Unraveling the Correlation between Solvent Properties and Sulfur Redox Behavior in Lithium-Sulfur Batteries

Figure 1 shows the cyclic voltammograms (CVs) of dissolved S₈ in nine representative solvents (or solvent mixtures), including DMSO, DMA, DMF, DOL, DME, TEGDME, ACN, sulfolane (TMS) and 1,4-dioxane (Diox). We converted the recorded potential to the Fc/Fc⁺ scale in order to eliminate solvent's influence on the Li/Li⁺ redox potential.⁵ As is quite apparent from Fig. 1, three groups of distinct CV patterns were observed which can be categorized based on (i) the number of oxidation and reduction peak, and (ii) the peak separation of the reduction peaks. Group 1: CVs recorded in DMSO, DMF, and DMA largely resemble each other and are consistent with the CVs reported in literature (DMSO,^15,19 DMF,²⁰ DMA),¹⁹ having three oxidation peaks and two reduction peaks with large peak separation (ΔE > 500 mV, see Figs. 1a–1c, CVs in blue). Group 2: CVs recorded in DME, DOL:DME (1:1,v:v), TEGDME, ACN, and TMS, showing only one oxidation peak and two reduction peaks with small peak separation (ΔE ≈ 200–300 mV, see Figs. 1d–1h, CVs in red). The 2^nd reduction peak in DOL:DME is less clear at 50 mV/s but is quite pronounced at a slow scan rate of 5 mV/s (Fig. 2c). Group 3: The CV recorded in Diox:DME (1:1, v:v) shows only one oxidation peak and only one reduction peak (see Fig. 1i, CV in green), which is consistent with CV collected at a slow scan rate of 5 mV/s as indicated in Fig. S1.

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Several studies have reported similar results for DOL:DME,^5,10 DME¹⁹ and ACN,¹⁹ while to the best of our knowledge CVs on a planar carbon electrode in TEGDME, TMS, and Diox:DME are not available in the literature. Qualitatively, we attribute the Group 1 to high-DN solvents, and Groups 2 and 3 to low-DN solvents. Although the solvents in Group 1 exhibit high values of DN, ɛ, and AN, we propose that actually DN would be the primary descriptor instead of ɛ or AN, because ACN which has a high ɛ and a high AN belongs to Group 2 and thus no trend can be established using ɛ or AN. We note that, Diox:DME (1:1, v:v) in Group 3 not only has a low DN but also the lowest dielectric constant ɛ (≈4, roughly estimated based on the work of Hall et al.)²¹ among all solvents. It is known that a solvent (mixture) with a dielectric constant approaching one would lead to an incompletely salt (charges) dissociation.²² Therefore, in group 3, the anion (polysulfide) is believed to strongly associate with cation and consequently, it would have less interaction with solvent molecules. That is, solvent molecules would have less impact on polysulfide stability via dipole-ion interaction (AN, DN) compared to it in a highly dissociated system. In addition to these CV classifications, we will further examine the correlations between each solvent property (ɛ, AN, DN) and (i) the onset potential of S₈-reduction, and (ii) the reversibility of the 2^nd oxidation peak.

The onset potential of S₈-reduction vs. AN of the solvent

A positive correlation was found between the onset potential of S₈-reduction and the AN of solvents (Fig. 2a), i.e. the higher the AN of the solvent, the higher the onset potential of S₈-reduction. The onset potentials of S₈ reduction were taken from the 1^st derivative of the current density (Fig. S2). The acceptor number was introduced by Mayer et al.,²³ seeking to empirically describe the electrophilic property of a solvent. The acceptor number is generally derived from ³¹P-NMR measurements of triethylphosphine oxide dissolved in the respective solvents and is considered as an indicator for the ability of the solvent to solvate anions. The first step of S₈-reduction is generally agreed to be the reduction of elemental S₈ to S₈^2–:^{5,10,15,24,25}

The solvation energy of the S₈²⁻ anion in high-AN solvents is greater than that in low-AN solvents due to the stronger electrophilic property of the high-AN solvents, which leads to a more positive reduction potential of S₈ to S₈²⁻ in high-AN solvents than in low-AN solvents (see. Equation 3).

Our observation is consistent with Mayer et al.,²³ showing that the AN of the solvent influences the half-wave potential (polargarphic) of the reduction of [Bu₄N]₃[Fe(CN)₆] (tetrabutylammonium hexacyanoferrate), which can also be rationalized using Equation 3.

The reversibility of the 2^nd oxidation peak vs. DN of the solvent

It is clear from Fig. 1 that the second redox pair (at ≈−1.5 V_Fc) is more reversible in solvents with high DN (e.g. DMSO, DMA, DMF, see Figs. 1a–1c, blue CVs) and appears irreversible in solvents with low DN (e.g. DME, DOL:DME, TEGDME, TMS, ACN, and Diox:DME). Note that there is no ambiguity between DN and dielectric constant, as this redox pair is irreversible in ACN (low DN, high ɛ). Due to the limited sample size and the inaccuracy of DN describing the solvation ability of solvent to Li⁺, it is not our intention to draw a linear correlation between DN and CV features. One is only able to qualitatively couple CV features such as oxidation peak number and reduction peak separation with the range of DN of the solvent, rather than with other properties such as AN and dielectric constant. Taking DMSO (high DN) as an example, the second redox couple exhibits a one-electron reversible process, as evidenced from the scan rate independent peak separation of ≈60 mV (Fig. 2b).²⁶ The assignment of the 2^nd redox pair in DMSO has been extensively discussed in the literature. After the 1^st reduction peak, during which S₈ is electrochemically reduced, other polysulfides are generated by disproportionation reactions as described in Equations 4, 5 and 6.^15,25,27,28

The 2^nd redox pair has been assigned to the electrochemical reduction and oxidation reaction between S₃^•−/S₃²⁻,^28–30 as shown in Equation 7.

Zou et al.¹⁰ have applied operando UV-Vis spectroscopy to show that the UV-Vis absorbance of S₃^•− (620 nm) decreases significantly as the electrode potential goes below ∼−1.5 V_Fc and increases drastically as soon as the electrode potential reverses, suggesting that the S₃^•−/S₃²⁻ redox process is relatively reversible. This is consistent with our observation of a fast and reversible 2^nd redox peak observed in DMSO (Fig. 2b).

In contrast, the oxidation reaction of the 2^nd redox pair is much less reversible in low-DN solvents, resulting in a less visible oxidation peak (Figs. 1d–1h). In addition, the potential of the 2^nd reduction peak shifts strongly with scan rate in a low-DN solvent like DOL:DME (Fig. 2c), indicating the irreversibility of the 2^nd redox process. Interestingly, the related oxidation peak can be clearly observed at the slow scan rate of 5 mV/s (located at −1.15 V_Fc, see Fig. 2c), indicating that the oxidation process exhibits sluggish electrode kinetics rather than poor chemical stability. The 2^nd redox pair in DOL:DME has been assigned to the reduction of S₄²⁻ based on the decreasing UV-Vis absorption at 420 nm (S₄²⁻).¹⁰ However, no increase of absorbance at other wavelength was observed in the operando UV-Vis study.¹⁰ This suggests that S₄²⁻ is electrochemically reduced to form species that are UV-Vis inactive (e.g. solid), which can be generalized to^10,11,14,31

In addition, considering the sluggish kinetics observed in low-DN solvents, we believe that this redox pair involves the formation of solid phases such as Li₂S₂/Li₂S from S₄²⁻. Consistent behavior was also observed in other solvents (Fig. S3), showing that the 2^nd oxidation peak is much more visible/reversible in high-DN solvents, e.g. DMF (DN = 26.6) and DMA (DN = 27.8), compared to low-DN solvents, e.g. ACN (DN = 14.1).

In addition to the CV analyses, we also exploited the rotating ring disk electrode technique to investigate the kinetics and Li-S reaction mechanism in various electrolytes, as we had done previously for DMSO and DOL:DME-based electrolytes.⁵ We observed that electrolytes with high-DN solvents and electrolytes with TBA⁺ cation (a strongly solvating cation) have always two well-defined reduction plateaus, among which the 1^st reduction wave was always accompanied with an electron transfer of ∼1.7 e⁻/S₈, estimated by applying the Levich-equation (see Fig. S4). This suggests a two-electron reduction of S₈ to S₈²⁻ (Eq. 3), indicating S₈²⁻ is more stabilized in such electrolyte environments, that is, with high-DN solvent and/or with strongly solvating cation (TBA⁺).^5,32

Other CV analyses such as peak current evaluation using the Randle-Sevcik equation are further illustrated in the supporting information (Fig. S5 and S6). The parameters used in the Levich equation for the analysis of the RRDE data, which are also useful for numerical modeling of Li-S batteries (e.g. the diffusion coefficient of dissolved S₈ in various electrolytes) are presented in the supporting information (Table S2). In short, two clear correlations between solvent properties and CV features were identified: 1) the onset potential of the first S₈-reduction peak increases with increasing AN, and 2) the reversibility of the second oxidation peak increases with increasing DN, owing to the formation of soluble polysulfides, rather than solid phase polysulfides, in high-DN solvents.

Here we employ UV-Vis spectroscopy to examine the polysulfide stability in different solvents and we show that the stability of various polysulfides (S_n^2–) is mainly dictated by the solvated cations, which can be manipulated by solvent donor number (DN), cation concentration, and the cation type (Li⁺, TBA⁺), as illustrated in Scheme 1.

Scheme 1. Summary of how polysulfide stability/speciation is affected by its interaction with cations and solvent molecules.

Effect of solvent donor number

Fig. 3a shows the UV-Vis spectra of a 5 mM concentration of polysulfides with a nominal stoichiometry of "Li₂S₈" in nine different solvents with 1 M LiTFSI. Clearly, high-DN solvents (blue lines labeled g-i) all have a strong absorption at 620 nm (corresponding to S₃^•−), 475 nm (S₆²⁻), 492 nm (S₈²⁻), and 350 nm (S₆²⁻),^{10,13,15,16,25} while low-DN solvents (red lines labeled a-f) all have similarly pronounced absorption maxima at 420 nm (S₄²⁻) without any absorption at 620 nm (S₃^•−). We note that TEGDME with lower DN of 16.6 has a higher absorption at 620 nm compared to DME (DN ≈ 20 or 24), which can be explained by 1) the chelate effect, the known cage structure formed by TEGDME that can better solvate Li⁺ cation^33,34 and 2) that donor number, an empirical parameter derived from the solvation of SbCl₅, cannot fully represent the solvation of Li⁺.³⁵ The distinct speciation of polysulfides in different solvents are consistent with the literature and can be well explained by the Pearson's Hard Soft Acid Base (HSAB) theory.³⁶ The Li ions solvated in high-DN solvents (strongly solvated Li⁺, soft acid) preferentially stabilize polysulfides with lower charge density (softer base, e.g. S₈²⁻, S₆²⁻, S₃^•−), whereas the Li ions solvated in low-DN solvents (poorly solvated Li⁺, hard acid) preferentially stabilize polysulfides with higher charge density (harder base, e.g. S₄²⁻). Here, we compare the hardness/softness (i.e. charge density) of different polysulfides based on reported theoretical studies. Both Steudel et al.³⁷ and Pascal et al.³⁸ have calculated the charge density of terminal and in-chain sulfur atoms in different polysulfides (summarized in Fig. S7). Although Steudel et al.³⁷ have focused their work on sodium-sulfur system at elevated temperature (600 K), their calculations were also conducted at 298 K to address the structure and atomic charges of isolated polysulfide dianions and anion radicals at 298 K. It was reported that regardless of the assumed nature of the continuum medium (e.g. vacuum or polarizable continuum model with dielectric constants 8 and 78), the negative charge density of terminal sulfur atoms in S_x²⁻-chains decreases in the following order S₂²⁻ > S₃²⁻ > S₄²⁻ > S₅²⁻ > S₆²⁻ > S₇²⁻ > S₈²⁻; in addition, it was calculated that that the negative charge density of S₃^•− would be even lower than that reported for S₈²⁻ (see comment to Fig. S7 in the SI).^37,38 Similar trend was also reported by Pascal et al.,³⁸ who calculated the average valence electron populations for the internal and terminal sulfur atom of Li₂S_x in a 12 TEGDME molecule environment (see Fig. S7). Although the absolute value of the negative charge density is different in different studies and also depends on the assumed surrounding continuum (see Fig. S7), the overall trend is still the same in all studies, namely that short-chain polysulfides (e.g. S₄²⁻) have a higher negative charge density on the terminal sulfur atoms than that in long-chain polysulfides (e.g. S₈²⁻) and in the S₃^•− radical. In other words, the negative charge is more strongly delocalized on long-chain polysulfides (S₈²⁻) and on S₃^•− radicals compared to that on short-chain polysulfides (S₄²⁻), which in turn implies that the softness of polysulfides decreases in the following order: S₃^•− > S₈²⁻ > S₆²⁻ > S₄²⁻ > S₃²⁻ > S₂²⁻. Therefore, the S₄²⁻ polysulfide (harder base) is better stabilized by weakly solvated Li⁺ (hard acid) prevalent in low-DN solvents, whereas S₃^•−, S₈²⁻, and S₆²⁻ (softer base) are better stabilized by strongly solvated Li⁺ (soft acid) prevalent in high-DN solvents.

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To confirm that the polysulfide stability is mainly affected by donor number rather than by the dielectric constant (ɛ)^5,16 or the acceptor number (AN), we further investigated the polysulfide speciation in a rather unique solvent (ACN) which has a low donor number (DN = 14.1, similar as TEGDME) but high dielectric constant (ɛ = 36) and acceptor number (AN = 18.9) which are close to those of DMSO (which, however, has also a very high DN; see Table S1). In Fig. 3a, we show that the speciation of polysulfides in ACN resembles that in the low-DN system (TEGDME) despite ACN has a completely different ɛ and AN compared to TEGDME. This clearly suggests that dielectric constant and acceptor number are not the critical parameters governing polysulfide stability/speciation in the presence of a high concentration of Li⁺ cations.

Effect of Li⁺ concentration

In contrary to our results, Bieker et al.¹⁶ reported that the UV-Vis spectrum of a nominal "Li₂S₈" stoichiometry in ACN resembles that of "Li₂S₈" in DMSO, and it was thus concluded that ɛ is the primary descriptor for polysulfide stability/speciation rather than DN. After careful analysis, we believe this discrepancy is related to a difference in the Li⁺ concentration. In our work, 1 M LiTFSI was added to the 5 mM "Li₂S₈" dissolved in ACN to mimic the practical Li-S battery environment, whereas no additional salt was used for the preparation of the 1 and 10 mM "Li₂S₈" containing ACN solution in the work by Bieker et al.¹⁶ To resolve this question, we evaluated UV-Vis spectra of 5 mM "Li₂S₈" in ACN with different concentrations of LiTFSI and without added LiTFSI (Fig. 3b). The sample of "Li₂S₈" in ACN without added LiTFSI salt (light blue) indeed shows a similar spectrum as "Li₂S₈" in DMSO (line h in Fig. 3a), with a high absorption at 620, 475, and 350 nm, quite analogous to what was reported by Bieker et al.¹⁶ On the other hand, the solution of "Li₂S₈" in ACN with 1 M LiTFSI presents a similar absorption spectrum as "Li₂S₈" in low-DN TEGDME and DOL:DME, with a pronounced absorption maximum at 420 nm. This experiment confirms our hypothesis that the Li⁺ concentration is responsible for the apparent discrepancy between our data and those by Bieker et al.¹⁶ We believe that when no additional "naked" Li⁺ is present, soft polysulfides (e.g. S₃^•−) can be stabilized by the surrounding ACN molecules owing to the high charge accepting ability of ACN (high AN of 18.9). That is, at extremely low cation concentrations, the stability of polysulfides is governed by the solvent molecules via dipole-anion interaction (solvent – S_n²⁻), instead of the cation-anion interaction (Li⁺(solvents)_n – S_n²⁻). However, with increasing Li⁺ concentration, the number of "naked" Li⁺ (hard acid) increases and the influence of the cation on polysulfide stability becomes significant, which shifts the equilibrium to stabilize hard polysulfides (e.g. S₄²⁻). As shown in Fig. 3b, with increasing Li⁺ concentration (0 M → 1 M), the absorption at 620 nm (S₃^•−) and at 475 nm (S₆²⁻)/492 nm (S₈²⁻) decreases gradually, while the absorption at 420 nm (S₄²⁻) increases. This experiment confirms our hypothesis and resolves the apparent discrepancy in the literature with regards to the speciation of polysulfides in ACN solvent.

Recently, several research groups have proposed a sparingly solubilizing electrolyte system for Li-S batteries,^4,39,40 aiming to limit the concentration of polysulfides on the order of 1 mM or less by occupying most of the solvent molecules with supporting salt, leaving none left to coordinate to polysulfide molecules.⁴ In addition, a high concentration of Li-salts are required to achieve sparingly solubilizing electrolyte such as ACN₂LiTFSI-TTE³⁹ and ACN₂-LiTFSI–HFE.⁴⁰ We have learned from Fig. 3b that more "naked" Li⁺ in the system will shift the polysulfides equilibrium to the one with higher charge density, namely shorter chain polysulfides (e.g. S₄²⁻). Although the solvation state of polysulfides are likely different in sparingly solubilizing electrolytes, the impact of Li⁺ cation on the polysulfide stability/speciation may still apply, that shorter chain polysulfides are preferably promoted by the cation-anion interaction in a highly concentrated electrolyte.

Effect of cation type

To further show that cations can very strongly affect polysulfide speciation, we replaced the 1 M Li⁺ cations (a hard acid) with 1 M TBA⁺ cations (a soft acid regardless of solvent)⁴¹ in the solution of "Li₂S₈" in ACN. As shown in Fig. 3c, the spectrum of "Li₂S₈"in ACN-TBATFSI resembles that in DMSO with 1 M LiTFSI (line h in Fig. 3a) where long-chain polysulfides are clearly dominating (e.g. 620 nm (S₃^•−), 475 nm (S₆²⁻), 492 nm (S₈²⁻)). This further confirms that large concentrations of cations and their type will affect the speciation of polysulfides.

To further distinguish the impact of donor number, dielectric constant, and acceptor number on the charge/discharge behavior of Li-S cells, we employ a two-compartment cell with a lithium metal anode and a cathode either based on a dissolved S₈ containing catholyte or based on a solid S₈/C composite cathode. The two-compartment cell is a closed system that confines polysulfides in the cathode and allows full reactions (long reaction time in hours), whereas CV and RRDE were conducted in an open system where polysulfides are freely to diffuse in a large amount of electrolyte (short reaction time in seconds). With this, we evaluate the Li-S cell behavior in ACN (DN = 14.1, ε = 35.95, AN = 18.9) and compare it first to that in DMSO (DN = 29.8, ε = 46.5, AN = 19.3) and then to that in commonly used electrolyte DOL (DN = 18, ε = 7.13):DME (DN = 24, ε = 7.1, AN = 10.2).

Figs. 4a and 4b show the voltage profiles of the catholyte (0.5 mM S₈) two-compartment cell in ACN (green) and DMSO (blue) at 0.5C and 2.9C (based on 1672 mAh/g_s ≡ 1C). Despite the fact that ACN and DMSO exhibit very similar dielectric constant and acceptor number, the catholyte two-compartment cell voltage profiles and discharge/charge potentials in ACN are significantly different from that in DMSO. The voltage plateau separation in the two-compartment cell is found to be well-correlated to the separation of the reduction peaks in cyclic voltammograms (Fig. 1). The significantly different voltage profiles observed in DMSO and ACN cannot be explained by their almost identical dielectric constant and acceptor number, but can be correlated to their differences in DN (ACN (14.1) vs DMSO (29.8)) as already discussed above. Consistently, DMSO-alike voltage profiles were also reported for other high-DN solvents, such as DMA (DN = 27.8)¹¹ and DMF (DN = 26.6).¹⁰

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In contrast, the cell voltage profiles with ACN based electrolyte is very similar to that in the low-DN solvent DOL:DME (average DN ∼20). Even using conventional S₈/C composite cathodes (albeit with relatively low loadings of 0.25–0.6 mg_s/cm²), the voltage profiles obtained in ACN and DOL:DME based electrolytes are still very similar (Fig. 4c; note that the larger hysteresis for high-loaded sulfur electrodes is due to the higher current densities in this case, as the C-rate is kept constant). Therefore, we conclude that the donor number – governing the effective charge density of the solvated cation (Li⁺) – is the primary descriptor determining the voltage profile (reaction potentials and peak separations) of Li-S batteries via dictating the speciation of polysulfides in different electrolytes. Similar findings were also reported by Schneider et al.,⁴² who observed distinctly different cell voltages in different solvents and attributed this to the considerably stronger solvation effect for small and hard lithium ions (indicated by the DN) compared to that for the polysulfide anions (indicated by AN).

Lastly, the discharge capacity achieved in ACN is similar to that of DOL:DME, which is higher than it is in DMSO. However, the discharge capacity of Li-S cells in DMSO is also much lower compared to that in other high-DN solvents such as DMF¹⁰ and DMA¹¹ measured under comparable conditions. Therefore, we believe that the limited discharge capacity in DMSO is related to its high viscosity (1.99 cp)¹⁸ compared to that of other solvents DMF (0.79 cp),¹⁸ DMA (0.93 cp),¹⁸ ACN (0.34 cp),¹⁸ and DOL:DME (average ∼0.5 cp),¹⁸ which significantly reduces the mobility of Li⁺ cations and soluble polysulfides and thus limits the growth of solid lithium sulfide in the electrode. Based on our observations, solvent viscosity show limited effect on polysulfide stability/speciation and the electrochemical redox behavior. Despite TMS (∼10.07 cp)¹⁸ has a much higher viscosity than ACN (∼0.34 cp),¹⁸ they both have shown similarity in redox behavior i.e. CV features (Figs. 1g, 1h, oxidation/reduction peak numbers, reduction peak separation, reduction onset potential and the reversibility of 2^nd oxidation peak) and polysulfide stability/speciation represented by UV-Vis spectra (Fig. 3a). We believe that viscosity mainly affects the transport behavior of polysulfide, which has great importance to the cell performance, such as rate capability (shown in Fig. 4) and ohmic resistance affecting energy efficiency. On the other hand, the polysulfide stability/speciation is determined by the cation-anion interaction and the dipole-anion interaction. In the nine solvents investigated, we observed that the cation-anion interaction has a stronger impact on the polysulfide stability over dipole-anion interaction. Therefore, we propose donicity would be the primary descriptor (but not the only one) determining the redox behavior of polysulfides in a well dissociated electrolyte system (reasonable dielectric constant required), and acceptor number can also regulate the redox pair, as exemplified by its influence on reduction onset potential (Fig. 2a).

In addition to solvent and the concentration of salt, the type of anions has been shown to influence the sulfur redox pair, as anions with different donicity may also contribute to the coordination of Li⁺.^43–45 For instance, Watanabe and co-workers⁴³ have shown a strong anionic effects on polysulfide solubility in solvate ionic liquid electrolytes, which is directly related to polysulfide shuttling. Furthermore, a strong influence of anions on the reaction intermediates were reported in the Li-O₂ system where NO₃⁻ with higher donicity is believed to assist the solvation of Li⁺, resulting in an increased capacity and toroid formation.⁴⁶ Efforts in understanding anion effect in Li-S redox chemistry and cell behavior are on-going and will be reported in future work.