Coupled In Situ NMR and EPR Studies Reveal the Electron Transfer Rate and Electrolyte Decomposition in Redox Flow Batteries

We report the development of in situ (online) EPR and coupled EPR/NMR methods to study redox flow batteries, which are applied here to investigate the redox-active electrolyte, 2,6-dihydroxyanthraquinone (DHAQ). The radical anion, DHAQ3–•, formed as a reaction intermediate during the reduction of DHAQ2–, was detected and its concentration quantified during electrochemical cycling. The fraction of the radical anions was found to be concentration-dependent, the fraction decreasing as the total concentration of DHAQ increases, which we interpret in terms of a competing dimer formation mechanism. Coupling the two techniques—EPR and NMR—enables the rate constant for the electron transfer between DHAQ3–• and DHAQ4– anions to be determined. We quantify the concentration changes of DHAQ during the “high-voltage” hold by NMR spectroscopy and correlate it quantitatively to the capacity fade of the battery. The decomposition products, 2,6-dihydroxyanthrone and 2,6-dihydroxyanthranol, were identified during this hold; they were shown to undergo subsequent irreversible electrochemical oxidation reaction at 0.7 V, so that they no longer participate in the subsequent electrochemistry of the battery when operated in the standard voltage window of the cell. The decomposition reaction rate was found to be concentration-dependent, with a faster rate being observed at higher concentrations. Taking advantage of the inherent flow properties of the system, this work demonstrates the possibility of multi-modal in situ (online) characterizations of redox flow batteries, the characterization techniques being applicable to a range of electrochemical flow systems.


INTRODUCTION
Redox flow batteries are a promising large-scale energy storage technology. The catholyte and anolyte are stored in two separate tanks and, when required, flow through a connected electrochemical cell where they undergo redox reactions, either storing or releasing charge. This allows energy storage and power generation to be decoupled. Organic redox-active molecules have emerged in recent years as promising electrolyte molecules for flow battery applications. 1−3 Since these molecules are comprised of earth-abundant elements, a high sustainability and low cost are expected. 4,5 However, for deep market penetration of these types of flow battery systems, the bottlenecks are the relatively low energy densities and short lifetimes when compared to those of other battery systems. 6 Therefore, understanding the reaction mechanisms involved is vital for further improvement of both the energy density and lifetime.
In a previous study, taking advantage of the inherent flow properties of a redox flow battery, we demonstrated two in situ NMR techniques to study these systems: online and operando NMR. In the online experiment, one of the electrolyte solutions is flowed through the NMR probe to study either the catholyte or anolyte while the cell is situated outside of the detection region. In contrast, the operando experiment consists of positioning a miniaturized cell within the detection region of the NMR probe to facilitate simultaneous study of both the catholyte and anolyte. By analyzing the bulk magnetic susceptibility shifts of the electrolyte peaks, we quantified the concentrations of radicals present during cycling and showed that the electrochemical reaction of 2,6-dihydroxyanthraquinone (DHAQ) proceeds through two single-electron transfers (DHAQ 2− → DHAQ 3−• and DHAQ 3−• → DHAQ 4− ), accompanied by intermolecular electron transfer between the anions themselves. The radical (i.e., semiquinone, DHAQ 3−• ) concentration was shown to be set by the comproportionation reaction: This equilibrium also dictates the difference in couples between the two one-electron-transfer reactions, allowing this difference to be estimated from a determination of the DHAQ 3−• concentration. Finally, we demonstrated that one of the electrolyte degradation reactions is electrochemical in nature. 7 The property of flow within these battery systems allows for simple implementation of multi-modal characterization. Here we move beyond our previous work and utilize this concept to couple EPR and NMR measurements. EPR spectroscopy has been applied to study in situ free radicals generated electrochemically since 1959. 8−12 Simultaneous electrochemical−EPR measurements allow not only for the identification of reaction intermediates and products but also for the elucidation of the reaction mechanism and kinetics. Note that in situ EPR studies of an operating flow battery have not been previously demonstrated, although EPR has previously been used to study the crossover of vanadyl ions. 13 Here, we report the coupled use of online EPR and NMR techniques to study anthraquinone-based flow batteries. They represent one of the most promising families of organic molecules for flow battery applications, offering fast electron transfer and excellent stability. 14−17 Two anthraquinone molecules, DHAQ and 4,4′-((9,10-anthraquinone-2,6-diyl)dioxy)dibutyrate (DBEAQ), are studied. We directly detect and quantify the anthraquinone radical species, reveal the electronic structures of the radicals, and determine the rate constant for the electron transfer between the singly and doubly reduced DHAQ anionsa parameter that we were unable to determine in the NMR studies. 7 The radical concentration is found to correlate with the overall DHAQ concentration (10, 100, and 200 mM), which we interpret in terms of a competing dimer formation mechanism. These overall concentrations are relevant for flow battery applications, where concentrations ranging from 0.01 to 3 M are generally used. 6 Finally, the coupled NMR spectroscopy allows for the decomposition of DHAQ to be followed and for the degradation to be quantitatively correlated to the capacity fade of the flow battery.

RESULTS AND DISCUSSION
A lab-scale flow battery was positioned outside the EPR and NMR magnets. Aqueous solutions of anthraquinone and potassium hexacyanoferrate(II and III) were used as the anolyte and catholyte, respectively. The evolution of anthraquinone was followed by EPR and NMR spectroscopies. The electrolyte solution was pumped from the reservoir to the electrodes, then through a flow EPR tube and an NMR tube, and back to the electrolyte reservoir (see Figure S1 for the setup). The round-trip time was 64 s. The residence time in the EPR detection region was 0.13 s, which is much longer than the electron spin−lattice relaxation time that is typically on the timescale of microseconds for semiquinones. 18 Two different concentrations of DHAQ were studied in fullcell batteries, namely 10 and 100 mM, with coupled in situ NMR and EPR experiments being performed for both concentrations. Since a large amount of data was generated from these in situ experiments, Figure 1 serves as a guideline to relate the data analyses presented in the following figures to the voltage profiles of the batteries.
Coupled In Situ NMR and EPR Experiments. Figure 2 presents the in situ 1 H NMR and EPR spectra of 10 mM DHAQ as a function of electrochemical cycling. On charging (reduction of DHAQ 2− anions) at 10 mA, the voltage of the battery increases from 1.15 V to a cutoff voltage of 1.6 V. In the NMR spectra, the proton signals A (defined in Figure 2a) have disappeared by the time the third spectrum has been acquired (i.e., between 192 and 288 s) after turning on the charging current and when 4% of DHAQ 3−• radical anions have formed. Signal B is significantly broadened and only just visible above the baseline under the conditions used here; this is in contrast to our prior work where this signal was resolved more clearly throughout the cycling, 7 which is ascribed to the lower concentration of DHAQ used in the present study. The loss of signals A (and B) is due to electron delocalization over the semiquinone DHAQ 3−• radical anion and the intermolecular electron transfer between the DHAQ 2− anion and the DHAQ 3−• . Note that signal C is barely observable due to a H-D exchange reaction with the solvent D 2 O molecule during prior electrochemical cycling.
In the EPR spectra, an EPR resonance centered at 337.78 mT develops (corresponding to a g-factor of 2.0046), which coincides with the disappearance of NMR signals A and B. This signal is assigned to the DHAQ 3−• radical anion. As charging continues, the EPR signal increases in intensity and broadens, reaching a maximum breadth and intensity at 50% state-of-charge (SOC), whereafter it decreases in intensity and sharpens. The broadening of signals is caused by Heisenberg spin exchange, i.e., the "flip-flop", dipolar-driven (zeroquantum) spin-exchange between two unpaired electrons  6 ] full cell as a function of time. During charge, a constant current of 10 mA was applied, followed by a voltage hold at 1.6 V. During discharge, a constant current of −10 mA (where the sign indicates the polarity of the electrodes) was applied, followed by a potential hold at 0.6 V. The charge−discharge cycles were repeated four times, then potential holds of 10 h each were applied at 1.6 and 1.7 V. (b) Voltage of a 100 mM DHAQ versus 150 mM K 4 [Fe(CN) 6 ] and 50 mM K 3 [Fe(CN) 6 ] full cell. During charge, a constant current of 150 mA was applied to a cutoff voltage of 1.7 V. During discharge, a constant current of −150 mA was applied to a cutoff voltage of 0.6 V. The 7th charge was followed by a voltage hold at 1.7 V for 20 h and another 20 charge/ discharge cycles. when they come into close proximity, and the intermolecular electron transfer. 19,20 As the voltage reaches 1.6 V, the EPR signal is still observable, but it continues to drop in intensity, reaching its minimum, and the voltage is held; this is accompanied by the appearance of the NMR signals of A″ and B″ from the doubly reduced DHAQ 4− . Note that a second voltage plateau is observed at 1.5 V. This plateau appears only after a voltage hold at 1.6 V for 2 h, and it was previously observed after a more prolonged voltage hold (see Extended Data Figure 8e in ref 7). Since there are no noticeable changes in the NMR and EPR signals that are observed, this voltage plateau is likely to be caused by ferrocyanide decomposition or water oxidation at the catholyte side. The study of the catholyte is outside the scope of the current study but certainly warrants future investigation. During discharge, reversible changes in the NMR and EPR spectra were observed. When the voltage decreases to and is held at 0.6 V, the EPR signal of DHAQ 3−• drops to below the detectable level (10 nM for the Magnettech benchtop spectrometer or 9 × 10 8 spins/G at a S/ N ratio of 3), in contrast to the detectable amount of residual DHAQ 3−• that remains throughout the high-voltage hold. This is due to the continual chemical oxidation of DHAQ 4− , as discussed in our previous study, 7 where the oxidant may be either trace amounts of oxygen gas that have permeated into the battery system or the solvent water itself. 7 The charge− discharge cycle was repeated five times, followed by longer potential holds of 10 h at 1.6 V and then 1.7 V ( Figure S2).
Determining the Radical Anion Concentration. The concentration of radical anions can be readily estimated by measuring the changes in the bulk magnetization from the solvent water resonance in the NMR spectra ( Figure S2, eq 7), 7 and with EPR, it can very simply be estimated by spin counting. In the latter method, the radical concentration is proportional to the double integral of the EPR signal, so the DHAQ 3−• radical anion concentration can be readily determined by calibrating the signal integral to that of a sample with a known concentration. We used 4-OH-TEMPO dissolved in water as the reference (see Figure S3 for the EPR spectra; the method of spin counting is described in detail in the SI). The concentration of DHAQ 3−• radical anions as a function of electrochemical cycling, estimated by both the NMR (b) and EPR (c) methods, is shown in Figure 3, with good consistency being seen between the two approaches. During charge, the concentration of DHAQ 3−• radical anions increases from 0 to 7 mM and then decreases to 0.2 mM. The changes are reversible during discharge. Larger fluctuations can be seen in the concentrations estimated by NMR than by EPR. This is due to errors from the phase and linewidth of the NMR signals, where a FWHM of 11 Hz corresponds to an error of ±3 mM. However, the similar numbers determined by the two methods for both 10 and 100 mM concentrations ( Figure 3d) help validate the previous NMR approach and our assumption that the effect of changes in pH and in water−quinone−salt interactions during cycling can be ignored when analyzing the bulk magnetic susceptibility shifts in the water resonance. 7 The concentrations of radical anions were measured for three total concentrations of DHAQ, as shown in Figure 3d, the maximum DHAQ 3−• fractional concentrations decreasing noticeably from 0.74 to 0.51 and 0.40 for the 10, 100, and 200 mM DHAQ solutions, respectively. The point at which the maximum value is observed shifts slightly toward higher SOCs: from 50.9, 56.1, and 59.6% SOC for 10, 100, and 200 mM DHAQ, respectively, where the SOC is defined by the oxidation state of DHAQ; i.e., 0% DHAQ 4− anions corresponds to 0% SOC and 100% DHAQ 4− corresponds to 100% SOC. This effect suggests that, besides the comproportionation reaction (eq 1) proposed in previous work, 7,15 additional reaction equilibria exist, which result in lower AQ 3−• fractional concentrations at higher concentrations. The strongest candidates for this are the dimerization equilibria,

d1
(2) ( 3) which have been shown to be important in quinone-based systems. 21−26 This overall concentration effect on the maximal radical concentration of quinones was studied as early as the 1930s. 27 As the EPR spectra are consistent with a single EPRactive spin system, the dimer does not appear to be paramagnetici.e., it does not consist of two weakly coupled (but still paramagnetic) spin S = 1 / 2 AQ 3−• monomers. Thus, the orientation and distance between two AQ 3−• monomers must be such that a stronger coupling between the two unpaired electrons results, leading to a total spin of S = 0, i.e., a dimer that is EPR inactive. Indeed, the early study reported an overall decrease in the magnetic susceptibility of a solution with concentration as a result of dimerization. 27 Overall, this suggests that reaction (2) is the predominant dimerization mechanism probed here: if dimers are formed via reaction (3), we might expect increased overall concentration to increase the dimer concentration and either to have little effect on radical concentration or, if reaction (2) also operates, to decrease radical concentration.
The implication of the dimerization for our study is that the apparent comproportionation reaction (eq 1) equilibrium constanti.e., that determined by measuring the radical concentrationnow depends on the initial AQ 2− concentration. (Note that the inherent equilibrium constant defined by eq 1 is independent of the initial AQ 2− concentration.) Thus, the calculated (apparent) voltage separation between the two one-electron couples will also depend on the initial concentration. However, as the AQ 2− concentration tends to zero, the influence of the dimerization tends to zero, and the calculated voltage separation tends to its true (inherent) value. In our previous work, 7 a voltage separation of 33 mV for the two one-electron couples was determined for a 100 mM DHAQ concentration (Table S1). It drops to 3.7 mV for the 200 mM solution, the marked asymmetry in the radical concentration with state of charge seen in Figure 3d also suggesting a second competing reaction associated with different kinetics. For the 10 mM DHAQ system reported here, the apparent voltage separation for the two one-electron couples has now increased (as expected) to 76 mV, which is close to the value of 60 mV reported for a low-concentration (5 mM) solution of DHAQ by simulating the cyclic voltammetry. 15 Further details of this calculation can be found in the SI, together with calculations performed to explore the effect of dimerization on the apparent voltage profiles. The calculations indicate that the extracted voltage separation at a 10 mM concentration is close to the limiting voltage separation (i.e., the voltage separation of the extrapolated to zero concentration) of approximately 79 mV. Further measurements and modeling are in progress to explore these coupled equilibria in more detail. However, we note that, while more measurements at much lower concentrations may provide further insight, side reactions involving oxidation of the DHAQ 4− anion further complicate the analysis.
Measuring the Rate Constant of Electron Transfer between DHAQ 3−• and DHAQ 4− Anions. In our previous study, we estimated the rate constant of intermolecular electron transfer between DHAQ 2− and DHAQ 3−• radical anions by measuring the line-broadening of NMR resonances A and C (see Figure 2a for species/resonances A and C), where the radical concentration was estimated from the charging current. However, we were unable to determine the rate constant for the electron transfer between DHAQ 3−• and DHAQ 4− anions (Figure 4a) due to the lack of a reliable estimation of the radical concentration at high voltages, where the decomposition reactions and chemical oxidation of DHAQ 4− occur. Now, with the incorporation of a more sensitive EPR technique, the radical concentration at high voltages can be readily estimated by spin counting, even in the presence of these side reactions, and thus the rate constant of intermolecular electron transfer between the DHAQ 3−• radical anion and the DHAQ 4− anion can be determined unambiguously.
In the slow exchange regime, 7 when the transverse relaxation rate of the paramagnetic species, R 2P , is much faster than the exchange rate, τ P −1 , i.e., R 2P ≫ τ P −1 , the transverse relaxation rate of the diamagnetic species, R 2ex , arising from the chemical exchange with the paramagnetic species, is given by where k ex is the bimolecular rate constant (or the electrontransfer rate constant) and [P] is the concentration of the paramagnetic species, i.e., the concentration of DHAQ 3−• radical anions. The exchange rate is related to the rate constant by where [D] is the concentration of the diamagnetic species, i.e., the concentration of DHAQ 2− and DHAQ 4− anions. The Journal of the American Chemical Society pubs.acs.org/JACS Article electron transfer was previously shown to be in the slowexchange regime for resonances A and C of the DHAQ 2− anion in a solution of 100 mM DHAQ. 7 Here the concentration of DHAQ was 10 mM, so following eq 5, the exchange rate τ P −1 is 10 times smaller than that at 100 mM, meaning that the slow-exchange regime is more easily achieved. Therefore, eq 4 can be used to determine the rate constant for the electron transfer. Figure 4b presents the NMR spectra and the concentrations of DHAQ 3−• radical anions during the voltage hold at 1.6 V. The linewidths of peaks A″ and B″ decrease as the concentration of DHAQ 3−• radical anion decreases. Following eq 4, the rate constant k ex is calculated and plotted as a function of time in Figure 4c. The values of k ex range from 1.5 × 10 5 to 2.4 × 10 5 M −1 s −1 , with an average of 2.0 × 10 5 M −1 s −1 . The values of k ex for the electron transfer between DHAQ 3−• and DHAQ 4− anions are on the same order of magnitude, i.e., 10 5 M −1 s −1 , as the electron transfer between DHAQ 2− and DHAQ 3−• radical anions (k ex ≈ 1.0 × 10 5 M −1 s −1 ). 7 Unpaired Spin Densities and Consequences for H/D Exchange. EPR spectroscopy can be used to quantify the (unpaired) electron density distribution over the radical anions by extracting the hyperfine coupling constants for the unpaired electron to the neighboring nuclear spins, since a linear relationship between hyperfine coupling constant A and the unpaired π-electron populations on the isotropic proton of the carbon atoms in a π-type organic radical has been shown previously. 28 This linearity should be applicable to the two anthraquinone radical anions studied here, i.e., DHAQ and DBEAQ. The values of A for the protons, as shown in Figure 5, were obtained by fitting the experimental spectra to the simulated ones. The simulation gives a set of hyperfine coupling constants but does not correlate the values to the specific protons. Therefore, the assignment was aided by the NMR observations and DFT calculations. 7 For DHAQ, the values of A for the protons are as follows: A H′ , and A I′ . Note that the values of A B′ , A G′ , A H′ , and A I′ extracted from the spectral fitting are smaller than the linewidths (0.34 MHz for DHAQ and 0.33 MHz for DBEAQ) used in the fits. Therefore, the electron spin densities on these protons are very small.
The H-D exchange can be seen in the in situ EPR spectrum when D 2 O was used as the solvent. As shown in Figure S4, during the galvanostatic cycling of 1 mM DHAQ at a current of 1 mA, EPR signals at 337.42 and 337.92 mT gradually decrease, while new EPR signals in the range of 337.53−337.85 mT develop. The best fit to the spectrum acquired at the end of electrochemical cycling (Figure 5b) was obtained by replacing the proton (I = 1 / 2 ) on the C′ position by a deuterium (I = 1). In contrast, when H 2 O was used as the solvent, there are no distinguishable changes in the in situ EPR spectra. These observations confirm that proton C′ is labile and undergoes an exchange reaction with the deuterium (or proton) from solvent water. In contrast, no H-D exchange occurs on DBEAQ molecules ( Figure S5).
Identifying and Quantifying Decomposition Products. To detect the decomposition products following electrochemical cycling of the battery with 10 mM DHAQ electrolyte, the battery voltage was held for 10 h either at 1.6 or 1.7 V, the latter being shown in Figure 6a. Holding the voltage is a commonly implemented cycling condition to ensure the complete reduction or oxidation of the electrolyte. 6 During the voltage hold, no decomposition products were detected in both the NMR and EPR spectra. As shown in Figure 6a, only 1 H NMR signals A″ and B″ of the DHAQ 4− anions are visible. However, in our previous study, decomposition products were observed from a 100 mM solution of DHAQ, 7 which suggests that the decomposition reaction is concentration-dependent. In another experiment, we cycled a battery with 100 mM DHAQ at 150 mA four times, followed by a voltage hold at 1.7 V for 20 h followed by a further 20 continuous cycles. Figure  6b presents the NMR spectra acquired during the voltage hold. New signals at 6.55, 6.65, 6.84, 7.14, 7.50, 7.88, and 8.02 ppm Journal of the American Chemical Society pubs.acs.org/JACS Article were observed, consistent with our earlier studies. 7 These signals are assigned to 2,6-dihyhroxyanthrone (DHA) and 2,6dihydroxyanthranol (DHAL). Since the formation of DHAL 2− is favored at high pH values, 29 the signals of slightly higher intensity at 6.55, 6.84, 7.50, and 7.88 ppm were tentatively assigned to DHAL 2− , as the pH value of the electrolyte solution is 14. The pH dependence of the ratio of these two species is still under systematic investigation. The in situ NMR spectra acquired before the voltage hold are shown in Figure  S6. The concentration of DHA/DHAL was then quantified: after a voltage hold for 10 h, 28% of the DHAQ decomposed. Assuming that decomposition occurs at a similar rate for the 10 mM DHAQ solution, 2.8 mM DHAQ should have decomposed and therefore 1.4 mM DHA or DHAL should have been produced, assuming a 1:1 ratio. These concentrations are above the detection limit of the NMR technique, but since no new NMR signals were observed, it suggests that no decomposition products were formed when 10 mM was used.
To confirm the assignment of the new peaks at 6.55, 6.65, 6.84, 7.14, 7.50, 7.88, and 8.02 ppm in Figure 6b, we synthesized DHA and DHAL and acquired their 1 H NMR spectra (blue color; Figure 6c). The expected eight doublets of the DHA and DHAL signals were observed, as highlighted by the green and red triangles. The eight doublets come from four pairs of closely bonded protons, which is further substantiated by the 2D 1 H homonuclear correlation spectrum (COSY), as shown by the four off-diagonal signals in Figure 6d. This is consistent with the bonding relationship of the protons in the DHA 2− and DHAL 2− anions, as shown in Figure 6e, where there are four pairs of closely bonded aromatic protons. Note that DHA 3− and DHAL 3− , which are resonance structures, were proposed in our previous work. 7 Since eight doublets were observed in the work presented in this paper, we propose that DHA 3− and DHAL 3− are in fact deuterated, forming DHA 2− and DHAL 2− anions which are tautomers. 30 The 2D NMR spectrum of the synthesized DHA and DHAL matches the 2D spectrum of the decomposition products (extended data Figure 8b in ref 7). The signals at 6.45, 6.50, 6.75, 7.20, 7.51 ppm, which are not highlighted in the 1D spectrum, likely come from the protons on the central ring and impurities from the synthesis. It is also possible that H-D exchange occurred on these protons after the sample was dissolved in D 2 O with 1 M KOH to acquire the NMR spectrum. The red spectrum in Figure 6c corresponds to the in situ spectrum acquired immediately after the voltage hold was stopped and the discharge was commenced. At this point, approximately 1% DHAQ 3−• radical anions were present, as estimated by the current passed. As discussed in the preceding section, the fast electron transfer between DHAQ 3−• and DHAQ 4− anions causes broadening of peaks A″ and B″, allowing the decomposition product signals (again, marked with green and red triangles) to be revealed as they remain unaffected by this broadening mechanism. The chemical shifts of the decomposition products at 6.55, 6.65, 6.84, 7.14, 7.50, 7.88, and 8.02 ppm match reasonably well to the chemical shifts of the as-synthesized DHA 2− and DHAL 2− anions at 6.59, 6.65, 6.86, 7.19, 7.51, 7.94, and 8.02 ppm.
Having observed and quantified the degradation, we next wanted to understand how much capacity fade is caused by the decomposition of the DHAQ 4− anions and whether the decomposition products are electrochemically active. After the five galvanostatic cycles and the voltage hold, the battery was discharged and charged at 150 mA for 20 cycles. At the end of the first discharge cycle, as shown in Figure 7a, a second voltage plateau appears at 0.7 V. Deducting this value from the redox potential of 0.5 V of [Fe(CN) 6 ] 4− /[Fe(CN) 6 ] 3− , gives a redox potential of −0.2 V vs SHE. Note that an irreversible oxidation peak at −0.2 V vs SHE has been reported for DHA at pH 14 in a cyclic voltammetry experiment, 31 consistent with our observation. Furthermore, this second oxidation plateau disappears during the subsequent cycles, suggesting that the oxidation reaction is irreversible. In the NMR spectra corresponding to the second plateau, as shown on the right in Figure 7a, the intensity of signals at 6.64 and 6.84 ppm decrease, while the intensity of signal at 7.49 ppm increases, which suggests that the DHA 2− or DHAL 2− anions have reacted further. In the subsequent cycles, no significant changes in the decomposition product signals were observed, the observed shift of the signals from the decomposition products being instead caused by the change of bulk The NMR measurements have been shown to be in the quantitative regime. 7 This enables us to track the concentration changes of the redox-active electrolyte and the decomposition products. During the voltage hold at 1.7 V for 100 mM DHAQ, a signal at 7.48 ppm grows in and is well separated from other signals. This signal is used to calculate the concentrations of DHA 2− or DHAL 2− anions. Signal A″ at 7.96 ppm is used to calculate the concentration of DHAQ 4− anions. However, it overlaps with the two signals of DHA 2− or DHAL 2− anions at 7.88 and 8.02 ppm; thus, the difference of signal integrals is taken and used for the calculation (see Methods for details). As shown in Figure 7b, the total concentration of DHA 2− and DHAL 2− anions increases from 0 to 43.0 mM, while the concentration of DHAQ 4− anions decreases from 90 to 54.0 mM. Figure 7c presents the capacity of the battery as a function of cycle numbers before and after the voltage hold. The capacity decreases from 93.5 mA h (the theoretical capacity is 96.4 mA h) before the voltage hold to 70.4 mA h after the voltage hold, after which it then drops to 57.1 mA h and continues to fade slowly afterward. The decrease from 70.4 to 57.1 mA h is caused by the irreversible electrochemical oxidation of DHA 2− or DHAL 2− , the total decrease in capacity from 93.5 to 57.1 mA h corresponding to a capacity fade of 38.9%. Since the concentration decrease of DHAQ during the voltage hold is 40.0%, it is reasonable to conclude that the decomposition reaction of the DHAQ 4− anions is the main cause for the capacity fade of the battery.

CONCLUSION
The use of in situ EPR and coupled online EPR/NMR metrologies to study flow batteries is demonstrated in this work. These methods allowed the formation of radical anions in anthraquinone-based flow batteries to be directly observed by EPR and the delocalization of the unpaired electron spin density over the DHAQ 3−• and DBEAQ 3−• radical anions to be determined. The concentrations of DHAQ 3−• radical anions were quantified by spin counting from the EPR analysis and by measuring the bulk magnetization from the NMR analysis, and consistent results were obtained when using these two methods. The fraction of the radical anions was found to be concentration-dependent, the fraction decreasing as the total concentration of DHAQ increases. This suggests that, besides the comproportionation reaction between DHAQ 2− and DHAQ 4− , additional reaction equilibria exist. The most likely candidate for this involves a dimerization in which the two unpaired electrons of the DHAQ 3−• radical anions are coupled, resulting in an EPR-silent anion (and a reduction in the susceptibility as measured by NMR). Further work will include exploring the concentration profiles of the various species with alternative methods. For example, complementary optical absorption spectroscopic measurements will be pursued to track dimer formation and loss of other species in the system. The role of dimer formation in the degradation mechanism remains another important question to be addressed. Journal of the American Chemical Society pubs.acs.org/JACS Article EPR is more sensitive toward low concentrations of radical anions, enabling a reliable measurement of the concentration of the DHAQ 3−• radical anions at high voltages. By simultaneously measuring the line-broadening of the 1 H resonances of DHAQ 4− , we were able to measure the rate constant for the intermolecular electron transfer from DHAQ 4− to DHAQ 3−• anion. The intermolecular electron transfer can be potentially used to relay electrons from the electrochemical cell to the electrolyte reservoir, thus reducing the pumping power and increasing the energy efficiency of the battery at the system level.
Decomposition of DHAQ 4− to DHA 2− and DHAL 2− anions was observed for a 100 mM DHAQ solution, but not for a 10 mM DHAQ solution, suggesting that the decomposition reaction is concentration-dependent. Our NMR analysis reveals that DHA 2− or DHAL 2− anions undergo irreversible electrochemical oxidation reactions in the voltage window of 0.6−1.6 V. Furthermore, by correlating the concentration of DHAQ to the capacity of the battery quantitatively, we show that the decomposition of DHAQ is the main cause of the capacity fade of the battery. The elementary reaction steps that lead to the formation of DHA 2− or DHAL 2− and their further oxidation warrant systematic investigation. For example, the potential dependence of the decomposition could be investigated by varying the potentials of the anode or cathode side separately with the incorporation of a third reference electrode. This would allow the reaction kinetics and the elementary reaction steps to be studied.
Coupling the in situ NMR and EPR techniques, we demonstrate the possibility of multi-modal characterizations of redox flow batteries. Other characterization techniques such as optical spectroscopy or mass spectrometry could be incorporated into this concept. These characterization techniques could then be further extended to study other flow electrochemical systems, for example, to study electrochemical CO 2 sequestration or water desalination.
Online EPR and NMR Setup. The setup consists of a flow battery (Scribner), two peristaltic pumps (MasterFlex L/S 07751-20, Cole-Parmer), an electrochemical cycler (SP-150, BioLogic SAS), a benchtop EPR (MS5000, Magnettech), and an NMR (300 MHz, Bruker) spectrometer ( Figure S1). The battery and the EPR spectrometer are positioned outside the 5 G line of the NMR magnet. The electrolyte is pumped through the flow battery, then flowed through the EPR and NMR magnets, and finally back to the electrolyte reservoir. The direction of flow is from the bottom to the top of both magnets. PFA tubes (1/16 in.) are used to connect the electrolyte reservoir, the battery, and the EPR and NMR sampling tubes. The time it takes for a round-trip from and back to the electrolyte reservoir is 64 s at a flow rate of 13.6 cm 3 min −1 . The time it takes for the electrolyte solution to travel from the electrolyte reservoir to the battery is 3 s, from the battery to the EPR detection region is 3 s, from the EPR to the NMR detection region is 29 s, and from the NMR detection regions back to the electrolyte reservoir is 29 s. To minimize heating of the aqueous solution by microwave irradiation, a flat EPR cell (E4503, Magnettech) is used. A customized adaptor made of polyether ether ketone (PEEK) is used to connect the flat EPR cell to the 1/16 in. tube. The cell is orientated in the resonator such that the strength of the magnetic field is maximized and the strength of the electric field is minimized across the sample. The volume of the cell in the excitation region of the microwave is 0.03 cm 3 (2.00 cm × 0.50 cm × 0.03 cm), giving a residence time of 0.13 s for the electrolyte solution at a flow rate of 13.6 cm 3 min −1 . Details of the NMR sampling tube are provided in our previous publication. 7 For the coupled in situ EPR and NMR experiment, 27 mL of 10 mM DHAQ was used as the anolyte, and 60 mL of 15 mM Spin Counting and EPR Parameters. The double integral, DI, of an EPR signal is proportional to the concentration of spins in the sample, C S , following 32 where C ns is a constant including the normalized spectrometer settings, i.e., sweep time and number of accumulations, P is the microwave power, B m is the modulation amplitude, Q is the resonator's quality factor, n B is the Boltzmann factor for temperature dependence, S is the total electron spin, v is the volume of the sample, and f(B 1 ,B m ) is the spatial distribution of microwave and modulation field in the sample. By measuring a standard sample of known C S , a linear relationship between DI and C S can be established. The concentration of a sample of interest can then be calculated from the DI of its EPR signal. A set of 4-OH-TEMPO solutions of concentrations ranging from 0.1 mM to 125 mM was prepared. H 2 O was used as the solvent. 4-OH-TEMPO has a spin quantum number of a half, i.e., S = 1 / 2 . EPR spectra were acquired using the flat cell under a flow rate of 13.6 cm 3 min −1 . This ensured that v and f(B 1 ,B m ) remained the same throughout the measurements. The magnetic field was swept from 332.5 to 342.5 mT. The sweep time was 60 s for a single scan. P was 0.5 mW, and B m was 0.001 mT. Q was recorded for each spectrum, in the range of 1670 ± 20. The first-derivative spectra ( Figure S3a) were integrated to generate the absorption spectra ( Figure S3b). Then the baselines of the absorption spectra were corrected by a fourth order polynomial fit after which the baseline-corrected spectra were integrated one more time to give the double integral, DI, which was fit linearly as a function of the concentrations of 4-OH-TEMPO ( Figure S3c,d), and a slope of 4725.7 mM −1 was obtained.
For the in situ measurement of DHAQ 3−• radical anions, the magnetic field was swept from 336.5 to 339 mT. The sweep time was 60 s per single scan. B m was 0.001 mT, and Q was recorded for each spectrum. Q was 1306 ± 5. The temperature of the resonator was kept at 29°C, and a time delay of 35 s was added between each scan. The in situ EPR spectra of the DHAQ 3−• radical anions were doubly integrated, following the above procedure. Normalizing the EPR parameters following eq 6 and dividing the double integral by 4725.7 mM −1 gave the concentration of the DHAQ 3−• radical anions.
The in situ measurement of DBEAQ was performed on an X-band spectrometer (EMX Micro, Bruker). The magnetic field was swept from 341.3 to 351.3 mT. The sweep time was 20 s per single scan. P was 2 mW, and B m was 0.01 mT.
The measured g-factors of DHAQ 3−• and DEBAQ 3−• radical anions were corrected by using the g-factor of 4-OH-TEMPO as the reference. The g-factor of 4-OH-TEMPO measured on the Magnettech instrument is 2.0057, while the value reported in literature is 2.0059. 33 A scaling factor of 1.0001 (2.0059/2.0057 = 1.0001) is therefore applied to the measured values using the Magnettech instrument. The corrected g-factor of DHAQ 3−• is 2.0046 (2.0044 × 1.0001 = 2.0046). The g-factors of DHAQ 3−• and DBEAQ 3−• measured by the Bruker instrument are 2.0077 and 2.0080, respectively, which were corrected to 2.0046 and 2.0049.
NMR Parameters. Pseudo-2D NMR experiments were performed by direct excitation with a 90°radio-frequency pulse. Each NMR spectrum is acquired by collecting 16 free induction decays (FIDs) with a recycle delay of 5 s. The pulse width for a 90°pulse was 27 μs. All spectra were referenced to the water chemical shift at 4.79 ppm before battery cycling starts.
Bulk Magnetization and Radical Concentrations. Bulk magnetization of the electrolyte solution is linearly proportional to the concentration of DHAQ 3−• radical anions. The derivation of the relationship between bulk magnetization, radical concentration (C rad ), and the change in chemical shift of water (Δδ S ) was provided in our previous work. 7 The concentration of DHAQ 3−• radical anions can be readily estimated by Calculation of Rate Constant for the Electron Transfer Reaction. The result derived for the slow exchange regime was used for the calculations of the rate constants for the electron transfer between DHAQ 3−• and DHAQ 4− anion. 7,34 When the concentration of radical anions is increased by Δ[P], the transverse nuclear relaxation of the nucleus is increased by ΔR 2ex . Following eq 8, ΔR 2ex is calculated by where FWHM is the full width at the half maximum of the NMR signal, measured in Hz. FWHM 0 is the full width at the half maximum of the NMR signal with a known concentration of radical anions, [P] 0 . The linewidth of the NMR signal during the voltage hold at 1.7 V for 10 h is chosen to be FWHM 0 , and it is equal to 26.7 Hz where [P] 0 is 0.02 mM. It takes 29 s for the flowing electrolyte to reach the NMR detection region from the EPR detection region. Within this time duration, some DHAQ 4− anions are oxidized to the DHAQ 3−• radical anions. Therefore, to obtain an accurate estimation of [P], we need to account for the increased concentration of DHAQ 3 Calculations of DHAQ, DHA, and DHAL Concentrations. The in situ NMR spectra were first baseline-corrected by a fourth-order polynomial function. The proton resonance at 7.48 ppm, which is well separated from the other peaks during the potential hold, was used for the calculations of DHA or DHAL concentrations. Note that we cannot differentiate the signals of DHA and DHAL, so the concentration calculated is for both of the molecules. The proton resonance at 7.96 ppm was used for the calculation of DHAQ 4− concentration. This signal overlaps with two signals of DHA or DHAL at 7.88 and 8.01 ppm. To deduct the integrals of these two signals, a spectrum taken immediately after the voltage hold was stopped (at 27.93 h, see Figure 7a) was used to establish the ratios of the integrals of these two signals to that at 7.48 ppm. This spectrum was chosen because the signal A″ of DHAQ 4− was broadened at this point to below the baseline due to the presence of approximately 1% DHAQ 3−• radical anions and the corresponding intermolecular electron transfer between DHAQ 3−• and DHAQ 4− . As such, the signals of DHA or DHAL can be accurately integrated since they are unaffected by the radical-induced broadening. A ratio of 1.19:1.37:1.00 was obtained after the deconvolution of the three signals at 8.01, 7.88, and 7.48 ppm ( Figure S6b). This ratio was used for the calculations of integrals at 8.01 and 7.88 ppm during the potential hold. The spectrum at the beginning of the potential hold (at 8.80 h, see Figure S6a) was used to calibrate the concentration since there are negligible decomposition products at this time. Signal A″ in this spectrum corresponds to 90 mM DHAQ 4− (excluding the 10% impurity in the sample, as specified by the manufacturer).
In situ NMR and EPR setup, additional 1 H NMR spectra, and EPR spectra of DHAQ, DBEAQ, and 4-OH-TEMPO, calculations of reaction equilibria including Figures S1−S6 and Table S1 (PDF)