Hole Polaron Diffusion in the Final Discharge Product of Lithium

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Hole Polaron Diffusion in the Final Discharge Product of Lithium-Sulfur Batteries Zhixiao Liu, Perla B. Balbuena, and Partha P. Mukherjee J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06869 • Publication Date (Web): 24 Jul 2017 Downloaded from http://pubs.acs.org on July 27, 2017

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The Journal of Physical Chemistry

Hole Polaron Diffusion in the Final Discharge Product of Lithium-Sulfur Batteries

Zhixiao Liu,1 Perla B. Balbuena,2,* Partha P. Mukherjee1,* 1

Department of Mechanical Engineering, Texas A&M University, College Station, TX, USA 2

Department of Chemical Engineering, Texas A&M University, College Station, TX, USA

Revised manuscript submitted to Journal of Physical Chemistry C July 2017

*

Correspondence: [email protected] (P. P. Mukherjee); [email protected] (P. B. Balbuena)

1 ACS Paragon Plus Environment


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Abstract Poor electronic conductivity of bulk lithium sulfide (Li2S) is a critical challenge for the debilitating performance of the lithium-sulfur battery. This study focuses on investigating the thermodynamic and kinetic properties of native defects in Li2S based on a first principles approach. It is found that the hole polaron p+ can form in Li2S by removing a 3p electron from an S2– anion. The p+ diffusion barrier is only 90 meV, which is much lower than the Li vacancy (V ) diffusion barrier. Hence p+ has the potential to serve as a charge carrier in the discharge product. Once the vacancy-polaron complex (V –2p+)

forms, the charge transport will be hindered due to the relatively higher diffusion barrier of the complex. Heteroatom dopants, which can decrease the p+ formation energy and increase V formation energy, are expected to be introduced to the discharge product to

improve the electronic conductivity.


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Introduction Lithium–sulfide (Li–S) batteries are considered as a competitive energy storage technique in the foreseeable future.1-3 A Li–S battery can deliver a theoretical capacity as high as 1675 mAh g-1 if the active material sulfur can be ultimately reduced to lithium sulfide (Li2S) during the discharge process. However, the final discharge product Li2S also brings critical challenges to Li–S batteries. Li2S is insoluble in the electrolyte, and solid Li2S cannot transfer free electrons.4-6 Fan et al reported that the precipitation of solid Li2S could passivate the surface of carbon fiber cathode and then leads to the decrease of the practical capacity.7 The high discharging current density and low operating temperature can even enhance the surface passivation.8 In this regard, it is important to understand the charge transport mechanism in solid Li2S. Plenty of efforts were performed to investigate charge transport mechanisms in solid LiO2, Li2O2, NaO2, and Na2O2, which are discharge products of lithium-air batteries (LABs) and sodium-air batteries (NABs).9-13 It was found that negatively charged Li vacancies (V ) and positively charged hole polarons (p+)

are main charge carriers due to their relatively low formation energies and diffusion barriers. Recently, we studied the charge transport mechanism in the intermediate discharge product Li2S2, and found that the positively charged hole polaron (p+) could serve as the charge carrier.14 Kim et al. studied the formation and diffusion of charged native defects in crystalline Li2S and argued that negatively charged Li vacancy (V ) is

the main charge carrier because of its low diffusion barrier. They also reported that negatively charged electron polaron (p–) cannot serve as the charge carrier due to the extremely high formation energy. In crystalline Li2S, the ionic state of each S atom is 2–,



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which apparently indicates that the outermost 3p orbitals are fully occupied. Therefore, it is difficult for S2– to accept another electron to form an electron polaron. The present work postulates a hole polaron (p+) conduction mechanism in crystalline Li2S. To the best of our knowledge, this work demonstrates for the first time that the hole polaron can serve as charge carrier in Li2S at the operating condition with a high applied potential and a high temperature. Crystalline Li2S has an anti-fluorite structure, in which S atoms occupied face-centered lattice sites and each S atom coordinates with four Li atoms which occupy tetrahedral interstitial sites. At first glance, it seems like polarons cannot form in crystalline Li2S because the Li–S system lacks d orbitals. However, electrons in Li2S are localized by S2- anions, and the 3p states have the potential to trap a hole polaron. In this work, it is hypothesized that once an S2- anion loses an electron, a hole polaron will appear at that site. The energy barrier of a single hole polaron diffusion is calculated to estimate the electronic conductivity. Computational Methods The Vienna Ab Initio Simulation Package (VASP)15-16 within the plane wave basis set approach17 was employed to verify the hypothesis of the hole polaron in this work. The projected augmented wave (PAW) approach was employed to describe electron-ion interactions,18 and the generalized gradient approximation (GGA) of the Perdew-BurkeErnzerhof (PBE) functional was used to describe the electron-electron exchange correlations.19 The Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional with = 0.5 was employed for calculating the defect formation energy because the conventional PBE functional always underestimates the electron localization.20 All calculations are performed with a (3× 3 × 3) supercell (including 324 atoms) with Γ-only k-point, and the


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energy cut-off is predefined to 400 eV. The criteria for structure relaxing is set to 0.02 eV Å-1. All calculations considered spin polarization. The hole polaron was formed by removing one electron from the system. For the hole polaron calculation, an initial perturbation was applied to an S atom and adjacent Li atoms for inducing the polaron formation.9 The diffusion barrier of the defect was calculated by the climbing image nudged elastic band (CI-NEB) method21-22 with five linearly interpolated images between the initial state and the final state. For all CI-NEB calculations, all atoms were allowed to be relaxed considering HSE06 and spin polarization. Results and Discussion First-principles calculations were performed to verify the hypothesis of the hole polaron. Figure 1(a) shows the formation energy of charged native defects in crystalline Li2S at the theoretically calculated equilibrium potential ( = 2.28 V) condition. Details for formation energy calculations are discussed in the supporting information. In Figure 1(a), the slope of each line represents the charge state of the native defect: the upward slope indicates a positively charged defect, while the downward slope represents a negatively charged defect. The vertical dash line represents the Fermi level which satisfies charge neutrality.23 At the equilibrium potential condition, the main charged defects are V and

p+, which have the lowest formation energy of 1.40 eV. Kim et al. also calculated the formation energy of Li vacancy , and found that the formation energy is 1.31 eV6 at the applied potential of = 2.4 V (this value was adopted from the galvanostatic intermittent titration technique (GITT) measurement24). The formation energy of each charged defect is also affected by the applied potential as shown in Figure S1. Figure 1(b) shows the p+ formation energy as a function of applied potential , and it is found that



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the formation energy decreases as the applied potential increases. It can be inferred that a large overpotential is expected to enhance the conductivity during the charging process. When the applied potential is lower than 2.12 V, V and V have the lowest formation energy; otherwise, V and p+ have the lowest formation energy.

Figure 1. (a) The formation energies of charged native defects in Li2S. The vertical dash line in Figure (a) represents the Fermi level which satisfies the neutrality of the system. The formation energy in (a) is calculated at the equilibrium potential = 2.28 V. (b) The formation energies of charged defects at the Fermi level as a function of applied potential . The vertical dashed line in Figure (b) represents the equilibrium potential. It is hypothesized that the hole polaron p+ is produced by removing a 3p electron from an S2– anion (schematically shown in Figure S2). For polaron calculations in the present study, a perturbation is added to the local structure because polarons always are associated with the distortion of the local structure.9-10, 25-26 The perturbation means a slight disorder of the local atomic structure. The present study shows that the magnetic moment of a (3×3×3) supercell with an extra positive charge (removing an electron) is 1 . Figure 2(a) shows the spin density around the polarized anion. The dumbbell shape of the isosurface suggests that the polarization is attributed to a 3p orbital. Bader analysis 2728

also shows that the ionic state of this polarized anion is -1. The average distance


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between Li+ cations and the S– anion is elongated to 2.67 Å, which is 0.19 Å longer than the distance between Li cations and normal S2– anions. The elongation is attributed to the weaker electrostatic attraction between Li+ cations and the S– anion. The total density of states (TDOS) of the (3×3×3) supercell with a hole polaron is plotted in Figure 2(b). It can be seen that metallic states are not present in the valence band; hence the polarondoped Li2S is not a band conductor. Also, the hole polaron states appear in the gap between the valence band maximum (VBM) and the conduction band minimum (CBM). The position of the hole polaron states is much closer to the VBM. These mid-gap states are also observed in the DOS of polaron-doped Li2O2.9 Banerjee and collaborators mapped the polaronic states in the V2O5 nanowire combining DFT calculations and experimental techniques.29 They also found that the polaron can induce mid-gap states, and these polaronic states can be evidenced by the hard X-ray photoemission spectroscopy (HAXPES) measurement. In Ref. 6, Kim et al. argued that the hole polaron was not stable in the Li2S (2 × 2 × 2) supercell, which conflicts with our results. To verify the reliability of the current results, we recalculated the hole polaron in the (2 × 2 × 2) Li2S supercell with different input parameters (400 eV cut-off energy with = 0.5 as used for the (3 × 3 × 3) supercell and 500 eV cut-off energy with = 0.48 as used in Ref. 6). All calculations demonstrated that the hole polaron is stable in the crystalline Li2S (Figure S3). Our study also examined the effects of the pseudopotentials on the hole polaron formation. The results demonstrated that the hole polaron can also form when the Perdew-Wang functional (PW91)30 with the HSE06 method is used to describe the electron exchangecorrelation interaction. Recently, Siegel and collaborators also found that O2- in MgO can



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be converted to a stable hole polaron by losing a 2p electron.31 Since S is the first-nearest downstairs neighbor of O in the periodic table, the S2- anion and O2- anion have similar orbital arrangement of the outmost electrons. (3s23p6 for S2- and 2s22p6 for O2-). For both anions, the outmost p orbitals are fully occupied and they can lose one electron to form a hole polaron.

Figure 2. Geometric and Electronic structures of hole polaron. (a) The red isosuface (3×10-3 |e|/Å3) represents the spin density distribution around the polarized S atom. The yellow sphere represents the S atom, and violet spheres represent Li atoms. The averaged distance between Li atoms and the polarized S atom is longer than 2.67 Å, while the normal Li–S bond length is 2.48 Å. (b) Total density of states (TDOS) of a (3×3×3) Li2S supercell with one hole polaron. The polarized states appear between the valence band and the conduction band. The previous study demonstrated that the hole polaron could diffuse in the bulk Li2O2 with a barrier as low as 68 meV.9 Our work employed a climbing image nudged elastic band (CI-NEB) method

22

to find the minimum energy path (MEP) for hole

polaron diffusion in crystalline Li2S. Two diffusion paths are proposed: (i) the hole polaron hops between two first nearest neighbor (1NN) sulfur anions along the [110] orientation with a hoping distance of 4.04 Å; (ii) the hole polaron hops between two second nearest neighbor (2NN) sulfur anions along the [100] orientation with a hopping 8 ACS Paragon Plus Environment

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distance of 5.72 Å. The energy profiles along the proposed diffusion paths are shown in Figure 3. The diffusion along [110] orientation is energetically preferred because of the relatively lower barrier of 90 meV. The barrier of the other diffusion path is 182 meV. The V diffusion barrier was also calculated in this study, and it was found that the MEP is 293 meV (Figure S4), which agrees well with the diffusion barrier barrier of V

(about 290 meV) calculated by Kim et al.

6

It can be inferred that the hole polaron

diffusion is facile due to the much lower diffusion barrier than V . Ceder and his

colleagues also searched the MEPs of the hole polaron diffusion in cathode materials LiFePO4 and LiMnPO4, and they found that the diffusion barriers are 170 meV and 303 meV, respectively.26 These results indicate that hole polarons are expected to be relatively mobile in solid Li2S.

Figure 3. Activation energies of the hole polaron diffusion along different directions.

The mobility of the hole polaron p+ can be estimated by Einstein relation

= , with =

(1) &'

exp $% (.


(2)


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Here ) is Boltzmann constant, T is temperature, d is the hopping distance, and is the vibration frequency which approximates to 1013 sec-1. Δ+ is the classical diffusion barrier shown in Figure 3. The contribution of the atomic vibration to the diffusion barrier is less than 1 meV when , > 200 K (Figure S5), so it is safely ignored in the current study. The effect of temperature on the mobility of p+ and V is shown in Figure 4(a). It can be

found that a higher temperature is helpful for enhancing the mobility of charged defects. At room temperature condition (T = 20 °C), the magnitude of V mobility is four orders

lower than the p+ mobility. Consequently, it can be expected that p+ is the main charge carrier due to its relatively low diffusion barrier and high mobility. Based on the carrier mobility, the conductivity of Li2S can be calculated by / = 01.

(3)

In Eqn. (3), c denotes the defect concentration. Figure 4(b) shows the electronic conductivity corresponding to p+ diffusion. Since the V mobility is too low in Li2S, we does not make a significant contribution to the conductivity. In principle, assumed that V

the conductivity is not a constant during the discharging/charging process, but dependent on the cell potential as shown in Figure 4(b). This behavior has also been found in Li-air batteries.32 The reason is that the p+ formation energy is a monotonically decreasing function cell potential. Figure 4(b) suggests that a higher operating temperature is expected to improve the electronic conductivity because the higher temperature is beneficial for increasing p+ concentration and enhancing p+ mobility (Figure 4(a)). At the room temperature (T = 20 °C) and equilibrium potential ( = 2.28 V) condition, the calculated electronic conductivity is 5.54×10-23 S cm-1 (Figure 4(b)). Kim et al. theoretically calculated the ionic conductivity of Li2S with the similar operating condition


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(T = 20 °C and Φ = 2.4 V), and found that the ionic conductivity is 1.9×10-26 S cm-1. For alkali metal oxides, the hole polaron also plays the role of the predominant charge carrier. The theoretically predicted Li2O2 electronic conductivity is 3×10-18 S cm-1, and the predicted Na2O2 electronic conductivity is 2×10-19 S cm-1.13 Lu et al. found that crystalline LiO2 can be the stable discharge product in the Li–O2 battery.33 A recent theoretical study reported that the electronic conductivity caused by hole polaron hopping is 3 × 104 S cm-1, which is much higher than the electronic conductivity of Li2O2.34 Compared to alkali metal oxides, the relatively lower electronic conductivity of Li2S can be attributed to the higher p+ formation energy and diffusion barrier. Figure 4(b) clearly shows that the bulk electronic conductivity is even lower than 5.54×10-23 S cm-1 during the discharging process ( < ). Under this condition, charges are difficult to migrate from the cathode to the electrolyte/Li2S interface to promote significant electrochemical reduction reactions. Hence the electrochemical reduction of soluble PSs to solid products should happen on the fresh cathode surface. The present theoretical findings indicate that the growth of Li2S precipitation during the discharging process should be a chemical reaction rather than an electrochemical reaction, as proposed by Fan et al based on their experimental findings.7 Two scenarios can happen during the charging process ( > ). Under a low overpotential condition, the delithiation and decomposition of Li2S should happen at the Li2S/cathode interface. In this case, the contact area will continually decrease and even disappear before the Li2S particle is fully converted to Li+ and S8, which can lead to irreversibly losing the active material. The other scenario is to charge the Li–S battery with a high overpotential. As shown in Figure 4(b), the electronic conductivity exponentially increases as the applied potential increases. Under a high



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charging overpotential, the high electronic conductivity can transfer charges to the electrolyte/Li2S interface where electrochemical reactions take place. In this case, the conversion of Li2S to S8can always happenat the electrolyte/Li2S interface during the entire charging process, which can mitigate capacity fade due to losing the active material.

Figure 4. (a) The effect of temperature on the mobility of hole polaron p+ and Li vacancy V . (b) The electronic conductivity as the function of applied potential. The vertical dashed line in Figure (b) represents the equilibrium potential = 2.28 V. According to Eqn. (3), a high electronic conductivity can be reached by increasing '

the concentration of hole polaron, and the concentration is proportional to exp $% 5 (. Hence, it is necessary to find an effective strategy to lower the formation energy of charge carrier and improve the electronic conductivity. Introducing heteroatom impurities is a promising method to increase the conductivity of the discharge products according to previous studies on lithium-air batteries. Matsuda et al. reported that Cl–-incorporated Li2O2 has an enhanced electronic conductivity to tolerate surface passivation, which consequently leads to a super improved practical capacity.35 Radin et al. investigated the role of heteroatom impurities in Li2O2, and found that heteroatoms can reduce the formation energy of charged defects, leading to the increase in conductivity.36


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The properties of a vacancy-polaron complex were also studied in this study. The complex was constructed by one V bridging two adjacent p+ ( V –2p+).

The

magnetic moment of the complex is 2 , and the ionic state of each polarized S atom is 1. Figure 5(a) depicts the spin density distribution in the complex. The shape of the isosurface indicates that each S loses a 3p electron, and the axis of the half-occupied 3p orbital points to the vacancy. The average Li–S distance in the complex is 2.63 Å, which is longer than the normal Li–S bond length in crystalline Li2S. The distance between these two polarized S– is 3.98 Å, which is shorter than the 4.04 Å distance between two 1NN S2-. The shorter S–S distance in the complex is attributed to the weaker electrostatic repulsion between the two S– anions. The diffusion behavior of the complex was also investigated in the current study. The position of the complex is represented by the position of the Li+ vacancy, and the complex moves with the vacancy. Two diffusion paths were proposed in this study: one diffusion path is the vacancy hopping to the 1NN Li+ along the [100] orientation; the other diffusion path is the vacancy hopping to the 2NN Li+ along the [110] orientation. CI-NEB simulations demonstrated that the MEP is the diffusion along the [100] orientation with a barrier of 0.83 eV. The complex diffusion along the [110] orientation has a higher barrier of 1.27 eV. The vacancy-polaron complex encounters a much higher diffusion barrier than the single hole polaron. The magnitude of the complex diffusion barrier is almost one order of magnitude larger than the single polaron diffusion. The single V diffusion is also studied in the present study. It is found

that diffusion barriers are 0.29 eV along the [100] orientation and 0.99 eV along the [110] orientation, respectively (Figure S3). These results suggest that once the complex forms in Li2S, the transport of charge carriers will be hindered. Ceder and his colleagues



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+ calculated the V –p complex diffusion in crystalline Li2O2, and they also found that the

complex diffusion barrier was much higher than the single polaron diffusion barrier 9. + The diffusion of the V –p complex was not studied in the current work, because the net + + –p is zero and the directional diffusion of V –p does not generate current. charge of V

A vacancy can trap the hole polaron in metal chalcogenides. Recently, Frodason et al. using DFT with a HSE hybrid functional predicted that a Zn vacancy could also trap polarons in ZnO.37 They found that the distance between two polarized O– anions were 3.69Å, which agreed well with the 3.75 Å inferred from electron paramagnetic resonance (EPR) measurements.37-39 In ZnO, the electronic configuration of the hole polaron (O– anion) is 2p5. Hence the polaron can be attributed to a paramagnetic center which can be easily observed by EPR.38 The electronic configuration of the polarized S2– is 3p5, which indicates EPR is a potential technique to map the hole polaron in Li2S. As discussed above, decreasing the formation energy of the hole polaron (in other words, increasing the concentration of the hole polaron) is one way to enhance the electronic conductivity. As shown in Figure 1(a), the x coordinate of the lowest cross point between the positive-slope curve and the positive-slope curve represents the hypothetical Fermi level, which is common throughout the cell.32 The Fermi level is included in Eqn. S1 for calculating the defect formation energy. The formation energy of hole polaron can be decreased by shifting the Fermi level to the left. Figure S6 schematically demonstrated that a negatively charged foreign dopant could shift the Fermi level to the left. The foreign dopant candidates can be Group V elements in the periodic table, such as N3- substituting S2- (N ) and P3- substituting S2- (P ). Recently, Li3N and P2S5 were used as additives to improve the performance of conventional Li–ion


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batteries and Li–S batteries.40-42 These additives can serve as the dopant sources in the Li–S battery, just as Co3O4 providing Co2+ dopants to Li2O2 for improving the conductivity.36 Also, N-decorated and P-decorated carbon cathodes can also serve as the dopant sources in Li–S batteries.43-50 It is worth noticing that the position of the dopant curve in Figure S6 is sensitive to the chemical potential of the dopant in the system. How dopants can enhance the electronic conductivity will be addressed in future work.

Figure 5. (a) The red isosurface (3×10-3 |e|/Å3) represents spin density distribution in the + -p complex. Yellow spheres represent S atoms, violet spheres represent Li atoms, and V the gray sphere represents the Li vacancy. (b) The energy barriers of the V –2p+ complex diffusion along different orientations. Conclusions In summary, first-principles calculations are performed to analyze the thermodynamic and kinetic properties of hole polaron in bulk Li2S. It is found that the hole polaron p+ can be formed by removing a 3p electron from S2– anion. At the equilibrium potential = 2.28 V, negatively charged Li vacancy V and hole polaron p+ are the predominant

native defects. The high charging overpotential can facilitate the formation of the hole polaron. MEPs of diffusion of charged defects are calculated in this study. The hole polaron prefers diffusing along [110] orientation with a 90 meV barrier, which is much lower than the V diffusion barrier. Therefore, p+ has the potential of serving as the

charge carrier in bulk Li2S. High applied potential and high temperature are beneficial for 15 ACS Paragon Plus Environment


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enhancing the electronic conductivity. The properties of V –2p+ properties are also

studied, and it is found that the complex can hinder the charge transport through the Li2S precipitation. The object of the present study is using the DFT simulation to investigate the charge diffusion in crystalline Li2S, and provide potential strategies for enhancing Li2S conductivity. It is worth noticing that the theoretical prediction should be validated by the experimental observation. We are planning a new work in which the DFT simulation and EPR characterization will be combined to investigate the effect of heteroatoms on the hole polaron formation and diffusion. Supporting Information Detailed computational methods and formulas for calculating the formation energies of charged defects; effect of applied potential on the formation energy; schematic diagram of the mechanism for hole palaron formation; isosurface of spin density distribution around the polaron; MEP for Li vacancy diffusion; contribution of the atomic vibration to the diffusion barrier; possible ways to increase the electronic conductivity are reported as Supplemental Information. This information is available free of charge via the Internet at http://pubs.acs.org. Acknowledgements: The information, data, or work presented herein was funded by the Office of Energy Efficiency and Renewable Energy (EERE), U.S. Department of Energy, under Award Number DE-EE0006832. Supercomputer resources from Texas A&M University High Performance Computer are gratefully acknowledged.


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Disclaimer: The information, data, or work presented herein was funded in part by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. References 1. Bruce, P. G.; Freunberger, S. A.; Hardwick, L. J.; Tarascon, J.-M., Li-O2 and Li-S Batteries with High Energy Storage. Nat. Mater. 2012, 11, 19-29. 2. Yin, Y. X.; Xin, S.; Guo, Y. G.; Wan, L. J., Lithium–Sulfur Batteries: Electrochemistry, Materials, and Prospects. Angew. Chem. Int. Ed. 2013, 52, 1318613200. 3. Manthiram, A.; Fu, Y.; Su, Y.-S., Challenges and Prospects of Lithium–Sulfur Batteries. Acc. Chem. Res. 2012, 46, 1125-1134. 4. Yang, Y.; Zheng, G.; Misra, S.; Nelson, J.; Toney, M. F.; Cui, Y., High-Capacity Micrometer-Sized Li2s Particles as Cathode Materials for Advanced Rechargeable Lithium-Ion Batteries. J. Am. Chem. Soc. 2012, 134, 15387-15394. 5. Eithiraj, R.; Jaiganesh, G.; Kalpana, G.; Rajagopalan, M., First‐Principles Study of Electronic Structure and Ground‐State Properties of Alkali‐Metal Sulfides–Li2S, Na2S, K2S and Rb2S. Phys. Status Solidi 2007, 244, 1337-1346. 6. Kim, D.-H.; Lee, B.; Park, K.-Y.; Kang, K., First‐Principles Study on Charge Transport Mechanism of Lithium Sulfide (Li2S) in Lithium‐Sulfur Batteries. Chem. Asian J. 2016, 11, 1288-1292. 7. Fan, F. Y.; Carter, W. C.; Chiang, Y. M., Mechanism and Kinetics of Li2S Precipitation in Lithium-Sulfur Batteries. Adv. Mater. 2015, 27, 5203-5209. 8. Liu, Z.; Mukherjee, P. P., Mesoscale Elucidation of Surface Passivation in the Li– Sulfur Battery Cathode. ACS Appl. Mater. Interfaces 2017, 9, 5263-5271. 9. Ong, S. P.; Mo, Y.; Ceder, G., Low Hole Polaron Migration Barrier in Lithium Peroxide. Phys. Rev. B 2012, 85, 081105. 17 ACS Paragon Plus Environment


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TOC Graphic


Hole Polaron Diffusion in the Final Discharge Product of Lithium

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