## Highlights

- •“One-stop” NMR method to quantify electrolyte evolution and inactive Li accumulation
- •Decomposition kinetics and new failure mechanism of advanced electrolytes
- •Apparent ETN of electrolyte decomposition reactions

## Context & scale

In non-aqueous batteries, such as lithium (Li)-ion batteries and Li metal batteries, the electrolyte decomposition reaction on anodes is regarded as the most intriguing and complicated phenomenon that dictates the stability of anodes. Amid the electrolyte decomposition reaction, the electron transfer number (ETN) is the pivot that intrinsically interconnects the ever-changing reactants (i.e., charges, electrolyte, and active Li) and products (i.e., solid electrolyte interphase [SEI]). However, the lack of an approach to quantify the ETN of electrolyte decomposition reactions impedes the complete comprehension of the electrolyte decomposition process. In this contribution, a simple but delicate method was established to gauge the apparent ETN of the decomposition reaction of each electrolyte component. The fully described electrolyte decomposition reaction affords directional insights into failure forecasting and electrolyte design.

## Summary

Solid electrolyte interphase (SEI) is pivotal in dictating the stability of anodes in non-aqueous batteries. However, electrolyte decomposition mechanism as an indispensable piece of the puzzle to construct a stable SEI is with few quantitative understandings. Herein, as a quantitative descriptor, the apparent electron transfer number (ETN) is acquired by a facile yet precise methodology in working lithium metal batteries with lithium bis(fluorosulfonyl)imide (LiFSI)-dimethyl carbonate (DMC)-based localized high-concentration electrolyte. Through accurate measurements of the electrolyte evolution and concurrently accumulated inactive Li by electrolyte quantitative nuclear magnetic resonance (ely-qNMR) and titration-qNMR, respectively, the decomposition rates of different electrolyte components and ETNs that define the fate of electrolyte can all be acquired in a “one-stop” fashion. The recognition of ETNs (1.0 for DMC and 5.1 for LiFSI) provides pioneering insights into the electrolyte decomposition mechanism and affords new visions for electrolyte design to promote the continuous rise of non-aqueous rechargeable batteries.

## Graphical abstract

## Keywords

## Introduction

Propelled by the challenge of climate change, the past decades have witnessed the rise of a clean energy revolution, which is underscored by the steady transition from fossil fuels to renewable and efficient energy. The formation of SEI results from decomposition reactions of electrolytes owing to the high reactivity of anodes, such as Li and lithiated graphite. SEI dictates the rate and uniformity of transport of Li ions at the anode/electrolyte interface and restrains continuous decomposition reactions of electrolytes, which rules the reversibility of anode, especially for Li metal batteries. Constructing a durable SEI has been pursued for more than 40 years and is still the focus of long-cycling non-aqueous batteries.

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^{, }As key devices to store and provide electrical power at demands for portable electronic devices, electrical vehicles, and so on, long-cycling rechargeable non-aqueous batteries are under intensive explorations.^{, }^{, }In terms of dictating the stability of batteries, solid electrolyte interphase (SEI), which embodies features of the anode/electrolyte interface in non-aqueous batteries, is regarded as the most important and the least understood part.^{7}

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^{,}Clearly, the electrolyte decomposition mechanism is a key piece of the puzzle of constructing a durable SEI, since SEI is composed of the decomposition products of solvents, Li salts, and additives. Tremendous efforts have been devoted to regulating the stability of SEI by electrolyte design, especially for Li metal batteries in the last decade. In retrospect, the attempts based on a trial-and-error method mainly fall into three trends: solvents, electrolyte additives, and solvation structure in electrolytes. Generally, ethylene carbonate is an indispensable co-solvent for stable SEI on graphite anodes, whereas ether solvents (but not all of them), such as dimethoxyethane, contribute to stable SEI on Li anodes. Electrolyte additives like fluoroethylene carbonate and LiNO Regulated solvation structure of Li ions as in high-concentration electrolytes (HCEs) and localized HCEs (LHCEs) has been also demonstrated to render robust anion-derived SEI.

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_{3}with preferential decomposition reactions act as film-formation agents enabling stable SEI.^{21}

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^{, }Despite the progress in the strategies, understanding the mechanism of electrolyte decomposition is largely deficient due to the complexity of electrolyte decomposition reactions and the limitation of the current trial-and-error method. A detailed and quantitative understanding of the electrolyte decomposition mechanism is highly expected to promote the rational design of stable SEI.In order to decipher the electrolyte decomposition mechanism, enormous attempts have been made from theoretical and experimental aspects. Computational methods such as density functional theory (DFT) and molecular dynamics (MD) can predict the reaction direction thermodynamically and gain valuable insights into the plausible reaction pathways. Meanwhile, quantifiable experimental evidence is necessary to prove the possible reaction pathways obtained from theoretical simulations. On the strength of characterization techniques such as X-ray photoelectron spectroscopy (XPS) and (cryo-) transmission electron microscope (TEM), the reaction products, namely the components of SEI, and their corresponding content and distribution are gradually identified, which affords necessary information to infer the decomposition mechanism of electrolytes.

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^{, }However, the spatial resolution of XPS (hundreds of micrometers) and TEM (dozens of nanometers) is appropriate for detecting reaction products at a local area, whereas the spatial distribution of SEI components is non-uniform from both horizontal and vertical orientation, which restricts and even misleads the identification of reaction products from an overall viewpoint. In contrast with reaction products, quantifying the changed amount of electrolyte components and the corresponding consumed electrons to acquire the electron transfer number (ETN) provides another emerging approach to decipher the electrolyte decomposition mechanism.Upon re-examining the decomposition process of electrolyte components, it is noticed that the content of consumed electrolyte components and reaction products are interconnected by transferred charge (Figure 1A). ETN, which is equal to the corresponding consumed electron divided by the molar changes of individual electrolyte components, is a vital parameter to infer electrolyte decomposition mechanisms. Nonetheless, the exact ETN is currently unknown because the existing experimental means cannot quantitatively measure the change of reactants simultaneously, i.e., the changed amount of electrolyte components and the corresponding consumed amount of electrons. For instance, the ETN of the decomposition reaction of lithium bis(fluorosulfonyl)imide (LiFSI) is still controversial.

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^{,}Therefore, ETN is a pivotal but missing descriptor to disclose electrolyte decomposition mechanism quantificationally.In this contribution, the apparent ETN is quantitatively determined by a delicately designed qNMR technique with the emphasis on the pre-acid-titration and cross-calibration treatment as well as the adoption of the anode-free battery configuration. By statistical regression analysis that builds the correlation between the consumed electrolyte and the irreversible Li inventory loss, the experimentally acquired ETN serves as a quantitative descriptor to grasp the mechanism behind battery performance and open up a new avenue to interpret electrolyte evolution, which fills the gap toward the quantitative understanding of electrolyte decomposition reaction in non-aqueous batteries.

## Results

### Procedure and calculation method for obtaining the absolute and relative amount of different electrolyte components

A highly anticipated LHCE (LiFSI: dimethyl carbonate (DMC): 1,1,2,2-tetrafluoroethyl 2,2,3,3-tetrafluoropropyl ether (HFE) = 1:1.5:2) is selected as the targeted electrolyte, which not only possesses a relatively simple electrolyte composition but also produces an anion-derived SEI with significantly improved reversibility of Li metal anodes.

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^{,}For the sake of quantifying apparent ETN, the absolute consumption of each electrolyte component and the associated Li inventory loss are indispensable parameters. First, to measure the content of electrolyte components, NMR provides easily discernible and quantifiable signals of the nuclei in solvent and anion molecules. Ideally, based on the integral area ratio to the known internal reference (2,4-dichlorobenzotrifluoride, DCBF), both the relative and absolute value of the residual solvent/anion can be determined by a single test, using uncycled samples as standards (Equations 1 and 2):

$\mathrm{A}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{e}:\phantom{\rule{0.25em}{0ex}}n{\left(\mathrm{Z}\right)}_{\mathrm{i}}=\frac{a{\left(\mathrm{Z}\right)}_{\mathrm{i}}/a{\left(\mathrm{D}\mathrm{C}\mathrm{B}\mathrm{F}\right)}_{\mathrm{i}}}{a{\left(\mathrm{Z}\right)}_{0}/a{\left(\mathrm{D}\mathrm{C}\mathrm{B}\mathrm{F}\right)}_{0}}\cdot n{\left(\mathrm{Z}\right)}_{0}$

(Equation 1)

$\mathrm{R}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}:\phantom{\rule{0.5em}{0ex}}\frac{n{\left(\mathrm{F}\mathrm{S}\mathrm{I}\right)}_{i}}{n{\left(\mathrm{D}\mathrm{M}\mathrm{C}\right)}_{\mathrm{i}}}=\phantom{\rule{0.25em}{0ex}}\left(\frac{a{\left(\mathrm{F}\mathrm{S}\mathrm{I}\right)}_{i}^{19\mathrm{F}}/\mathrm{N}{\left(\mathrm{F}\mathrm{S}\mathrm{I}\right)}^{19\mathrm{F}}}{a{\left(\mathrm{D}\mathrm{C}\mathrm{B}\mathrm{F}\right)}_{i}^{19\mathrm{F}}/\mathrm{N}{\left(\mathrm{D}\mathrm{C}\mathrm{B}\mathrm{F}\right)}^{19\mathrm{F}}}\right)/\left(\frac{a{\left(\mathrm{D}\mathrm{M}\mathrm{C}\right)}_{i}^{1\mathrm{H}}/\mathrm{N}{\left(\mathrm{D}\mathrm{M}\mathrm{C}\right)}^{1\mathrm{H}}}{a{\left(\mathrm{D}\mathrm{C}\mathrm{B}\mathrm{F}\right)}_{i}^{1\mathrm{H}}/\mathrm{N}{\left(\mathrm{D}\mathrm{C}\mathrm{B}\mathrm{F}\right)}^{1\mathrm{H}}}\right)$

(Equation 2)

Here,

*n*(Z)_{i}and*a*(Z)_{i}stand for the molar quantities and integral area of electrolyte species Z at the*i*cycle, and N(Z) stands for the number of specifc atoms per molecule. The detailed calculation for$\text{}\mathit{n}{\left(\text{Z}\right)}_{0}$ can be found in the experimental procedures section.As for the Li inventory loss (i.e., the loss of active Li), the anode-free configuration serves as an appropriate device that faithfully reflects the total Li inventory loss under a practical battery operating condition, which is mostly induced by the irreversibility of the anode when Li metal is not excessive. However, apart from the continuous consumption of anions and solvents, the Li inventory also irreversibly converts into SEI-covered inactive Li metal (Li Other alternative techniques, such as electron paramagnetic resonance (EPR), and mass spectrometer (MS)-based titration, are also able to quantify the inactive Li

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^{0}) due to the fracture of deposited Li, as illustrated in Figure 1B. To accurately assign the irreversible capacity to corresponding electrolyte decomposition, the contribution and influence from the electronically inactive Li^{0}should be deducted beforehand. Recently, a simple titration gas chromatography (TGC) method has been proposed to quantify the inactive Li^{0}by using D_{2}O as the titrant.^{39}

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*in situ*and*operando*solid-state NMR,^{41}

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^{0}through the gas or solid product detection. However, the aforementioned studies mainly concern the remnant Li metal yet lack information about the concurrent evolution of liquid electrolyte and its interconnection to battery performance. In contrast, although qNMR has been employed on the electrolyte quantification in several systems, the effect of the remaining inactive Li^{0}and the error induced by the sample preparation has yet been properly considered.Therefore, a “one-stop” methodology was proposed (Figure 2) to integrate the electrolyte quantification and the inactive Li

^{0}titration technique. The rigorous method ensures precise measurement of the evolution of electrolyte components and the correlative consumed charges simultaneously. In comparison with previous works, our approach uniquely distinguishes the decomposing rate of different electrolyte components, paving the way for accurately acquiring apparent ETN by subsequent multiple regression of multiple sets of data.### Experimental working flow for qNMR measurements

The detailed working flow of the “one-stop” qNMR technique comprises the steps of battery cycling, electrolyte extraction, acid titration, and NMR measurements (Figure 3A). To ensure statistical reproducibility and predictability, multiple battery cycles are required to repeatedly form new SEI and rack up the changes of electrolyte, considering that the formation of SEI is self-limited, which may only consume limited electrolytes in a single cycle. After battery cycling, the dissembled cell is quickly transferred into a sample tube containing deuterated solvent (deuterated dimethyl sulfoxide [DMSO-d6]), titrant (maleic acid [MA]), and relaxation enhancer (chromium(III) acetylacetonate [Cr(acac)

_{3}]) to extract the remaining electrolyte from cycled cells. After fully mixing, a portion of the mixture is then transferred into an NMR sample tube containing DCBF, which acts as the internal reference for both^{1}H- and^{19}F-NMR spectroscopy (Figure 3B). The nuclei of each substance show distinct and well-separated chemical shifts in the spectra, as can be seen in the Figures S1 and S2, which ensures the base for quantification. As regards, batteries at different states of health (SOH), i.e., cycle number, the NMR spectra of varied statuses of electrolyte are plotted in Figure 3C. In the subsequent spectra analysis, the evolution of the characteristic signal response in^{1}H-NMR and^{19}F-NMR, highlighted in the enlarged spectra shown in Figure 3D, reflects the decomposition of solvents and anions, whereas the changes in the peak area of titrant reveal the amount of inactive Li^{0}without interference to other signals in the electrolyte quantitative nuclear magnetic resonance (ely-qNMR) (Figure 3E). In conjunction with the information of irreversible capacity generated from the battery data, the apparent ETN can be obtained by multiple regression of multiple sets of data.Although qNMR is a powerful tool to distinguish and quantify the electrolyte components, the condition for qNMR of electrolyte has been seldom well treated, leading to flawed and even misleading results. A careful pre-test of qNMR is thus implemented to ensure accurate and unambiguous measurements. To begin with, the knowledge of the longitudinal relaxation time (T1) for all of the nuclei is requisite for establishing a reliable and reproducible qNMR measurement. It is worth noting that with the addition of the relaxation enhancer, the longest T

_{1}is reduced by 8–20 times as shown in Figures S4 and S5, which guarantees the base for precise measurements of the substance abundance. During the electrolyte extraction process, the excessive titrant would react with the remnant inactive Li^{0}, which not only provides the information about the content of inactive Li^{0}but also eliminates the error caused by the persistent consumption of the electrolyte with exposed inactive Li^{0}(Figures S6–S8). Except for the Li^{0}induced error, the uncertainty is also affected by the weighing process, which is exaggerated when the procedure involves several weighing and transfer steps. Therefore, a cross-calibration process is adopted to mitigate the error, by taking advantage of the residual DMSO solvent signal as the in-built internal reference to normalize the divergence, as confirmed in Figures S9 and S10. Altogether, the overall standard deviation of the parallel samples was reduced by 70%. Note that the peak area of HFE diluent is not discussed herein due to the minimal decomposition during the repeated cycling, as confirmed in preliminary experiments with pouch cells (Figures S11–S13).In virtue of the proper design, the newly developed method can unambiguously obtain multi-information (i.e., the solvent consumption, the anion consumption, the accumulation of inactive Li, and total Li inventory loss) of a single cell without modification of the testing instrument. Based on those, decomposition rates of different electrolyte components, the source of irreversible capacity decay, and the ETN that defines the fate of electrolytes can all be acquired in a “one-stop” fashion.

### Decomposition rate of different electrolyte components and the accumulation of inactive Li^{0}

As stated above, depending on the unique environment of each nucleus, the evolution of solvents and anions is obtained by the cross-calibrated integral area of characteristic signals in

^{1}H and^{19}F spectra, respectively. As shown in Figure 4A, the decomposition of anion molecules, in comparison with solvents, obviously dominates the SEI forming process in the LHCE, which has already been confirmed by both theoretical calculations and experimental characterizations. Beyond the confirmation of known phenomena, the ely-qNMR also enables quantitative analysis of the kinetics of electrolyte decomposition reactions. Interestingly, the consumption of both solvent and salt is found to be linearly correlated to cycle number at the testing condition, which can be rationalized by the fact that the newly exposed anode area is similar in each cycle and thus consumes the same amount of electrolyte per cycle. Supposing that the decomposition kinetics is unchanged during the span of testing, the electrolyte decomposition plot is linearly fitted and extrapolated to the uncycled state. Specifically, the slope of the plot suggests a higher decomposing rate of the anion (0.14 μmol per cycle) than that of the solvent (0.09 μmol per cycle). Apart from the consumption rate, the nonzero intercept of anion decomposition (∼2.08 μmol) also hints that at the first cycle, an extra amount of SEI is formed mostly from anion reduction, whereas the solvent (∼0.15 μmol) has almost no contribution.Due to the higher consumption of salts, the relative solvent-to-salt ratio keeps increasing and deviating from the pristine composition as shown in Figure 4B, which also results in the dropping of effective concentration. Based on the decomposition rates of different electrolyte components, the solvent-to-salt ratio ($\mathrm{\alpha}$) at the

where

*i*cycle can be described by the following relationship (Equation 3), of which the simulated curve (the dashed line in Figure 4B) fits well with the experimental data:$\mathrm{\alpha}=\frac{n{\left(\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}\right)}_{0}-r\left(\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}\right)\cdot i}{n{\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)}_{0}-r\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)\cdot i-\text{\Delta}n{\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)}_{0}}$

(Equation 3)

where

*n*(Solvent)_{0}and*n*(Anion)_{0}stand for the initial amount of electrolyte components, $\text{\Delta}$*n*(Anion)_{0}stands for the extra decomposition at the first cycle, and*r*(Solvent) and*r*(Anion) stand for the consumption rate of electrolyte components. According to previous studies, the solvent-to-salt molar ratio dictates the solvation structure and thus the battery performance. Typically, the solvation structure with anions, namely contact ion pair (CIP) and aggregate (AGG), will only prevail when solvent-to-anion molar ratio is lower than 3 in the DMC-based LHCEs. A fixed and low solvent-to-anion molar ratio (less than 3) is highly expected to maintain the stable performance of batteries. However, due to the unbalanced consumption rates, the solvation structure, as well as the battery performance, will gradually change along with the evolution of solvent-to-anion molar ratio upon long-term cycling, which may serve as an important indicator for SOH prediction.To further unveil the trend and influence of electrolyte evolution, the Equation 3 is rearranged as follows:

where ${\alpha}_{0}$ stands for the initial solvent-to-salt ratio, and

$\begin{array}{cc}\frac{\alpha}{{\alpha}_{0}}& =\frac{1}{{\alpha}_{0}}\cdot \frac{{\alpha}_{0}\cdot n{\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)}_{0}-\beta \cdot r\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)\cdot i}{n{\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)}_{0}-r\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)\cdot i-\text{\Delta}n{\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)}_{0}}\\ & =\frac{\beta}{{\alpha}_{0}}\cdot \frac{\frac{{\alpha}_{0}}{\beta}\cdot n{\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)}_{0}-r\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)\cdot i}{n{\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)}_{0}-r\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)\cdot i-\text{\Delta}n{\left(\mathrm{A}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\right)}_{0}}\end{array}$

(Equation 4)

where ${\alpha}_{0}$ stands for the initial solvent-to-salt ratio, and

*β*stands for the relative consumption rate of solvent to salt. Based on Equation 4, the relative deviation from the initial solvent-to-salt ratio can be expressed as a function of $\beta /{\alpha}_{0}$. Intriguingly, the simulated trends indicate that a $\beta /{\alpha}_{0}$ close to 1 is required to sustain a consistent electrolyte composition for stable performance, as shown in Figure 4C. Accordingly, $\beta /{\alpha}_{0}$ can serve as a guiding parameter that reflects the tolerance to repeated cycling and instructs the rational design for a long-lasting electrolyte.For titration-qNMR, a one-to-one reaction ratio between the acid titrant and the exposed inactive Li is guaranteed by the excessive amount of titrant. As shown in Figure S14, the inactive Li which may offset the titrant changes. The formation of LiH is highly dependent on the electrolyte composition. As has been reported, the LiH formation is negligible in the LiFSI-DMC-based localized HCE system. Therefore, at least in the studied system, the LiH would not affect the conclusion. It is possible that in other LiH-rich electrolyte systems the LiH will be a concern. In this regard, the integral of MA also has almost no changes (0.4%) after 2 h of mixing with LiH (Figures S15 and S16). Therefore, by taking the advantage of the relatively slow reaction rate between MA and those SEI components, the titration-qNMR can somehow selectively reflect the amount of inactive metallic Li

^{0}calculated by the changes of titrant matches well with the results obtained from the TGC method, verifying the feasibility of the titration-qNMR method. To rule out the concern of parasitic reactions between the titrant and SEI components such as lithium hydroxide (LiOH), lithium oxide (Li_{2}O), lithium floride (LiF), and lithium carbonate (Li_{2}CO_{3}), excessive SEI components are mixed with the dissolved titrant in deuterated solvent for 2 h. The negligible changes of the titrant indicate that the above SEI components have minimal influence on the titration-qNMR (<0.1%; Figure S15), which can be attributed to the weak acidity of organic acid and the limited dissociation in non-aprotic DMSO-d6 solvent. In addition to the conventional SEI components, lithium hydride (LiH) has also been observed recently in the anode,^{48}

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^{0}in anode-free batteries, without interference from SEI.With the above assurances, the amount of accumulated inactive Li

^{0}can be assuredly captured by the changes of the titrant, as shown in Figure 4D. The accumulation of inactive Li^{0}also follows the linear relationship to the cycle number, except for the initial cycles (before 10 cycles) that exhibit a large amount of remaining Li^{0}(Figures S17 and S18), which is due to the over-plating during the first cycle. At the same time, by adding an excessive amount of organic acid as the titrant, the inactive Li^{0}can also be reflected by the changes of the titrant. As summarized in Figure 4E, continuous plating/stripping processes wear out the electrolyte and active Li, resulting in the unbalanced consumption of solvents and salts as well as the accumulation of the inactive Li^{0}. Based on the results of ely-qNMR and titration-qNMR, the correlation and contribution of the consumed solvent/anion to the Li inventory loss can thus be decoded.### Acquisition of apparent ETN of the solvent and anion

As stated earlier, the Li inventory loss can be manifested by the battery data from the anode-free configuration (Figures S19 and S20). As shown in Figure 5A, the capacity retention of a typical anode-free cell is plotted, where the commonly used Coulombic efficiency (CE) is converted to the relevant accumulated irreversible capacity. Not surprisingly, the capacity decay is also linearly dependent on the cycle number and the total deposition capacity, which is in line with the qNMR results. On account of the finding that the evolution of electrolyte components is compliant with the trend of capacity decay patterns or vice versa, the knowledge of ETN may open up the possibility for applications such as online SOH monitoring, by judicious combinations of other non-destructive techniques.

Under the testing condition, the capacity fading rate is around 9.4 μAh per deposition capacity in mAh. Thereinto, it is noticed a plateau exists before 10 cycles in Figure 5A, which does not reflect the real capacity fading of the anode but is due to the superfluous Li plated at the first cycle. Given that the reversibility of the anode is consistent over the period, which is confirmed by the consistent CE in Li | Cu cells in Figure S21, the actual Li inventory loss can be uncovered by extrapolating the linear fitted line (the dashed line in the plot). Meanwhile, the extrapolated irreversible capacity line intersects with the axis of the zero cycle at 0.27 mAh. Based on the reported formation mechanism of inactive Li

^{0}, which is believed to form mainly during the discharging process, the Li inventory loss at the intercept can be directly correlated to the electrolyte decomposition. Therefore, the intercept at the zero cycle is ascribed to the extra SEI forming process during the first charging process, which is also reflected by the lower CE during the first cycle in the Li | Cu cells (Figure S14). Combined with the aforementioned extra anion consumption at the first cycle (2.1 μmol in Figure 4A), the ETN for the anion decomposition can be preliminarily calculated by dividing the corresponding irreversible capacity (0.27 mAh) by salt consumption (2.1 μmol) and the Faraday constant (26.8 Ah/mol), which equals to about 4.8 mol_{e}/mol_{anion}.The fluctuations of battery performance (Figure 5B) and the varied testing conditions, such as cycle number and current density, necessitate a statistical analysis of multiple tests to assert whether there is a representative ETN as a universal conclusion. For each qNMR test, the Li inventory loss caused by electrolytes, i.e., the irreversible capacity converted into SEI (irre. capacity ${\left(\mathrm{L}{\mathrm{i}}^{+}\right)}_{i}$), and the corresponding consumption of the solvent and LiFSI, i.e., $\mathrm{\Delta}n{\left(\mathrm{D}\mathrm{M}\mathrm{C}\right)}_{i}$ and $\Delta n{\left(\mathrm{L}\mathrm{i}\mathrm{F}\mathrm{S}\mathrm{I}\right)}_{i}$, are collected as shown in Table S1. By plotting all data points from different testing conditions in the same plot, an obvious trend is observed as shown in Figure 5C. Given that there are two explanatory variables, namely the decomposition of solvents and salts, a multiple regression fitting is conducted to provide a statistically credible result of ETN by the following equation:

${\left(\begin{array}{ll}\begin{array}{l}\Delta n{\left(\mathrm{D}\mathrm{M}\mathrm{C}\right)}_{1}\\ \Delta n{\left(\mathrm{D}\mathrm{M}\mathrm{C}\right)}_{2}\\ \dots \end{array}& \begin{array}{l}\Delta n{\left(\mathrm{L}\mathrm{i}\mathrm{F}\mathrm{S}\mathrm{I}\right)}_{1}\\ \Delta n{\left(\mathrm{L}\mathrm{i}\mathrm{F}\mathrm{S}\mathrm{I}\right)}_{2}\\ \dots \end{array}\\ \Delta n{\left(\mathrm{D}\mathrm{M}\mathrm{C}\right)}_{\mathrm{n}}& \Delta n{\left(\mathrm{L}\mathrm{i}\mathrm{F}\mathrm{S}\mathrm{I}\right)}_{\mathrm{n}}\end{array}\right)}^{}\left(\begin{array}{l}{z}_{\mathrm{D}\mathrm{M}\mathrm{C}}\\ {z}_{\mathrm{L}\mathrm{i}\mathrm{F}\mathrm{S}\mathrm{I}}\end{array}\right)=\left(\begin{array}{l}\mathrm{I}\mathrm{r}\mathrm{r}\mathrm{e}.\phantom{\rule{0.5em}{0ex}}\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}{\left(\mathrm{L}{\mathrm{i}}^{+}\right)}_{1}\\ \mathrm{I}\mathrm{r}\mathrm{r}\mathrm{e}.\phantom{\rule{0.5em}{0ex}}\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}{\left(\mathrm{L}{\mathrm{i}}^{+}\right)}_{2}\\ \dots \\ \mathrm{I}\mathrm{r}\mathrm{r}\mathrm{e}.\phantom{\rule{0.5em}{0ex}}\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}{\left(\mathrm{L}{\mathrm{i}}^{+}\right)}_{\mathrm{n}}\end{array}\right)$

Along with the preliminarily estimated ETN of the anion (

*z*_{LiFSI}$\phantom{\rule{0.25em}{0ex}}\approx \phantom{\rule{0.25em}{0ex}}$4.8 mol_{e−}/ mol_{anion}), the fitted ETN by binary regression analysis is approximated to be 1.0 (*z*_{DMC}) and 5.1 (*z*_{LiFSI}) for the solvent and anion, respectively, with a coefficient of determination around 95% (detailed procedure can be found in the experimental procedures section):$\mathrm{Irre}.\phantom{\rule{0.25em}{0ex}}\mathrm{capacity}{\left({\mathrm{Li}}^{+}\right)}_{i}=\{\begin{array}{l}1.0\phantom{\rule{0.25em}{0ex}}\times \phantom{\rule{0.25em}{0ex}}F\phantom{\rule{0.25em}{0ex}}\times \phantom{\rule{0.25em}{0ex}}\mathrm{\Delta}n{\left(\mathrm{DMC}\right)}_{i}\\ 5.1\phantom{\rule{0.25em}{0ex}}\times \phantom{\rule{0.25em}{0ex}}F\phantom{\rule{0.25em}{0ex}}\times \phantom{\rule{0.25em}{0ex}}\mathrm{\Delta}n{\left(\mathrm{LiFSI}\right)}_{i}\end{array}$

This experimental evidence, for the first time, provides a clue for quantitively understanding the electrolyte decomposition process as well as its correlation to SEI formation. When considering a total of N possible decomposing reaction pathways for solvent/anion molecules, which possess different ETNs ( as for DMC, it may have 1 or 2 electron transfer per molecule based on the observation of products. Taking both the acquired ETN and the previous literature into consideration, the predominant SEI forming mechanism can be inferred as follows:

*z*_{i}) and consume a certain amount of solvent/anion molecules (*n*_{i}) during each cycle, the $\mathrm{apparent}\phantom{\rule{0.25em}{0ex}}\mathrm{ETN}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}\sum \left({z}_{i}{n}_{i}\right)/\sum {n}_{i}$, reflecting the averaged results of all the possible reaction pathways in a given time. For LiFSI, the possible decomposition reaction pathway involves either 4 electrons or up to 16 electrons;^{27}

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$4{\mathrm{Li}}^{+}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}4{e}^{-}\phantom{\rule{0.25em}{0ex}}+{\left({\mathrm{FSO}}_{2}\right)}_{2}{\mathrm{N}}^{-}\phantom{\rule{0.25em}{0ex}}\to \phantom{\rule{0.25em}{0ex}}2\mathrm{LiF}\phantom{\rule{0.25em}{0ex}}+{\left({\mathrm{LiSO}}_{2}\right)}_{2}{\mathrm{N}}^{-}$

(Equation 5)

$4{\mathrm{Li}}^{+}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}4{e}^{-}\phantom{\rule{0.25em}{0ex}}+{\left({\mathrm{FSO}}_{2}\right)}_{2}{\mathrm{N}}^{-}\phantom{\rule{0.25em}{0ex}}\to \phantom{\rule{0.25em}{0ex}}\mathrm{LiF}\phantom{\rule{0.25em}{0ex}}+{\mathrm{Li}}_{2}\mathrm{O}+{\mathrm{LiSO}}_{2}\mathrm{F}+\phantom{\rule{0.25em}{0ex}}{\mathrm{NSO}}^{-}$

(Equation 6)

$2{\mathrm{Li}}^{+}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}2{e}^{-}+\phantom{\rule{0.25em}{0ex}}2{\mathrm{CH}}_{3}{\mathrm{OCO}}_{2}{\mathrm{CH}}_{3}\phantom{\rule{0.25em}{0ex}}\to \phantom{\rule{0.25em}{0ex}}2{\mathrm{CH}}_{3}{\mathrm{OCO}}_{2}\mathrm{Li}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}{\mathrm{CH}}_{3}{\mathrm{CH}}_{3}$

(Equation 7)

Statistically, the apparent ETN of anion indicates that anions are inclined to undergo mostly 4 electron reactions that generate LiF and Li does not affect the conclusion and the validity of the method since the variables here are reactant changes instead of the solid and gaseous products. It is also worth noting that the fitting also accords well with the results at other C-rates, which indicates that the ETN of DMC and LiFSI is independent and non-interfering to one another. Besides, the electrolyte samples without HFE are also investigated and included in the study to further demonstrate that HFE does not affect the validity of the finding, as shown in Table S1. This finding supports the

_{2}O (like Equations 5 and 6), whereas the other reaction pathways with 8–16 electron transfer that generate other fragments like Li_{3}N or Li_{2}S take place less frequently. As for the solvent, the apparent ETN of DMC decomposition suggests the inclination to the one-electron reaction mechanism that generates lithium alkyl carbonate (CH_{3}OCO_{2}Li) and ethane (Equation 7). The gas generation, which has been reported as a common issue in lithium batteries,^{51}

*a priori*knowledge that the decomposition products of DMC and LiFSI have no interaction or inter-reaction between each other.Bridging by the apparent ETN, the contribution of individual electrolyte components to the Li inventory loss can be properly assigned in Figure 5D. Although anion-derived SEI is in favor of high reversibility of Li plating/stripping, the consumption rate of anion is larger than that of solvents at the same time, which changes the pristine solvation structure of electrolytes. The contradiction implies that there is still room to improve battery performance by rationally devising electrolytes to reduce the ETN of anion and hence generate SEI with a minimum consumption content of anions. Combining the decomposition kinetics and the ETN, the trend of the irreversible capacity loss at different SOHs can thus be analyzed, which suggests that the overall CE can be improved from 99.0% to 99.5% by simply suppressing the decomposition of anions at the first cycle and reducing the ETN of anion from 5.1 to 2.1. However, a further improvement of CE to above 99.9% not only requires the ETN of anions to approach 1 but also demands a halved consumption rate of anions and a minimum formation of inactive Li

^{0}. In addition to anions, solvents also contribute significantly to the Li inventory loss even at such a low solvent-to-salt ratio when the solvent-to-salt ratio increases during cycles. Altogether, a perfect electrolyte is supposed to have an intrinsic low ETN, a low consumption rate, and a balanced kinetic-component configuration (*β*/*α*_{0}).Therefore, combining the electrolyte changes and correlative capacity loss in an anode-free configuration, the apparent ETN of electrolyte decomposition reactions on Li metal anode is calculated via statistical regression analysis. Not only the contribution of individual electrolyte components to the Li inventory loss can be assigned and predicted but also the kinetics of electrolyte decomposition can be inversely deduced by reversing the calculation process with the knowledge of ETN, which paves the way for the prediction of the aforementioned failure. Last but not the least, the apparent ETN also opens up a new dimension for evaluating the potential of electrolytes and distinguishing the related contribution to SEI formation at different SOHs. For instance, calendar aging has recently been identified as the main origin of substantial SEI formation and lithium inventory loss when the battery is stored at high state of charge (SOC) and high temperature. Through proper experiment design, such as increasing the aging duration or the number of aging, our approach can be applied to the calendar aging scenario by comparing the aged condition and non-aged conditions.

## Discussion

Apparent ETN to quantitatively describe the decomposition mechanism of electrolyte components was acquired by a simple but delicate qNMR method, which gauges the electrolyte evolution and accumulated inactive Li

^{0}simultaneously in a “one-stop” fashion. Through proper pre-treatments, i.e., relaxation-enhancement, acid titration, and cross-calibration, the decomposition rates of different electrolyte components were also rigorously quantified. The discrepancy in decomposing rates of anions (0.14 μmol per cycle) and solvents (0.09 μmol per cycle) leads to the descending concentration during long-term cycling, which will profoundly alter the solvation structure as well as the composition and thus lead to the unstable anode/electrolyte interface and eventually battery failure. Except for the new failure mechanism, the fully described electrolyte decomposition reaction by ETN (1.0 for DMC and 5.1 for LiFSI) and the decomposition kinetics afford a new perspective to evaluate electrolyte and even forecast battery lifetime. The finding that the anion account for a major part of irreversible capacity also suggests the potential advantage of an anion with an inherent low ETN. Given that the universality of the methodology is not limited by the type of electrolyte, it is expected that the concept of ETN can also be applied to other types of anodes (graphite and silicon-based anodes) and other electrolyte components (co-solvents, functional additives, and diluents), serving as a quantitative descriptor to disclose the electrolyte decomposition mechanism and directly link up electrolyte with the battery performance. Therefore, the method established herein can not only shed light on the quantitative understanding of electrolyte decomposition reactions and irreversible Li inventory loss but may also refresh the recognition in the functionality of electrolyte components. Since the method is easy to be implemented into other batteries as a standard inspection method, it is also hoped that the scientific insights obtained in this work can inspire the rational electrolyte evaluation of other types of rechargeable batteries.## Experimental procedures

### Resource availability

#### Lead contact

Further information and requests for resources should be directed to and will be fulfilled by the lead contact, professor Qiang Zhang ( zhang-qiang@mails.tsinghua.edu.cn ).

#### Materials availability

This study did not generate new unique reagents.

### Materials

DMSO-d6 (99.9%, with 0.03% tetramethylsilane), LiH (99%), Li

_{2}CO_{3}(99.5%), and Li_{2}O (99.99%) were purchased from Anhui Zesheng Technology. LiF (>99.5%) and LiOH (99.99%) were purchased from Beijing InnoChem Science & Technology. MA (≥99%), DCBF (≥98%), and Cr(acac)_{3}(≥97%) were purchased from Adamas Reagent. Battery-grade LiFSI (99.9%), DMC (99.9%), and HFE (99.9%) were purchased from Suzhou Duoduo Chemical Technology. All the solvents and Li salts were used as received.LiNi

_{0.5}Co_{0.2}Mn_{0.3}O_{2}(NCM523) cathode (punched into disks with a diameter of 13 mm) with an area capacity of ∼2.7 mAh cm^{−2}(measured value) was acquired from Guangdong Canrd New Energy Technology. The ratio of active material, conductive additive, and binder is 96:2:2. Polyethylene (PE) separator (punched into 19 mm disks) was purchased from Asahi Kasei Technosystem. Copper foil (punched into 16 mm disks, 9 μm in thickness) was purchased from Hefei Kejing Materials Technology. All materials were kept and used in an Ar-filled glove box with oxygen and water contents below 0.1 ppm.### Sample preparation for qNMR measurements

LHCE was prepared by mixing LiFSI, DMC, and HFE with a molar ratio of 1.0:1.5:2.0. The diluent used to extract electrolytes for NMR measurements was prepared by adding 0.5 mM relaxation enhancer (Cr(acac)

_{3}) and 100 mM titrant (MA) in DMSO-d6. All the coin cells (2025-type) were assembled in an Ar-filled glove box. The Cu | NCM anode-free coin cells were assembled and added with a controlled amount of electrolytes (20 μL). The Cu | NCM anode-free pouch cells (7 × 4 cm^{2}) were fabricated with one piece of double-side-coated cathode and two Cu foil in a dry room at a dew point of −60°C with the addition of 0.5 mL electrolytes. The cells were cycled galvanostatically using a Neware battery tester (CT-4008t, Shenzhen, China) within a voltage range of 2.8–4.3 V at 25°C. After cycling, the coin cell was then disassembled in an Ar-filled glove box. All the parts of the disassembled cell were quickly transferred into a centrifugal tube containing 2 mL of diluent. After the inactive Li metal was all reacted by the titrant (∼5 min), the centrifugal tube was shaken for 5 min and then rested for 2 h to mix thoroughly and evenly. As for pouch cells, 2 mL of the diluent was injected into the pouch cell and then kneaded for 5 min. Then, 0.6 mL of the extract was transferred into an NMR tube containing 20 μL internal reference (DCBF) for NMR measurements.### Details for qNMR measurements

Considering the solubility and the volatility, DMSO-d6 and DCBF were selected as the solvent and internal reference, respectively. By measuring the T1 of the slowest relaxing signal (0.85 s), the relaxation delay (d1) should be larger than 4.25 s to ensure full relaxation between the pulses. To guarantee accuracy,

^{1}H-NMR and^{19}F-NMR spectra were acquired using a 90° pulse angle with a d1 of 15 s on a JNM-ECZ400S spectrometer. The scan range was set to be 120% of the interested signal range with the transmitter offset at the center of signals. The scan number was 8, which was able to obtain a signal-to-noise ratio at least above 800 for each signal (>2,000 for DCBF and DMC peaks in^{1}H-NMR and >800 for DCBF and LiFSI in^{19}F-NMR). At least 3 samples were used for each batch. Since the most of resonances are well separated as shown in Figures S1 and S2, the area extraction and integration were done by using the automatic peak selection and integration method provided in JEOL Delta software, with the same integration width for each signal. Special notice is that sometimes the peaks of HFE may interfere with the baseline in MA integration, which requires further peak fitting using the Voigt function.### Details for qNMR calculations

The integration of each signal was normalized by the integral of the internal reference (DCBF). As mentioned in the main text, the relative ratio of salt versus DMC can be directly calculated by the normalized ratio without other post-processing. Although the amount of electrolyte added ($n{\left(Z\right)}_{add}$) is known, there is supposed to exist inevitable electrolyte loss during cell assembly and disassembly. The actual $n{\left(Z\right)}_{0}$ can be calculated based on the known amount of DCBF and the actual ratio of electrolyte to DCBF:

where the density ${\mathrm{\rho}}_{\mathrm{DCBF}}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}1.48\phantom{\rule{0.25em}{0ex}}\mathrm{g}\phantom{\rule{0.25em}{0ex}}{\mathrm{mL}}^{-1}$, volume of electrolyte ${V}_{\mathrm{DCBF}}\phantom{\rule{0.25em}{0ex}}$= 0.02 mL, molecular weight MW

$n{\left(\mathrm{Z}\right)}_{0}=a{\left(\mathrm{Z}\right)}_{0}/a{\left(\mathrm{DCBF}\right)}_{0}\times \left(\frac{{\text{\rho}}_{\text{DCBF}}\times {\text{V}}_{\text{DCBF}}}{{\text{MW}}_{\text{DCBF}}}\right)$

where the density ${\mathrm{\rho}}_{\mathrm{DCBF}}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}1.48\phantom{\rule{0.25em}{0ex}}\mathrm{g}\phantom{\rule{0.25em}{0ex}}{\mathrm{mL}}^{-1}$, volume of electrolyte ${V}_{\mathrm{DCBF}}\phantom{\rule{0.25em}{0ex}}$= 0.02 mL, molecular weight MW

_{DCBF}= 215 g ${\mathrm{mol}}^{-1}$. Whereas for the absolute value, the data should be firstly calibrated by the in-built calibrant (residual^{1}H signal of DMSO-d6) to avoid the error caused by the weighing, considering that the residual solvent ratio is a constant in the same batch of solvent. Specifically, all the peaks were calibrated by the correction factor $\text{\gamma}=\frac{a{\left(\mathrm{DMSO}\right)}_{i}/a{\left(\mathrm{DCBF}\right)}_{i}}{a{\left(\mathrm{DMSO}\right)}_{0}/a{\left(\mathrm{DCBF}\right)}_{0}}$, based on the ratio of DMSO/DCBF in an untested zero cycle cell as the standard (the detailed deduction can be found in supplemental information under Figure S10). Therefore, the effective molar quantities of the Z species were calculated as follows:$n{\left(\mathrm{Z}\right)}_{i}=a{\left(\mathrm{Z}\right)}_{i}/a{\left(\mathrm{DCBF}\right)}_{i}\times \frac{{\text{\rho}}_{\text{DCBF}}\times {\text{V}}_{\text{DCBF}}}{{\text{MW}}_{\text{DCBF}}}/\text{\gamma}$

### ETN multiple linear regression procedure

The multiple linear regression is performed by inputting the consumption of solvent, the consumption of anion, and the irreversible capacity from electrolyte decomposition (as shown in Table S1) into the MATLAB curve fitting tool as X, Y, and Z data. A custom equation Z = (z

_{1}X + z_{2}Y)/F, where the Faraday constant F = 26.8 mAh/mol, was adopted to fit the plot, using the default least-squares algorithm without other restrains.## Data and code availability

- •This paper does not report original code.
- •All data reported in this paper will be shared by the lead contact upon request.

## Acknowledgments

This work was supported by the National Key R&D Program of China ( 2021YFB2500300 and 2021YFB2400300 ), National Natural Science Foundation of China ( 22108149 ), China Postdoctoral Science Foundation ( 2021M691755 and 2021M700404 ), Tsinghua University Initiative Scientific Research Program , and Beijing Institute of Technology Research Fund Program for Young Scholars . Figure 3A was partly generated using Wikimedia Commons, provided by Database Center for Life Science, licensed under a Creative Commons Attribution 3.0 unported license.

### Author contributions

Q.Z., M.-Y.Z., and X.-Q.Z. conceived and designed the experiments. M.-Y.Z. assembled the coin cells, and M.-Y.Z. and P.S. assembled the pouch cells. M.-Y.Z., L.-P.H., and X.-Q.Z. performed the electrochemical tests. M.-Y.Z., J.X., and X.-Q.D. performed NMR measurements. M.-Y.Z. and J.-F.D. conducted the TGC measurements. Q.Z. supervised the whole project. All authors participated in data analyses and discussions. M.-Y.Z., X.-Q.Z., B.-Q.L., J.-Q.H., and Q.Z. co-wrote the manuscript with input from all authors.

### Declaration of interests

A patent application has been submitted based on the methodology reported herein.

## Supplemental information

- Document S1. Figures S1–S21, Table S1, and Note S1

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## Article Info

### Publication History

Published: August 4, 2022

Accepted:
July 8,
2022

Received in revised form:
April 15,
2022

Received:
March 8,
2022

### Identification

### Copyright

© 2022 Elsevier Inc.