Enhancing electrochemical intermediate solvation through electrolyte anion selection to increase nonaqueous Li–O₂ battery capacity

Significance

The Li–air battery has attracted significant interest as a potential high-energy alternative to Li-ion batteries. However, the battery discharge product, lithium peroxide, is both electronically insulative and insoluble in nonaqueous electrolytes. It therefore passivates the battery cathode as it is uniformly deposited and disallows the battery to achieve even a modest fraction of its potential electrochemical capacity. Our objective is to circumvent this challenge by enhancing the solubility of electrochemically formed intermediate species. We present a rational basis for electrolyte (i.e., solvent and salt) selection for nonaqueous Li–air batteries and demonstrate a selection criterion for an electrolyte salt that increases the stability of Li⁺ in solution, thereby triggering a solution-based process that allows significantly improved battery capacities.

Abstract

Among the “beyond Li-ion” battery chemistries, nonaqueous Li–O₂ batteries have the highest theoretical specific energy and, as a result, have attracted significant research attention over the past decade. A critical scientific challenge facing nonaqueous Li–O₂ batteries is the electronically insulating nature of the primary discharge product, lithium peroxide, which passivates the battery cathode as it is formed, leading to low ultimate cell capacities. Recently, strategies to enhance solubility to circumvent this issue have been reported, but rely upon electrolyte formulations that further decrease the overall electrochemical stability of the system, thereby deleteriously affecting battery rechargeability. In this study, we report that a significant enhancement (greater than fourfold) in Li–O₂ cell capacity is possible by appropriately selecting the salt anion in the electrolyte solution. Using ⁷Li NMR and modeling, we confirm that this improvement is a result of enhanced Li⁺ stability in solution, which, in turn, induces solubility of the intermediate to Li₂O₂ formation. Using this strategy, the challenging task of identifying an electrolyte solvent that possesses the anticorrelated properties of high intermediate solubility and solvent stability is alleviated, potentially providing a pathway to develop an electrolyte that affords both high capacity and rechargeability. We believe the model and strategy presented here will be generally useful to enhance Coulombic efficiency in many electrochemical systems (e.g., Li–S batteries) where improving intermediate stability in solution could induce desired mechanisms of product formation.

The lithium–oxygen (Li–O₂) battery has garnered significant research interest in the past 10 y due to its high theoretical specific energy compared with current state-of-the-art lithium-ion (Li-ion) batteries (1, 2). Consisting of a lithium anode and an oxygen cathode, the nonaqueous Li–O₂ battery operates via the electrochemical formation and decomposition of lithium peroxide (Li₂O₂). The ideal overall reversible cell reaction is therefore

$$2\text{Li}+{\text{O}}_2\mathrm{\leftrightarrow }{\text{Li}}_2{\text{O}}_2\left(2{\text{e}}^{-}\hspace{0.5em}\text{process}\right)U=2.96\text{V}.$$ [1]

One challenge preventing the realization of a modest fraction of the Li–O₂ battery’s high theoretical specific energy is that the discharge product, Li₂O₂, which is generally insoluble in aprotic organic electrolytes, is an insulator (3–5). As Li₂O₂ is conformally deposited on the cathode’s carbon support during discharge, it electronically passivates the cathode, resulting in practical capacities much smaller than theoretically attainable (6). Recently, two reports described the engineering of electrolytes to circumvent this passivation and improve Li–O₂ battery discharge capacity. Aetukuri et al. suggested that adding ppm quantities of water to a 1,2-dimethoxyethane (DME)-based electrolyte increases the solubility of intermediates during Li₂O₂ formation (7). This increased solubility allows a reduced oxygen species shuttling mechanism that promotes deposition of Li₂O₂ aggregated toroid structures. The diffusion of the intermediates away from the electrode surface allows the surface to remain electronically accessible to Li⁺ and O₂, promoting more Li₂O₂ growth, thereby leading to an increase in cell capacity. Of note, this increase in cell capacity with water content in the electrolyte is also consistent with reports by Gasteiger and coworkers (8, 9). Aetukuri et al. reason that this increase could be attributed to water’s significantly higher Gutmann Acceptor Number (AN) than DME, as the AN is a measure of a solvent’s Lewis acidity, and thus quantifies its ability to efficiently solubilize negatively charged species, such as the potential discharge product intermediate, superoxide (O₂⁻) (10). In a related analysis, Johnson et al. showed that an electrolyte solvent with a higher Gutmann Donor Number (DN), a measure of Lewis basicity (11), is more likely to induce toroid formation due to increased Li⁺ stability in solution, inducing solubility of O₂⁻ (12). Johnson et al. further confirmed the presence of O₂⁻ ions in Li⁺-bearing high-DN electrolytes using surface-enhanced Raman spectroscopy (12).

Whereas water and certain organic solvents increase cell capacity via this solution mechanism, there is evidence that both decrease electrolyte stability. Water impurities in Li-ion electrolytes are known to enhance parasitic electrochemical side reactions, and Aetukuri et al. and Cho et al. showed that adding ppm quantities of water in Li–O₂ batteries leads to a decrease in electrolyte stability and increase in irreversible reactions with the lithium anode (7, 13). Furthermore, using quantitative measures of battery rechargeability, high-DN solvents, such as DMSO and N-methyl pyrrolidone, have been observed to be less stable than low-DN solvents, such as acetonitrile and DME (14). Recently, Khetan et al. used a thermodynamic analysis to show that an organic solvent's ability to induce the solution mechanism is anticorrelated with its stability toward nucleophilic attack (15). Thus, Li–O₂ cells would benefit from an appropriately engineered electrolyte that both induces Li₂O₂ intermediate solubility and maintains or exceeds present electrolyte stability.

In this article, we describe the importance of the lithium salt anion in enhancing the solvation of electrochemically formed intermediate species during Li–O₂ battery discharge, thereby enhancing discharge capacity. We present a study on two common Li–O₂ battery salts, lithium bis(trifluoromethane) sulfonimide (LiTFSI) and lithium nitrate (LiNO₃), dissolved in DME. These salts were selected because Schmeisser et al. found that TFSI⁻ and NO₃⁻ anions provided different DN in ionic liquids with common cations (NO₃⁻-containing ILs having higher DN than TFSI⁻-containing ILs). We also specifically selected NO₃⁻ because of its reported positive influence on Li–O₂ battery rechargeability compared with the more commonly used TFSI⁻ (16, 17). We found that electrolytes containing a high concentration of NO₃⁻ exhibited higher donicity, as verified using ⁷Li NMR, and provided an increase in battery capacity greater than fourfold compared with a battery using exclusively TFSI⁻ as the electrolyte anion, while not decreasing battery rechargeability, as measured using quantitative oxygen consumption and evolution. To theoretically quantify this enhancement, we propose an Ising model description of the solvation shell of Li⁺. This analysis indicates that the origin of this enhanced solution process is due to the formation of ion pairs (Li⁺–NO₃⁻) in a DME solvent. The theoretical analysis further predicts that ion-pair formation and the associated enhancement in capacity would not be observed when DMSO is used as a solvent, which was subsequently confirmed experimentally. We generalize this analysis to provide a rational basis for selection of electrolyte (solvent + salt) combinations for use in Li–O₂ batteries. We believe these results will have profound implications not only for Li–O₂ batteries, where a practical outcome of the solubility is an enhancement in battery capacity, but also for other electrochemical systems (e.g., lithium–sulfur batteries) in which intermediate solvation may induce desired mechanisms of product formation.

Results and Discussion

To characterize the effects of the electrolyte salt anion on discharge performance, Li–O₂ cells were prepared with electrolytes of varying concentrations of LiNO₃ and LiTFSI salts, totaling 1.0 M Li⁺, in DME. Cell design and preparation are detailed in SI Appendix and follow those described previously (18).

Fig. 1A presents representative galvanostatic discharge profiles of these Li–O₂ cells as a function of the LiNO₃ salt concentration. Fig. 1A (Inset) shows the average cell capacity for each LiNO₃ salt concentration. Cell capacity increases more than fourfold over the LiNO₃ concentration range studied, clearly indicating the substantial effect of the Li⁺ counterion on cell capacity.

Fig. 1.

(A) Representative galvanostatic discharge profiles of Li–O₂ cells (450 μA/cm² under a 1.5-atm O₂ atmosphere to a 2-V cutoff). (Inset) Capacity dependence on LiNO₃ concentration. (B) Li₂O₂ discharge yield as a function of LiNO₃ electrolyte concentration. (C) ⁷Li chemical shift of electrolyte solutions, versus a 3 M LiCl in D₂O standard, as a function of electrolyte LiNO₃ concentration. A less negative chemical shift represents a shift down-field. A 1.0 M Li⁺ concentration was used for all electrolytes (DME used as the solvent), and the LiTFSI:LiNO₃ ratio was varied. The LiNO₃ concentration for each cell is provided in the figure. As an example, the cell labeled “0.1 M LiNO₃” contained 0.1 M LiNO₃ and 0.9 M LiTFSI. Error bars are 1 SD of multiple experiments.

Scanning electron microscopy (SEM) was performed on discharged cathodes to investigate changes in Li₂O₂ morphology, and hence changes in discharge mechanism, with increasing LiNO₃ concentration. Fig. 2 presents SEM images of a pristine cathode (Fig. 2A) and images of cathodes from cells of identical electrolyte compositions as those studied in Fig. 1, but discharged at 45 μA/cm² (Fig. 2 B–F). When comparing Fig. 2 A–C, the pristine, 0 M LiNO₃, and 0.01 M LiNO₃ cathodes appear indistinguishable. This implies a conformal coating of discharge product on the 0 M LiNO₃ and 0.01 M LiNO₃ cathodes, and is consistent with previous reports for 1 M LiTFSI in DME (7, 19).

Fig. 2.

(A) SEM image of pristine XC72 carbon cathode before discharge. (B–F) Discharged cathodes from cells using 1 M total Li⁺ concentration, with 0 M LiNO₃ (1 M LiTFSI), 0.01 M LiNO₃, 0.1 M LiNO₃, 0.5 M LiNO₃, and 0.7 M LiNO₃, respectively. Cells were discharged at 45 μA/cm² to 0.9 mAh/cm² or a 2-V cutoff voltage. All cells had at least 0.5 mAh/cm² capacity. (Scale bars, 1 μm.)

A conformal coating of discharge product is indicative of a predominant thin-film Li₂O₂ surface deposition mechanism. Originally outlined by Laoire et al., this mechanism is described by the following elementary steps (20, 21):

$${\text{Li}}^{+}+{\text{e}}^{-}+{\text{O}}_2^{*}\mathrm{\leftrightarrow }{\text{LiO}}_2^{*},$$ [2]

$${\text{Li}}^{+}+{\text{e}}^{-}+{\text{LiO}}_2^{*}\mathrm{\leftrightarrow }{\text{Li}}_2{\text{O}}_2^{*}\text{and}/\text{or}{2\text{LiO}}_2^{*}\mathrm{\leftrightarrow }{\text{Li}}_2{\text{O}}_2^{*}+{\text{O}}_2,$$ [3a,b]

where “*” denotes a species adsorbed to the cathode/Li₂O₂ surface. Importantly, in the LiTFSI/DME electrolyte, LiO₂* is insoluble and therefore remains adsorbed to the electrode surface, where a second charge transfer step (reaction 3a) or a disproportionation reaction (reaction 3b) results in the conformal Li₂O₂ coating observed in Fig. 2 B and C (2, 19–23).

As the LiNO₃:LiTFSI ratio increases, the discharge morphology changes perceptibly. As seen in Fig. 2D, when using 0.1 M LiNO₃, nodular morphologies appear on the cathode surface. Increasing the LiNO₃ concentration to 0.5 M and 0.7 M finds these structures replaced with increasingly larger toroid structures, as seen in Fig. 2 E and F, respectively.

As described previously, the toroid morphology observed in Fig. 2 D–F is indicative of a solution mechanism of Li₂O₂ growth proceeding through solubility of the LiO₂ intermediate (7, 12, 24). The dissolution of LiO₂* into lithium cations and the redox active superoxide anion, O₂⁻, follows the equilibrium reaction (7):

$${\text{LiO}}_2^{\ast }\leftrightarrow {\text{Li}}^{+}\left(\text{sol}\right)+{\text{O}}_2^{-}\left(\text{sol}\right).$$ [4]

Solvated O₂⁻ can then diffuse in solution to a growing Li₂O₂ toroid, where it can combine with Li⁺ to form adsorbed LiO₂* on the toroid surface. LiO₂* can subsequently undergo disproportionation according to Eq. 3b, leading to the formation of Li₂O₂ on the toroid surface (7). The observed toroid formation on discharged cathodes from cells using high LiNO₃:LiTFSI ratios supports the enhancement of this solution mechanism with increasing LiNO₃ concentration.

In further support of the solution mechanism, increasingly larger toroid structures were observed with decreasing current density in cells using 0.5 M LiNO₃ (0.5 M LiTFSI) (SI Appendix, Fig. S1). This observation is consistent with previous reports where Li₂O₂ toroid formation was observed at low currents in electrolytes that promoted the solution Li₂O₂ formation mechanism (7, 12, 24).

Of note, we find that Li₂O₂ yield, as measured using an established peroxide titration technique (18), is generally unaffected by the electrolyte compositions studied here (Fig. 1B), although a slightly higher Li₂O₂ yield may be observed at high LiNO₃ concentrations. Differential electrochemical mass spectrometry was also used, as described previously (18), to quantify the reversibility of the electrochemical reactions (SI Appendix, Fig. S2). The ratio (OER:ORR) of the amount of oxygen evolved during charge (OER) to the amount of oxygen consumed during discharge (ORR), an important metric of reversibility, is statistically equal for a cell using 1 M LiTFSI and a cell using 0.5 M LiNO₃:0.5 M LiTFSI (OER:ORR ∼0.82). Furthermore, only ¹⁸O₂ is evolved on charge after a discharge under ¹⁸O₂ of a cell using 0.5 M LiN¹⁶O₃:0.5 M LiTFSI, confirming that NO₃⁻ does not participate in the cathode reaction other than to induce solubility of the intermediates. This result agrees with a similar experiment using pure LiTFSI-based electrolytes (19), implying that electroactive O₂ remains associated during both Li₂O₂ formation and oxidation.

With a change in anion clearly inducing a solution Li₂O₂ growth mechanism, it can be reasoned that the NO₃⁻ anion is affecting LiO₂ solubility via enhanced Li⁺ solvation. The electrolyte anion can affect the electrolyte's overall donicity [quantified by the Gutmann DN, a measure of Lewis basicity (11)], in turn affecting the electrolyte's ability to solubilize LiO₂* through enhanced solvation of Li⁺. We used ⁷Li NMR to probe the electron donicity felt by Li⁺ ions in our LiNO₃:LiTFSI in DME electrolytes as a proxy measurement of the relative effect of the anion on electrolyte DN.

Using NMR as a proxy for DN is a well-known technique, with Erlich and Popov first proposing ²³Na NMR as an effective measurement for a solvent’s DN (25). Erlich and Popov reasoned that a down-field ²³Na shift resulted from stronger interaction between the solvation shell molecules and the cation, thereby decreasing the cation’s shielding. The environment of Li⁺ in LiNO₃:LiTFSI in DME electrolytes cannot be determined via ²³Na NMR, as adding NaClO₄ to the electrolytes causes a white precipitate to crash out of solution [likely NaNO₃, as dissolving NaClO₄ in an anhydrous solvent containing LiNO₃ has been proposed as a method for making anhydrous LiClO₄ (26)]. However, we reason that ⁷Li NMR, in place of ²³Na NMR, can serve as a reasonable proxy of the relative donicity of Li⁺ electrolytes in a single solvent.

Fig. 1C shows the ⁷Li chemical shift, referenced to an external standard of LiCl in D₂O, of each LiNO₃:LiTFSI in DME electrolyte. As LiNO₃ concentration increases, the ⁷Li peak shifts down-field, or becomes less shielded. Cahen et al. showed that the ⁷Li chemical shift of a lithium salt may display a concentration dependence, contingent, to a first approximation, on the DN of the solvent and the DN of the anion (27). The DN of an electrolyte containing a low-DN solvent and a high-DN anion, like Br⁻ (DN = 33.7 kcal/mol) in acetonitrile (DN = 14.1 kcal/mol), exhibits an anion concentration dependence [DN values from Linert et al. (28)]. Conversely, electrolytes comprising a high-DN solvent with a relatively low DN anion, like ClO₄⁻ (DN = 8.44 kcal/mol) in dimethyl sulfoxide (DN = 29.8 kcal/mol), do not exhibit a DN dependence on anion concentration. These trends agree with Linert et al., who found via solvatochromic dyes that the effective DN of an electrolyte depended on an interplay between the DN of the solvent, DN of the anion, and AN of the solvent (28). For example, if the solvent’s DN was larger than the anion’s DN, then the electrolyte comprising the two had a DN similar to its solvent’s DN.

If LiNO₃ indeed has a higher DN than DME, then increasing the concentration of LiNO₃ will increase the number of NO₃⁻ interacting with any particular Li⁺, which in turn will lead to an increase in the electrolyte’s DN. Thus, we reason that the presence of a concentration dependence on ⁷Li chemical shift, as seen in Fig. 1C, indicates NO₃⁻ serving an active role in the electrolyte’s donicity, and the increasingly down-field shift of ⁷Li with increasing LiNO₃ concentration represents increasing donicity.

In contrast, Fig. 3 shows that indeed LiNO₃:LiTFSI salts in the high-DN solvent dimethyl sulfoxide do not exhibit a substantial change in ⁷Li shift with increasing LiNO₃ concentration, and, as therefore expected, no statistically significant capacity increase is observed in DMSO-based electrolytes as the LiNO₃:TFSI ratio increases. To confirm the general correlation between enhanced Li⁺ solvation and Li–O₂ battery capacity, another high-DN anion, Br⁻, was studied. As expected, similar trends in ⁷Li NMR chemical shifts and Li–O₂ battery capacity are observed between 0.5M LiBr:0.5M LiTFSI and 0.5 M LiNO₃:0.5 M LiTFSI in DME and DMSO-based electrolytes (SI Appendix, Fig. S10).

Fig. 3.

(A) ⁷Li chemical shift of DMSO and DME-based electrolytes, versus a 3 M LiCl in D₂O reference, as a function of electrolyte LiNO₃ concentration. A less negative chemical shift represents a shift down-field. A 1.0 M Li⁺ concentration was used for all cell electrolytes, and the LiTFSI:LiNO₃ ratio was varied. (B) Discharge profiles (45 μA/cm², 2-V cutoff) for cells employing DMSO and DME-based electrolytes. Labels correspond to discharges of cells using the following electrolytes: 1. 1 M LiTFSI in DME, 2. 0.5 M LiNO₃:0.5 M LiTFSI in DME, 3. 1 M LiTFSI in DMSO, and 4. 0.5 M LiNO₃:0.5 M LiTFSI in DMSO.

We note, however, that extreme care must be taken when using NMR techniques to compare and quantify solvent DNs, particularly between dislike solvent classes, such as protic and aprotic solvents, as was discussed by Gal and Laurence (29). For the current study, our interest is only in the relative changes of the Li⁺ chemical environment as a function of anion composition in a single aprotic solvent (both for DME and DMSO), such that ⁷Li NMR provides useful qualitative, if not quantitative, values for comparison.

To provide a quantitative basis for the role played by the electrolyte anion, we present a revised thermodynamic model for the solution electrochemical process. The solution-mediated electrochemical growth of Li₂O₂ is triggered by the dissolution reaction given in Eq. 4. The free-energy change involved in this dissolution reaction is given by

$${\text{ΔG}}_{\text{sol}}={\text{G}}_{{\text{Li}}_{\text{sol}}^{+}}+{\text{G}}_{{\text{O}}_{2,\text{sol}}^{-}}-{\text{G}}_{{\text{LiO}}_2^{*}}\hspace{0.17em},$$ [5]

where ${\text{G}}_{{\text{Li}}_{\text{sol}}^{+}}$ is the free energy of the Li⁺ ions in the electrolyte, ${\text{G}}_{{\text{O}}_{2,\text{sol}}^{-}}$ is the free energy of O₂⁻ ions in the electrolyte, and ${\text{G}}_{{\text{LiO}}_2^{*}}$ is the free energy of the adsorbed LiO₂ on the Li₂O₂ surface during discharge.

To understand the role of the salt anion on the equilibrium of the dissolution reaction, we need to explore the stabilization of the solvated intermediates in the presence of the anion. The presence of the anion can influence the free energy of Li⁺ ions. To a first approximation, the free energy of the Li⁺ ions and thus the free energy of LiO₂ dissolution is largely dependent on the species that are present in the Li⁺ first solvation shell (30, 31). To be consistent with the experimental data presented in Figs. 1–3, we explicitly model an electrolyte that contains a mixture of LiNO₃ and LiTFSI such that the total Li⁺ concentration is maintained at 1 M. The concentration of ${\text{O}}_2^{-}$ ions in the solution is expected to be much lower than the Li⁺ and salt anion concentrations (7). Thus, we do not expect ${\text{O}}_2^{-}$ ions to play a significant role in the solvation of Li⁺. Hence, to a first approximation, the solvation shell of Li⁺ will comprise only solvent molecules and salt anions (${\text{NO}}_3^{-}\hspace{0.17em}$ and TFSI⁻). The exact composition of the solvation shell will depend on the energetics of the interactions of the Li⁺ ion with the solvent and the anions. To determine the composition of the first solvation shell and in turn the free energy of stabilization, we develop a modified Ising model for the site occupancy in the solvation shell of Li⁺ (32). The Ising model formalism, originally developed to describe magnetism, provides a systematic basis for treating the energetics of interaction between Li⁺ and the solvent and salt anions (33).

In this model, we develop a site occupancy variable to describe each of the solvation shell sites of Li⁺. The Hamiltonian that governs the solvation shell of Li⁺ is given by

$$\text{H}={\text{h}}_1{\displaystyle \sum _{\text{i}=1}^{\text{N}}{\mathrm{n}}_{\mathrm{i}}}+{\text{h}}_2{\displaystyle \sum _{\text{i}=1}^{\text{N}}{\mathrm{m}}_{\mathrm{i}}}+{\text{h}}_3{\displaystyle \sum _{\text{i}=1}^{\text{N}}{\mathrm{l}}_{\mathrm{i}}}+{\text{J}}_{11}{\displaystyle \sum _{\langle \text{i},\text{j}\rangle }{\mathrm{n}}_{\mathrm{i}}{\mathrm{n}}_{\mathrm{j}}}+{\text{J}}_{22}{\displaystyle \sum _{\langle \text{i},\text{j}\rangle }{\mathrm{m}}_{\mathrm{i}}{\mathrm{m}}_{\mathrm{j}}}+{\text{J}}_{33}{\displaystyle \sum _{\langle \text{i},\text{j}\rangle }{\mathrm{l}}_{\mathrm{i}}{\mathrm{l}}_{\mathrm{j}}}+{\text{J}}_{12}{\displaystyle \sum _{\langle \text{i},\text{j}\rangle }{\mathrm{n}}_{\mathrm{i}}{\mathrm{m}}_{\mathrm{j}}}+{\text{J}}_{21}{\displaystyle \sum _{\langle \text{i},\text{j}\rangle }{\mathrm{m}}_{\mathrm{i}}{\mathrm{n}}_{\mathrm{j}}}+{\text{J}}_{13}{\displaystyle \sum _{\langle \text{i},\text{j}\rangle }{\mathrm{n}}_{\mathrm{i}}{\mathrm{l}}_{\mathrm{j}}}+{\text{J}}_{31}{\displaystyle \sum _{\langle \text{i},\text{j}\rangle }{\mathrm{l}}_{\mathrm{i}}{\mathrm{n}}_{\mathrm{j}}}+{\text{J}}_{23}{\displaystyle \sum _{\langle \text{i},\text{j}\rangle }{\mathrm{m}}_{\mathrm{i}}{\mathrm{l}}_{\mathrm{j}}}+{\text{J}}_{32}{\displaystyle \sum _{\langle \text{i},\text{j}\rangle }{\mathrm{l}}_{\mathrm{i}}{\mathrm{m}}_{\mathrm{j}}},$$ [6]

where i = 1 to N represent sites in the solvation shell of a Li⁺ ion and$\langle \text{i},\text{j}\rangle$ represents the nearest-neighbor pair in the solvation shell. The occupation variables “n,” “m,” and “l” represent the occupancy of a site by the solvent, the ${\text{NO}}_3^{-}\hspace{0.17em}$ anions, and the TFSI⁻ anions, respectively. For any site “i” occupied by the solvent, n_i = 1, m_i = 0, and l_i = 0 and similarly for other cases. Thus, at any given site, ${\mathrm{n}}_{\mathrm{i}}+{\mathrm{m}}_{\mathrm{i}}+{\mathrm{l}}_{\mathrm{i}}=1$, i.e., each site is occupied by either solvent or a salt anion. In our model, h₁ represents the interaction energy between a Li⁺ ion and a solvent, h₂ represents the interaction energy between a NO₃⁻ anion and Li⁺, and h₃ represents the interaction energy between a TFSI⁻ anion and Li⁺. The coupling constant J₁₁ represents the interaction between neighboring solvent molecules in the Li⁺ solvation shell. Likewise, J₂₂ and J₃₃ represent the interactions between neighboring NO₃⁻ and neighboring TFSI⁻ anions, respectively. The symmetry assumption is invoked, which yields J₁₂ = J₂₁, J₁₃ = J₃₁, J₂₃ = J₃₂. The cross-coupling terms J₁₂, J₁₃, and J₂₃ represent interactions between neighboring ${\text{NO}}_3^{-}\hspace{0.17em}$ and solvent molecules, neighboring TFSI⁻ and solvent molecules, and neighboring ${\text{TFSI}}^{-}$ and ${\text{NO}}_3^{-}\hspace{0.17em}$ anions, respectively.

The exact model is not easily analytically tractable; however, we can invoke the mean-field approximation, described in SI Appendix. The mean-field approximation is valid under the assumption that the Li⁺ ions are uniformly distributed in solution and each site in the solvation shell experiences an averaged effect of other species present in the electrolyte. The coordination number z of the solvation shell is expected to be independent of species (anions or solvent) occupying the solvation shell. The mean-field approximation replaces the nearest-neighbor interaction (n_in_j) by the average interaction (n_i$\langle \text{n}\rangle$), where assuming spatial invariance, the average occupation of species in the shell can be defined as $\langle \text{n}\rangle =1/\text{N}{\displaystyle {\sum }_{\text{i}=1}^{\text{N}}\langle {\mathrm{n}}_{\mathrm{i}}\rangle }$.

The interaction term h₁ is dependent on the donating tendency of the solvent molecule to the Li⁺ ions in solution. The free energy of Li⁺ ions can be expressed in terms of the half-wave potential of Li/Li⁺ couple and it has been shown that the half-wave potential of Li/Li⁺ couple is a function of the DN of the solvent (34). Hence the Li⁺–solvent interaction energetics (h₁) can be expressed as a function of the DN of the solvent. Similarly, we assume that the terms h₂ and h₃ can be expressed as a function of the DN. There is an additional contribution to h₂ and h₃ that depends on the concentration of the ${\text{NO}}_3^{-}\hspace{0.17em}$ and TFSI⁻ anions. This arises due to a change in the reference chemical potential of the ${\text{NO}}_3^{-}\hspace{0.17em}$ and TFSI⁻ anions to account for the configurational entropy associated with that concentration. The coupling constant J₁₁ is a weak attractive van der Waals interaction between solvent molecules, and is estimated to be an order of magnitude less than the donor interactions h₁, h₂, and h₃. The constants J₂₂, J₃₃, and J₂₃ are representative of the repulsive interaction between neighboring anions in the Li⁺ solvation shell and are of the same order of magnitude as h₁, h₂. The coupling constants J₁₂, J₁₃ for the interaction between a solvent molecule and the respective anion can be described by the electron accepting tendency of the solvent and can therefore be determined by the solvent’s AN. As we are accounting for the coupling constants in terms of the overall donating and accepting tendencies of the solvent, the overall coordination number is already included in the model, i.e., z = 2.

Solving SI Appendix, Eqs. S4 a–c, we derive analytical expressions for the average occupation numbers of the solvent molecules and the anions in the first solvation shell of the Li⁺ ion as functions of the DN of the solvent, DN of the anion, and anion concentration. From the occupation numbers, we can determine the overall free energy of Li⁺ ions in solution using the mean-field relation:

$${\text{G}}_{{\text{Li}}^{+}}=\langle \text{n}\rangle {\text{h}}_1\left({\text{DN}}_{\text{sol}}\right)+\langle \text{m}\rangle {\text{h}}_2\left({\text{DN}}_{{\text{NO}}_3^{-}},{\text{c}}_{{\text{NO}}_3^{-}}\right)+\langle \text{l}\rangle {\text{h}}_3\left({\text{DN}}_{{\text{TSFI}}^{-}},{\text{c}}_{{\text{TFSI}}^{-}}\right).$$ [7]

The developed model requires the DN of ${\text{NO}}_3^{-}\hspace{0.17em}$ and TFSI⁻ anions to determine the occupation numbers. We use the values determined by Schmeisser et al. via ²³Na NMR for ionic liquids with common cations, as discussed earlier (35). Although the quantitative nature of these measurements is still under debate (29), we believe the trends can be well captured from these values. Schmeisser et al. find that TFSI⁻ has a very low DN of 11.2 kcal/mol whereas ${\text{NO}}_3^{-}\hspace{0.17em}$ has a DN of 22.2 kcal/mol (35). Using these values, we can determine the occupation shell of Li⁺ as a function of the ${\text{NO}}_3^{-}\hspace{0.17em}$ anion concentration. As is shown in Fig. 4A, the solvation shell is completely dominated by DME and ${\text{NO}}_3^{-}\hspace{0.17em}$ anion. As the ${\text{NO}}_3^{-}$ anion has a higher DN than DME (DN = 20 kcal/mol), we observe a strong concentration dependence on the ${\text{NO}}_3^{-}$ anion. This suggests that increasing ${\text{NO}}_3^{-}$ anion concentration will lead to a displacement of low-DN solvents like DME in the Li⁺ solvation shell. As we increase the concentration of ${\text{NO}}_3^{-}$ in DME, a higher number of ${\text{NO}}_3^{-}$ ions occupy the Li⁺ solvation shell until the electrostatic repulsion of ${\text{NO}}_3^{-}\hspace{0.17em}$ ions becomes dominant, leading to a saturation in the number of anions that occupy the first solvation shell.

Fig. 4.

(A) Occupation of the solvent (red line), TFSI⁻ (green line), and ${\text{NO}}_3^{-}\hspace{0.17em}$(blue line) in the Li⁺ solvation shell and (B) the Li⁺ solvation energy (eV) as a function of the concentration of the ${\text{NO}}_3^{-}\hspace{0.17em}$ anion. The rate enhancement of the solution process, ${\mathrm{r}}_{\mathrm{S}}\sim \text{exp}\left(\left(-{\text{ΔG}}_{\text{sol}}\right)/\text{kT}\right)$, is marked on the right y axis of B. The Li⁺ free energy is normalized relative to that of the case with 1 M LiTFSI. There is a rate enhancement, ${\mathrm{r}}_{\mathrm{S}}$, by a factor of ∼4 as the concentration of ${\text{NO}}_3^{-}\hspace{0.17em}$ is increased from 0.1 to 0.5 M.

The corresponding change in the free energy of Li⁺ as a function of ${\text{NO}}_3^{-}\hspace{0.17em}$ concentration in DME is shown in Fig. 4B. The free energy of Li⁺ as evaluated from the model is well-correlated with the experimentally measured NMR ⁷Li chemical shift, as shown in SI Appendix, Fig. S8. This proves that the thermodynamic analysis developed in this work accurately captures the effect of the change in anion concentration in the Li⁺ solvation shell. Due to a higher DN of the ${\text{NO}}_3^{-}\hspace{0.17em}$ anion, there is an overall increase in Li⁺ solvation energy; this is accompanied by an enhancement of the rate of the solution process given by $r_S\sim \text{exp}\left(\left(-{\text{ΔG}}_{\text{sol}}\right)/kT\right)$. This shows that at 0.5 M LiNO₃:LiTFSI, we would expect an approximately fourfold enhancement in the rate of the solution process. The rate enhancement, $r_S\hspace{0.17em}\sim \hspace{0.17em}\text{exp}\left(\left(-{\text{ΔG}}_{\text{sol}}\right)/kT\right)$, as calculated from the model, shows a positive correlation with the observed capacity enhancement as shown in SI Appendix, Fig. S9.

The model developed can be generalized to map out the entire electrolyte design space. A contour map of the Li⁺ stabilization as a function of varying DN of solvent and anion is shown in Fig. 5 and the corresponding contour map of the occupation of the solvent in the solvation shell in shown in SI Appendix, Fig. S5. This generalization analysis assumes a constant AN chosen to be the average of DME and DMSO and a 50:50 salt blend of LiTFSI and a varying electrolyte anion. The contour map shows that there is an enhancement when using low-DN solvent, such as DME, and high-DN salt anion, such as ${\text{NO}}_3^{-}\hspace{0.17em}$ ions. However, an interesting prediction of this generalized analysis is that there is no benefit in using high-DN salt anions in a high-DN solvent such as DMSO (a more detailed analysis of the DMSO case is reported in SI Appendix). This suggests that there is no ion-pair formation in a DMSO solvent and hence, almost no associated change in discharge capacity. This is in excellent agreement with the experiments presented in Fig. 3. To emphasize this agreement, our model predicts that in DMSO, the NO₃⁻ anion does not enter the Li⁺ solvation shell, and hence there is no change in the Li⁺ solvation free energy (SI Appendix, Figs. S3 and S4).

Fig. 5.

Contour plot showing the free energy of Li⁺ for electrolytes with varying DN of the solvent and salt anion, in kcal/mol. The free energy is normalized relative to that of DME and 1 M LiTFSI. The electrolyte is considered to be a 50:50 mixture of LiTFSI and a salt consisting of Li⁺ and the labeled salt anion in the labeled solvent. The blue region corresponds to those electrolytes incapable of triggering the solution process whereas the red region corresponds to those that can trigger the solution process.

The contour map suggests that using a higher DN anion than NO₃⁻ can lead to even greater enhancement of Li⁺ solvation, and therefore a study on bromide’s (Br⁻) effect on Li⁺ solvation and Li–O₂ capacity was performed (28). Our model predicts that for an electrolyte consisting of DME as a solvent and LiTFSI and LiBr as the salt blend, there is a greater stabilization of Li⁺ compared with the LiTFSI and LiNO₃ salt blend of similar concentration, as shown in SI Appendix, Fig. S11. The results from the model are consistent with ⁷Li NMR chemical shifts (SI Appendix, Fig. S10A presents the LiBr ⁷Li NMR results). We also find a capacity enhancement with the 0.5 M LiBr:0.5 M LiTFSI electrolyte over the 1 M LiTFSI electrolyte (SI Appendix, Fig. S10B). Of note, the capacity enhancement obtained in our LiBr and LiNO₃ studies are statistically similar, although using Li⁺ solvation arguments alone, the LiBr-containing cells would be expected to have higher capacities at similar electrolyte concentrations. However, in addition to the free energy of dissolution, ${\text{ΔG}}_{\text{sol}}$, other factors, such as O₂ solubility, and the diffusion coefficients of O₂⁻ and Li⁺, govern the overall rate for the solution process and, thereby, the overall capacity enhancement due to the solution process. These other factors likely contribute to suppress the capacity gains expected solely from enhanced solvation when employing the LiBr electrolyte compared to the LiNO₃ electrolyte.

The contour map presented in Fig. 5 provides a rational basis for selection of the total electrolyte, i.e., solvent and anion. An important conclusion of the contour map is that there is minimal capacity enhancement by changing the electrolyte anion in high-DN solvents. We have demonstrated this conclusion using two examples of high-DN anions (${\text{Br}}^{-}$, ${\text{NO}}_3^{-}$) showing almost no enhancement in solvation in a high-DN solvent such as DMSO as shown in SI Appendix, Figs. S3 and S12. However, there is tremendous scope in tuning the electrolyte anion in low-DN solvents to obtain high discharge capacities. Given that it should be simpler to identify anions stable to the Li–O₂ cathode electrochemistry than high-DN solvents (36, 37), anion selection in combination with low-DN solvents potentially provides a route to avoid the unfavorable capacity/stability trade-off observed in high-DN solvents, such as DMSO (14, 15, 38, 39).

Conclusions

In conclusion, we have demonstrated Li⁺ counterion influence on promoting the solubility of electrochemical intermediates during a Li–O₂ battery discharge without further compromising electrolyte stability. Specifically, Li–O₂ batteries using electrolytes of LiNO₃ and LiTFSI in DME displayed increased capacity and increased toroid formation with increasing LiNO₃ concentration. We ascribe intermediate solubility to enhanced stability of Li⁺ in solution by anions with higher effective donor numbers than that of the solvent, thereby also inducing increased stability of the electrochemically formed anion, O₂⁻, in solution. This strategy can potentially be combined with current efforts to identify novel, stable electrolytes, including those in which organic molecules are entirely removed from the electrolyte [a fascinating idea being explored by researchers at Liox Power, Inc. (40)], to develop a practical electrolyte that could enable high-energy, long-life Li–air batteries. Further, we have developed a generalized model that predicts Li⁺ solvation shell occupation and the resulting stability of Li⁺ in electrolytic solutions. We envision this strategy for intermediate stabilization to be generally applicable to numerous nonaqueous systems in which stabilization of desired intermediates may lead to improved electrochemical efficiency. For example, in Li–S batteries, polysulfide intermediate speciation could potentially be controlled by simply tuning the Li⁺ salt anion, perhaps providing a route for increased sulfur utilization.