Full cell measurements

The QBFB comprised a mixture of commercially available and custom-made components. Circular endplates were machined out of solid aluminium. Current collectors were 3 inch × 3 inch pyrolytic graphite blocks with interdigitated flow channels (channel width = 0.0625 inch, channel depth = 0.08 inch, landing between channels = 0.031 inch, Fuel Cell Technologies). Pretreated 2 cm2, stacked (×6) Toray carbon paper electrodes (each of which is about 7.5 μm uncompressed) were used on both sides of the cell. Pretreatment consisted of a 10 min sonication in isopropyl alcohol followed by a five hour soak in a hot (50 °C) mixture of undiluted sulphuric and nitric acids in a 3:1 volumetric ratio. Nafion 212 (50 μm thick) was used as a proton-exchange membrane (PEM, Alfa Aesar), and PTFE gasketing was used to seal the cell assembly. Membrane pretreatment was done according to previously published protocols7. Six bolts (3/8”, 16 threads per inch) torqued to 10.2 N m completed the cell assembly, and PTFE tubing was used to transport reactants and products into and out of the cell. The cell was kept on a hot plate and wrapped in a proportional integral derivative (PID)-controlled heating element for temperature control. On the positive side of the cell, 120 ml of 3 M HBr and 0.5 M Br 2 were used as the electrolyte solution in the fully discharged state; on the negative side, 1 M AQDS in 1 M H 2 SO 4 was used. HBr was used on the negative side instead of H 2 SO 4 for stability testing results displayed in Extended Data Fig. 9. State-of-charge calculations are based on the composition of the quinone side of the cell. 2,7-Anthraquinone disulphonate disodium salt 98% (TCI) was flushed twice through a column containing Amberlyst 15H ion-exchange resin to remove the sodium ions. Measurements shown here were done at 40 °C. March centrifugal pumps were used to circulate the fluids at a rate of approximately 200 ml min−1. For characterization, several instruments were used: a CH Instruments 1100C potentiostat (which can be used up to ±2 A), a DC electronic load (Circuit Specialists) for galvanic discharge, a DC regulated power supply (Circuit Specialists) for electrolytic characterization, and a standard multimeter for independent voltage measurements. The cell was charged at 1.5 V until a fixed amount of charge ran through the cell. During this process, the electrolyte colours changed from orange to dark green (AQDS to AQDSH 2 ) and from colourless to red (Br− to Br 2 ). Periodically, the open circuit potential was measured, providing the data inset in Fig. 1b. Also, at various SOCs, potential–current behaviour was characterized using the equipment described above: a fixed current was drawn from the cell, and the voltage, once stabilized, was recorded (Fig. 1b). For the cycling data in Fig. 2b, the potentiostat was used for constant-current (±0.5 A cm−2) measurements with cut-off voltages of 0 V and 1.5 V. For the cycling data in Fig. 2a, a more dilute quinone solution (0.1 M as opposed to 1 M) was used. Here, the half-cycle lengths were programmed to run at constant current for a fixed amount of time, provided the voltage cut-offs were not reached, so that half of the capacity of the battery was used in each cycle. The voltage cut-offs were never reached during charging, but were reached during discharge. Current efficiencies are evaluated by dividing the discharge time by the charge time of the previous half-cycle.

As shown in Fig. 2, current efficiency starts at about 92% and climbs to about 95% over ∼15 standard cycles. Note that these measurements are done near viable operating current densities for a battery of this kind. Because of this, we believe this number places an upper bound on the irreversible losses in the cell. In any case, 95% is comparable to values seen for other battery systems. For example, ref. 19 reports vanadium bromide batteries with current efficiencies of 50–90%, with large changes in current efficiency observed for varying membrane conditions. Our system will probably be less dependent on membrane conditions because we are storing energy in anions and neutral species as opposed to cations, which Nafion can conduct reasonably well.

In Fig. 2b we illustrate the capacity retention of the battery (that is, the number of coulombs available for discharge at the nth cycle divided by that available for discharge at the (n − 1)th cycle) to be 99.2% on average, which is quite high and provides direct evidence that our irreversible losses are below 1%. If we attribute all of this loss (the 0.78% capacity fade per cycle) to some loss of redox-active quinone, it would be equivalent to losing 0.0006634 moles of quinone per cycle. If we attribute all of the loss to bromine crossover (which would react with the hydroquinone and oxidize it back to quinone), this corresponds to a crossover current density of 1.785 mA cm−2, which is within the range of the widely varying crossover values reported in the literature20. Note that these crossover numbers can be very sensitive to membrane pretreatment conditions. It is also important to mention that, to determine very accurate current efficiencies, detailed chemical analyses of the electrolyte are necessary.

Half-cell measurements

These were conducted using a BASi Epsilon EC potentiostat, a BASi Ag/AgCl aqueous reference electrode (RE-5B, 3 M KCl filling solution) and a Pt wire counter electrode. Rotating disk electrode (RDE) measurements were conducted using a BASi RDE (RDE-2) and a 3 mm diameter glassy carbon disk electrode. Electrode potentials were converted to the standard hydrogen electrode (SHE) scale using E(SHE) = E(Ag/AgCl) + 0.210 V, where E(SHE) is the potential versus SHE and E(Ag/AgCl) is the measured potential versus Ag/AgCl. 2,7-Anthraquinone disulphonate disodium salt 98% was purchased from TCI and used as received. 1,8-Dihydroxy-anthraquinone-2,7-disulphonic acid was made according to the literature procedure21. The electrolyte solution was sulphuric acid (ACS, Sigma) in deionized H 2 O (18.2 MΩ cm, Millipore). The Pourbaix diagram (plot of E0 versus pH) shown in Extended Data Fig. 4 was constructed using aqueous 1 mM solutions of AQDS in pH buffers using the following chemicals: sulphuric acid (1 M, pH 0), HSO 4 −/SO 4 2− (0.1 M, pH 1–2), AcOH/AcO− (0.1 M, pH 2.65–5), H 2 PO 4 −/HPO 4 2− (0.1 M, pH 5.3–8), HPO 4 2−/PO 4 3− (0.1 M, pH 9.28–11.52), and KOH (0.1 M, pH 13). The pH of each solution was adjusted with 1 M H 2 SO 4 or 0.1 M KOH solutions and measured with an Oakton pH 11 Series pH meter (Eutech Instruments).

RDE studies

All RDE data represent an average of three runs. Error bars in Extended Data Figs 2 and 3 indicate standard deviations. Before each run, the glassy carbon disk working electrode was polished to a mirror shine with 0.05 µm alumina and rinsed with deionized water until a cyclic voltammogram of a solution of 1 mM AQDS in 1 M H 2 SO 4 showed anodic and cathodic peak voltage separation of 34 to 35 mV (39 mV for DHAQDS) at a sweep rate of 25 mV s−1. The electrode was then rotated at 200, 300, 400, 500, 700, 900, 1,200, 1,600, 2,000, 2,500 and 3,600 r.p.m. while the voltage was linearly swept from 310 to 60 mV (250 to −100 for DHAQDS) at 10 mV s−1 (Extended Data Fig. 1). The currents measured at 60 mV (−100 for DHAQDS) (that is, the diffusion-limited current density) versus the square root of the rotation rate (ω) is plotted in Extended Data Fig. 2. The data were fitted with a straight line, with the slope defined by the Levich equation as 0.620nFAC O D2/3ν−1/6, where n = 2, Faraday’s constant F = 96,485 C mol−1, electrode area A = 0.0707 cm2, AQDS concentration C O = 10−6 mol cm−3, kinematic viscosity ν = 0.01 cm2 s−1. This gives D values of 3.8(1) × 10−6 cm2 s−1 for AQDS and 3.19(7) × 10−6 cm2 s−1 for DHAQDS. The reciprocal of the current at overpotentials of 13, 18, 23, 28, 33, 38 and 363 mV was plotted versus the reciprocal of the square root of the rotation rate (Fig. 3b and Extended Data Fig. 2). The data for each potential were fitted with a straight line; the intercept gives the reciprocal of i K , the current in the absence of mass transport limitations (the extrapolation to infinite rotation rate). A plot of log 10 (i K ) versus overpotential was linearly fitted with a slope of 62 mV (AQDS) and 68 mV (DHAQDS) defined by the Butler–Volmer equation as 2.3αRT/nF (Extended Data Fig. 3), where R is the universal gas constant, T is temperature in kelvin and α is the charge transfer coefficient. This gives α = 0.474(2) for AQDS and 0.43(1) for DHAQDS. The x-intercept gives the log of the exchange current i 0 , which is equal to FAC O k 0 , and gives k 0 = 7.2(5) × 10−3 cm s−1 for AQDS and 1.56(5) × 10−2 cm s−1 for DHAQDS.

Stability studies

AQDS (50 mg) was dissolved in 0.4 ml of D 2 O, and treated with 100 µl of Br 2 . The 1H and 13C NMR spectra (Extended Data Figs 5a, b and 6a, b) were unchanged from the starting material after standing for 20 h at 25 °C. AQDS (50 mg) was then treated with 1 ml of 2 M HBr and 100 µl of Br 2 . The reaction was heated to 100 °C for 48 h and evaporated to dryness at that temperature. The resulting solid was fully dissolved in D 2 O giving unchanged 1H and 13C NMR (Extended Data Figs 5c and 6c); however, the 1H NMR reference was shifted due to residual acid. These results imply that bromine crossover will not lead to irreversible destruction of AQDS.

Sulphonation of anthraquinone and electrochemical study

9,10-Anthraquinone was treated with H 2 SO 4 (20% SO 3 ) at 170 °C for 2 h according to a literature procedure8. The resulting red solution, containing roughly 37% AQDS, 60% 9,10-anthraquinone-2,6-disulphonic acid and 3% 9,10-anthraquinone-2-sulphonic acid, was diluted and filtered. A portion of this solution was further diluted with 1 M H 2 SO 4 to ∼1 mM total anthraquinone concentration. The cyclic voltammogram (Extended Data Fig. 8) is similar to that of pure AQDS, though the anodic/cathodic peak current density is broadened due to the presence of the multiple sulphonic acid isomers.

Theory and methods

We used a fast and robust theoretical approach to determine the E0 of quinone/hydroquinone couples in aqueous solutions. We employed an empirical linear correlation of ΔH f , the heat of formation of hydroquinone at 0 K from the quinone and hydrogen gas, to the measured E0 values22. Following the treatment of ref. 22, the linear correlation is described as ΔG = −nFE0, where ΔG is the difference in total free energy between quinone and hydroquinone, n is the number of electrons involved in the reaction and F is the Faraday constant. The entropy contributions to the total free energies of reaction have been neglected because the entropies of reduction of quinones are found to be very similar22,23, and the E0 of the oxidation–reduction system is linearly expressed as (−nF)−1ΔH f + b, where b is a constant. It was also assumed that the reduction of quinones takes place in a single-step reaction involving a two-electron two-proton process9,24. The total free energies of molecules were obtained from first-principles quantum chemical calculations within density functional theory (DFT) at the level of the generalized gradient approximation (GGA) using the PBE functional25. The projector augmented wave (PAW) technique and a plane-wave basis set26,27 as implemented in VASP28,29 were employed. The kinetic energy cut-off for the plane-wave basis was set at 500 eV, which was sufficient to converge the total energies on a scale of 1 meV per atom. To obtain the ground-state structures of molecules in the gas phase, we considered multiple initial configurations for each molecule and optimized them in a cubic box of 25 Å using Γ-point sampling. The geometries were optimized without any symmetry constraints using the conjugate gradient (CG) algorithm, and the convergence was assumed to be complete when the total remaining forces on the atoms were less than 0.01 eV Å−1.

The search for conformational preference through theoretical calculations for each hydroxylated quinone is crucial because of the significant effects of intramolecular hydrogen bonds on the total free energies of the molecules30. Three-dimensional conformer structures for each quinone/hydroquinone molecule were generated using the ChemAxon suite (Marvin 6.1.0 by ChemAxon, http://www.chemaxon.com) with up to 25 conformers generated per molecule using the Dreiding force field31. The conformers generated were used as input structures for the DFT geometry optimization employed for determining ΔH f , which in turn is used to estimate E0 and .

To calculate the E0 of the hydroxy-substituted AQDS molecules (Fig. 3c), the correlation between ΔH f and E0 was calibrated from experimental data on six well-characterized quinones32. Specifically, we used the experimental values of the aqueous E0 and computed ΔH f of 1,2-benzoquinone, 1,4-benzoquione, 1,2-naphthoquinone, 1,4-naphthoquinone, 9,10-anthraquinone and 9,10-phenanthrene33. The training set ensures that the calibration plot addresses most classes and aspects of quinones, including two quinones each from 1-ring (benzoquinone), 2-ring (naphthoquinone) and 3-ring (anthraquinone and phenanthrene) structures. In addition, the experimental values of E0 of the training set spanned 0.09 V (9,10-anthraquinone) to 0.83 V (1,2-benzoquinone), providing a wide range for E0 (Extended Data Fig. 7). The linear calibration plot for E0 yields an R2 = 0.97 between the calculated ΔH f and E0 (Extended Data Fig. 7).

The values of the quinones in water were calculated using the Jaguar 8.0 program in the Schrödinger suite 2012 (Jaguar, version 8.0, Schrödinger). The standard Poisson–Boltzmann solver was employed34,35. In this model, a layer of charges on the molecular surface represents the solvent. was calculated as the difference between the total energy of the solvated structure and the total energy of the molecule in vacuum. A more negative value for corresponds to a quinone that is likely to have a higher aqueous solubility. An absolute prediction of the solubility is not readily available, as the accurate prediction of the most stable forms of molecular crystal structures with DFT remains an open problem36.

Cost calculations