Materials. All reactions were performed using standard Schlenk and glovebox (Vigor) techniques under argon atmosphere. All chemicals were purchased from Energy Chemical Inc, stored in an Argon glovebox. Toluene were distilled from sodium/benzophenone prior to use, and other chemicals were used as commercially available without further purification. Deionized water was purged overnight using Ar before use.
Synthesis of NDI. The cationic Naphthalene diimide derivative NDI was synthesized following the literature procedure.63 1,4,5,8-naphthalene tetracarboxylic dianhydride (NTDA) (1 g, 3.73 mmol) was dissolved in 120 mL dry toluene under N2 atmosphere and heated to 90°C, and N, N-dimethyl-1,3-propanediamine (3 mL, 23.84 mmol) was added dropwise over 10 min. The reaction mixture was heated at 120°C for 24 h. The crude mixture was concentrated on a rotary evaporator, and the yellow crystalline NDI-1 was purified by recrystallizing from ethanol. Yield: 1 g (61%). A mixture of NDI-1 (1 g, 2.29 mmol), methyl chloride (5ml, 90.61 mmol), and 50 ml dry DMF were added. The solution was sealed in a pressure vial with a Teflon bushing and heated at 85°C for 12 h. The resulting suspension was cooled, collected by vacuum filtration, washed with DMF, acetone, and ether, and then dried in a vacuum to give NDI at 60°C overnight. A gray solid. Yield: 1.1 g (89%). 1H NMR (400 MHz, D2O) δ 8.59 (d, J = 2.4 Hz, 4H), 4.23 (t, J = 6.9 Hz, 4H), 3.57–3.48 (m, 4H), 3.14 (s, 18H), 2.32–2.22 (m, 4H). 13C NMR (101 MHz, D2O) δ 164.09, 131.02, 126.01, 64.03, 52.91, 37.65, 21.39. HRMS (ESI) m/z: [M − 2Cl]2+ calcd for C26H34N4O4 233.1285; found 233.12779.

Synthesis of PDI. The cationic perylene diimide derivative PDI was synthesized following the literature procedure.65 3,4,9,10-Perylenetetracarboxylic dianhydride (PTCDA) (2 g, 5.10 mmol) and N, N-dimethyl-1,3-propanediamine (6 mL, 47.68 mmol) were dissolved in 80 mL dry isobutanol and heated at 90°C for 24 h with stirring under N2 atmosphere. The crude product was filtered, washed with deionized water and ethanol. The obtained residue was treated with 5% aqueous NaOH solution at 90°C for 30 min to remove the unreacted raw material The suspended mixture was filtered, washed with water and ethanol, and dried under vacuum to give the product as red solid PDI-1. Yield: 2.6 g (90%). To a mixture of PDI-1 (2 g, 3.57 mmol), methyl chloride (8 ml, 144.98 mmol), and 150 ml dry toluene were added. The solution was sealed in a pressure vial with a Teflon bushing and heated at 105°C for 12 h. The resulting suspension was cooled, collected by vacuum filtration, washed with toluene, and ether, and then dried in a vacuum to give PDI at 60°C overnight. A brown-red. Yield: 2.2 g (93%). 1H NMR (400 MHz, CF3COOD) δ 8.94 (s, 8H), 4.62 (s, 4H), 3.81 (s, 4H), 3.37 (s, 18H), 2.61 (s, 4H). 13C NMR (101 MHz, CF3COOD). δ 165.93 (s), 136.37 (s), 133.24 (s), 129.41 (s), 126.44 (s), 124.48 (s), 121.85 (s), 64.88 (s), 53.22 (s), 37.92 (s), 21.84 (s). HRMS (ESI) [M − 2Cl]2+ calcd for C36H38N4O4 295.1441; found 295.14421.

Synthesis of TPDI. Compound TPDI was synthesized according to the literature.62 3,4,9,10-Perylenetetracarboxylic dianhydride (PTCDA) (1.62 g, 4.13 mmol) and N, N-dimethyl-1,3-propanediamine (30 mL, 201 mmol) were added and heated at 100°C for 28 hours, and then the temperature was gradually increased to 170°C over 4 hours. The mixture was then cooled to room temperature, and a mixture of ethanol and diethyl ether (1:3) was added. The resulting precipitate was collected by suction filtration, washed with diethyl ether, and dried under vacuum. A red solid TPDI-1. Yield: 2.4 g (90%). To a mixture of TPDI-1 (1.38 g, 2.13 mmol), water (6 ml), 85% formic acid (6.4 mL), and 30% formaldehyde (4.4 mL) were added. The solution was stirred at room temperature for 1 h and then heated at 120°C for 16 hours. Caution: at that time, the mixture would produce a lot of carbon dioxide, so it should be deflated slowly after the reaction. The solution was cooled to room temperature and then precipitated with ethyl ether, further to be centrifuged. The residue was dried under a vacuum. A red solid TPDI-2. Yield: 1.9 g (86%). A mixture of TPDI-2 (1.5 g, 1.45 mmol), dry MeOH (60 mL), and Na2CO3 (1 g) was stirred at room temperature for 12 h and then added methyl iodide (3 mL, 48.19 mmol), heated at 60°C for 12 h. The mixture was then cooled to room temperature and then precipitated with ethyl ether. The resulting precipitate was collected by suction filtration, washed with diethyl ether, and dried under vacuum. The product was exchanged for chloride by column anion exchange with Amberlite® IRA-900 chloride from anion exchange resin to give TPDI. A red solid. Yield: 1.39 g (90%). 1H NMR (400 MHz, CF3COOD) δ 8.95 (dd, J = 8.1 Hz, 8H), 5.10 (s, 4H), 4.56 (s, 20H), 4.35 (s, 8H), 3.60 (s, 36H). 13C NMR (101 MHz, CF3COOD). δ 167.80 (s), 136.82 (s), 133.39 (s), 129.63 (s), 126.73 (s), 124.66 (s), 121.57 (s), 54.43 (s), 53.64 (s), 52.02 (s), 49.62 (s), 44.23 (s), 35.56 (s). HRMS (ESI) [M − 3Cl]2+ calcd for C50H74N8O4 283.5272; found 283.52952.

Synthesis of 1,1`-bis[3-(trimethylammonio)-propyl]-4,4`-bipyridinium tetrachloride - [(NPr) 2 V]Cl 4 . Compound [(NPr)2V]Cl4 was synthesized according to the literature20. In a 250 mL N2 purged Schlenk flask, 4,4`-bipyridine (2.0 g, 12.8 mmol) was combined with (3-bromopropyl)trimethylammonium bromide (10 g, 38.3 mmol) in 15 mL of DMSO and stirred at 100°C for 3 h. The resulting precipitate was collected by suction filtration, washed with cold DMSO and acetonitrile. The product was exchanged for chloride by column anion exchange with Amberlite® IRA-900 chloride form anion exchange resin to give [(NPr)2V]Cl4. A white solid. Yield: 4.48 g (70%). 1H NMR (400 MHz, D2O) δ 9.09 (s, 2H), 8.51 (s, 2H), 4.74 (s, 2H), 3.47 (d, J = 4.4 Hz, 2H), 3.08 (d, J = 2.3 Hz, 9H), 2.57 (s, 2H).
Synthesis of (Ferrocenylmethyl)trimethylammonium Chloride – FcNCl.
FcNCl was synthesized according to a reported method.66 (Ferrocenylmethyl)dimethylamine (10 g, 41.2 mmol), methyl chloride (49.4 mL, 445.3 mmol), and 25 mL dry CH3CN were added to a round-bottom flask, which was stirred at RT overnight. The product was collected by filtration, washed with 10mL ether for 3 times, and dried under vacuum. A yellow solid. Yield: 10.9 g (90%). 1H NMR (400 MHz, D2O) δ 4.49 (t, J = 1.8 Hz, 2H), 4.40 (t, J = 1.8 Hz, 2H), 4.37 (s, 2H), 4.25 (s, 5H), 2.92 (s, 9H).
Materials Characterization. NMR spectra spectrum were collected using a Bruker 400 MHz NMR spectrometer. UV-Vis measurements were performed using a DH-2000-BAL Scan spectrophotometer. The cyclic voltammetry (CV) in solution were measured using CHI660E B157216. The Linear sweep voltammetry (LSV) was measured on a rotating disk electrode (RDE) device (Pine Instruments Co., USA, 0.1963 cm2). Electrochemical Impedance analysis (EIS) was performed using an Autolab electrochemical workstation (AUT86797-302N, Metrohm instruments, Switzerland). High-resolution mass spectra (HRMS) were collected on a Bruker maxis UHR-TOF mass spectrometer in an ESI positive mode. EPR was measured using a Bruker A300-9.5/12 instrument at room temperature in dry degassed methanol. The EPR parameters for the experiments are as follows: modulation frequency = 100 kHz, modulation amplitude = 1.0 G, time constant = 81.92 msec, conversion time = 80.00 msec, center field = 3514.503 G, sweep width = 1000 G, microwave attenuation = 26.3 dB, microwave power = 0.00471 mW. All battery tests were conducted under an Ar atmosphere. The flow battery was tested at RT on a battery tester (NEWARE instrument, CT-4008T-5V12A-S1-F). All photographs were taken using a Nikon D5100 digital camera.
Solubility tests. The solubility of imide derivatives was tested in 2 M NaCl solutions by UV-Vis spectrum.67 Firstly, adding imide derivatives into 2 M NaCl solutions until no further solid could be dissolved. A saturated solution of imide derivatives was obtained after centrifugation. Then take a small amount of the saturated solution and diluted it with a known magnification. The concentration was measured by the UV-Vis spectrum. Finally, the concentration was calculated according to a pre-calibrated absorbance-concentration curve of known concentrations of imide derivatives.
The cyclic voltammogram (CV) studies. All electrochemical CV experiments were carried out in 0.5 M NaCl electrolyte solutions. Redox potential was referenced to NHE. The glassy carbon electrode (d = 3 mm) was used for the working electrode, which was polished using Al2O3 suspended in deionized H2O, then rinsed with deionized H2O, and dried with airflow. The platinum sheet (1 cm2) was used for the counter electrode. The reference electrode consisted of a silver wire coated with a layer of AgCl and suspended in a solution of 3 M KCl electrolyte (Ag/AgCl, vs. NHE).
The electrochemical kinetics studies. All linear sweep voltammetry (LSV) studies were conducted using a CHI660E and a Pine in a three-electrode configuration. A glassy carbon rotating electrode (5 mm diameter) was used as the working electrode along with a platinum sheet counter electrode and an Ag/AgCl reference electrode same as used in LSV studies. Before data collection, the electrolyte was purged by Ar for 20 minutes to remove the oxygen dissolved in the electrolyte. LSV scans were recorded at a scan rate of 5 mV s− 1.
The diffusion coefficient (D, cm2 s− 1) was determined by the slope of the fitted Levich equation (Eq. 1).
$${i}_{l}=0.620nFAc{D}^{2/3}{v}^{-1/6}{\omega }^{1/2} \left(1\right)$$
where \({i}_{l}\) was the mass transfer limiting current from RDE tests, n was the electron transfer number, Faraday’s constant F = 96485 C mol− 1, electrode area A = 0.1963 cm2, concentration c = 1×10− 6 mol cm− 3, kinetic viscosity v = 9×10− 3 cm2 s− 1 (0.5 M NaCl aqueous solution), ω represented rotate speed (rad/s).
The electron transfer constant (\({k}_{0}\), cm s− 1) was calculated from the Koutecký-Levich equation (Eq. 2).
$${i}^{-1}={{i}_{l}}^{-1}+{{i}_{k}}^{-1}={\left(0.620nFAc{D}^{2/3}{v}^{-1/6}{\omega }^{1/2}\right)}^{-1}+{\left(nFA{k}_{0}c\right)}^{-1} \left(2\right)$$
where \(i\) represented the measured current, \({i}_{k}\) was the kinetic current (no mass transfer), which can be obtained from the butler-volmer equation (Eq. 3).
$${\eta }=\frac{2.303RT}{\alpha nF}\text{l}\text{o}\text{g}{i}_{0}-\frac{2.303RT}{\alpha nF}\text{l}\text{o}\text{g}i \left(3\right)$$
where \({\eta }\) represented over potential, \({i}_{0}\) was the exchange current, \(\alpha\) was the transfer coefficient, R is the universal gas constant (8.314 J K− 1mol− 1), and T is the temperature (298 K). When η was equal to 0, \({i}_{0}\) can be obtained and \({k}_{0}\) can be calculated by the following equation (Eq. 4).
$${k}_{0}=\frac{{i}_{0}}{FAc} \left(4\right)$$
Theoretical Calculations. To simulate the experimental UV-Vis in water, the Polarizable Continuum Model (PCM) as a self-consistent reaction field (SCRF) was used for the calculation of equilibrium geometries, vibrational frequencies, and excited state calculations. The geometries for the ground state of these compounds were optimized at the B3LYP hybrid functional and 6-311 + G(d) basis set for all atoms.35 The calculated maximum absorption wavelength (λTD-DFT), oscillator strength (f), molecular orbitals (MOs) involved in the main transitions were reported in this work. It should be pointed out that the structures of all stationary points were fully optimized, and frequency calculations were performed at the same level. The frequency calculations confirmed the nature of all revealed equilibrium geometries: there were no imaginary frequencies. The simulated UV–Vis spectra for optimized molecules were performed at the time-dependent density functional theory (TD-DFT/B3LYP) at the ground-state equilibrium geometries in water solution, in association with the 6-311 + G(d) basis set. All of the above computational calculations reported in this work were performed using the Gaussian 09 code.21,68 The volume was estimated using Marching Tetrahedron (MT) mothed, based on the vdW surface defined by ρ = 0.001 au isosurface, using the Multiwfn code.69 NMR chemical shifts for Nucleus-independent chemical shift (NICS)70,71 values were calculated at the points shown using the GIAO72 method.
Permeability measurements. The membrane permeability of active materials was measured with a homemade H-tube, assembling with two L-shaped glass tubes, two glass stoppers, one metal clip, and two gaskets separated by a piece of AMV membrane. The flange and gasket diameter is 17 mm. 20 mL solution of 0.02 M NDI (PDI, or TPDI) in 2 M NaCl was placed on one storage tank as the donating side, while the other storage tank filled with 20 mL 2 M NaCl was used as the receiving side. The whole device was placed on the agitator, and the magneton was added for stirring at all times. The crossover of active materials was periodically monitored by measuring the concentration of the solution in the receiving side by UV-Vis (test every two days).
The permeability of active materials was calculated using Fick’s law (Eq. 5).
\(\text{p}= \frac{\text{ln}\left(1-\frac{2{C}_{t}}{{C}_{0}}\right)\left(-\frac{{V}_{0}l}{2A}\right)}{t}\) \(\left(5\right)\)
Where P is the permeability (cm2 s− 1), Ct is the concentration measured at the receiving side at time t, C0 (0.02 M) is the initial concentration of active materials at the donating side. V0 (20 mL) is the initial volume on either the receiving or donating sides. A (2.19 cm2) is the effective membrane area. l (50 µm) is the thickness of the AMV membrane. t is the time (s).
In-suit UV-Vis spectra. The UV-Vis, computer, Neware instrument, and flow battery were connected in the glove box. Anolyte was stored in a customized cuvette (1 cm*1 cm*10 cm) and catholyte was stored in a sample bottle. The concentration of arylene diimide derivatives and FcNCl used are 10− 5 M and 2*10− 5 M for in-situ UV-Vis spectrum and their solution volume are 8mL and 20 mL, respectively. The flow rate is 30 ml min− 1. The current density is 0.5 mA cm− 2. The data is recorded quickly during charging and discharging.
Full cell tests. A home-made full battery was assembled with two steel plates, two polytetrafluoroethylene insulation plates, two Cu plate collectors, two graphite plates, and two graphite-felts, which are separated by AMV membrane. For NDI/FcNCl-based and TPDI/FcNCl-based AORFB, the active area is 9 cm2. For PDI/FcNCl-based AORFB, the active area is 4 cm2. The electrolyte materials with the same concentration are dissolved in 2 M NaCl. For one-electron storage, the anolyte and catholyte are 8 mL and 10 mL respectively. For two-electron storage, the anolyte and catholyte are 8 mL and 20 mL respectively. The electrolytes are pumped into the cell at a flow rate of 60 mL min− 1 through a peristaltic pump (BT100M, Baoding Chuang Rui Precision Pump Co., Ltd.). The reservoirs are purged with Ar to displace any O2 in the system and then sealed.
Electrochemical Impedance Spectroscopy (EIS). The Potentio-controlled Electrochemical impedance spectroscopy (EIS) of batteries were obtained by Nava with a frequency range from 0.01 Hz to 10 kHz.