Understanding the Aqueous Solubility of Anthraquinone Sulfonate Salts: The Quest for High Capacity Electrolytes of Redox Flow Batteries

Dissolving high concentrations of organic molecules in water has become a ubiquitously important task in the research of redox flow batteries (RFBs). A large variety of organic molecules have been exploited to replace vanadium salts in the most mature RFB systems so that a wide adoption of the technology will be constrained by the high and volatile cost of vanadium salts.^1,2 Among them, quinone,^3–5 nitroxyl radicals,⁶ and phenothiazine⁷ have all demonstrated outstanding performance with low redox potentials, high chemical stabilities, and low permeabilities through ion-selective membranes. Although solubility seems a less important property since RFBs aim at stationary energy storage, a low solubility and a bulky electrolyte will burden a RFB with a high cost of balance-of-site,⁸ hurting their chance to compete with the ever mature lithium-ion batteries.

However, the approach to design highly soluble molecules has relied largely on the intuition of synthetic chemists in favor of small, highly charged molecules, in a sharp contrast to the methodic designs for other properties like the redox potential. The most comprehensive theoretical study so far is an investigation into the aqueous solubility of quinone by Er et al.⁹ They applied density functional theory to study the solvation energy of quinone derivatives to elucidate the impact of functional groups. Similar strategies have been employed to predict the solubility of molecules in non-aqueous solvents.¹⁰ However, the models, which consider the equilibria between neutral molecules in vacuum and in water, hardly capture the physical process of the dissolution. Most of these molecules have conjugated structures, which take charged functional groups like sulfonate or phosphonate to dissolve well. The dissolution thus involves dissociation after breaking bonds in the solid, rather than the simple solvation of neutral molecules. Research has shown a strong dependence of the solubility of quinone molecules on their counter cations.^11,12 Another study has suggested that frustrated formation of ionic crystals could be responsible for a highly soluble bis-quinone derivative,¹² stressing the need of considering the solid phase when dealing with solubility.

Here, we use anthraquinone sulfonate salts as model systems to understand factors that determine their aqueous solubility. We synthesize 15 salts and measure with UV–vis spectroscopy their solubilities, falling a wide range of 1 mM to 1.2 M. We further perform single-crystal X-ray diffraction (XRD) to understand the impact from the solid structure of the salts. The results reveal insights into the design of highly soluble molecules for aqueous RFBs.

We focus on anthraquinone sulfonate salts for the following reasons. First, a variety of anthraquinone sulfonates are commercially available. Second, anthraquinone derivatives have demonstrated their potential in aqueous RFBs with rapid charge transfer kinetics, low redox potentials and high solubilities.^3,4,13 Third, they represent the typical structure of molecules for RFB applications, a redox-active but hydrophobic core functionalized with hydrophilic, anionic groups. At last, sulfonates have a sufficiently low pKa, so unlike other anionic groups (e.g. hydroxyl), the salts dissociate fully in water, which simplifies the aqueous speciation and eliminates the need to control the pH of the solution.

The three anthraquinone sulfonate molecules studied here are shown in Fig. 1. They are 2,7-anthraquinone-disulfonate (2,7-AQDS²⁻), 2-anthraquinone-sulfonate (AQS⁻), and 1,5-anthraquinone-disulfonate (1,5-AQDS²⁻), all purchased as sodium salts. The cations we choose are Na⁺, K⁺, Mg²⁺, Ba²⁺ and Ca²⁺, as they do not hydrolyze in water. With the combination of the above anions and cations, we can investigate how solubility depends on factors such as the number and the position of charged functional groups, the cations, and the structure of the solid salt.

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We follow two general procedures when preparing the quinone salts. The quinone molecules come as sodium salts, which first need to be purified through recrystallization. Take the preparation of 2,7-AQDS²⁻ salts for examples. We add to a concentrated 2,7-AQDSNa₂ solution a small amount of chloride salt with a different cation. If precipitate appears (in the cases of Ca²⁺ and Ba²⁺), we will collect it, wash it with deionized water, and dry it for solubility measurement. If the salt dissolves (in the cases of K⁺ and Mg²⁺), we will instead use the acid form (2,7-AQDSH₂) as the precursor, attained through ion exchanging the sodium salt. For the potassium salt, the acid is reacted with an exact amount of KOH for neutralization. For the magnesium salt, we neutralize the acid an excess amount of 4MgCO₃·Mg(OH)₂, which does not dissolve in a neutral solution. The supernatants after neutralization thus contain only the metal cation and the quinone, which is confirmed by measuring the pH of the solution. The supernatants are then dried for the salts.

We measure the solubilities with the light absorption of quinone that is independent of its counter cations when diluted to a low concentration. Compared to other common methods of solubility measurements such as gravimetry and elemental analysis, the use of spectroscopy offers a combination of high precision, convenience, and low material consumption, the last of which allows us to examine more than a dozen of compounds within reasonable time. The as-prepared salts are added to water at 50 °C, stirred, until deemed supersaturated. The mixture is then cooled down and filtered. The eluent is diluted for UV–vis spectroscopy. A calibration curve is established with the sodium salts of the quinone molecules. We assume Beer–Lambert's law for dilute solutions of these salts, whose absorbance (A) follows

$$\begin{eqnarray}&&A=\varepsilon CL,\end{eqnarray} \tag{ 1 }$$

where ε is the molar attenuation coefficient derived from the calibration, C the concentration of the quinone, and l the path length. UV–vis spectra for the three quinone molecules are shown in Fig. 1, where strong adsorption can be found at ∼260 nm, which was chosen to measure the solubility of quinone salts.

Table I summarizes all the results. They fall in a wide range from below 1 mM to above 1 M. The solubility of a salt apparently depends on the following a trend of Mg²⁺ > Na⁺ > K⁺ > Ca²⁺ > Ba²⁺, and the quinone anion with a trend of 2,7-AQDS²⁻ ≫ 1,5-AQDS²⁻ > AQS⁻. It is remarkable that the magnesium salts, instead of the most exploited sodium salts, are the most soluble ones for all three quinone molecules.

To understand the above trends, we invoke the thermodynamic cycle that separates the dissolution into steps of sublimation and hydration. The Gibbs free energy of dissolution (ΔG_diss) thereby comprises the sum of the hydration energy of ions (ΔG_h,i), minus the cavitation energy for water to accommodate the solute (ΔG_c) and the lattice energy of the salt being dissolved (ΔG_l), as in

$$\begin{eqnarray}&&{\rm{\Delta }}{G}_{diss}=\sum {\rm{\Delta }}{G}_{h,i}-{\rm{\Delta }}{G}_{c}-{\rm{\Delta }}{G}_{l}.\end{eqnarray} \tag{ 2 }$$

All ΔG's will be discussed in terms of their magnitudes. The contribution of ΔG_c is typically small in fully dissociated compounds,¹⁴ so we crudely leave it out of the discussion. The hydration energy of cations can be found in literature.¹⁵ The hydration energy of the quinone anions and ΔG_l's depend on the structures of the anions and the solids, respectively. Our approach here does not account for the inter-dependent nature of these terms of energies, and we will only compare contributions from the same type of ΔG. Nonetheless, we will show below that even with these simplifications, the discussion provides plenty insights into the aqueous solubility of the molecules.

The impact of the metal cations can be understood by considering their hydration energies and the lattice energies. The order of Mg²⁺ > Na⁺ > K⁺ follows the order of $\tfrac{1}{2}$ΔG_h,Mg2+ > ΔG_h,Na+ > ΔG_h,K+,¹⁵ where the factor of a half comes from the fact that the dissolution of one mole of quinone anions releases 50% fewer divalent cations. On the other hand, the low solubility of calcium and barium salts, despite the high hydration energies of Ba²⁺ and Ca²⁺, are likely the results of the high lattice energies. The lattice is held together by the dispersive forces among the conjugated structures and the Coulombic forces among the ions. The dispersive forces in the salts should be similar to that in anthraquinone, whose lattice energy (114 kJ mol⁻¹)¹⁶ is much lower than those of ionic organic salts.^17,18 Therefore, the Coulombic forces between the sulfonates and the metal cations should dominate the lattice energies.

The above insights allow us to empirically connect the solubilities of a quinone sulfonate salt and a sulfate salt if they share the same metal cation. Underlying this connection is the fact that the dissolutions of the two salts have the same hydration energy of the cation and the assumption that similar Coulombic forces exist in the two solids given the similarity between sulfates and sulfonates. The correlation is demonstrated for all the salts in Fig. 2, where a cation that makes a sulfate soluble also renders a highly soluble quinone sulfonate. This correlation will be a convenient first assessment when we design the composition of a RFB electrolyte, which should by no means be limited to sulfonated quinone.

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The differences between 2,7-AQDS²⁻ and 1,5-AQDS²⁻ salts root in the lattice energies, as the two anions are unlikely to differ significantly in their hydration energies. To support this interpretation, we grew the single crystals of the two sodium salts from water solutions with an ethanol layer on top. Single-crystal XRD reveals their structures as in Fig. 3. Compared to 2,7-AQDSNa₂, 1,5-AQDSNa₂ displays more complicated bonds to the sodium cations; the adjacent sulfonate and carbonyl groups chelate one cation, and another sulfonate has a short bond with another cation (Na2A-O1A, 2.2844(14) Å) indicative of a strong Coulombic force. Therefore, slight differences in the positions of functional groups can result in a major difference in the lattice structures, leading to the different solubilities.

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The hydration energies are responsible for the differences between the 2,7-AQDS²⁻ and AQS⁻ salts. Not only is the dissolution of 2,7-AQDS²⁻ favored energetically because of its high charge, it also brings more cations to the solution. The lattice energy does not play an as-important role, since we would expect the divalent 2,7-AQDS²⁻ to result in a more stable crystal. At last, the comparison between the 1,5-AQDS²⁻ and AQS⁻ salts embodies the challenge in predicting their aqueous solubilities, as the benefit from the high hydration energy of the divalent 1,5-AQDS²⁻ is countered by the high lattice energy of the salts, leading to solubilities similar to those of AQS⁻ salts.

An immediate application of the above results is in the design of a high-capacity neutral quinone electrolyte. 2,7-AQDS²⁻, the most soluble quinone out of the three, has been applied to the negative sides of acid RFBs.^19–21 If applied in a neutral RFB to take advantage of the lower redox potential, the routine choice of a cation would be either Na⁺ or K⁺, given the small size, the compatibility with other active materials in the positive side, and the high conductivity in a cation-selective membrane (e.g. Nafion). However, if aimed at a high capacity, our measurement suggests Mg²⁺. Therefore, we carried out cyclic voltammetry of a dilute solution of 2,7-AQDSMg (Fig. 4), which confirms its electrochemical reversibility.

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However, at a higher concentration, the reduction of 2,7-AQDS²⁻ leads to the precipitation of Mg(OH)₂, which precludes its application in a neutral RFB. The reaction goes as

$$\begin{eqnarray*}&&\begin{array}{l}M{g}^{2+}+2,7-AQD{S}^{2-}+2{H}_{2}O+2{e}^{-}\to Mg{\left(OH\right)}_{2}\\ \,\,\,\,\,+\,2,7-{H}_{2}AQD{S}^{2-},\end{array}\end{eqnarray*}$$

which is spontaneous given the pKa of the reduced quinone and the association constant of Mg(OH)₂.²² In another words, the reduced quinone renders the solution weakly basic, where Mg²⁺ hydrolyzes and precipitates. As a result, when we electrolyze a solution of 1 M 2,7-AQDSMg in a homemade H-cell, we immediately observe precipitation (the inset of Fig. 4), the XRD characterization of which confirmed the formation of solid Mg(OH)₂. Although we can buffer the solution to prevent the precipitation, it would introduce a large number of ions to limit the solubility of quinone and defeat the purpose of using 2,7-AQDSMg. The same issue will occur to other quinone molecules, but not to a molecule that does not involve protons in its electrochemical reaction, such as derivatives of methyl viologen.²³

We use three sulfonated anthraquinone molecules and fifteen different salts to investigate factors underlying their aqueous solubilities. The results emphasize the need to consider the cations and the lattice structures when designing quinone salts, which likely applies to other redox-active organic salts intended for high-capacity RFB electrolytes. We recommend that a computed descriptor, including the hydration energy and the lattice energy, must be used with precaution when explaining or predicting solubilities. Instead, we suggest using the solubility of common inorganic salts as a convenient tool to estimate the solubility of organic salts and to understand solubility trends.

Experimental

Acknowledgments