Revealing Charge Transport Mechanisms in Li2S2

Letter pubs.acs.org/JPCL

Revealing Charge Transport Mechanisms in Li2S2 for Li−Sulfur Batteries Zhixiao Liu,† Perla B. Balbuena,*,‡ and Partha P. Mukherjee*,† †

Department of Mechanical Engineering and ‡Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, United States

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S Supporting Information *

ABSTRACT: Besides lithium sulfide (Li2S), lithium persulfide (Li2S2) is another solid discharge product in lithium−sulfur (Li−S) batteries. Revealing the charge transport mechanism in the discharge products is important for developing an effective strategy to improve the performance of Li−S batteries. Li2S2 cannot transport free electrons due to its wide bandgap between the valence band maximum (VBM) and conduction band minimum (CBM). However, electron polarons (p−) and hole polarons (p+) can appear in solid Li2S2 due to the unique molecular orbital structure of the S2− anion. The 2 thermodynamic and kinetic properties of native defects are investigated. It is found that negatively charged Li vacancies (V−Li) and p+ are the main native defects with a low formation energy of 0.77 eV. The predominant charge carrier is p+ because p+ has a high mobility. The electronic conductivity related to p+ diffusion is dependent on temperature, and high temperatures are preferred to increase the conductivity.

R

reduced to insoluble products (as shown in reactions iv and v), which precipitate onto the cathode surface. Both soluble PSs and solid products bring critical challenges that prevent Li−S batteries from commercialization. The “shuttle effect” can transport soluble long-chain PSs to the anode side. In the anode side, long-chain PSs react with the Li metal surface, leading to an irreversible capacity loss.7,8 A variety of experimental and computational efforts have been made to find practical strategies to mitigate this harmful shuttle effect.9−14 The insoluble Li2S product is an electronic insulator, which can passivate the active surface area for electrochemical reactions.15 Enhancing the mobility of charge carriers in discharge products could be a promising method to improve the electrochemical performance according to previous studies on lithium−air batteries (LABs).16−18 Kim et al. investigated the thermodynamic and kinetic properties of charged defects in crystalline Li2S, and found that the negatively charged Li vacancy (V−Li) is the main charge carrier.19 Although the activation energy for V−Li diffusion is only 0.29 eV, the low vacancy concentration prevents Li2S from achieving high conductivity. Kim et al. suggested introducing heteroatom dopants into Li2S to increase the concentration of charge carriers.19 Li2S2 is the only solid intermediate discharge product in Li−S batteries, but the nature of solid Li2S2 has not been understood clearly. Crystalline Li2S2 is not a stable phase according to the equilibrium Li−S phase diagram.20 Siegel and collaborators found that Li2S2 could be converted into Li2S to lower the bulk

echargeable lithium−sulfur (Li−S) batteries attract considerable attention due to their high specific capacity and low cost.1,2 The electrochemical reaction mechanism of Li−S batteries is different from lithium-ion batteries (LIBs). In commercial LIBs, transition metal oxides always serve as Li storage materials in the cathode side and graphite is the conventional anode material. The cathode material experiences Li intercalation during the discharging process and deintercalation during the charging process.3 However, the specific capacity is limited by those of the intercalation materials (372 mAh g−1 theoretical capacity for graphite and 272 mAh g−1 theoretical capacity for LiCoO2). By contrast, Li−S batteries can deliver a theoretical capacity as high as 1675 mAh g−1 if sulfur is completely reduced to the final discharge product Li2S. The Li−S battery involves complex multistep electrochemical reactions:4 2Li+ + 2e− + S8 ↔ Li 2S8 ,

2.39 V vs Li0/Li+

2Li+ + 2e− + 3Li 2S8 ↔ 4Li 2S6 ,

2.37 V vs Li0/Li+

2Li+ + 2e− + 2Li 2S6 ↔ 3Li 2S4 ,

2.24 V vs Li0/Li+

(i) (ii)

(iii)

2Li+ + 2e− + Li 2S4 ↔ 2Li 2S2 ,

2Li+ + 2e− + Li 2S2 ↔ 2Li 2S,

≈2.2 V vs Li0/Li+

2.15 V vs Li0/Li+

(iv) (v)

From reactions i∼iii, S8 molecules are electrochemically reduced to long-chain lithium polysulfides (LiPSs) as Li2Sx (with 4 ≤ x ≤ 8). These long-chain PSs can dissolve into many aprotic electrolytes.5,6 Long-chain PSs can be subsequently © 2017 American Chemical Society

Received: December 29, 2016 Accepted: March 6, 2017 Published: March 6, 2017 1324

DOI: 10.1021/acs.jpclett.6b03063 J. Phys. Chem. Lett. 2017, 8, 1324−1330

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The Journal of Physical Chemistry Letters Gibbs free energy of the system.21 But the reduction reaction of Li2S2 to Li2S is kinetically slow.1 The crystal structure of Li2S2 was not known until recently. In Siegel et al.’s work, the Li2S2 Gibbs free energy was calculated based on a Li2O2−like crystal structure (space group p63/mmc).21 By using an evolutionary algorithm and first-principles calculations, Feng et al. first predicted a possible Li2S2 crystal structure belonging to the space group p1.22 Later, Yang et al. also predicted a Li2S2 crystal structure with space group p42/mnm.23 It was found that the energy of p42/mnm structure was lower than that of the p1 structure, without considering the energy contributed by the atoms vibrations. Recently, the p1 structure was experimentally detected by using an operando X-ray diffraction (XRD) technique.24 Recently, Li2S particles were used to fabricate composite cathode for Li−S batteries. Li2S can be treated as the Li source in the Li−S cell to couple with Li metal-free anodes, such as Si25 anode and metal oxide anodes.26,27 According to our firstprinciples calculation results, the lithiation of α-S8 to Li2S is always accompanied by about 40% volume expansion. This huge volume expansion can mechanically destroy the integrity of the cathode framework.28 On the other hand, the Li2S cathode experiences the volume contraction during the initial delithiation process, which could prevent the cathode framework from mechanical damage.25 However, Li2S also suffers from the poor ionic and electronic conductivity. Cui and coworkers reported that activating the initial delithiation process needs to overcome a huge potential barrier of approximately 1 V.25 Revealing charge transport mechanisms in the solid lithium sulfides of Li−S battery is crucial to improving the performance of Li−S batteries. Enhancing charge transport can not only tolerate surface passivation, but also reduce charging overpotential. In this paper, a first-principles analysis technique, which has been successfully used to study charge transport in the products of metal-air batteries,16,29−31 is employed to investigate charge transport in solid Li2S2. This study adopts the p1 structure predicted by Feng et al. because the p1 structure is more stable at room temperature according to calculations based on first-principles atomistic thermodynamics. Figure S1 clearly demonstrates that p42/mnm Li2S2 is stable only when the temperature approaches 0 K. The total density of states (TDOS) of p1 Li2S2 is plotted in Figure 1, which shows that Li2S2 is a semiconductor. The calculated bandgap is about 1.7 eV based on the generalized gradient approximation (GGA) of the Perdew−Burke−Ernzerhof (PBE) functional. 32 The bandgap of p1 Li2S2 is close to the bandgap of p42/mnm Li2S2 (1.8 eV), and much less than the bandgap of Li2S (3.5 eV) calculated by Eithiraj.33 Conventional GGA+PBE simulations always underestimate the bandgap. In this regard, the Heyd−Scuseria−Ernzerhof (HSE06) hybrid functional is employed to improve the bandgap calculation.34 With HSE06, the calculated Li2S2 bandgap is about 2.8 eV, which is also much less than the 5.08 eV Li2S bandgap reported by Kim et al.19 The narrower bandgap indicates that Li2S2 has more intrinsic charge carriers than Li2S. Native defects are sometimes helpful for enhancing electronic conductivity. Nørskov and his colleagues found that the neutral Li vacancy (V0Li) makes Li2O2 conductive.35 This phenomenon is also theoretically observed in crystalline Li2S. The presence of V0Li makes the valence band shift upward. Consequently, the Fermi level can cross the valence band, which represents a p-type conductor (Figure S2). However, V0Li

Figure 1. Total density of states of perfect Li2S2 and Li2S2 with neutral native defects. The neutral Li vacancy is generated by removing a Li atom from a (3 × 3 × 2) supercell; and the neutral S2 vacancy is generated by removing a S2 dimer from (3 × 3 × 2) supercell. The energy level is referenced to Fermi energy.

in Li2S requires a vacancy formation energy (Ef) higher than 3 eV, which indicates that it is difficult to generate V0Li in pristine Ef

( ) ∼ 10

Li2S practically (exp − κT

−52

at T = 293 K), and

introducing heteroatoms are expected to reduce the vacancy formation energy.36 However, for the Li2S2 crystal, the presence of either V0Li or V0S2 does not affect the position of Fermi level. The Fermi level in these defective systems is still above the valence band maximum (VBM) but below the conduction band minimum (CBM), as shown in Figure 1. From the TDOS in Figure 1, it can be inferred that Li2S2 cannot transport free electrons from the cathode substrate to the electrolyte/Li2S2 interface for electrochemical reactions. Beyond free electrons, charged defects and polarons can also potentially serve as charge carriers to support electrochemical reactions at the interface.16,29−31,37,38 Figure 2 shows the diffusion barriers of charged native defects along different crystal orientations. The diffusion barrier is calculated by the climbing image nudged elastic band (CI-NEB) method.39 For negatively charged Li vacancy (V−Li), four diffusion paths are proposed (Figure S3). Diffusion paths along the [010] and [100] orientations are in a Li2S2 (001) plane. A Li vacancy can also hop from one (001) plane to the adjacent (001) plane via two consecutive paths, which are named [001]-in and [001]out. Figure 2a shows that V−Li interplane diffusion always encounter high energy barriers. The V−Li [100] diffusion barrier is 0.95 eV and the [010] diffusion barrier is 0.83 eV. Diffusion along the [001] orientation is energetically favored. The barriers of [001]-in diffusion and [001]-out diffusion are 26 and 148 meV, respectively. Similarly to V−Li diffusion, V2+ S2 intraplane diffusion along the [001] direction is also the energetically favored path with a barrier as low as 0.46 eV (Figure 2b). V2+ S2 interplane diffusion along [100] has a 0.71 eV barrier, and the diffusion along the [010] direction encounters the highest energy barrier of 1.20 eV. Regardless of the diffusion path, V−Li − always diffuses faster than V2+ S2 because VLi requires smaller activation energy to overcome the barrier. The vacancy diffusion is evaluated by swapping the positions between a 1325

DOI: 10.1021/acs.jpclett.6b03063 J. Phys. Chem. Lett. 2017, 8, 1324−1330

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Figure 2. Energy barriers of (a) V−Li and (b) V2+ S2 diffusion along different orientations.

vacancy and its adjacent ion. The higher diffusion barrier of V2+ S2 can be attributed to the larger size of the S2− anion. 2 + Li2S2 bulk consists of S2− 2 molecular ions and Li ions. Figure S4 shows the electronic structure of an S2 molecule. Similarly to the O2 molecule, 12 electrons in a S2 molecule occupy σs, σ*s , σp, πp, and π*p orbitals. In an isolated S2 molecule, the antibond orbital π*p is half occupied. In Li2S2 bulk, Li 2s electrons are transferred to πp* orbital of S2, leading to S2− 2 . The antibonding σp* orbital is still empty in S2− 2 , and this orbital can accept an extra electron to form an electron polaron p−. On the other hand, π* orbital can donate an electron to form a hole polaron p+ (Figure S5). The formation of p− can be demonstrated by the slight distortion of the local atomistic structure. It is found that the S−S bond of the S2 anion who accepts the extra electron is elongated to 2.74 Å, which is 0.64 Å longer than nonpolarized S2 anions. The elongation of the bond length is also observed in the electronically polarized O−O pair in Li2O2.37 For the electron polaron, the extra electron is localized at the antibond σ*p orbital as proposed in Figure S5. The occupation of antibonding orbital weakens the intermolecular interactions, leading to the increase of the bond length. Electronic structure analysis also provides evidence to support this hypothesis. Bader analysis40 demonstrates that the ionic state of the elongated S−S pair is −3. Figure 3a depicts the spin density around the elongated S−S pair. It can be seen that the spin density distributes along S−S axis, and these two spin isosurfaces exclude each other. The shape of the spin density isosurfaces indicates that the extra electron is localized at the antibonding σp* orbital. This work also suggests that the S−S bond can hold a hole polaron p+. The formation of p+ is also associated with the distortion of the local atomistic structure. In contrast to p−, p+ can reduce the bond length of the polarized S−S pair to 2.01 Å. This result coincides with the hypothesis that the hole polaron p+ is formed by removing an antibonding electron from the S2− 2 , resulting in a shorter bond length due to a weaker S−S exclusion. It is also found that the magnetic moment of the distorted structure is 1 μB. It is hypothesized that removing an electron from the π*p orbital leads to an unpaired electron as schematically shown in Figure S5. The hypothesis is verified by the spin density distribution shown in Figure 3b. It can be seen that the spin density isosurfaces from different S atoms excluded each other and distribute aside the S−S axis. The pattern of spin density distribution coincides with the shape of the π*p orbital, which proves that one electron is removed from the πp* bond. It is worth noting that the averaged Li−S bond length around p+ is also elongated to 2.68 Å. The reason is that

Figure 3. Spin density of (a) electron polaron and (b) hole polaron in a (3 × 3 × 2) supercell. Violet spheres represent Li atoms and yellow spheres represent S atoms, respectively. Green spheres represent S atoms associated with the polaron.

the electrostatic repulsion between Li+ and p+ weakens the Li− S ionic bonds. The diffusion behavior of polarons is also studied in the present work. Figure 4 shows the energy barriers of different diffusion paths. The proposed polaron diffusion paths are the same that were proposed for V2− S2 diffusion. The preferred − diffusion path for p is also along the [001] direction with an energy barrier of 0.69 eV. The energy barrier for diffusion along the [100] direction is only 0.02 eV higher than the diffusion along the [001] direction. The electron polaron p− diffusion along the [010] direction is kinetically slower than the other 1326

DOI: 10.1021/acs.jpclett.6b03063 J. Phys. Chem. Lett. 2017, 8, 1324−1330

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Figure 4. Energy barriers of polaron diffusion along different directions.

two diffusion paths as shown by the higher diffusion barrier of 0.89 eV. It is interesting that p+ can almost freely move in Li2S2. For p+, the diffusion barrier along [001] direction is 13 meV, which is much lower than the barriers of p− diffusion. The interplane diffusion barriers are even less than 10 meV. The present simulation demonstrates that the diffusion barriers are 6 meV for the [010] and [100] directions. In Li2O2 and Na2O2, it was shown that p+ also has much lower diffusion barrier than p−.31,38 The mobility of charge carriers can be estimated by the Einstein relation as eD μ= (1) κT

Figure 5. (a) Mobility of different charged native defects. (b) Ionic conductivity and electronic conductivity as the function of temperature. The ionic conductivity corresponds to V−Li diffusion, and the electronic conductivity corresponds to p+ diffusion.

where κ is Boltzmann constant, T is temperature, and D is the diffusion coefficient of the charge carrier. ⎛ ΔE ⎞ ⎟ D = νd 2 exp⎜ − ⎝ κT ⎠

Fermi level, which is the energy level makes the system satisfy charge neutrality. This approach was employed by Siegel and collaborators to investigate charge carrier concentration in crystalline Li2O2.16,42 It is worth noting that the relative position of the VBM to the Fermi level (Δϵ) is dependent on the applied potential Φ as reported by Luntz and collaborators.43−45 The applied potential-dependent Fermi level can be aligned by either metal−insulator−metal (MIM) modeling44,45 or using experimental values.43 Using this alignment approach, Luntz et al. found that Fermi level in Li2O2 is ∼0.35 eV above the VBM at the equilibrium potential (Δϵ(Φ0) = 0.35 eV). The Fermi level reported by Luntz et al. is closer to the VBM than the value (≈ 2 eV) reported by Siegel et al.42 According to eq S5, a lower Fermi level can reduce the formation energy of a positively charged hole polaron, and increase the formation energy of a negatively charged Li vacancy. It can be inferred that the current study about Li2S2 may underestimate the electronic conductivity and overestimate the ionic conductivity. − The calculated ionic conductivity (corresponding to VLi diffusion) and electronic conductivity (corresponding to p+ diffusion) are shown in Figure 5b. The calculated ionic conductivity is 1.5 × 10−25 S cm−1, which is very close to the ionic conductivity of Li2S crystal.19 This low ionic conductivity can be attributed to the relatively high V−Li diffusion barrier. The electronic conductivity of Li2S2 is 15 orders of magnitude larger than the ionic conductivity at room temperature, which indicates that p+ is the predominant carrier to transport charge through the precipitation film during the charging/discharging

(2) 13

Here v is the vibration frequency which approximates to 10 s−1, d is the hoping distance, and ΔE is the diffusion barrier. From Figure 2 and Figure 4, we know that the diffusion barrier is direction-dependent. Therefore, the harmonic mean value is calculated to estimate the mobility of different charged defects, as shown in Figure 5a. It is found that p+, as the positive charge carrier, has the highest mobility with a magnitude of 10−1 cm2 V−1 s−1 due to its extremely low diffusion barrier. The negative charge carriers, p−and V−Li, have mobilities of around 10−16 ∼ 10−15 cm2 V−1 s−1 at room temperature, and the mobility could be enhanced by increasing temperature. The formation energies of charged defects are calculated in this study to estimate the conductivity of Li2S2 (Figure S6). It is found that p+ and V−Li are predominant charged native defects with the formation energy Ef = 0.77 eV. The conductivity can be estimated by the following equations:41 σ = ceμ (3) and

⎛ Ef ⎞ c = c 0 exp⎜ − ⎟ ⎝ κT ⎠

(4)

V−Li

+

0

Here c is the concentration of or p , and c is the concentration of Li+ or S2− 2 in the perfect Li2S2 crystal. The formation energy Ef is calculated according to eq S5 in the Supporting Information. In the present study, the Fermi level for the formation energy calculation (eq S5) is a hypothetical 1327

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carrier in Li2S2, n-type heteroatom doping, which can decrease the formation energy of p+, is expected to be an effective strategy to improve the conductivity of crystalline Li2S2.

process. It is also found that the increase of temperature is helpful for achieving a higher conductivity, which can consequently lead to a smaller Ohmic drop. Mikhaylik and Akridge experimentally studied the effect of temperature on the performance of Li−S batteries, and they found that the battery could reach a higher discharge voltage at a higher temperature.46 Figure S7 proposes a scenario describing charge transport and electrochemical reactions. During the discharging 2− process, the long-chain S2− m are reduced to short chain Sn (m > n) by taking electrons from the Li2S2 surface. Simultaneously, hole polarons are created at the electrolyte/Li2S2 interface. Hole polarons then diffuse to the Li2S2/cathode interface due to the potential gradient, and disappear there by combining with electrons from the cathode. During the charging process, hole polarons are created at the Li2S2 interface and then transported to the electrolyte/Li2S2 interface to activate oxidation reactions. Previous experimental and theoretical studies demonstrated that crystalline Li2S2 is not thermodynamically stable. Siegel and co-workers predicted that solid Li2S2 could be converted into α-S8 and Li2S via the disproportionation reaction to minimize the Gibbs free energy of the system.21 However, in their model, only the bulk Gibbs free energy was considered. It is worth noting that the surface Gibbs free energy makes a significant contribution to the total Gibbs free energy of a particle, especially the nanosized regime. Ceder and co-workers have developed a first-principles thermodynamic model, which takes into account both the bulk Gibbs free energy and surface Gibbs free energy, to study the nanoscale stabilization of sodium oxides in Na−O2 batteries.47 It was found that the stable phase changes from NaO2 to Na2O2 with increasing the size of the sodium oxide nanoparticle. Inspired by this work (see ref 47), we would like to suggest that Li2S2 could potentially be stabilized in nanoscale confined structures. If the electrochemical reaction is stopped at the Li2S2 step, the battery can still deliver a theoretical capacity of 837 mAh g−1, with an equilibrium potential of 2.2 V vs Li/Li+. Converting α-S8 to Li2S2 is accompanied by only 5% volume expansion according to the present calculation results, which indicates that Li2S2 precipitation will generate less mechanical damage in the carbon-based cathode framework. Compared to Li2S, another advantage of Li2S2 is its relatively higher electronic conductivity. If Li2S2 nanoparticles, as the active material, are impregnated into a porous nanostructure, the Li−S battery can have a lower potential barrier for activating the initial delithiation process. In summary, a first-principles approach is performed to understand the charge transport mechanism in crystalline Li2S2. Electronic structure analysis shows that Li2S2 is a semiconductor that cannot transport free electrons. Native defects can serve as carriers to deliver charge from the cathode to the PSs in the electrolyte. The thermodynamic and kinetic properties of negatively charged Li vacancy (V−Li), positively − charged S2 vacancy (V2+ S2 ), electron polaron (p ), and hole + polaron (p ) are estimated in this study. It is found that V−Li and p+ are the predominant charged native defects in Li2S2. The present calculations show that p+ has a much higher mobility than V−Li because p+ diffusion requires extremely low activation energy (∼10 meV). Li−S batteries should avoid low-temperature operating conditions because the high temperature can increase the electronic conductivity of Li2S2. A good electronic conductivity can mitigate the surface passivation caused by the precipitation of discharge products. Since p+ is the main charge

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COMPUTATIONAL METHODS All calculations were performed using the Vienna Ab initio Simulation Package (VASP)48,49 based on density functional theory (DFT)50,51 within the plane wave basis set approach.52 The cutoff energy of the plane wave basis set was set to 400 eV The projector augmented wave (PAW) method was employed to describe electron−ion interactions, and the generalized gradient approximation (GGA) of the Perdew−Burke− Ernzerhof (PBE) functional32 was employed used to describe the electron−electron exchange correlations. Heyd−Scuseria− Ernzerhof (HSE06) hybrid functional34 with α = 0.25 was employed for calculating the defect formation energy because conventional DFT always underestimates the electron localization. Equations for calculating the formation energy are discussed in the Supporting Information. The HSE06 hybrid functional was also employed for calculating the electronic structures and searching minimum energy paths for defect diffusion.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b03063. Gibbs free energies of Li2S2 with different crystal structures (Figure S1); TDOS of Li2S (Figure S2); proposed paths for defect diffusion (Figure S3); electronic structure of S2 molecule (Figure S4); polaron formation mechanism (Figure S5); defect formation energy (Figure S6); proposed scenarios of polaron transport during charging/discharging processes (Figure S7) (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (P.P.M.). *E-mail: [email protected] (P.B.B.). ORCID

Perla B. Balbuena: 0000-0002-2358-3910 Partha P. Mukherjee: 0000-0001-7900-7261 Notes

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. The authors declare no competing financial interest. 1328

DOI: 10.1021/acs.jpclett.6b03063 J. Phys. Chem. Lett. 2017, 8, 1324−1330

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ACKNOWLEDGMENTS 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 DEEE0006832. Supercomputer resources from Texas A&M University High Performance Computer are gratefully acknowledged.

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