. Molton, C. Duboc, J. Lepreetre, S. Patoux, F. Alloin, Lithium/sulfurcell discharge mechanism: an original approach for intermediate speciesidentification, Anal. Chem. 84 (2012) 3973–3980.
[32] Y.M. Sun, N. Liu, Y. Cui, Promises and challenges of nanomaterials for lithium-based rechargeable batteries, Nature Energy 1 (2016) 16071.
[33] G. Kresse, J. Hafner, Norm-conserving and ultrasoft pseudopotentials for first-rowand transition elements, J. Phys. Condens. Matter 6 (1994) 8245.
[34] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation madesimple, Phys. Rev. Lett. 77 (1996) 3865.
[35] S. Grimme, S. Ehrlich, L. Goerigk, Effect of the damping function in dispersioncorrected density functional theory, J. Comput. Chem. 32 (2011) 1456–1465.
[36] F. Zhou, M. Cococcioni, C.A. Marianetti, D. Morgan, G. Ceder, First-principlesprediction of redox potentials in transition-metal compounds with LDAþU, Phys.Rev. B 70 (2004) 235121.
[37] F. Ding, A. Rosen, K. Bolton, Size dependence of the coalescence and melting of ironclusters: a molecular-dynamics study, Phys. Rev. B 70 (2004) 075416.
[38] C. Casewit, K. Colwell, A. Rappe, Application of a universal force field to organicmolecules, J. Am. Chem. Soc. 114 (1992) 10035–10046.
[39] H.C. Andersen, Molecular dynamics simulations at constant pressure and/ortemperature, J. Chem. Phys. 72 (1980) 2384–2393.
[40] Y.C. Wang, J. Lv, L. Zhu, Y.M. Ma, CALYPSO: a method for crystal structureprediction, Comput. Phys. Commun. 183 (2012) 2063–2070.
[41] T. Yu, Z.Y. Zhao, L.L. Liu, S.T. Zhang, H.Y. Xu, G.C. Yang, TiC3 monolayer with highspecific capacity for sodium-ion batteries, J. Am. Chem. Soc. 140 (2018)5962–5968.
[42] Z.H. Cui, E. Jimenez Izal, A.N. Alexandrova, Prediction of two-dimensional phase ofboron with anisotropic electric conductivity, J. Phys. Chem. Lett. 8 (2017)1224–1228.
[43] T.T. Li, C. He, W.X. Zhang, A novel porous C4N4 monolayer as a potential anchoringmaterial for lithium-sulfur battery design, J. Mater. Chem. 7 (2019) 4134–4144.
[44] H.R. Jiang, W. Shyy, M. Liu, Y.X. Ren, T.S. Zhao, Borophene and defectiveborophene as potential anchoring materials for lithium-sulfur batteries: a first-principles study, J. Mater. Chem. 6 (2018) 2107–2114.
[45] T. Shen, J.-C. Ren, X. Liu, S. Li, W. Liu, van der Waals stacking induced transitionfrom Schottky to ohmic contacts: 2D metals on multilayer InSe, J. Am. Chem. Soc.141 (2019) 3110–3115.
[46] K. Mathew, R. Sundararaman, K. Letchworth-Weaver, T. Arias, R.G. Hennig,Implicit solvation model for density-functional study of nanocrystal surfaces andreaction pathways, J. Chem. Phys. 140 (2014) 084106.
[47] K. Mathew, R.G. Hennig, Implicit Self-Consistent Description of Electrolyte in Plane-Wave Density-Functional Theory, 2016.
[48] G. Zhang, H.J. Peng, C.Z. Zhao, X.H. Chen, L.D. Zhao, P. Li, J.Q. Huang, Q. Zhang,The radical pathway based on a lithium-metal-compatible high-dielectricelectrolyte for lithium-sulfur batteries, Angew. Chem. Int. Ed. 57 (2018)16732–16736.
[49] G. Gao, E.R. Waclawik, A. Du, Computational screening of two-dimensionalcoordination polymers as efficient catalysts for oxygen evolution and reductionreaction, J. Catal. 352 (2017) 579–585.
[50] W. Zhang, D. Cheng, J. Zhu, Theoretical study of CO catalytic oxidation on free anddefective graphene-supported Au-Pd bimetallic clusters, RSC Adv. 4 (2014)42554–42561.
[51] H.L. Xin, A. Vojvodic, J. Voss, J.K. Norskov, F. Abild-Pedersen, Effects of d-bandshape on the surface reactivity of transition-metal alloys, Phys. Rev. B 89 (2014)115114.
[52] A. Dal Corso, Projector augmented-wave method: application to relativistic spin-density functional theory, Phys. Rev. B 82 (2010) 075116.
[53] H. Liu, A.T. Neal, Z. Zhu, Z. Luo, X.F. Xu, D. Tomanek, P.D. Ye, Phosphorene: anunexplored 2D semiconductor with a high hole mobility, ACS Nano 8 (2014)4033–4041.
[54] N.H. Miao, B. Xu, L.G. Zhu, J. Zhou, Z.M. Sun, 2D intrinsic ferromagnets from vander Waals antiferromagnets, J. Am. Chem. Soc. 140 (2018) 2417–2420.
T. Li et al. Energy Storage Materials 25 (2020) 866–875
[55] J.H. Jung, C. Park, J. Ihm, A rigorous method of calculating exfoliation energiesfrom first principles, Nano Lett. 18 (2018) 2759–2765.
[56] X. Liang, A. Garsuch, L.F. Nazar, Sulfur cathodes based on conductive MXenenanosheets for high-performance lithium-sulfur batteries, Angew. Chem. 127(2015) 3979–3983.
[57] Z.W. Seh, J. Yu, W.Y. Li, P. Hsu, H.T. Wang, Y.M. Sun, H.B. Yao, Q.F. Zhang, Y. Cui,Two-dimensional layered transition metal disulphides for effective encapsulation ofhigh-capacity lithium sulphide cathodes, Nat. Commun. 5 (2014) 5017.
[58] A. Allred, Electronegativity values from thermochemical data, J. lnorg. Nucl. Chem.17 (1961) 215–221.
875
[59] E. Sanville, S.D. Kenny, R. Smith, G. Henkelman, Improved grid-based algorithm forBader charge allocation, J. Comput. Chem. 28 (2007) 899–908.
[60] E. Cha, M.D. Patel, J. Park, J. Hwang, V. Prasad, K. Cho, W. Choi, 2D MoS2 as anefficient protective layer for lithium metal anodes in high-performance Li-Sbatteries, Nat. Nanotechnol. 13 (2018) 337.
[61] C. He, G. Liu, W.X. Zhang, Z.Q. Shi, S.L. Zhou, Tuning the structures and electrontransport properties of ultrathin Cu nanowires by size and bending stress using DFTand DFTB methods, RSC Adv. 5 (2015) 22463–22470.
