Solvation-property relationship of lithium-sulphur battery electrolytes – Nature Communications

Solvation free energy measurement of electrolytes

Measurement of the solvation free energy of Li+ is at the core of this study. In a recent study, we introduced a method to experimentally characterise the relative solvation free energy of electrolytes22. It employs potentiometry of an electrochemical cell with symmetric Li metal electrodes but asymmetric electrolytes in the two half cells. The half reactions consist of the Li/Li+ redox couple. Because the identical electrode terms cancel out, only the Li+ terms solvated in two different electrolytes remain, and the resulting net reaction is the transfer of Li+ between two electrolytes. The change in free energy in this process, which is the difference in the solvation free energies of Li+ in different electrolyte environments, gives rise to an electromotive force that can be measured. By holding one electrolyte as a reference electrolyte, it is possible to characterise and compare the solvation free energy of various electrolytes relative to a reference electrolyte. It is important to note that while the standard notion for solvation free energy is defined for the dilute limit, in this work, we consider practically more relevant finite concentrations where the solvation free energy includes the concentration effects. In essence, our measured concentration-dependent solvation free energy is the chemical potential of dissolved ions.

In this study, we examine a series of ether-based electrolytes with moderate to high solvating power (Fig. 1b). Ethers are the most commonly used class of solvents for Li-S batteries, as other classes such as carbonates are unstable with the LiPS23. Adding fluorinated solvents with low solvating power or increasing concentration could tune the solvation energy, further balancing excessive side reactions and sluggish kinetics4. In addition, this range of electrolytes allows for an appropriate window to probe the thermodynamics; for example, we find that weakly (sparingly) solvating electrolytes tend to have overbearing kinetic limitations at room temperature (Supplementary Fig. 1).

We can identify a few trends in the measured Li+ solvation energies of different electrolytes. First, as salt concentration increases, we observe a more positive solvation energy that corresponds to weaker solvation. This is aligned with the Nernst equation, as the chemical potential of Li+ is higher at elevated concentrations. Second, mixtures of 1,2-dimethoxyethane (DME) and 1,1,2,2-tetrafluoroethyl-2,2,3,3-tetrafluoropropyl ether (TTE) solvents show that greater amounts of TTE leads to weaker (more positive) solvation free energies. This is in agreement with the fact that TTE acts as a diluent, rendering the electrolyte as a local high concentration electrolyte24. As the amount of TTE increases, the local concentration of Li+ increases, producing a more positive solvation energy. Third, the solvation strength of solvents increases in the order of 1,3-dioxolane (DOL)-DME-tetraethylene glycol dimethyl ether (G4), which is in agreement with previous reports in the literature19,25,26.

Solvation effect on Li-S battery voltage profile

The thermodynamic voltage is a core property of a battery. Battery voltage, alongside capacity, dictates the energy content of a battery cell. Battery voltage also impacts the compatibility and stability of other battery components. From a practical perspective, the thermodynamic voltage profile is an important indicator of the battery’s state of charge during operation, which will indicate how much charge remains in the battery at any given moment. Although the thermodynamic voltage is unaffected by the electrolyte in most Li-based battery chemistries, the Li-S battery is different: it has a unique chemistry with active materials in both solid and solvated phases, allowing the electrolyte to play a role in the reaction thermodynamics. Indeed, different voltage profiles for different electrolytes have been observed27,28, which can have profound implications on the energy density of the battery, but the mechanism remains unclear. We use the measured solvation free energies to draw quantitative relationships to the Li-S battery voltage plateaus and propose a mechanism.

Figure 2a displays the discharge voltage profiles for two electrolytes: 1 M LiTFSI DME and 1 M LiTFSI DME-TTE (1:1 vol). The discharge c-rate is C/20, which makes the overpotential negligible and the profiles are essentially reflective of the thermodynamic properties. We can see that both electrolytes have two plateaus, with the first above 2.2 V and the second below 2.2 V. We observe that when TTE is added as a diluent, which weakens the solvation, the 1st plateau is lowered and the 2nd plateau is elevated. The trend holds for the series of ether-based electrolytes, where we see lower 1st plateau and higher 2nd plateau with weaker solvation (Fig. 2b, c, Supplementary Fig. 2), in agreement with previous observations27,28,29. This correlation can be extended to strongly solvating solvents such as dimethyl sulphoxide (DMSO) (Supplementary Fig. 3). The average voltages show a weak correlation with weaker solvation, which suggests that the voltage of the 2nd plateau, which has a larger capacity, bears greater weight on the average voltage (Supplementary Fig. 4).

Fig. 2: Effect of solvation free energy on Li-S battery voltage profiles.

a Voltage profiles of 1 M LiTFSI DME and 1 M LiTFSI DME-TTE (1:1 vol) in Li-S batteries. b Correlation of 1st plateau voltage vs. solvation energy, showing decreasing voltage with weaker solvation. c Correlation of 2nd plateau voltage vs. solvation energy, showing increasing voltage with weaker solvation. d Proposed mechanism of the solvation free energy effect on Li-S battery voltage profile. e Molecular dynamics simulation of unclustered Li+ in the two electrolytes, showing that DME with stronger solvation has a larger fraction of unclustered Li+. f Diffusivity of Li and toluene and the ratios of the two parameters, showing that the less clustered DME has higher diffusivity.

In an effort to explain this correlation, the proposed mechanism is illustrated in Fig. 2d. The fully charged high energy state is composed of elemental Li and S, and the fully discharged state is Li2S23. The free energies of the two end states are the same irrespective of the electrolyte as they are solid phases. The intermediate state is the solvated LiPS, whose free energy is deeply dependent on the solvation strength of the electrolyte. For the strong solvation case, the strong interaction with the electrolyte stabilises the LiPS and lowers its free energy, whereas the opposite case is true for the weak solvation case, where the free energy is higher. For both cases, the first plateau represents the reaction from elemental Li and S to solvated high order LiPS23. The low free energy of LiPS for the strong solvation case results in a large difference in free energies (∆G1,ss). Because the free energy change upon this reaction is directly related to the negative of the cell voltage, E1,ss, the 1st plateau of the strong solvation case has a relatively high voltage compared to the weak solvation case. The energetics of LiPS affect the second plateau as well, which represents the transformation of low order LiPS to Li2S. For the strong solvation case with low free energy of LiPS, ∆G2,ss and E2,ss are small, which leads to the low 2nd plateau voltage compared to the weak solvation case. In essence, solvation free energy of LiPS species dictates the change in free energy from Li+S to LiPS, and LiPS to Li2S, which respectively determine the first and second plateau voltages.

These differences are intertwined with the solvation structure. We compared two electrolytes with different solvation strengths, 0.1 M Li2S6 in DME and DME-TTE 1:1, using molecular dynamics and diffusion-ordered spectroscopy-nuclear magnetic resonance (DOSY-NMR). (Supplementary Fig. 57). For the weakly solvating solvent formulation, DME-TTE 1:1 was used to ensure sufficient solubility of 0.1 M Li2S6 for the DOSY-NMR experiment. We find that DME, which provides strong solvation, is effective in dissociating Li+ and has a relatively high percentage of unclustered Li+ compared to DME-TTE (Fig. 2e). These results are further corroborated by Fig. 2f. As unclustered Li+ content increases in strongly (highly) solvating DME, Li+ self-diffusivity increases. Even when accounting for the viscosity differences that are reflected in toluene diffusivities, the Li/Tol diffusivity ratio is higher for DME case, further validating the differences in solvation structure that we find in MD simulations.

It is important to note that the proposed mechanism in Fig. 2d is a simplified model. It is well-established that LiPS is a series of Li2Sx compounds that are in equilibrium with each other23, and the reaction pathway involves multiple LiPS lithiation reactions. Describing the precise reaction pathway and the involved LiPS species is an nontrivial task. However, we believe that our model circumvents this problem by describing the species as a single band of LiPS. This simplification is reasonable for explaining the shifts in voltage profiles, because all soluble LiPS species are likely to be affected in similar ways by different solvating environments; in weak solvation the entire band is shifted upwards in energy whereas the opposite is true for strong solvation. The premise is supported by the fact that solubilities of different LiPS species are higher in strongly solvating solvents4. The intricate relationship between solvation energy and solubility will be discussed in the next section.

Polysulphide solubility and Li-S battery cyclability

The solubility of polysulphides is a key factor in Li-S battery performance, including cycle and calendar life, self-discharge, and internal resistance4. We prepared electrolytes saturated with Li2S6, as shown in Fig. 3a, where electrolytes with stronger solvation appear darker. We deployed UV-Vis spectroscopy to quantify the solubility of the LiPS (Fig. 3b), which confirmed that solubility decreases with weaker solvation—a finding extensively discussed in the literature4. As a note, tetraethylene glycol dimethyl ether (G4) was not included in this list because it led to significantly different polysulphide speciation and a peak in shorter wavelengths, which is known to be the S3•- radical anions that form in strongly solvating electrolytes4,29,30.

Fig. 3: Effect of solvation free energy on polysulfide solubility and Li-S battery cyclability.
figure 3

a Digital photograph of electrolytes saturated with Li2S6. b Solubility of Li2S6 in the electrolytes quantified with UV-Vis spectroscopy. c Correlation of the negative of the natural log of the solubility constant with solvation energy. d, e Correlations of Li-S battery CE averaged over 150 cycles and initial discharge capacity with solvation energy, showing that both metrics increase with weaker solvation.

Although different parameters such as donor number and dielectric constant have been considered as descriptors for polysulphide dissolution and its effect on battery properties, there has not been a single parameter that sufficiently describes the phenomenon. Because solvation free energy directly governs the solvation behaviour and is a descriptor in fundamental thermodynamic relationships, we believe it describes solvation and solubility more accurately. The solubility constant Ksp is related to the free energy of dissolution ∆Gdiss through Eq. (1)31.

$${Delta G}_{{diss}}=-{RT} , {{{{{mathrm{ln}}}}}},({{{{{mathrm{K}}}}}}_{{sp}})$$


Gdiss includes the negative of the lattice energy of Li2S6, which is a constant for all electrolytes, and the solvation energy terms of the individual species, leading to Eq. 2 that shows that solvation energy is proportional to the negative of natural log of the solubility constant. Although the solvation free energy term that we measure constitutes that of Li+, here we assume that it scales with the solvation free energy of all species, meaning that a strong solvating solvent for Li+ will be a strong solvating solvent for other ionic LiPS species. In addition, cations generally have smaller ionic radii and have larger solvation energies than anions and are likely to dominate the solvation energy of salts32.

$${Delta G}_{{solv}}^{L{i}^{+}}propto {-{{{{mathrm{ln}}}}}} ,({{{{{mathrm{K}}}}}}_{{sp}})$$


There may be several possible dissociation modes, as shown in Eqs. (3)–(5), and the equilibrium constant expression will vary depending on the reaction. Our data shows that the dissociation of Li2S6 most closely resembles Eqs. (3), (4), particularly the dissociation of Li2S6 into Li+ and LiS6 (Fig. 3c, Supplementary Fig. 8). Despite the excellent fit, it is important to note that Li+ and LiS6 will not be the only species in equilibrium. Li2S6, S62- and other speciation of polysulphides will also be present, although these species may not constitute the majority30,33.

$${{{{{{rm{Li}}}}}}}_{2}{{{{{{rm{S}}}}}}}_{6}left(sright)leftrightarrow {{{{{{rm{Li}}}}}}}_{2}{{{{{{rm{S}}}}}}}_{6},({sol})$$


$${{{{{{rm{Li}}}}}}}_{2}{{{{{{rm{S}}}}}}}_{6},left(sright)leftrightarrow {{{{{{rm{Li}}}}}}}^{+}left({sol}right)+{{{{{{rm{LiS}}}}}}}_{6}^{-},({sol})$$


$${{{{{{rm{Li}}}}}}}_{2}{{{{{{rm{S}}}}}}}_{6},left(sright)leftrightarrow 2{{{{{{rm{Li}}}}}}}^{+}left({sol}right)+{{{{{{rm{S}}}}}}}_{6}^{2-}({sol})$$


Polysulphide solubility is well known to have profound effects on battery performance4,23. We find that electrolytes with weak solvation and low LiPS solubility have high CE20. This is attributed to the shuttling effect to the metallic Li and the alleviation of this effect as LiPS solubility decreases4,20. We observe a similar trend with the initial discharge efficiency increasing with weaker solvation (Fig. 3e, Supplementary Fig. 9). This is somewhat surprising as polysulphide solubility is not expected to affect the amount of active material available. We believe that this is again related to the polysulphide shuttling effect; as polysulphide reacts with Li metal to form lithium-rich LiPS23, active S is lost in the form of insoluble Li2S or Li2S2 on the anode or undergoes self-discharge, reducing the discharge capacity.

Although weaker solvation is beneficial in improving CE and the initial discharge capacity, it can take a toll on the kinetics. Supplementary Fig. 10 shows that the 2nd plateau overpotential, obtained through the differences between cycling at 0.05C and 0.2C, increases with weaker solvation. This may be a result of insufficient concentration of LiPS that act as redox mediators to accelerate the charge-transfer reaction13,34. The kinetics seems to be play an important role in cycling stability as well, seen by the fact that capacity retention does not increase with weaker solvation, but rather peaks between solvation energies of −10 to −12 kJ mol−1 (Supplementary Fig. 11), a phenomenon that corroborates with recent findings35. In addition, if solvation is further weakened and LiPS solubility is further suppressed, kinetic effects can take over where the discharge capacity decreases with weaker solvation (Supplementary Fig. 1)4,23. Therefore, regulating solvation strength is crucial for balancing electrochemical stability and kinetics to achieve optimal battery performance. With that, it is also important to note that solvation energy is not the sole factor in governing these properties; details in molecular structures and chemical reaction pathways that lead to different passivation layers are important contributors that must be taken into account for a holistic understanding.

Lithium metal anode cyclability, morphology and interphase

When the anode has excess inventory of Li, as is the case for most Li-S batteries, the cell CE does not reflect that of the Li metal anode. However, the side reactions at the Li metal-electrolyte interface is undeniably important for the battery performance, as it leads to electrolyte dry-out, impedance build-up and the need for more excess Li and electrolyte that reduces the energy density4. We examined the Coulombic efficiencies of six electrolytes with and without Li2S6 using a modified Aurbach method (Supplementary Fig. 12). The Aurbach method commonly used to assess the Li metal CE cannot be used directly when LiPS exists in the electrolyte. In a Li-Cu cell with an open circuit potential >2 V upon assembly, LiPS reduction reaction takes place prior to Li deposition, hindering accurate assessment of Li metal CE (Supplementary Fig. 13). We employed a modified protocol that replaces Cu with thin Li (20 μm) on Cu that circumvents the initial LiPS reduction reaction. 1 M LiTFSI G4, 1 M LiTFSI DME and 2 M LiTFSI DME, which possess relatively strong solvation and suffer instabilities at the Li metal anode, had CE results too low for the measurement and are not included in the plot (Fig. 4a).

Fig. 4: Solvation effects on Li metal cyclability, morphology and interphase.
figure 4

a Li || Cu CE of electrolytes with and without LiPS. b, c Correlations of Li || Cu CE with solvation energy, showing increasing CE with weaker solvation, while the addition of LiPS leads to lower CE. dg SEM micrographs of Li plated on Cu with 1 M LiTFSI DME and 1 M LiTFSI DME-TTE 1:1 with and without LiPS. h XPS elemental ratios of the SEI of the Li plated on Cu with 1 M LiTFSI DME and 1 M LiTFSI DME-TTE 1:1 with and without LiPS.

Figure 4b shows that the CE of electrolytes without LiPS increases with weaker solvation, in agreement with previous observations (Supplementary Fig. 14)22,36,37. When the electrolyte is saturated with LiPS (Fig. 4c, Supplementary Fig. 15), which resembles the case of a Li-S battery with lean electrolyte (E/S ratio ≤ 5 mg μL−1), a similar trend is observed except that the CE is overall lowered by about 3%. This result is surprising as LiPS is known to have a synergetic effect with LiNO3 to stabilise the Li metal anode38. We conjecture that without LiNO3, LiPS does not have stabilising effects and even has detrimental effects. This is supported by the scanning electron microscopy (SEM) images in Fig. 4d, e. It shows that 1 M LiTFSI DME without LiPS has areas of bare Cu, whereas the same electrolyte with LiPS has the entire active surface covered with Li metal. This suggests that the Li plated in 1 M LiTFSI DME has a smaller surface area, which corroborates the higher CE. Similar phenomena have been previously reported, where Li depositing in islands rather than covering the entire surface area has been correlated with improved CE39,40. A similar relationship can be observed for the 1 M LiTFSI DME-TTE 1:1 case, shown in Fig. 4f, g. A potential mechanism is that LiPS promotes Li nucleation over Li growth, which leads to the formation of small nuclei, increasing the overall surface area and side reactions. It is possible that an electrolyte decomposition layer on the current collector prior to Li deposition may lead to different nucleation behaviour. An alternative mechanism may be related to surface energy of Li in contact with the electrolyte. It has been suggested that the solvation energy of the electrolyte can dictate the Li surface energy at the Li-electrolyte interface, thereby impacting the morphology of Li37. It could be that the presence of LiPS alters the solvation energy that the high surface area Li morphology is favoured. Interphase chemistries were analysed with X-ray photoelectron spectroscopy (XPS) in Fig. 4h. We observe that the SEI is more inorganic-rich with higher fluorine and sulphur content when TTE is added to the electrolyte, which is consistent with literature reports24. When LiPS is incorporated into the electrolyte, the SEI becomes relatively richer in sulphur, which likely stems from the decomposition of LiPS.

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