A DFT Investigation on the Origins of Solvent-Dependent Polysulﬁde Reduction Mechanism in Rechargeable Li-S Batteries

: The lithium-sulfur (Li-S) battery is one of the promising energy storage alternatives because of its high theoretical capacity and energy density. Factors governing the stability of polysulﬁde intermediates in Li-S batteries are complex and are strongly a ﬀ ected by the solvent used. Herein, the polysulﬁde reduction and the bond cleavage reactions are calculated in di ﬀ erent solvent environments by the density functional theory (DFT) methods. We investigate the relationship between the donor numbers (DN) as well as the dielectric constants ( ε ) of the solvent system and the relative stability of di ﬀ erent polysulﬁde intermediates. Our results show that the polysulﬁde reduction mechanism is dominated by its tendency to form the ion-pair with Li + in di ﬀ erent organic solvents.


Introduction
Lithium-sulfur (Li-S) batteries, with their high theoretical energy density of 2600 Wh/kg, are attracting much attention as future energy storage systems in various fields, including portable electronic devices, hybrid to full electric vehicles (EVs), and large-scale power grids [1,2]. Since the sulfur cathode could undergo multiple electron transfer events during the Li-S battery operations, a high theoretical capacity (1675 mAh/g) can be achieved. In comparison, the conventional intercalated LiCoO 2 cathode in the lithium-ion batteries (LIB) shows a capacity of around only 140 mAh/g [3]. The abundant quantity and the low cost of the sulfur resources on earth also guarantee economic advantages of Li-S batteries [4][5][6]. Overall, the predicted high efficiency and the environmental compatibility of the Li-S batteries have made them the most promising candidate to overcome the intrinsic limitation of the common batteries for the next generation rechargeable energy storage system [4,[7][8][9].
However, the development on the application of Li-S batteries is hindered by various problems, including the shuttle effect [9][10][11][12] and the dendrite formation at the anode [13,14], etc. The combined effects of the physical properties, such as viscosity, conductivity, and safety issues of the electrolyte system [15,16], the salt additives [17], electrode materials [18][19][20][21], interface stabilities [22][23][24][25], etc., have been the subject of intense investigations in the past decade aiming for the practical and sustainable scaling of high-performance Li-S batteries [26,27]. The physical environment of a Li-S battery is an extremely complicated system and the plethora of experimental attempts are still largely based on trial and error. Large-scale theoretical simulations have also been carried out to improve the fundamental understanding of the structural and transport behaviors of the intermediates, the interaction between the electrolyte and the reacting species, and the adsorption event at the electrode surfaces [28][29][30][31][32][33].
In principle, the selection of the solvent and the electrolyte system is critical to the battery performance since the sulfur reduction mechanisms [10,[34][35][36] depend strongly on the dissolution, diffusion and disproportionation reactions of soluble polysulfides in the solvent environment [5,9,[37][38][39][40][41][42][43][44]. The chain length distribution of the polysulfide species intimately affects the diffusion coefficients, the conductivities, clustering, and even the extent of the shuttle effect [12,28,29]. Meanwhile, the major polysulfide species may exist in different forms [44] depending on the solvent system [38,43,45], the ionic additives [46], and even the concentrations [43]. For example, a previous study has shown that different alkali-metal cations could stabilize polysulfides of different length, e.g., S 4 2− or S 3 2− [38]. It was also observed that the radical polysulfide species are favored at lower sulfur concentrations, while the doubly charged, dimerized polysulfide species are favored at higher sulfur concentrations [43] in accordance with chemical equilibrium. For the more fundamental solvent effect, different theories have been suggested to rationalize experimental observations. For example, the most stable polysulfide intermediate may exist as S 3 − radicals in dimethyl sulfoxide (DMSO), or as S 4 2− in the mixed solvent system, 1,3-dioxane:1,2-dimethoxyethane (DOL:DME) [38,47]. A different study reported that polysulfide radicals (i.e., S 4 − ) can be selectively stabilized in ether-based electrolytes, such as in tetraethylene glycol dimethyl ether (TEGDME), and polyethylene oxide (PEO) [43,48]. These phenomena were tentatively correlated with the dielectric constant (ε) and/or the donor number (DN) of the solvent system. Nevertheless, a microscopic understanding is lacking. In general, the ε of the solvent is related to the stability of polar or ionic solute species, and the DN is directly related to the complexation between the cation and the solvent molecules. Therefore, a single parameter may not offer a comprehensive explanation to the observed tendency of the dominant polysulfide species. A more profound understanding of the multiple polysulfide reduction pathways in different electrolytes is necessary.
In this work, we focus on the interaction between polysulfides, lithium ions, and the solvent system. The structures of the polysulfides and the lithium polysulfides (LiPSs) in different solvent systems are simulated, and various possible reduction pathways of these species are characterized. We consider both the implicit solvent model and the explicit solvent binding with Li + . Our results shall help establish the dominant factors of polysulfide stabilities, which may be applied to solvent system optimization in Li-S battery design.

Results and Discussions
The optimized geometries of polysulfides (PS) and lithium polysulfides (LiPS) in DMSO are shown in Supplementary Figure S1 and Figure 1, respectively. Note that the overall geometries are similar in different solvents. The lengths of S-S bonds are in the range of 1.99 to 2.19 Å for both PS's and LiPS's, and the lengths of Li-S bonds are in the range of 2.37 to 2.44 Å. The overall geometry and the detailed geometry parameters are consistent with previously reported values [29,33,[49][50][51]. We then consider the electrochemistry profile and compute the reduction potentials for major polysulfide reduction reactions, as shown in Supplementary Table S1. Note that since the mixed-solvent system DOL:DME cannot be easily simulated by the implicit solvent model, we adopt the THF solvent system which has a similar molecular motif and dielectric constant (ε THF = 7.43) value with DOL and DME (ε DOL = 7.3 and ε DME = 7.2). As can be expected, the calculated reduction potentials increase in solvents with higher dielectric constant as the anions are stabilized in polar solvents. Overall, the computed theoretical values are consistent with the cyclic voltammogram experimental values.

Solvent-Dependent PS Reaction Pathways
To further explore the reactions of PS in different solvents, we consider some possible reaction pathways (Reactions (1)-(8) in Table 1) based on the results from UV-Vis spectroscopy [38,52,53], and we calculate their reaction free energies (∆G). In solvents with medium to low polarity (ε < 10), it has been proposed that the PS species may exist as neutral lithium polysulfides (LiPS) [44]. Therefore, the aforementioned reaction pathways between the undissociated LiPS reactants are also considered as Reactions (9)-(16) in Table 2.

Solvent-Dependent PS Reaction Pathways
To further explore the reactions of PS in different solvents, we consider some possible reaction pathways (Reactions (1)- (8) in Table 1) based on the results from UV-Vis spectroscopy [38,52,53], and we calculate their reaction free energies (∆G). In solvents with medium to low polarity (ε < 10), it has been proposed that the PS species may exist as neutral lithium polysulfides (LiPS) [44]. Therefore, the aforementioned reaction pathways between the undissociated LiPS reactants are also considered as Reactions (9)-(16) in Table 2. Therefore, for the initial S 8 2− decomposition step, several crucial reactions are considered as shown by Reactions (1)- (4). Although the neutral cyclic S 5 molecules and the radical anions S 5 − have not been experimentally observed in solution or in the solid state [44], their existence cannot be completely ruled out and are therefore considered as the decomposition product within the first few steps (Reaction (2)). Further decompositions of the short-chain PS species (S 6 2− ) are proposed to proceed by Reactions (5) and (6). The origins of the observed species may also come from disproportionation reactions such as Reactions (7) and (8). In general, for the same reaction, the reaction Gibbs free energy may monotonously decrease (Reactions (1) and (3)), or increase (Reactions (2) and (4) and are all likely to proceed. The existence of the decomposed products S 6 2− (Reaction (1)) and S 3 − (Reaction (2)) have been observed experimentally [38]. The S 6 2− may also easily undergo a bond cleavage to form two S 3 − radical anions, as shown by the slightly exothermic Reaction (5).
In comparison, the decomposition of S 6 2− to form S 4 2− (Reaction (6)) involves a higher reaction energy (0.62 eV) and its occurrence is deemed more unlikely. The experimentally [11] observed S 4 2− may result from the reduction of the S 4 − product in Reaction (4). Similarly, the relatively higher reaction Gibbs free energies involved in the disproportionation reactions in Reactions (7) and (8) have rendered these pathways rather improbable. Unlike the reactions between the ionic species as in Table 1, the ∆G's for neutral reactants are much less dependent on the ε, as the numerical values of the ∆G's for the same reaction are all relatively similar in different solvents in Table 2. In solvents with low ε, e.g., DIOX or THF, the polysulfide intermediates are expected to exist as the neutral bound LiPS species. For these systems, the results indicate that the more probable decomposition pathways are Reaction (9) followed by Reaction (14), in which the Li 2 S 8 species first decompose into Li 2 S 6 , and then to Li 2 S 4. Recall that the major species observed in DOL:DME are S 8 2− and S 4 2− [38], which is consistent with our calculation results. Other reaction pathways generating the LiS 3 (Reactions (10), (13), and (15) in Table 2) are deemed less probable due to their high endothermic characters (∆G > 0.5 eV).

The Effect of Solvent Donor Number (DN)
In a few cases, it has been observed that a high dielectric solvent may also facilitate the reaction pathway of the LiPS rather than the dissociated PS [38]. It has been proposed that, other than the dielectric constant, the donor number (DN) is another important factor governing solvent reactions. The donor number, defined as the negative enthalpy value for the 1:1 adduct formation in the dilute solution of a Lewis base and the standard Lewis acid antimony pentachloride (SbCl 5 ) in the non-coordinating solvent 1,2-dichloroethane [54], is a parameter describing the cation coordinating power of solvents. To quantify the effect of the DN, we calculate the average binding energies (E b ) for three high dielectric solvent systems, with moderate to high donor numbers. The estimated coordination numbers and the optimized geometries are shown in Table 3 and Supplementary Figure  S2, respectively. The cutoff binding energy for the predicted maximal coordination number (n p ) is set as −0.30 eV based on the experimental observation of [Li-(DMSO) 4 ] + [46]. As can be expected, the value of n p increases with the DN. The calculated small coordination number for Li + in ACN (n p = 2) indicates that the Li + cations are less solvated in ACN than the solvents with higher DN, such as in DMSO (n p = 4). In other words, the more unshielded Li + cations in ACN may lead to a stronger attraction to the PS anions. As a result, the chemical equilibrium is expected to shift towards the bound LiPS ion pairs and their respective reaction pathways. This could explain the experimental observation that ACN, despite its intrinsic high dielectric constant (ε = 35.69), behaves like DOL:DME with dominant species S 8 2− and S 4 2− , or more accurately, the Li 2 S 8 and Li 2 S 4 [55].
The one-electron thermodynamic reduction potentials (E red ) are calculated by the following equation [59,60]: where ∆G sol represents the Gibbs free energy of reduction in the solvated environment, F is the Faraday constant and 1.46 V is the absolute reduction electrode potential of Li/Li + . The reaction free energies (∆G) are calculated at 298 K. The average binding energies of explicit solvent molecules with Li + (E b ) are calculated by the following equation: where E tot , E Li+ , and E solvent are the computed free energies of the solvated lithium ion-solvent complex, the solvated lithium cation and the solvent molecules, respectively.

Conclusions
We perform computational investigations to quantify the influences of the DN and the ε of the solvent system to the relative stability of the polysulfide intermediates in Li-S batteries. The theoretical reduction mechanisms of the PSs under different solvation situations in different solvent systems are shown in Scheme 1. In general, the higher the DN and ε of the solvent, the more favorable the dissociated PS to the bound LiPS, and vice versa. Our theoretical calculations predict different major species when the reduction reactions proceed in the dissociated PS or the bound LiPS state. Our results confirm and rationalize the experimentally observed stability of S 6 2− and S 3 − in solvents with high DN and high ε, and the observed stability of Li 2 S 8 and Li 2 S 4 in solvents with low DN and low ε. For solvents with a high ε but a low DN, e.g., acetone, the two states shall exist in a chemical equilibrium and the dominant species will depend on the competing forces between solvation and coordination. We hope these results offer a clearer microscopic picture and will inspire the future optimization of the electrolyte systems.
Catalysts 2020, 10, x FOR PEER REVIEW 6 of 9 the dissociated PS to the bound LiPS, and vice versa. Our theoretical calculations predict different major species when the reduction reactions proceed in the dissociated PS or the bound LiPS state.
Our results confirm and rationalize the experimentally observed stability of S6 2− and S3 − in solvents with high DN and high ε, and the observed stability of Li2S8 and Li2S4 in solvents with low DN and low ε. For solvents with a high ε but a low DN, e.g., acetone, the two states shall exist in a chemical equilibrium and the dominant species will depend on the competing forces between solvation and coordination. We hope these results offer a clearer microscopic picture and will inspire the future optimization of the electrolyte systems.