The Lithiation and Delithiation Processes in Lithium-Sulfur Batteries

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C: Energy Conversion and Storage; Energy and Charge Transport

The Lithiation and Delithiation Processes in Lithium-Sulfur Batteries from Ab Initio Molecular Dynamics Simulations Claire Arneson, Zachary D. Wawrzyniakowski, Jack T. Postlewaite, and Ying Ma J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00478 • Publication Date (Web): 09 Apr 2018 Downloaded from http://pubs.acs.org on April 9, 2018

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The Journal of Physical Chemistry

The Lithiation and Delithiation Processes in Lithium-Sulfur Batteries from Ab Initio Molecular Dynamics Simulations

Claire Arneson, Zachary D. Wawrzyniakowski†, Jack T. Postlewaite†† and Ying Ma* Materials Science and Engineering, University of Wisconsin-Eau Claire, Eau Claire, WI 54701, United States

Abstract Lithium-sulfur (Li-S) batteries are a promising alternative to the Li-ion technology due to their high theoretical capacity and low cost. Unlike intercalation compounds, the sulfur cathode undergoes a series of complex electrochemical reactions that give rise to substantial structural and morphological changes. Here we report ab initio molecular dynamics simulations of the lithiation and delithiation reactions that are important in Li-S batteries. The lithiation is studied on two low energy surfaces, (100) and (001), of sulfur (S8), while delithiation is studied on the (111) surface of lithium sulfide (Li2S). The effect of electrolyte is included by constructing interfacial systems between these surfaces and dimethoxyethane (DME), a widely used liquid electrolyte. During both lithiation and delithiation, a layer-by-layer reaction pattern is revealed. The evolution of atomistic structure and reaction voltage during lithiation and delithiation is studied, and the microscopic reaction mechanisms are analyzed. Dissolution of lithium polysulfides into the electrolyte is also observed in our simulations, which is attributed to the strong interaction between lithium polysulfides and electrolyte molecules in the form of lithium bonds. Studies of the delithiation process in Li2S confirm that the experimentally observed initial charge barrier is of kinetic origin.

†Present address: Chicago Kent College of Law, Illinois Institute of Technology, 565 W Adams St., Chicago, Il 60661 ††Present address: Department of Physics, University of Wisconsin-Madison, 1150 University Ave., Madison, WI 53706

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1. Introduction Lithium ion batteries (LIBs) are widely used as the energy storage device in portable consumer electronics,1 although their limited energy density is still a major challenge.2-3 Even after decades of development, current LIB technology can only deliver a maximal specific capacity of about 300 mAh/g,4 which hinders its applications in a few key markets such as extended-range electric vehicles.5 The cathode materials used in LIBs have a layered structure and lithium ions are inserted or extracted. Such an intercalation chemistry is essential for the stability and cyclability that are required for successful commercialization; however, it is also the underlying reason that is responsible for the limited capacity. Sulfur, one of the most abundant elements on earth, offers a theoretical capacity of 1,672 mAh/g, the highest of all known solid cathode materials.4 Unlike intercalation compounds, in which the cathode structure remains stable, a series of complex electrochemical reactions take place in sulfur and the structural stability requirement is relieved, leading to a much improved capacity. Besides the high capacity, a sulfur cathode is also appealing due to its low cost and environmental compatibility. For these reasons, sulfur is among the most promising cathode materials and lithium-sulfur (Li-S) batteries have been the subject of extensive research efforts.616

In fact, the concept of elementary sulfur as a cathode material was originated 17 even before

the introduction of the first intercalation cathode.18 Unfortunately, the electrochemical reactions in sulfur lead to the formation of various lithium polysulfides. Soluble polysulfides Li2Sn (3≤n≤ 8) intermediates can shuttle between the electrodes, resulting in poor Coulombic efficiency and capacity fading.19-21 The formation of insoluble products, Li2S2 and Li2S, that block the electrochemical reaction is again a serious problem.22-23 The sulfur cathode itself also suffers from poor electronic conductivity.16 To address these problems, various nanocomposites, including sulfur-carbon,24-28 sulfurgraphene,29-32 and sulfur-polymer composite materials,33-35 have been developed to facilitate rapid ionic and electronic transport. Novel cell configurations involving the insertion of an interlayer to trap polysulfides have been proposed.36-37 To expedite these efforts in improving the electrochemical performance of Li-S batteries, numerious studies have been devoted to the understanding of the reaction meachansim during charge (delithiation) and discharge (lithiation). Overall, the cell reaction during lithiation can be described by: 2 + → (1), 2 ACS Paragon Plus Environment

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and the reaction sequence is generally believed to be: → → → → → →

(2).

However, the actual reaction sequence is extremly complicated, and many intermediate molecular species that deviate from those listed in Eq. (2) may appear. Two voltage plateaus occuring around 2.2-2.3 V and 1.9-2.1 V appear on the voltage profile, which is often explained by a two-step reaction model: 38-39 + 4 → 2 , (3a)

2 + 8 → 4 ↓ +2 . (3b) The first plateau requires 4 electrons for each cycloocta sulfur ring, or 0.5 e-/sulfur, while the second plateau corresponds to a 1.0 e-/sulfur process. Although most experimentally observed second voltage plateaus start at around 0.5 e-/sulfur, which is consistent with this two-step model, the first plateau extends to only around 0.25 e-/sulfur, followed by a sloping region. In other words, the first step actually includes two different reaction mechansims, which can be explained by a four-region-reduction model.40 In this model, the first region is a 0.25 e-/sulfur process corresponding to the reduction of the cycloocta sulfur ring and the formation of soluable Li2S8 at the voltage of 2.2-2.3 V: + 2 → . (4a) The disolved Li2S8 is then further reduced and lower-order lithium polysulfides form through + 2 → + , (4b) which is also a 0.25 e-/sulfur process corresponding to the observed sloping regin. The reduction of low-order polysulfides to form Li2S2 is the third region that corresponds to the voltage plateau at 1.9-2.1V, followed by the fourth region of the formation of Li2S with a rapid decline in the cell voltage. In both models, a specific capacity of around 1.5 e-/sulfur (~1256 mAh/g) is accessible while the remaining 0.5 e-/sulfur capacity can hardly be achieved due to the low electrochemical acitivity of Li2S. Upon delithiation, lithium ions are extracted from Li2S under an external field, and an almost flat voltage pleteau is observed initially, followed by a gradual increase in the voltage. The reaction pathway during delithiation is believed to be different from that during lithiation, although the exact mechanism is not clear. While significant progress has been made, our current understanding of Li-S batteries is far from complete. A fundamental understanding of the complex electrochemical reactions during charge and discharge is still lacking. Advanced characterization tools and methodologies 3 ACS Paragon Plus Environment


could help to enhance our understanding;41-42 however, the physical and chemical processes involved are often beyond the detection limit of current characterization tools. Given the microscopic nature of the problem, few, if any, characterization tools have the necessary resolution to address these questions. Adding further to the complexities, the electrochemical reactions in the cathodes lead to constant changes in the reaction pattern, necessitating an in situ experimental technique.43 Computational approaches, in principle, can be used to provide the much needed insight.44-45 Many high-level quantum chemical and density function theory (DFT) calculations have been reported, although most of the studies are focused on the equilibrium structures and energetics of the various molecular species involved in the reaction. The dynamic processes that lead to the structural changes and formation of various polysulfides are relatively unknown. Molecular dynamics (MD) simulation is a powerful tool to study the dynamics involved in the reaction, and the lithiation processes in a solid sulfur cathode,46 as well as the short-chain sulfur in microporous graphene structure,47 have been recently studied using reactive MD simulations. However, results from such classical MD simulations depend critically on the quality of the empirical interatomic potentials. Ab initio molecular dynamics (AIMD) simulation requires no empirical parameters, although the time and length scales that can be accessed are often limited. A number of AIMD studies on the Li-S chemistry have been reported, although the number of lithium ions are often held constant.48-50 To the best of our knowledge, the dynamic processes during discharge and charge, where the cathode structure evolves as a function of the number of lithium ions added (lithiation) or removed (delithiation) at a given rate, have not been studied using AIMD simulations and are the main focus of the present study. Such a method can certainly be extended to study more complex electrochemical reactions and/or with increased time and length scales to reveal the effects of system size, charge/discharge rate, etc, which will be the subject of future studies. It should be noted that “lithiation” and “delithiation” have been used traditionally to describe the intercalation and de-intercalation processes in electrode materials. However, such a terminology has seen widespread usage in conversion type electrode materials as well.51-55 For this reason, we use “lithiation” to describe the process where lithium ions diffuse to and react with the cathode, and “delithiation” to describe the process where lithium ions leave the cathode under an external field. In this work, AIMD simulations were used to study the structural evolution during lithiation in a sulfur cathode, and new atomistic insights regarding the 4 ACS Paragon Plus Environment

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formation of lithium polysulfides were obtained. The delithiation process in Li2S, which is the discharged product, was also studied. Interestingly, Li2S can also be used as the cathode with a theoretical capacity of 1,166 mAh/g. The use of Li2S is appealing as it enables a lithium metalfree anode, although a large potential barrier is required on the initial charge to activate the insulating Li2S particle. Such an activation barrier is thought to be kinetic in nature, which is confirmed by our simulations based on the calculated values of charge voltage as a function of lithium removal.

2. Computational Methods Experimentally, the cathode materials are often used in the form of nanoparticles of ~100 nm, and simulating such a system is a formidable task for any first principles methods. To reduce the computational cost, the energies of several low-index surfaces were determined first and the lithiation processes were studied on selected low energy surfaces. For surface energy calculations, the surface system was constructed by removing the periodic boundary condition along the z direction, which is the surface norm, and adding a vacuum layer that is 10 Å in length. In this way, two free surfaces were created with one on the bottom and one on the top. First principles DFT calculations were performed using a plane wave basis set. The exchange correlation potential was described by a generalized gradient approximation with the PerdewBurke-Ernzerhof parameterization.56 The projector augmented wave method57 was applied as implemented in the Vienna ab initio simulation package (VASP).58-59 The surface structures were relaxed until the force on each atom was less than 0.02 eV/Å, and then the total energies were obtained. For each surface orientation, slabs of different thicknesses were studied to ensure convergence in the calculated surface energies and the surface energies were extracted as described in literature.60 Small particles of cathode materials are often embedded in a conductive carbon matrix. Depending on the size and geometry of the carbon matrix, distinctive voltage profiles may be observed, indicating different reaction patterns that can be attributed to the reduction of shortchain sulfur or sulfurized carbon.52, 61 The present study focuses on the reaction pattern in traditional Li-S system with elemental sulfur and liquid electrolyte, where the use of carbon matrix is mainly to provide necessary electrical conductivity since both S8 and Li2S are poor electrical conductors.16, 61 Although the presence of carbon matrix leads to lowered capacities 5 ACS Paragon Plus Environment


and sometimes increased polarization, the sulfur reduction mechanism is not expected to be significantly impacted. As a result, carbon matrix is not included in our simulations.

Figure 1. Computational setup for (a) the S8 (100)/electrolyte interface and (b) the Li2S (111)/electrolyte interface.

Electrolyte is also a critical component in a battery that provides the necessary transport pathway for lithium ions. The liquid electrolyte is often a mixture of multiple solvents and different lithium salts. Although the solvent molecules and the salt ions do not participate in the electrochemical reactions directly, recent studies suggested strong interactions between lithium ions and solvents containing oxygen atoms such as Dimethoxyethane (DME) and 1,3-dioxolane (DOL).49, 62 To further understand the molecular origin of such interactions and identify their role in lithiation and delithiation, the effects of electrolyte were included explicitly in our simulations by constructing the cathode/electrolyte interface. For simplicity, only DME molecules are studied, although the effect of DOL is similar because both solvents contain oxygen atom. The computational setups including the electrolyte are given in Figure 1. The dimension of the crystalline region is around 25 Å, while that of the electrolyte is around 15 Å The liquid structure was generated by randomly adding electrolyte molecules to the system at the experimental 6 ACS Paragon Plus Environment

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density, followed by a conjugate gradient structural relaxation with the crystalline part frozen. The temperature of the liquid was then raised gradually to 300 K in 2 ps using AIMD calculations. To allow for cathode-electrolyte interaction, the crystalline part, except for the bottom 10 Å of the crystal, was unfrozen and relaxed together with the liquid for another 2 ps to form the equilibrium cathode/electrolyte interface. Note that the frozen bottom crystal was used to simulate the bulk environment. With such a computational setup, the lithiation and delithiation processes were studied only along the top interface. During lithiation, lithium ions were added randomly along the top interface, and during delithiation, randomly selected lithium ions were removed. The system remains to be charge neutral as the adding or removing of a lithium ion was compensated by an incoming or outgoing electron. After each addition/removal of lithium ion, the system is equilibrated for a total of 2 ps, during which the system evolves structurally and reaches the new equilibrium. Different time periods for equilibration, including 0.5 ps, 1.0 ps, 2.0 ps, and 3.0 ps have been tested, and 2 ps is chosen to ensure that the calculated energies are converged and at the same time the computational cost is reasonable. The lithiation and delithiation rate of 1 lithium ion / 2 ps is actually very high if compared to experimental rates, similar to those reported previously.63-64 It is partially due to the limited time scale that is accessible to atomistic simulations, but at the same time it should be noted that the simulated rate does not directly correlate to experimental ones due to the fact that the diffusion process of lithium ions in the electrolyte, which is one of the key rate-limiting factors,65 is not included in our simulation. For this reason, the actual rate simulated is much lower, and the obtained reaction pattern is still reliable because lithium diffusion in the electrolyte is not likely to impact the electrochemical reaction that takes place within the cathode.

3. Results and Discussion 3.1 Surface energies The equilibrium shape and the surface termination of nanoparticles are determined by the surface energies, and our calculations started from the determination of low energy surfaces. Because crystalline sulfur is made up of individual cycloocta rings and the breaking of the S-S bond requires additional energy,66 surface models for S8 were constructed keeping all ring structures complete. The calculated energies for various low index surfaces in S8 and Li2S are 7 ACS Paragon Plus Environment


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listed in table 1. No solvation effect was considered as the impact of solvation on the surface energies was small.66 For S8, many surfaces exhibit low energies, which is consistent with the fact that no cycloocta sulfur ring is broken and the intermolecular interactions are van der Waals. Surface energies in Li2S are much larger due to the stronger interatomic bonding in Li2S. The lowest energy surface is (111), which is expected to be the dominate surface in Li2S nanoparticles. Our results are consistent with previously published data,66-67 and small variations in some surface orientations may be a result of minor differences in the computational details such as the pseudopotential used and the size of the k-point grid.

Table 1. Summary of calculated surface energies. Previously published data (Ref. 64 for S8 and Ref. 65 for Li2S) are included for comparison.

System

S8

Li2S

Surface energies (meV/Å2)

Surface

Previously published

orientation

This work

(001)

12

12

(010)

16

16

(100)

11

11

(011)

18

16

(110)

10

13

(111)

13

17

(100)

142

148

(110)

32

37

(111)

21

23

results66-67

3.2 The lithiation process on the S8 surfaces Most of the surfaces in S8 are close in energy because these surfaces differ only in the relative orientation of the cycloocta sulfur ring. It is expected that the lithiation process on different surfaces would also be similar, and any differences should be a result of the relative orientation of the ring. For comparison, the (100) and (001) surfaces, surfaces with low energies but different ring orientations, were selected to study the lithiation process. Figure 2 shows the 8 ACS Paragon Plus Environment

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interface structures between these surfaces and the electrolyte. In the case of the (100) surface, lithium diffusion is perpendicular to the plane of the cycloocta sulfur ring (Figure 2a), while in the case of the (001) surface, lithium diffusion is parallel to the ring (Figure 2b). In both cases, layers of sulfur rings can be identified, and the (100) surface has two rings per layer, while the (001) surface has four rings per layer.

Figure 2. The structure of the (a) S8 (100)/electrolyte, (b) S8 (001)/electrolyte, and (c) Li2S (111)/electrolyte interfaces. Note that any atoms outside of the simulation box (indicated by the black lines) are periodic images that are plotted to complete the electrolyte molecule or the cycloocta sulfur ring structure.

The lithiation process was simulated by adding lithium ions randomly along the interface. For each lithium ion added, the system was equilibrated for 2 ps, and the energy was calculated by averaging over the last half of the trajectory. The reaction voltage is determined using

(5),

where n is the number of lithium ions added, E(Li) is the cohesive energy per atom for BCC Li, E0 is the average energy for the interface system with no lithium added, and E(nLi) is the averaged energy for the system with n lithium ions added. Figure 3 plots the calculated voltage as a function of the number of lithium ions. To ensure convergence in the averaged energies and thus the calculated voltage, at least three different configurations for each number of lithium ion were studied for the S8 (100) surface and the averaged voltage, as well as the standard deviation, is shown in Figure 3a. Although larger deviations were observed for the cases with only one or two lithium ions, the standard deviation decreased to around ±0.05 V. The initial, large deviations can be explained by the differences in the initial positions of the randomly generated 9 ACS Paragon Plus Environment


lithium ions, and as more lithium ions were added to the system, the electrochemical chemical reaction involving S8 started, leading to a converged voltage profile. For the (001) surface of S8 (Figure 3b), only a single configuration was studied due to the increased system size and thus the higher computational cost. However, it is expected that the obtained results are accurate to within a standard deviation comparable to that of the (100) surface.

Figure 3. The calculated voltage as a function of the number of lithium ions (a) added to the S8 (100) surface, (b) added to the S8 (001) surface, and (c) removed from the Li2S (111) surface. In (a) the error bars represent the standard deviation of the average voltage calculated from at least three different configurations.

The obtained voltage profiles clearly show different regions corresponding to different reaction mechanisms. Initially, a high voltage of around 2.5 V can be seen for both (100) and (001) surfaces (Figures 3a and 3b) with up to two lithium ions in the system. Structural analysis reveals that although some of the cycloocta sulfur rings open up, the overall ring structure is maintained, as shown in Figure 4a for the (100) surface and Figure 5a for the (001). Since only a few S-S bonds were broken, the energy penalty was small, leading to a high reaction voltage. Because the structural changes in cycloocta sulfur rings were minimal, this initial high voltage stage can be described as an interfacial reaction whose reaction voltage is determined by the structure of the S8-electrolyte interface and the position of lithium ions along the interface. Such an interfacial reaction was subsequently dominated by the electrochemical conversion of cycloocta sulfur ring as more lithium ions were added to the system. A voltage plateau of around 2.2 V can be identified on the voltage profile, which extends from 3 to 4 lithium ions in the case of the (100) surface, and from 3 to 8 in the case of the (001) surface. Representative atomistic 10 ACS Paragon Plus Environment

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structures for this region are given in Figures 4b and 5b for the (100) (with 3 lithium ions) and (001) (with 6 lithium ions) surfaces, respectively. An intermediate region, from 5 to 8 lithium ions for the (100) and from 9 to 16 for the (001) surface, appears on the voltage profile where small fluctuations are observed. Representative atomistic structures are given in Figures 4c and 5c for the (100) (with 6 lithium ions) and (001) (with 12 lithium ions) surfaces, respectively. The discharge voltage finally approaches another plateau of around 2.0 V, and representative structures are given in Figure 4d for the (100) surface (with 10 lithium ions) and Figure 5d for the (001) surface (with 22 lithium ions). For the (100) surface, the lithiation process was studied up to a total number of 12 lithium ions, while for the (001) surface, the lithiation process was studied with up to 24 lithium ions.

Figure 4. Representative atomistic structure of the S8 (100)/electrolyte interface during different stages of the reaction. (a), (b), (c), and (d) correspond to systems with 1, 3, 6, and 10 lithium ions, respectively. 11 ACS Paragon Plus Environment


Figure 5. Representative atomistic structure of the S8 (001)/electrolyte interface during different stages of the reaction. (a), (b), (c), and (d) correspond to systems with 1, 6, 12, and 22 lithium ions, respectively.

The number of lithium ions simulated in this study may seem to be rather small, however, the lithium concentration studied is actually comparable to experiments, considering that the electrochemical reaction is mostly localized on the top layer of the cycloocta sulfur ring on both surfaces. As shown in Figure 4 and Figure 5, the cycloocta sulfur rings in the second layer are only slightly distorted. Focusing on the first layer, 12 lithium ions for the (100) surface, which has two cycloocta sulfur rings per layer, correspond to a discharge capacity of 0.75 e-/sulfur, 12 ACS Paragon Plus Environment

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while 24 lithium ions for the (001) surface, which has four cycloocta sulfur rings per layer, correspond to the same discharge capacity. Note that the theoretical capacity of S8, 1,672 mAh/g, is equivalent to 2 e-/sulfur, and only around 1.5 e-/sulfur capacity is experimentally accessible.

Figure 6. The calculated voltage as a function of capacity (e-/Sulfur) for (a) the S8 (100) surface, (b) the S8 (001) surface, and (c) the Li2S (111) surface. The three different regions, I, II, and III in (a) and (b) are described in the text.

Including only the first layer of cycloocta sulfur rings, the voltage profiles shown in Figure 3 for (100) and (001) surfaces are recast into Figure 6, which plots the calculated voltage as a function of discharge capacity. For both the (100) and (001) surfaces, three distinct regions can be identified. The first region (Figures 6a and 6b, region I) is consistent with the 2.2-2.3 V plateau observed experimentally, except for the initial high voltages. As discussed earlier, the initial high voltage is a result of the interface effects that depend on the structure of the electrolyte molecules and the position of lithium ions. In other words, the use of a different electrolyte could lead to different initial voltages, which has been reported experimentally.68 The voltage of 2.2-2.3 V corresponds to the reduction of the cycloocta ring, leading to the formation of various lithium polysulfides. At this stage of reaction, as the lithium concentration is low, high order lithium polysulfides, such as Li2S8, are expected to form (Eq. 4a). Structurally, one of the cycloocta sulfur rings breaks into smaller pieces that are attached to lithium ions, as shown in Figure 4b for the (100) surface with 3 lithium ions and Figure 5b for the (001) with 6 lithium ions. Interestingly, although the overall stoichiometry is close to Li2S8, our simulations reveal many possible reaction products that are in the form of LixSy, for example (Li3S8)+, (LiS8)-, (LiS5)-, etc. These molecules are spatially isolated, and each molecule is formed by chemical bonding between Li+ and the negatively charged sulfur atom (Figures 4b and 5b). Anion species 13 ACS Paragon Plus Environment


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such as (LiS8)- and (LiS5)- are a result of Li+ ion deficiency, while cation species such as (Li3S8)+ are a result of extra Li+, which has also been observed in a recent first principles study.49 Such a variation in the reaction products is not surprising considering that lithium ions are randomly inserted into the system. However, the net energy change, including the energy penalty due to the breaking of cycloocta sulfur ring and the energy decrease due to the formation of Li-S bonds, is quite similar in all these cases, leading to a constant voltage plateau. In other words, the reaction described in Eq. (4a) is rather simplified, and our AIMD simulations suggest a distinct mechanism where the reduction of a cycloocta sulfur ring can be, in general, described by: + → + .

(6)

Note that if ≠ 8, a separate cluster will form, which can be seen from Figure 4b where a S3 molecule is observed. The voltage plateau is then an average resulting from many such reactions that take place locally at different cycloocta sulfur rings, and the actual reaction depends on the number of available lithium ions that diffuse to the ring, i.e., the local lithium concentration. Due to the difference in such a local concentration, the reaction products, LixSy, can be in the form of anions, cations, or neutral molecules. The total charge of all the non-neutral molecules is balanced, and the system remains charge neutral. Non-neutral species give rise to a net electric field that drives the migration of these molecules, leading to the formation of thermodynamically more stable neutral lithium polysulfide species, for example, Li2S8.49 In other words, LixSy are intermediate reaction products that could be short-lived. These molecules are observed since our simulations sampled a time scale that is hardly accessible to experimental techniques. Although only limited theoretical and experimental data support the existence of such intermediate species,21 our simulation provides another evidence. As many of these intermediate molecules are smaller, they are expected to diffuse with relative ease. Thus, the design of a physical polysulfide trap should consider the confinement of these intermediate species. As more lithium ions diffuse into the system, polysulfides formed from Eq. (6) are further reduced, resulting in a second voltage plateau region (Figure 6, region III) at around 2.0 V. Since the lithium concentration is much higher at this stage of reaction, increased lithium-lithium repulsion leads to a lower voltage plateau. Structurally, many lithium polysulfide molecules, LixSy, are formed, and these molecules and electrolyte molecules move towards each other (Figures 4d and 5d) due to the strong polar interactions. Electrolyte molecules are also observed 14 ACS Paragon Plus Environment

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to diffuse into the second layer (Figure 4d), indicating the dissolution of lithium polysulfide into the electrolyte. Indeed, our simulations show that the average positions of sulfur atoms in the first layer move into the electrolyte by 1.49 Å and 1.73 Å for the (100) and (001) surface, respectively. Given sufficient time for diffusion, it is expected that the lithium polysulfides formed within the first layer would diffuse into the electrolyte, which opens the door for continued lithium diffusion into the bulk, thus creating a layer-by-layer reaction process. These results are distinct from a recent study that reported the formation of large polysulfide complex with a network structure,69 which is unlikely to dissolve. We believe that the inclusion of electrolyte molecules in the simulation is the key reason for the observed difference. In fact, many lithium ions in the current study are observed to be attracted to oxygen ions in the electrolyte molecule, forming strong lithium bonds that are an analog of hydrogen bonds.62 Such a lithium bond chemistry could be the initial driving force for the dissolution of lithium polysulfides, which subsequently diffuse away as a result of the concentration gradient towards the anode, resulting in the notorious polysulfide shuttle effects. Recent computational studies have also shown similar strong lithium-oxygen bonding in both DME and DOL.49 Thus, an efficient polysulfide trapping mechanism must overcome this strong lithium bond interaction. For any lithium polysulfides that remain in the cathode, continued lithiation will eventually lead to the formation of Li2S2 and Li2S particles that could block the lithium transport pathway into sulfur, leading to a rapid decline in the voltage profile. Unfortunately, simulations of such processes require a much longer time scale and were not studied. An intermediate region (Figure 6, region II) is observed with a sloping voltage, which is, again, a result of the uneven distribution of lithium ions. Besides the randomly created lithium positions along the interface that contribute to the uneven distribution, the layer-by-layer reaction process further amplifies the spatial variation in lithium concentration that is expected to decrease from the outer S8 layers into the inner layers. Initially, the reaction is dominated by the reduction of cycloocta sulfur rings with a reduction voltage of 2.2-2.3 V, corresponding to the first voltage plateau. This plateau carries a capacity of 0.5 e-/sulfur; however, beacause of the spatial variation of lithium concentration, some cycloocta sulfur rings have already been reduced to lithium polysulfides and continued reduction takes place at a voltage of 2.0 V, resulting in a lowering of the observed voltage in this intermediate region. As more cycloocta sulfur rings start the second reaction at 2.0 V, the voltage continues to decrease until the second reaction 15 ACS Paragon Plus Environment


dominates with a voltage plateau of 2.0 V. The staring position of this intermediate region, as well as the experimentally observed voltage for this region, depends on the overall competition of the two reaction mechanisms. It is expected that this region appears earlier on the discharge curve for later cycles as compared to the first one due to the pre-existing lithium polysulfides formed during the first cycle. Higher discharge rates will also lead to earlier appearance of this region, as higher rates decrease time for concentration-driven diffusion and thus increase the spatial variation. Both are consistent with experimental observations.70 Increased spatial variation also leads to the earlier formation of Li2S2 and Li2S, resulting in much reduced recoverable capacities.70 The above described reaction patterns are consistent with the four-region-reduction model,40 although the fourth region, which corresponds to quick voltage drop due to the formation of Li2S2 and Li2S, was not simulated due to computational restriction. Interestingly, different atomistic insights are obtained. The first voltage plateau is attributed to the reduction of cycloocta sulfur rings, which is similar to the reaction described in Eq. 4a, although many intermediate molecules, instead of Li2S8, formed as given in Eq. 6. The second plateau corresponds to the reduction of lithium polysulfides. Because it starts at 0.5 e-/sulfur, the overall lithium to sulfur ratio is 1:2. As such, the lithium polysulfides can be described by a formula of Li4S8. However, it should be pointed out that such a chemical formula represents only the average stoichiometry, and the acutal molecules formed vary significatly based on the local lithium concentration. Reduction of these molecules gives rise to the second voltage plateau of 2.0 V, forming either Li2S2, or Li2S: + 4 → 4 7a ! + 12 → 8 7% Reaction 7a corresponds to a 0.5 e-/sulfur capacity, while reaction 7b corresponds to 1.5 e-/sulfur. These two mechanisms compete with each other, and experimentally a capacity of around 1.0 e/sulfur can be realized. Again, Li4S8 in Eq. 7a and 7b only represents an average stoichiometry. The first reaction, Eq. 6, gives the initial 0.5 e-/sulfur capacity, however a sloping region is often observed as reaction 7a and 7b starts due to the uneven spatial distribution of lithium ions. These atomistic insights suggest the importance of local lithium concentraion, and the variation in such a concentration leads to the formation of various intermediate species, the competition of different reaction mechansims, and thus the overall reaction pattern. It also explains the variation

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in the experimentally observed charge/discharge profiles, as the local lithium concentration cannot be precisely controlled experimentally.

3.3 The delithiation process on the Li2S (111) surface After the formation of Li2S, an external voltage is required to drive lithium ions out, completing a charge-discharge cycle. This delithiation process is modeled by removing randomly selected lithium ions along the Li2S (111)/electrolyte interface at the same rate as discharging (1 Li/ 2 ps). The initial computational setup is given in Figure 1b. Only the (111) surface is studied since the (111) surface is low in energy and thus is expected to dominate. For each lithium ion removed, the system was equilibrated for 2 ps, while the energy was calculated by averaging over the last half of the trajectory. The reaction voltage is calculated by

(8),

where n is the number of lithium ions removed, E(Li) is the cohesive energy per atom for BCC Li, E(-nLi) is the averaged energy for the system with n lithium ions removed and E0 the average energy for the interface system with no lithium removed. As such, the voltage given in Eq. 8 is considered to be the thermodynamic equilibrium voltage, which is plotted in Figure 3c as a function of number of removed lithium ions. Structural distortions are localized around the removed lithium ions. The initial structure, as shown in Figure 7a, clearly shows the repeating Li2S layers along the surface norm. Within each layer, lithium ions are slightly above and below sulfur atoms, creating sublayers of Li-S-Li. In the current setup, each sublayer contains 9 atoms. Figure 7b shows the structure after the removal of 10 lithium ions. Even though all lithium ions in the first sublayer are removed, structural distortions are mainly localized within the first Li2S layer, indicating good structural stability of Li2S and, at the same time, poor electrochemical activity. The top layer, after the removal of 10 lithium ions, resembles the structure of a few lithium polysulfide, which could serve as the nuclei for the growth of polysulfide. Continued removal of lithium ions then leads to the growth of the polysulfide, consistent with a two-phase reaction model.



Figure 7. The atomistic structure of Li2S (111)/electrolyte interface with (a) no lithium removed and (b) 10 lithium ions removed.

Since the reaction also shows a layer-by-layer pattern, and the charge curve in Figure 3c is recast into Figure 6c considering only the first layer. An initial large voltage barrier of around 2.8-2.9 V is observed, which can be explained by the use of the perfect crystal in the present simulation. The presence of defects, as well as the finite size of nanoparticles, could result in a lower charge voltage, which is confirmed by the quick decrease in the voltage after the removal of a few lithium ions. The voltage reaches a plateau at 2.3-2.4V, which should be the true reaction voltage because the presence of defects is inevitable. Even the initial voltage of 2.8-2.9 V, which reflects the thermodynamic limit to remove lithium ions from an infinitely large perfect surface of Li2S, is significantly less than the experimentally observed initial voltage of 3.45 V, confirming that such a barrier must originate from poor kinetics.71 This two-phase reaction model also suggests that pre-existing polysulfides on the Li2S surface, for example, those formed from previous cycles, could help to reduce the initial voltage due to a decreased nucleation barrier, which is also consistent with experimental observations.

4. Conclusions Using ab initio molecular dynamics simulations, the lithiation on the (100) and (001) surfaces of S8 and delithiation on the (111) surface of Li2S, with the presence of electrolyte molecules, have been studied. The atomistic structure and reaction voltage as a function of the 18 ACS Paragon Plus Environment

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number of lithium ions were determined, and both systems show a layer-by-layer reaction pattern. For S8, the simulated reaction pattern corroborates the four-region reaction model, although new microscopic reaction mechanisms were revealed. The reduction of S8 gives rises to many smaller LixSy polysulfide molecules, which corresponds to the first voltage plateau at 2.2-2.3 V. Reduction of various polysulfides with an overall stoichiometry of Li4S8 corresponds to the second voltage plateau of 2.0 V, and an intermediate sloping region is found in between the two plateaus. This intermediate region is a result of variation in the local lithium concentration such that the two reduction mechanisms overlap. Our simulations also show that cycloocta sulfur rings diffuse into the electrolyte after the formation of lithium polysulfides as a result of strong lithium bonds, which is responsible for polysulfide shuttle effects. For Li2S, the removal of lithium ions corresponds to a voltage plateau of around 2.3-2.4 V, which confirms that the experimentally observed initial charge voltage of 3.45 V is a result of poor kinetics. These results provide a detailed microscopic view of the electrochemical reactions that are important in Li-S batteries, and the new atomistic insights obtained, including the formation of various intermediate species, the competition of different reaction mechanisms, and the importance of local lithium concentration, could help to improve our understanding of the complex electrochemical processes observed in these batteries.

Author information Corresponding Author *Email: [email protected] ORCID Ying Ma: 0000-0003-3408-5703 Acknowledgement This work used the Extreme Science and Engineering Discovery Environment (XSEDE) High Performance Computing Cluster Comet at the San Diego Supercomputing Center through allocations TG-DMR160048 and TG-DMR160036. The authors would like to thank the Center for High Throughput Computing (CHTC), University of Wisconsin-Madison, and the Blugold Supercomputing Cluster at the University of Wisconsin-Eau Claire for providing additional computational resources.



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The Lithiation and Delithiation Processes in Lithium-Sulfur Batteries

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