Decoupling the solubility of redox active species and the energy density of redox flow batteries using supersaturated, phase-change electrolytes

Abstract

Redox flow batteries (RFBs), with their characteristic decoupling of power density and energy capacity, are scalable energy storage systems that can help smooth out the intermittency of solar and wind power on the electric grid. Among the many different redox couples considered in RFBs, the cerium (Ce) redox couple, Ce(IV)/Ce(III), is particularly attractive due to its high standard potential (1.61 V vs. standard hydrogen electrode, SHE) and the relative abundance of Ce in Earth's crust (as abundant as lead). Ce-based RFBs, such as the Zn–Ce system, have been scaled up and commercialized, but meeting ever-lower energy storage cost targets (<$50 kW h⁻¹) requires significantly higher Ce electrolyte energy density. Herein, in a departure from previous studies that utilize acid-supported Ce electrolyte solutions (e.g., sulfuric acid), we have developed a new phase-change Ce electrolyte with ammonium sulfate (AS) as the supporting electrolyte. The solubility of Ce(IV) was enhanced to 1.23 M by optimizing the ratio between the Ce salt and AS. This ∼40% increase in energy density was found to be a function of solution chemistry, with complementary effects of Ce(IV) hydrolysis with water and complexation with anions. This cost-effective Ce electrolyte was paired with the titanium (Ti) redox couple to demonstrate a high-energy-density, low-cost Ce-based RFB. During cycling, part of the Ce was precipitated to form a slurry in the electrolyte. This slurry was succesfully cycled and reoxidized to the more soluble Ce(IV) form. 20 cycles (75 minutes per cycle) of the phase-change Ti–Ce RFB was demonstrated with a final energy efficiency > 70%.

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Introduction

Redox flow batteries (RFBs) have attracted significant attention due to their ability to decouple energy capacity from power output, making them ideal for large-scale energy storage systems.¹ While all-vanadium RFBs remain the most widely studied and applied, the high cost of raw materials and relatively low output potential drive forward the research on other redox couples.^2,3 In the meantime, the development of aqueous inorganic RFBs is usually limited by the poor solubility of active species. As the most abundant and inexpensive rare earth element,⁴ cerium (Ce) has a broad range of applications, such as automotive catalysts,⁵ wastewater treatment,⁶ alloy synthesis,⁷ and therapeutic agents.⁸ The Ce redox couple, Ce(IV)/Ce(III), has been utilized in electrochemical energy storage due to its high redox potential.⁹ More specifically, it has been successfully incorporated into aqueous RFBs working as the positive side¹⁰ and has been coupled with Zn, Pb, H₂, V, and Ti to yield a variety of RFBs.¹¹ Zn–Ce RFB was even commercialized by Plurion before they shut down due to the 2008 economic crisis. To our best knowledge, in previous studies, Ce species were dissolved in traditional acidic supporting electrolytes to enhance stability and kinetics, with the Ce solubility limited to (at best) 0.9 M.^12,13 Ce solubility in sulfuric acid (H₂SO₄) has been shown to decrease as the acid concentration increases, which is usually explained by the “common ion effect”,¹⁴ while an inverse relationship between Ce(III) and Ce(IV) solubility could be seen in methanesulfonic acid (CH₃SO₃H).¹⁵ Due to the limitation of Ce solubility in acidic electrolytes, the concentration of active species in aqueous RFBs using the Ce redox couple is usually below 1 M. Some reports exist of cerium redox in non-aqueous electrolytes, such as acetonitrile, but the very low solubility (0.05 M in this case¹⁶) makes these systems far from practical.

The study of solubility enhancement in aqueous inorganic RFBs is much more scarce compared to studies on organic actives,¹⁷ and most of the existing research is focusing on vanadium (V) RFBs.¹⁸ The group of Prof. Skyllas-Kazacos has conducted a comprehensive study on the effects of different additives on supersaturated V electrolytes. They first proposed the idea of using “stabilizing agents” that do not promote V solubility but postpone precipitation by adsorbing to the nucleation sites to inhibit crystal growth.¹⁹ According to their research, the ammonium (NH₄⁺) and phosphate (PO₄³⁻) ions were shown to work best as precipitation inhibitors.²⁰ Unlike this study, the amount of effective additives in their studies was very low (e.g., 1 to 5 wt%), which makes complexing an unlikely mechanism because it requires a comparable concentration between metal ions and complexing agents.

Building on our success developing the titanium (Ti)–Ce RFBs utilizing methanesulfonic acid as the supporting electrolyte and aiming to break through the existing Ce solubility limitation, we screened a series of non-acidic supporting electrolytes, and a solution of ammonium sulfate (AS) was found to enable Ce(IV) solubility as high as 1.23 M. Unlike prior studies where trace amounts of additives were added into conventional acidic electrolytes, AS is the only component of the electrolyte here apart from the dissolved Ce salt. Due to the high charge-to-radius ratio of Ce(IV), it easily hydrolyses with water when the solution pH is relatively high.²¹ The near-neutral environment of the AS solution favors Ce(IV) hydrolysis and the release of protons, thus reducing the pH. The resultant low-pH environment drives the protonation of the Ce counterion sulfate (SO₄²⁻) to form bisulfate (HSO₄⁻), and the complexation between Ce(IV) and HSO₄⁻ tends to form a stable structure where the ratio of Ce(IV) to HSO₄⁻ is 1 : 3.²² The synergistic effect of Ce(IV) hydrolysis, the resultant pH reduction, and the formation of bisulfate anions, enabling favorable complexation, serves as the foundation for our supersaturated electrolyte. This new Ce(IV) electrolyte was paired with the same concentration of Ti in AS, leading to a new type of RFB. Upon cycling, the Ce(III) ion exhibited much lower solubility compared to Ce(IV) and precipitated out of solution, but we were able to circulate the resultant slurry through the RFB and convert the Ce(III) back to dissolved Ce(IV). This phase-change cycling was carried out for 20 cycles with no irreversible capacity fade and an energy efficiency (EE) higher than 70% at 50 mA cm⁻² operating current density. Thus, we demonstrated a new Ce-based, slurry aqueous inorganic RFB with a theoretical energy density of 33 Ah L⁻¹.

Materials and methods

Chemicals

Ce(SO₄)₂·xH₂O (Alfa Aesar, 98%), TiOSO₄ (Sigma-Aldrich, 34%), and VOSO₄ (Sigma-Aldrich) were used as the raw Ce(IV), Ti(IV), and V(IV) materials, respectively. H₂SO₄ (Sigma-Aldrich, 99%) and CH₃SO₃H (Sigma-Aldrich, 99%) were used as the supporting electrolytes. The original Ce(IV), Ti(IV), and V(IV) solutions were prepared by first dissolving the required amount of AS in deionized water, then adding the corresponding amount of metal salt into the AS solution. A stirring bar was used to speed up the dissolution.

Characterization methods

Ce L_III-edge X-ray absorption near-edge structure (XANES) spectra were obtained using an easyXAFS 300+ X-ray spectrometer.²³ The second harmonic of a spherically-bent Ge(211) crystal was used to select the incident beam energy, which was detected using a silicon drift detector. Ce(SO₄)₂ dissolved in AS solution was injected into a sample cell consisting of a 0.25 mm thick PTFE ring shim (25.4 mm outer diameter, 15.9 mm inner diameter) sealed on both sides with Kapton tape. CeO₂ and Ce₂(SO₄)₃ were ground in a mortar and pestle, spread as a uniform layer on cellulose tape, and then stacked in six layers for measurement to optimize absorbance. Data were collected in transmission mode with the energy calibrated using a Cr metal foil, and the first inflection point of the Cr K-edge set to 5989 eV. The spectrum of Ce(SO₄)₂ was obtained from the XAS Database at the Canadian Light Source (https://xasdb.lightsource.ca, sample ID: id12345). Data were calibrated and normalized in the Athena²⁴ interface to IFEFFIT.²⁵ Raman spectroscopy was performed using a Renishaw inVia confocal Raman spectrometer equipped with a 514 nm laser excitation source. The laser power at the sample surface was set to 2 mW, and spectra were obtained by focusing the laser beam on the surface plasmon-coupled emission (SPCE) working electrode using a 50× objective lens with a numerical aperture of 0.9 and an exposure time of 30 s. Ultraviolet-visible spectroscopy (UV-Vis) was conducted using a Varian Cary 50Bio. The absorption spectra were obtained between 190 and 1100 nm at a scan rate of 600 nm min⁻¹. A quartz cuvette with a path length of 10 mm was used, and the supporting electrolyte solution without Ce(IV) was used to do baseline correction before running each sample.

Electrochemical measurements

Cyclic voltammetry (CV) was conducted using WaveNowXV Potentiostat Bundles (PINE Research). A three-electrode setup was used for the measurements: carbon paper (CP, AvCarb MGL190, Fuel Cell Store) or carbon felt (CF, GFA 6, SGL Group) with a 1 cm² surface area as the working electrode, Ag/AgCl as the reference electrode, and platinum wire as the counter electrode. The potential window of CV was 0 to 2 V vs. Ag/AgCl, and different scan rates (e.g., 2.5, 5, 7.5, and 10 mV s⁻¹) were selected for further calculation. The results were analyzed using the Nicholson–Shain (N–S) and Klinger–Kochi (K–K) equations to obtain the diffusion coefficient (D₀) and standard reaction rate constant (k₀).^26–28 More details for the calculation process are provided in the Results and discussion section.

Redox flow battery tests

All tests were conducted using an 857 Redox Flow Cell Test System (Scribner). CF with a 6 mm thickness was cut into a 5 × 5 cm segment, leading to a 25 cm² surface area. Raw and heat-treated (500 °C, 8 h, air atmosphere) CF were used as the positive (Ce) and negative (Ti) side electrodes, respectively. The separator was a quaternized cardo-poly(ether ketone)-based anion-exchange membrane functionalized with trimethylamine (QPEK-C-TMA AEM), developed by our group; the synthesis details are provided in previous studies.²⁹ A serpentine-type flow field with enlarged inlet and outlet was used, as shown in SI Appendix, Fig. S1. A total of 50 mL of electrolyte was used for each side. Since the original Ce(IV) and Ti(IV) electrolytes were in fully charged and discharged states, respectively, a V–Ti RFB was assembled by pairing V(IV) and Ti(IV) electrolytes and a single, full charge was operated at 50 mA cm⁻² until the cell reached cut-off potential (2 V) to obtain a fully charged Ti electrolyte, which contains mostly Ti(III). Next, this Ti electrolyte was paired with the Ce(IV) electrolyte for the cycling test in a sequence of discharge followed by charge–discharge. More details about the electrolyte composition and test protocol are provided in the SI Appendix.

Results and discussion

Determination of Ce(IV) electrolyte composition

Solutions of different chemicals containing NH₄⁺, PO₄³⁻, or –NH₂ were screened for their effects on Ce(SO₄)₂ solubility as shown in Table 1. The AS solution was the only candidate that had a positive effect on Ce(IV) solubility, with the solubility of Ce(IV) in other solutions being even lower than that in pure water. It was apparent that both NH₄⁺ and SO₄²⁻ play a role in promoting Ce(IV) solubility, as the substitution of either would disable the effect (e.g., both Na₂SO₄ and NH₄Cl solutions, resulting in poor Ce(IV) solubility). In optimizing the Ce(SO₄)₂ and AS system, the ratio of NH₄ to SO₄ was varied and found to have a significant impact on Ce(IV) solubility, as shown in Table 2. Note that we have used NH₄ and SO₄ instead of NH₄⁺ and SO₄²⁻ to denote all different species of ammonium (e.g., NH₃ and NH₄⁺) and sulfate (e.g., SO₄²⁻ and HSO₄⁻) in solution. The optimum ratio of NH₄ to SO₄ was determined to be 0.6 and this resulted in the highest observed Ce(IV) solubility of 1.23 M. Moreover, it is noteworthy that when the ratio of NH₄ to SO₄ was fixed (i.e., at 0.6 : 1), the Ce(IV) solution remained stable only when the Ce(IV) content reached a relatively high level (solutions 1 and 4, solutions 5 to 8, Table 2). The mechanism of this phenomenon is further discussed.

Table 1 Effects of different supporting electrolytes on the Ce(SO₄)₂ solubility^a

Additive	Effect	Ce(IV) conc.^a (M)
a The “−” sign in the Ce(IV) concentration column indicates that for the given type of supporting electrolyte, the lowest amount of Ce(SO4)2 in the dissolution experiment was not able to fully dissolve.
(NH4)2SO4	+	1.23
H2SO4	−	0.5
H3PO4	−	—
Na2SO4	−	—
CF3SO3H	−	—
Ce(NH4)4(SO4)4	−	0.1
NH4Cl	−	—
CH3COONH4	−	—
NH4SCN	−	—
(NH4)2S2O8	−	—
NH4SO3NH2	−	—

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Table 2 Effects of the ratio of the ammonium and sulfate on the Ce(IV) electrolytes

Solution #	Ratio of NH4 to SO4	Nominal^a Ce(IV) conc. (M)	Condition
a The nominal concentration indicates the concentration before accounting for the volume expansion during the dissolution process. Unlike conventional solution preparation, which utilizes a volumetric flask, we only used a beaker to facilitate the dissolution. On the other hand, a volumetric flask requires that the initial solution volume be smaller than the target number when transferring into the flask, and even this small amount of water might result in a discrepancy in the solubility limitation. In that case, we first calculated the required amount of AS and Ce(SO4)2 for an expected volume (e.g., 1.4 M Ce in 100 mL solution), then added the amount of water that was just enough to dissolve everything, then the final solution volume (114 mL) was measured and the actual concentration recalculated: 1.4 × 100/114 = 1.23 M.
1	0.6 : 1	1.4	Dissolved and stable for 21 days
2	0.55 : 1	1.4	Not dissolved
3	0.65 : 1	1.4	Not dissolved
4	0.6 : 1	1	Dissolved and precipitated within 1 day
5	1 : 1	0.1	Not dissolved
6	1 : 1	0.2	Not dissolved
7	1 : 1	0.3	Not dissolved
8	1 : 1	0.4	Dissolved
9	1.82 : 1	0.05	Dissolved and precipitated within 1 day

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Physicochemical characterization

The XANES spectrum of 1.23 M Ce(SO₄)₂ in 1.05 M AS (Fig. 1A) displayed white-line peaks at 5730.0 and 5737.5 eV, consistent with Ce(IV). The peak at 5737.5 eV had greater intensity than at 5730 eV, similar to solid Ce(SO₄)₂ and distinct from CeO₂. The peak intensity ratio of CeO₂ is similar for crystalline and amorphous forms,^30,31 as well as Ce(OH)₄,³² consistently distinct from Ce(IV) in the electrolyte solution, which also had a more pronounced pre-edge feature at 5720 eV and lacked the shoulder at 5726.5 eV found in CeO₂ (SI Appendix, Fig. S2A). The intensity minimum at 5732.5 eV was deeper for Ce(SO₄)₂ dissolved in AS compared to solid Ce(SO₄)₂ (SI Appendix, Fig. S2B), similar to what is reported for dissolved 0.1 M Ce(IV) in 2 M H₂SO₄.³³ The spectrum of Ce(SO₄)₂ dissolved in AS is clearly distinct from the trivalent sulfate, Ce₂(SO₄)₃ (SI Appendix, Fig. S2C). A linear-combination fit of the XANES spectrum of 1.23 M Ce(SO₄)₂ in 1.05 M AS to the spectra of the standards yielded 99.1% ± 0.4% Ce(SO₄)₂ and 0.9% ± 0.4% Ce₂(SO₄)₃, demonstrating that cerium in solution is predominantly >99% Ce(IV) (SI Appendix, Fig. S2D). The small Ce(III) component may be a fitting artifact needed to account for the spectral differences between dissolved and solid-phase Ce(SO₄)₂, as was previously observed.³³ This demonstrated that Ce(IV) dissolved in AS electrolyte occurs in a similar coordination state to that in a H₂SO₄ electrolyte and did not form oxide or hydroxide phases. Raman spectra for different Ce(IV) and blank solutions are shown in Fig. 1B. The original spectra were normalized based on the peak intensity of the silicon wafer, which occurred at 520 cm⁻¹. A totally symmetric ν₁-SO₄²⁻ peak located at around 980 cm⁻¹, representing unassociated SO₄²⁻, was observed for the blank AS solution, which is consistent with previous literature, indicating that the AS solution is an ideal model for a “free” sulfate system.³⁴ After Ce(SO₄)₂ was dissolved in AS, the ν₁-SO₄²⁻ peak intensity decreased and completely disappeared at higher Ce(SO₄)₂ concentrations, and no HSO₄⁻-related peak was generated, indicating an interaction between sulfate and Ce⁴⁺. Another bending mode, ν₄-SO₄²⁻, located at 615 cm⁻¹ in AS solution, showed a significant blueshift to 665 cm⁻¹, as presented in Fig. 1B. A previous study on supersaturated MgSO₄ solution has shown that a similar blueshift is related to the formation of contact ion pairs (CIPs).³⁵ This finding implies that instead of the total sulfate species concentration, an efficient binding between sulfate species and Ce(IV) is essential for obtaining a supersaturated Ce(IV) solution. On the other hand, when the concentration of Ce(SO₄)₂ was fixed at 0.123 M and the supporting electrolyte was varied, the ν₁-SO₄²⁻ peak intensity of Ce(SO₄)₂ in AS solution was most prominent, indicating a higher degree of free SO₄²⁻ (ESI Appendix, Fig. S3). The spectrum of Ce(SO₄)₂ in H₂SO₄ was nearly identical to that of H₂SO₄, which presented no ν₁-SO₄²⁻ peak but a tiny HSO₄⁻ peak at around 1047 cm⁻¹. Neither free SO₄²⁻ nor HSO₄⁻ was present when Ce(SO₄)₂ was dissolved in water, indicating a strong interaction between sulfate and Ce(IV). The fact that the solubility of Ce(SO₄)₂ in water was limited (less than 0.7 M) suggests that the complex stability is highly sensitive to the structure. The UV-vis spectra of Ce(IV) in AS and H₂SO₄ are depicted in Fig. 1C, where the Ce(IV) concentration had to be diluted about 1000-fold to obtain clear absorption peaks. With a significant difference in pH value (3.71 in AS vs. −0.02 in H₂SO₄), a clear redshift of the absorption peak from 272 to 317 nm was found after AS was substituted by H₂SO₄. A consistent redshift was observed when the supporting electrolyte consisted of different ratios of AS and H₂SO₄ (Fig. 1D). Likewise, Ce(IV) was found to be complexed more strongly with sulfate species in H₂SO₄ than methanesulfonate in CH₃SO₃H, with an absorption peak of 320 vs. 210 nm,³³ indicating a stronger complexation with a shift toward longer wavelength. In Fig. 1D, as the ratio between AS and H₂SO₄ decreased from infinity (only AS) to zero (only H₂SO₄), the pH was lowered while the sulfate species concentration was fixed. The redshift suggests that the binding affinity between Ce(IV) and the sulfate species is higher in a low-pH environment.

Fig. 1 (A) Ce L_III-edge XANES spectra of 1.23 M Ce(SO₄)₂ in a 1.05-M AS solution compared with the Ce(SO₄)₂, Ce₂(SO₄)₃ and CeO₂ standards. (B) Low-frequency Raman spectra of different concentrations of Ce(SO₄)₂ in 1.05 M AS. (C) UV-vis spectra of 0.615 mM Ce(SO₄)₂ in AS and H₂SO₄. (D) UV-vis absorption peak of 0.3075 mM Ce(SO₄)₂ in solutions with different ratios of AS to H₂SO₄ (SA). (E) High-frequency Raman spectra of 1.05 M AS and 1.23 M Ce(SO₄)₂ in 1.05 M AS. (F) Plots of intensity vs. hydrogen bonding type after 1.23 M Ce(SO₄)₂ was dissolved in 1.05 M AS.

Ce(IV) hydrolysis and complexation

The complexation between Ce and anions, especially in acidic supporting electrolytes, has been studied extensively.^36–38 In some recent studies, it has been found that in H₂SO₄, Ce(IV) tends to complex with HSO₄⁻ and the dominant structure is [Ce(IV)(H₂O)₆(HSO₄)₃]⁺.²² In aqueous solutions containing sulfate species, the speciation relationship between SO₄²⁻ and HSO₄⁻ is influenced by the dissociation equilibrium constants of H₂SO₄, and HSO₄⁻ is the dominant species when the pH is low, i.e., the dissociation of the first proton in H₂SO₄ is normally considered complete, but that of the second one is sluggish (SI Appendix, Section S2.1). Thus, a stable structure is obtained by the complexation between Ce(IV) and HSO₄⁻ instead of SO₄²⁻, whose quantity is negligible. In AS solutions, however, SO₄²⁻ would be the dominant species rather than HSO₄⁻ due to the much higher pH (5.4) of the solution, and proton dissociation from NH₄⁺ is unfavorable under neutral and acidic environments (SI Appendix, Section S2.2). As tabulated in the SI Appendix, Table S1, the pH of the AS solution decreased significantly after Ce(SO₄)₂ was dissolved, ensuring that most of the SO₄²⁻ ions were protonated to form HSO₄⁻. The cause of this dramatic pH reduction upon Ce(SO₄)₂ dissolution was further examined.

The hydrolysis of Ce(IV) in aqueous solution is considered to be very strong.³⁹ In an ideal solution where the anions do not complex with Ce(IV), the general reaction for Ce(IV) hydrolysis with water is as follows:

Ce⁴⁺ + iH₂O ↔ Ce(OH)_i⁴⁻ⁱ + iH⁺, (1)

where i is the hydration level with values between 0 and 4. The corresponding equilibrium constant, K_i, is defined as follows:

Using the values from previous literature,^40,41 the speciation abundance of different Ce(IV) compounds as a function of pH was generated (SI Appendix, Section S2.3 and Fig. S5). At higher pH, the hydrolysis of Ce(IV) is more prominent, indicating that it should be considered when AS is used as the supporting electrolyte. The Ce(IV) structure (e.g., [Ce(IV)(H₂O)₆(HSO₄)₃]⁺) proposed in previous studies did not consider this hydrolysis reaction, which could be explained by the following: (1) the pH of the supporting electrolyte used in those studies were low enough to retard Ce(IV) hydrolysis; (2) the Ce(IV) concentration used was very low (e.g., 0.25 mM), making it unnecessary to account for the pH change caused by Ce(IV) hydrolysis.²² In our study, however, the Ce(IV) concentration and the corresponding pH change indicated that a significant amount of Ce(IV) hydrolysis was taking place in the solution. When AS was the only supporting electrolyte, all protons were released by Ce(IV), and the number of protons released by each Ce(IV) was calculated from pH, Ce(IV), and sulfate concentration. Taking the electrolyte with the highest Ce(IV) concentration as an example, i.e., 1.23 M Ce(SO₄)₂ in 1.05 M AS, the concentration of total protons was calculated as follows:

TOT H⁺ = TOT SO₄ + 10^−pH₂ − 10^−pH₁ = 4.955 M, (3)

where pH₁ (5.4) and pH₂ (−0.16) represent pH values before and after Ce(SO₄)₂ dissolution, and the term TOT SO₄ represents the protons captured by SO₄²⁻ to form HSO₄⁻ because the latter is the dominant sulfate species at such a low pH. Then, two ratios could be easily obtained as follows:

The first ratio indicates that for each Ce(IV), four protons were released due to hydrolysis. The second ratio indicates that a complex could be attained where the ratio of Ce(IV) to HSO₄⁻ (following SO₄²⁻ protonation after Ce(IV) hydrolysis) is three, which coincides with a previous investigation.²² The occurrence of strong hydrolysis with water is supported by the Raman spectral signals at high Raman shift, indicating OH vibrations and hydrogen bonding in water molecules. As shown in Fig. 1E, in the Raman shift range between 2800 and 3800 cm⁻¹, the overall intensity after Ce(SO₄)₂ dissolution was significantly lower than that of the AS solution. In this range, the Raman spectrum of water can be deconvoluted into five bands centered at 3004, 3227, 3431, 3565, and 3633 cm⁻¹, respectively (details in the SI Appendix, Section S2.4).⁴² However, it has been reported that NH₄⁺ presents two stretching bands at 3061 and 3131 cm⁻¹.⁴³ Since the percentage of water hydrogen bonding at 3004 cm⁻¹ (single donor–double acceptor, DAA) is very small, the deconvolution was still performed based on all five bands, but the quantitative comparison was made by excluding the band at 3004 cm⁻¹. The deconvoluted results are shown in the SI Appendix, Fig. S6, and the intensities of four other types of hydrogen bonding were normalized based on the peak area of the AS solution, as illustrated in Fig. 1F. The intensities of the double donor–double acceptor (DDAA, 3227 cm⁻¹) and single donor–single acceptor (DA, 3431 cm⁻¹) were reduced to less than 50%, and that of free OH vibrations (3633 cm⁻¹) was nearly eliminated. The notable decrease in hydrogen bonding intensity indicates that water molecules are more structured by hydrolysis and complexation. Hence, we propose a new pathway for Ce(IV) dissolution and complexation in AS solutions that combines both hydrolysis with water and complexation with HSO₄⁻, to form the possible complex [Ce(OH)₄(HSO₄⁻)₃]³⁻, as depicted in Fig. 2. The bonding strength between Ce(IV) and HSO₄⁻ becomes weaker due to the negative charge carried by the hydroxide (OH⁻) ions, reducing the likelihood of Ce(IV)–sulfate precipitation and thus increasing Ce(IV) solubility. Similar calculations and analysis were performed on all three supporting electrolytes (water, H₂SO₄, and AS) with a lower Ce(IV) concentration (0.123 M) (SI Appendix, Section S2.5). In water, the ratio of Ce to sulfate was fixed at 1 : 2, suggesting that the stable structure, which requires a ratio of 1 : 3, was never achieved. As a result, the solution would tend to precipitate relatively quickly, as shown in the SI Appendix, Fig. S7. In H₂SO₄, the majority of total protons came from the acid itself instead of Ce(IV) hydrolysis, revealing that hydrolysis was thermodynamically unfavorable. At a relatively low concentration (e.g., 0.123 M Ce), the sulfate from Ce(SO₄)₂ could be fully protonated by H₂SO₄ and Ce(IV) hydrolysis, leading to the formation of stable Ce(IV) complex structures (the ratio of sulfate to Ce is much higher than 3). As the concentration of Ce(SO₄)₂ or H₂SO₄ is increased, however, free SO₄²⁻ starts to be non-negligible in the system, which competes with HSO₄⁻ to bind with Ce(IV) and precipitate as Ce(SO₄)₂ solid. This is a manifestation of the common-ion effect, wherein the solubility of Ce(SO₄)₂ decreases as the H₂SO₄ concentration increases.¹⁴ Notably, the calculation results for 0.123 M Ce(SO₄)₂ in 1.05 M AS suggest that eight protons were released, much higher than the highest number from hydrolysis with water (four). Thus, at this intermediate Ce(IV) concentration, NH₄⁺ can be hydrolyzed by Ce(IV) to release protons and a complex with –NH₃ can be formed. The participation of NH₄⁺ supports the earlier observation that the same concentration of Ce(SO₄)₂ was not able to dissolve in Na₂SO₄. The presence of free SO₄²⁻ in this solution (pH = 1.63) implies that the solution was not stable and would precipitate, and this was indeed observed experimentally as shown in the SI Appendix, Fig. S8. At even higher Ce(IV) concentrations (1.23 M), the protons from water hydrolysis were abundant and ammonium was re-protonated and detached. Based on the analysis above, a low pH environment that results in HSO₄⁻ being the dominant species of sulfate is key for a stable Ce(SO₄)₂ solution. Ce(IV) concentration and stability were found to be a function of the pH, and increase at low pH, but only if the acidity is generated by Ce(IV) hydrolysis instead of the addition of any acidic supporting electrolyte. Thus, the improved solubility is a result of the complementary and synergistic effects of Ce(IV) hydrolysis and complexation. We, herein, propose a new criterion for Ce(SO₄)₂ solubility in aqueous solution: the sulfate content does not decide the solubility, but a favorable complex between Ce(IV) and other species (i.e., water and HSO₄⁻) plays the key role. The low pH of the final solution is a prerequisite since it makes sure that HSO₄⁻ is the dominant sulfate species, but the low pH should come from Ce(IV) hydrolysis (e.g., in AS) to form Ce(OH)_i⁴⁻ⁱ intermediates, and not the solvent itself (e.g., H₂SO₄). A more quantitative study (e.g., density functional theory calculation and extended X-ray absorption fine structure) will be conducted in our future work to prove the Ce(IV) complex coordination.

Fig. 2 Schematic of the Ce(IV) hydrolysis and possible complexation coordination in an AS solution.

Electrochemical characterization

In this study, CP and CF were selected as candidates for electrodes on the Ce side. In our previous study,⁵¹ CF was proven to be degraded by the methanesulfonic acid-based Ce(IV) electrolyte, shown by the vanishing of the anodic peak and shifting of the cathodic peak towards the negative direction after CF was immersed in the Ce electrolyte for 24 h. A similar stability test was conducted in this study. The CVs revealed that with the AS supporting electrolyte, both peak positions and redox currents on CF electrodes remained stable after immersion in the Ce(IV) electrolyte for 24 h, as shown in Fig. 3B. The decrease in the oxidizing nature of Ce(IV) in AS (compared with the CH₃SO₃H supporting electrolytes) was attributed to the stronger complexation with sulfate species and hydrolysis with water, which made Ce(IV) more stable and harder to be reduced chemically. The comparison between the CVs of CP and CF in Fig. 3A and B and the SI Appendix, Table S2 demonstrates significant performance differences: better reversibility on CP (smaller peak separation) and enhanced reactivity on CF (higher peak currents).⁴⁴ The improved apparent kinetics on CF is attributed to its higher surface area, while the increased reversibility on CP is attributed to differences in surface functionalization (additional fundamental studies are needed, but are outside the scope of this study). Similarly, raw CP and HT CP, raw CF and HT CF were immersed in the Ce(IV)–AS electrolyte, and both anodic and cathodic peak currents dropped significantly for HT CF, indicating poor oxidative stability, as depicted in Fig. 3D and F. We hypothesize that the deterioration of HT CF in the Ce(IV) electrolyte was facilitated by the oxygen functional groups produced on the surface during thermal pretreatment. Based on these results, CF was selected as the electrode for the Ce side.

Fig. 3 CV plots of different carbon electrodes with 0.123 M Ce(SO₄)₂ in 1.05 M AS: (A) CP before and after immersion at 2.5 mV s⁻¹; (B) CF before and after immersion at 2.5 mV s⁻¹; (C) CF before immersion; (D) HT CF before immersion; (E) CF after immersion; and (F) HT CF after immersion.

The CVs of CF at different scan rates were analyzed to obtain the diffusion coefficients of the Ce complexes and the reaction rate constants. As shown in Fig. 3C, the peak potential separations at all scan rates were higher than 59 mV and increased with scan rate, suggesting that the Ce redox reaction was not readily reversible.⁴⁵ The N–S equation was used to calculate D₀ as follows:

i_p = 2.99 × 10⁵n^3/2α^1/2AC₀D^1/2₀ν^1/2 (6)

where i_p is the peak current, n is the number of electrons transferred during the reaction, α is the electron transfer coefficient, A is the electrode surface area, C₀ is the Ce concentration in bulk electrolyte, D₀ is the diffusion coefficient, and ν is the scan rate.^26,27 The transfer coefficient, α, was calculated using the following equation:where R is the universal gas constant (8.314 J mol⁻¹ K⁻¹), T is the temperature, F is Faraday's constant (96 485 C mol⁻¹), E_p is the peak potential, and E_p/2 is the half-peak potential.⁴⁶ The α values are tabulated in the SI Appendix, Table S3, and a clear deviation from 0.5 indicates that the reaction is irreversible. Similarly, the K–K equation was used for obtaining k₀ as follows:where k₀ is the standard rate constant, E₀ is the standard electrode potential, which was calculated from the average of cathodic and anodic peak potentials. The corresponding N–S and K–K plots are depicted in the SI Appendix, Fig. S9, from which the slope was used to calculate the value of D₀ and k₀, as tabulated in the SI Appendix, Table S4.

Ti–Ce RFBs test

The optimized Ce electrolyte was tested on CF electrodes in a Ti–Ce RFB. First, the Ti electrolyte was reduced to Ti(III) in a V–Ti cell configuration to enable us to cycle it with Ce(IV). The theoretical time for a single full charge of the V–Ti RFB was calculated to be 1.32 h, which was close to the actual duration (1.2 h), suggesting that all Ti(IV) was reduced to Ti(III) (ESI Appendix, Section S2.6). The QPEK-C-TMA AEM utilized in this study has been applied to several RFB systems with Ce, Ti, and V,^12,51–53 and the permselectivity was proven to be excellent without unwanted crossover. The high-frequency resistance (HFR), which includes ionic or contact resistance of different components in RFB,⁴⁷ is shown in Fig. 4A for the initial stage of Ti–Ce RFBs cycling. A significant fluctuation of HFR during discharge was observed with a peak value higher than 500 mΩ at the beginning of the discharge process. To put this in perspective, the HFR in all-V RFB cells is typically around 50 mΩ; thus, it is not a major performance limiter.^48,49 When a constant-current plus constant-voltage protocol was used, the large ohmic polarization in the early phase of discharge would bring the cell potential to the cut-off condition immediately, forcing the system into the next constant-voltage stage and lowering the energy efficiency (EE) (Fig. 4B). As the discharge proceeded, however, the HFR decreased to a more reasonable level (100 mΩ), which led to a remarkable phenomenon: the discharge current density in the constant-voltage phase was promoted to more than two times that of the constant-current stage (50 mA cm⁻²), indicating that significant discharge capacity was not utilized in the constant current (CC) stage (Fig. 4C). The hypothesis that this pronounced HFR was due to the precipitation of nanoparticles of Ce(III) stemmed from the low solubility of Ce(III) in sulfate environment being incorrect, as the HFR was not affected by increases in flowrate that would be expected to sweep away particulate precipitates inside the cell (see HFR as a function of electrolyte flowrate in SI Appendix Fig. S11). The conductivity of both Ce and Ti electrolytes is tabulated in the SI Appendix, Table S5, and the values were comparable with electrolytes of other RFBs.⁵⁰ Thus, the increase in HFR was traced back to the structure of the Ce(IV) complex in solution. As discussed earlier, Ce(IV) was bound with HSO₄⁻ to form a complex that is much larger than HSO₄⁻. Since an AEM was used in RFB tests, the transport of negative charge through the separator was required to maintain electroneutrality. Nonetheless, the substantial steric bulk and local positive charge of Ce(IV) would hamper this process, resulting in a high HFR. To discuss the effects of this complex on electrochemical reaction kinetics, the solvent reorganization energy, λ, which is the amount of energy required to re-organize the solvent configuration of the reactant to the state of the product, was calculated using eqn (9).⁵⁵ In this equation, α is the electron transfer coefficient, F is Faraday's constant (96 485 C mol⁻¹), E₀ is the standard potential of the considered reaction, which is the average of anodic and cathodic peak potential in CV, and ϕ_r is the potential at the plane of the reaction site versus the bulk solution. Since the reaction was assumed to occur at the surface of the electrode, E ≈ ϕ_r. Taking the CV of 10 mV s⁻¹ in Fig. 3C as an example, where α_c was 0.209 and E₀ was 1.1 V, the corresponding solvation overpotential, λ/F, was calculated to be 0.945 V. Given that the difference between the maximum applied potential (2 V) and E₀ was less than the solvation overpotential, the Ce complex is unlikely to be desolvated, indicating that the Ce(IV) complex was undergoing an outer-sphere electron transfer. In other words, the active redox couple at the positive electrode consisted of Ce complexes with different oxidation states rather than desolvated Ce⁴⁺ and Ce³⁺. The fact that the active species was in a bulky complex form also explains the steric bulk inducing high HFR. As the discharge advanced, more Ce(IV) was reduced to Ce(III) and free HSO₄⁻ was gradually released owing to the deficiency of Ce(III) in complexing with sulfate. Consequently, the HFR fell as the ionic charge carrier changed from the Ce(IV) complex to the far less bulky HSO₄⁻ ion. This postulation successfully correlates the HFR behavior with the proposed Ce(IV) structure in AS solution.

Fig. 4 Ti–Ce RFBs tests: (A) HFR, (B) cell voltage, and (C) current density with a constant-current + constant-voltage protocol; and (D) HFR, (E) cell voltage, and (F) current density with a constant-voltage + constant-current + constant-voltage protocol. Catholyte: 1.23 M Ce(SO₄)₂ in 1.05 M AS and anolyte: 1.23 M TiOSO₄ in 1.9 M AS after a full reduction to Ti(III).

To ensure that the majority of the discharge was concentrated in the constant-current phase, a short (2 min) constant-voltage (CV) step of 2 V was added before the constant-current segment with the intention of attenuating the HFR so that the following constant-current stage was terminated by mass transport polarization instead of ohmic polarization. As depicted in Fig. 4E and F, a discharge curve dominated by a constant-current phase was achieved with this new protocol, and the test showed an average EE of 70.2% and was operated consistently for more than 12 h. No second plateau was observed in Fig. 4E, further supporting that V was not crossing into the Ti side during the pre-charging of the V–Ti cell. The move from a typical CC–CV to a CV–CC–CV discharge profile is expected to have minimal impact on eventual grid integration. Grid applications require constant AC power output with frequency matching.^56–59 The battery management system (BMS) and the power conditioning system (PCS) are designed to ensure this and account for the typical constant DC current-constant DC voltage discharge profiles of batteries. The power conditioning systems coupled to a battery typically incorporate a DC–DC converter to ensure that the DC voltage output from the battery is within the optimal input range for the DC-to-AC converter. The AC output is, in turn, subject to a grid following (GFL) or grid forming (GFM) control scheme.⁶⁰ Thus, these systems will ensure that the AC output to the grid will be within acceptable parameters, even when a portion of the discharge happens at a constant DC voltage. After that, both EE and discharge capacity degraded due to the clogging of the tube and flow-field channel induced by Ce precipitation (SI Appendix, Fig. S12). The Ce precipitation was also detected in the CF electrode; the weight of CF after the cycling test was nearly doubled (SI Appendix, Table S6), and clear Ce deposition on graphite fiber was observed by scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) (SI Appendix, Fig. S13 and S14). However, if the precipitate and clogging inside the cell and tube were removed, the performance degradation would be entirely reversed, as shown in Fig. 5, proving that the performance degradation was mainly caused by clogging and not by other modes of irreversible capacity fading. The entrance and exit of flow field in this study was already enlarged compared with the conventional design (Fig. S1A), and the RFB test with the conventional flow field was not even able to finish a typical cycle, as shown in Fig. S15. Future work will focus on other strategies to prevent battery failure from clogging (e.g., by increasing channel widths of flow field and porosity of electrodes). Although the cycling performance shown here was worse than in our previous study using non-AS supporting electrolytes,^51,54 the high theoretical energy density (33.0 Ah L⁻¹) still indicates great potential for further development and application. Some alternative positive electrodes, e.g., Pt–Ti, will also be tested in future work to examine the role of the oxidative nature of Ce(IV) on the performance of the system. Notably, we have demonstrated diurnal cycling and cycling over several months using carbon felt-based positive electrodes with no deleterious effects.^12,51,54 The oxidative nature of Ce(IV) may even sustain catalytic oxygen functional groups on the positive electrode surface (originally generated by thermal treatment).

Fig. 5 Ti–Ce RFB performance with a constant-voltage + constant-current + constant-voltage protocol with clogging removed after the 15th cycle. The capacity fading between cycles 8 and 16 was reversible and due to the clogging of the cell tubing and electrode pores by the Ce precipitate, as seen in the ESI Fig. S12. The original capacity was recovered once the precipitates were washed off into the electrolyte tanks. Catholyte: 1.23 M Ce(SO₄)₂ in 1.05 M AS and anolyte: 1.23 M TiOSO₄ in 1.9 M AS after a full reduction to Ti(III).

Conclusions

The application of the Ce redox couple in RFBs is restricted by the low solubility of Ce. In this work, we developed a supersaturated Ce(IV) electrolyte with 1.23 M active species enabled by an ammonium sulfate-supported electrolyte. Complementary Ce(IV) hydrolysis and complexation were determined to be the primary factors contributing to this high solubility. In the AS solution, Ce(IV) was highly hydrolyzed with water to release protons, which reduced the pH and assisted in the formation of HSO₄⁻, and the strong complexation between Ce(IV) and HSO₄⁻ resulted in a stable structure, proposed as [Ce(OH)₄(HSO₄⁻)₃]³⁻. Notably, the operating current density and associated energy efficiency are higher than comparable cerium-based flow batteries observed in previous studies,¹¹ while simultaneously operating with a 40% higher Ce specific energy. Ti–Ce RFBs based on this electrolyte exhibited very high specific capacity (practically achieved 19 Ah L⁻¹ out of a nominal capacity of 33.0 Ah L⁻¹), energy efficiency over 70%, and no irreversible capacity fading, thus making the case for its use in grid-scale energy storage.

Author contributions

JX: conceptualization, data curation, formal analysis, investigation, methodology, validation, visualization, writing-original draft, and writing-review and editing; SS: conceptualization, formal analysis, methodology, writing-original draft, and writing-review and editing; JGC: data curation, writing-original draft, and writing-review and editing; VR: conceptualization, formal analysis, funding acquisition, methodology, project administration, resources, supervision, validation, visualization, writing-original draft, and writing-review and editing.

Conflicts of interest

The authors currently have no financial interests that may be perceived to influence the conclusions presented in this work. Some of the authors are seeking intellectual property protections on aspects of one or more technologies described in this report through the Office of Technology and Management (OTM) at Washington University in St. Louis (WUSTL).

Data availability

All data associated with these studies are represented in the manuscript and its supplementary information (SI). The raw data are available from the corresponding author upon reasonable request. Supplementary information is available. See DOI: https://doi.org/10.1039/d6ta01059h.

Acknowledgements

JX, SS, and VR would like to acknowledge the support of the Advanced Research Projects Agency-Energy (ARPA-E), the US Department of Energy, under the award no. DE-AR0000768 as a part of the Integration and Optimization of Novel Ion Conducting Solids (IONICS) program and the McKelvey School of Engineering, Washington University in St. Louis, and the Roma B. & Raymond H. Wittcoff Distinguished University Professorship. Yin-Yuan Huang is thanked for assistance with the Raman spectroscopy measurement. The work of JGC was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Critical Minerals and Materials program, under the Award Number DE-SC0022213. Elaine Flynn is thanked for assistance with sample preparation for the XANES analysis.

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