Selective ion transport through hydrated micropores in polymer membranes

Synthesis of cPIMs

To an AO-PIM-1 solution (2 wt% in dimethyl sulfoxide) was added an anhydride in one portion (5 mol eq. relative to the repeating unit of AO-PIM-1). After full dissolution of the anhydride, the mixture was stirred at 30 °C for a further 4 h; then, potassium ethoxide was added (13 mol eq. relative to the repeating unit of AO-PIM-1). The mixture was vigorously stirred at room temperature for 1 h and then poured into 400 ml water. Hydrochloric acid was added dropwise to the solution until the pH reached 1–2. The precipitate was filtered, suspended in 0.5 M aqueous H₂SO₄ and heated to reflux for 4 h. The powder was collected by filtration, washed with deionized water and acetone, and briefly dried in air at 110 °C for 1 h to yield a free-flowing yellow powder. Extended drying was found to afford insoluble polymers, probably owing to anhydride formation among carboxylic acid groups.

This reaction was previously reported for synthesizing small drug molecules³⁴ but had not been explored for polymer construction. When used in postpolymerization modifications, the reaction efficiency remained high under ambient conditions, with full conversion achieved in a few hours. Three commercially available, low-cost anhydrides (succinic anhydride, phthalic anhydride and diphenic anhydride) were used in the synthesis to attach ethyl-, phenyl- and biphenyl-containing pendant groups to the polymer backbones. More details are available in Supplementary Information.

Membrane fabrication

Polymer powders were dissolved in dimethyl sulfoxide at concentrations of 4–10 wt% and centrifuged at 12,000 rpm for 10 min to remove insoluble impurities. Free-standing membranes were fabricated by casting polymer solutions on to glass plates or in glass Petri dishes, followed by solvent evaporation at 60 °C over 2 days. Polymer membranes were peeled off the glass substrates by immersion in water. Membranes in K⁺ ion form were obtained by deprotonation and ion exchange in 1 M aqueous KOH at room temperature overnight, followed by washing and immersion in deionized water or a suitable electrolyte solution three times, with each immersion lasting at least 6 h. Film thickness was measured with a micrometer.

For thin film composite (TFC) membranes, polymer solutions were prepared by dissolving polymer powders in tetrahydrofuran at concentrations of 0.5 or 3 wt% in an autoclave at 160 °C for 2 h. The solutions were dried over anhydrous MgSO₄ and centrifuged at 12,000 rpm for 10 min to remove undissolved impurities. Porous polyacrylonitrile (PAN) ultrafiltration membranes were used as the substrate to provide mechanical support. To enhance hydrophilicity, PAN membranes were hydrolysed in 1 M KOH solution (H₂O/EtOH, 1:1 by volume) for 1–2 h at 40 °C before use. TFC membranes were prepared by spin-coating 1 ml of polymer solution on to PAN membranes. This procedure was repeated once to ensure a defect-free surface morphology, resulting in a selective layer with a thickness of 70–100 nm for 0.5 wt% polymer solutions at 1,000 rpm and around 1 µm for 3 wt% polymer solutions at 500 rpm. The thickness of the selective layer was characterized by atomic force microscopy and scanning electron microscopy. TFC membranes fabricated with 0.5 wt% polymer solutions were used for pressure-driven water permeation tests, whereas those with 3 wt% cPIM-Ph solutions were used for cross-over tests. Before use, TFC membranes were pretreated in 1 M aqueous KOH at room temperature overnight for deprotonation and ion exchange of cPIM thin layers, followed by washing and immersion in deionized water or a suitable electrolyte solution three times, with each immersion time lasting at least 6 h.

Gravimetric uptake and dimensional swelling ratio

Membrane samples were dried at 110 °C under vacuum for 12 h, quickly placed in a sealed glass vial and weighed with a high-precision analytical balance to obtain the dry mass. These samples were immersed in deionized water or an electrolyte solution at room temperature for 24 h. The mass of fully hydrated samples was measured after the excess surface water had been quickly wiped off with tissue paper. Water/electrolyte uptake was calculated according to equation (1):

where W_hydrated and W_dry are the masses of fully hydrated and dry membrane samples, respectively. Hydration numbers of carboxylate groups were derived from the uptake normalized by ion-exchange capacity.

The linear swelling ratio in liquid electrolytes was determined from the difference in linear dimensions between the hydrated (l_hydrated) and dry (l_dry) free-standing membranes, measured using a micrometer, and was calculated according to equation (2):

Linear swelling ratios under different relative humidities were measured with a Semilab SE-2000 variable-angle spectroscopic ellipsometer within the spectral range of 248 nm to 1,653 nm in a controlled humidity chamber. Samples were prepared by spin-coating the polymer solution on to Au-coated silicon wafers to obtain a thickness of around 600 nm. All ellipsometry data were analysed with Semilab SEA software, using the Tauc–Lorentz and Gauss dispersion laws for optical model fitting. As ellipsometry measured the volumetric change of the membrane samples (V), the linear swelling ratio was calculated according to equation (3):

Hydration capacity is a thermodynamic property of polar and charged functionalities, and the overall membrane hydration is, in general, linearly proportional to the amount of such functional groups present in the polymer, while also being influenced by external salt concentration and temperature. Hence, various electrolyte concentrations and temperatures were deployed to evaluate gravimetric uptake and dimensional swelling.

Ionic conductivity

The apparent through-plane ionic conductivity was measured by two-electrode EIS with an a.c. bias of 10 mV and a frequency range of 0.2 MHz to 10 Hz. Membrane samples were pretreated in 1 M aqueous KOH to fully deprotonate carboxylic acid groups and then soaked in 1 M aqueous KCl three times, with each immersion time lasting at least 6 h. The membranes were then sandwiched between two stainless steel electrodes and sealed with coin cells (type 2032), with extra electrolyte solution added. The assembled coin cells were placed in a temperature-controlled oven for conductivity measurement.

For highly conductive membranes with an areal resistance less than 2 Ω cm² (cPIM-1, cPIM-Et, cPIM-Ph and pretreated Nafion), different layers of membranes were stacked to afford varied thickness, and the stacked membranes were subjected to EIS measurements^35,36. The stack thickness was linearly fitted with areal resistance to derive the slope as the ionic conductivity, avoiding contributions to membrane resistance from contact and electrode resistance.

For membranes with an areal resistance greater than 2 Ω cm² (cPIM-BP and as-received Nafion), the ionic conductivity was calculated on the basis of a single measurement according to the following equation:

where R_m is the apparent resistance measured from Nyquist plots, L is the membrane thickness, A is the active membrane area (2.00 cm²) and R_m represents resistance from contact and electrode resistance (0.2 Ω cm²) measured from a shorted cell without membrane and verified by the stacking method.

Apparent ion transference number

V–I curves were measured in an H-shaped cell using two Ag/AgCl electrodes (3.0 M KCl) and recorded with a potentiostat (Biologic SP-150). In the middle of the cell, a membrane was sandwiched using two O-rings to separate the two compartments. The apparent ion transference number (t) was calculated from the zero-current potential (V₀), which is equal to the membrane potential, using the following equation:

where k_B is the Boltzmann constant, z is the ion charge number, T is the Kelvin temperature, e is the elementary charge, Î”C is the ratio of high concentration to low concentration (ΔC = 10), and γ_high and γ_low are the activity coefficients of the high-concentration solution and the low-concentration solution³⁷, respectively.

Cross-over

The cross-over of redox-active molecules was measured using stirred H-shaped cells. Membranes were sandwiched between two O-rings and placed in the middle of H-shaped cells with an effective membrane area of 1.54 cm². Feed and permeate solutions were 0.1 M redox-active molecules dissolved in 1 M aqueous KCl (or KOH) solution and 1 M aqueous KCl (or KOH) solution, respectively. Constant stirring was applied to alleviate concentration polarization near membrane surfaces. The concentration change of the permeate solution for K₄Fe(CN)₆ cross-over was monitored by taking 0.1 ml aliquots to 9.9 ml 2 wt% aqueous HNO₃ for inductively coupled plasma mass spectrometry (ICP-MS) measurements, whereas for the cross-over of organic molecules, aliquots were taken without dilution for ultraviolet–visible spectroscopy analysis and recycled back to the permeate solution. The permeation rate (flux) of ions and redox molecules across the membrane follows Fick’s first law:

where J is the permeation rate (mol cm^−2 s^−1), V is the solution volume (ml), A is the effective membrane area (1.54 cm²), C is the concentration of the permeate solution (mol cm^−3) and t is the diffusion time (s). As C₂ ≪ C₁ (hence C₁ − C₂ ≈ C₁), under the assumption that boundary resistances next to the membrane are negligible, Fick’s first law can be simplified as:

where p is the permeability (cm²â€‰s^−1), C₁ is the concentration of the feed solution (mol cm^−3) and l is the membrane thickness (cm).

Free-standing membrane samples were used for cross-over tests with a typical membrane thickness of around 50 µm, except for cPIM-Et, which had a thickness of 120 µm. However, the cross-over rate for 50-µm-thick cPIM-Ph membranes was too slow to be detected within a reasonable testing period. For example, in the tests for K₄Fe(CN)₆ cross-over, the concentration on the permeate side remained below the ICP-MS detection limit even after 100 days. Although estimates based on equipment detection limits can provide a upper limit for cross-over rates, they lack accuracy. To address this, TFC membranes with a 1.1-µm-thick cPIM-Ph layer were fabricated for cross-over tests, allowing reliable quantification of the permeation rate within a reasonable timeframe. The results are summarized in Supplementary Table 3. Transport resistance from the porous PAN support in TFC membranes was negligible; for example, it exhibited a K₄Fe(CN)₆ permeation rate of 0.28 mmol l^−1 h^−1, several orders of magnitude faster than that of TFC membranes.

Pressure-driven water permeation

Water permeation tests were performed using a dead-end stirred cell (Sterlitech) at various pressures in the range of 1–9 bar. The effective membrane area of the dead-end cell was 12.56 cm². Before measurement of water flux under different pressures, a pressure of 20 bar was applied for at least 6 h until steady permeance was achieved. At least three independent TFC membrane samples were tested to confirm the reproducibility.

NMR spectroscopy

NMR experiments were performed on a Bruker Avance III spectrometer equipped with a 7.0 T superconducting magnet operating at a ¹H frequency of 300.13 MHz and at a sample temperature of 302.5 ± 0.3 K unless stated otherwise. ¹H pulsed gradient stimulated echo (PGSTE) NMR was performed using a 5 mm ¹H radiofrequency coil and ⁷Li PGSTE NMR using a 10 mm ⁷Li radio-frequency coil, both in a Bruker diff30 probe with a maximum gradient strength of 17.7 T m^−1. ¹H NMR spectra were acquired for each hydrated cPIM sample with a 10 kHz spectral width, four signal averages and a repetition time of 5 s. Chemical shifts were referenced externally to the water peak in a spectrum of 1 M LiCl in water, as this was sufficient for the intention of measuring the line widths, but chemical shift values may have varied owing to random drift during shimming and are not necessarily accurate. The \({{T}}_{2}^{\ast }\) relaxation times were calculated from the full width at half maximum values for each peak³⁸, which were found by fitting to a Lorentzian function using dmfit software³⁹.

Sample preparation

Polymer films were pretreated in 1 M aqueous LiOH overnight, followed by washing and immersion in 1 M aqueous LiCl more than three times, for at least 6 h each time. Fully hydrated polymer samples were quickly rolled up and placed into NMR glass tubes (Norell, 5 mm) after the excess surface water had been wiped off with tissue paper.

Self-diffusion coefficient

¹H and ⁷Li PGSTE NMR experiments with bipolar gradients were used to measure the self-diffusion coefficients of water molecules and ions in hydrated polymer membrane samples. Of note, Li⁺ self-diffusion coefficients were measured, rather than K⁺, because of the relatively low receptivity, gyromagnetic ratio or sensitivity of ³⁹K, ⁴⁰K and ⁴¹K. Self-diffusion coefficients were calculated from a plot of signal intensity, S_G, against the gradient strength, G, using the Stejskal–Tanner equation:

where S₀ is the signal intensity when G = 0, γ is the gyromagnetic ratio, δ is the gradient pulse length and Δ is the observation time between gradient pulses.

Typical parameters for ¹H PGSTE NMR experiments were 16 gradient steps, spectral width (SWH) = 10,000 Hz, δ = 0.57 ms and a minimum of 28 signal averages. Typical 90° pulse lengths fell in the range 7.5–9.0 μs. Experiments were carried out over a range of observation times, Δ = 5.9, 6.5, 7.0, 7.5, 8.0, 10, 15, 20 and 30 ms. Typical parameters for ⁷Li PGSTE NMR experiments were eight gradient steps, SWH = 20,000 Hz and δ = 1 ms, with a minimum of 256 signal averages. Typical 90° pulse lengths were around 17.5 μs. Experiments were carried out at observation times of Δ = 8, 10, 12, 15, 20, 30, 50, 75, 100 and 120 ms. Maximum gradient strengths, G_max, were chosen to minimize S_G/S₀. Error bars were determined from the average standard deviation of three repeats of experiments in which Δ = 10 and 50 ms. ⁷Li PGSTE NMR experiments were also performed on cPIM-Et and cPIM-Ph at temperatures 289.5, 293.5, 298.0, 302.5 and 306.5 ± 0.3 K. Eight gradient steps were used with δ = 1.5 ms, Δ = 30 ms and G_max = 17 T m^−1, with SWH = 20,000 Hz and 256 signal averages.

To assess the presence of restricted diffusion, the MSD over time, ⟨[r′(t) − r(0)]²âŸ©, was determined from the measured diffusion coefficient, D, using the Einstein definition⁴⁰

and was plotted as a function of the observation time, Δ.

Molecular simulation

All-atomistic molecular dynamics simulations were performed in the Large-scale Atomic/Molecular Massively Parallel Simulator⁴¹. Polymer and ion interactions were described by the OPLS-AA forcefield, and water was described by the TIP4P/EW model^42,43. Water bonds and angles were restrained using the SHAKE algorithm⁴⁴. A short-range cutoff of 12 Å was used for non-bonded interactions, and long-range coulombic interactions were implemented with the particle–particle particle–mesh technique. A timestep of 1.0 fs was used. The forcefield combination and equilibration scheme used in this work have been previously validated for ionic polymers, showing good agreement with experimental densities and X-ray scattering data^45,46. The detailed procedure for construction of the polymer models is available in Supplementary Information.

Pore-size analysis

The pore networks formed in the dry and hydrated models were analysed using the Zeo++ package⁴⁷. All structural analyses were the average of five independent models with frames captured every 1 ns over a total 20 ns of molecular dynamics. This was done to capture a statistical representation of polymer conformations as well as the dynamic flexibility of the hydrated models. For the hydrated models, water and ions were considered part of the mobile phase and were removed from each frame before geometric analysis. Pore size distributions were measured with a 1 Å probe and 60,000 Monte Carlo samples. The specific volume occupied by the polymer chains (V_vdW) was determined by sampling the polymer box using a probe size of zero. Fractional free volume was calculated on the basis of the volume of the simulated box (V_box) and V_vdW using the following equation⁴⁸:

Degree of percolation

Water network characterization used the average of five independent models across 20 ns of molecular dynamics simulation sampled every 1 ns, using a distance-based clustering algorithm. Given the xyz coordinates of the water phase, any two water molecules were considered to be in an interconnected pathway if the distance between their oxygen atoms was within 3.5 Å. This distance was chosen to encompass the entire first peak in the oxygen–oxygen RDF for the TIP4P water model. We calculated both the average number of clusters in each system and the fraction of water molecules in the largest cluster. The degree of percolation was defined as the percentage of water molecules in the largest cluster over all water molecules.

Radial distribution functions

RDFs, g_ab(r) between two groups of atoms, a and b, within the polymer models were calculated using the MDAnalysis package over trajectories of 20 ns with frames every 10 ps.

We also calculated the radial number density distribution function (n_ab(r)) for a more direct comparison between systems with different numbers of atoms, where ρ is the number density of observed atoms:

Self-diffusion coefficient

Mean square displacement (MSD) was plotted every 10 ps over a trajectory of 20 ns. Self-diffusion coefficients (D_self) were then extracted from the slope of the linear portion of the MSD according to the Einstein relation, where d is the dimensionality (in our case, 3), by the following equation:

Pore surface composition

To characterize the per-atom distribution along the pore surfaces, visual pore size distributions were generated using the Zeo++ package⁴⁷ with a 1-Å probe, and the Euclidean distances between pore spheres and polymer atoms were calculated. Atoms located within 1 Å of any pore sphere were identified as pore surface atoms, whereas any outside this range were identified as being buried within the polymer matrix. This analysis was performed for a single snapshot; minor fluctuations will have occurred with motion of the systems.

Neutron scattering

Fixed window scan

Fixed window scans (FWS) were acquired on BASIS (SNS, USA) from 30 to 333 K at a heating rate of 0.13 K min^−1. The scattering signal was integrated at either ΔE = 0 (elastic; EFWS) or around an arbitrarily chosen energy range (inelastic; IFWS) with an integration width equivalent to E_res.

EFWS can be used to identify the temperature at which relaxation processes become detectable within the spectroscopic timescale, indicated by a change in slope. Under the assumption of harmonic oscillations (T ≤ 100 K, for which the Debye–Waller approximation is valid), EFWS is also effective for calculating the temperature dependence of the MSD, ⟨u²âŸ©, of hydrogen atoms:

IFWS can differentiate between local (for example, rotational and/or nanoconfined) and diffusive motions. Local motions are characterized by Q-independent maxima in the inelastic intensity, whereas diffusive motions show Q-dependent maxima. IFWS analysis can also be used to estimate activation energy.

where B is a constant accounting for the resolution function, ω_off is the energy offset, τ is the relaxation time (with τ₀ the high T limit), A₀ is the elastic incoherent structure factor, k_B is the Boltzmann constant and E_A is the activation energy⁴⁹.

Quasielastic neutron scattering

QENS profiles of cPIM-Et and cPIM-Ph were acquired at two facilities to capture dynamics across different timescales: (1) BASIS (SNS, USA)⁵⁰ with an E_res of 3 μeV, covering the nanosecond timescale (~0.02 < τ < 2 ns); and (2) LET (ISIS, UK)⁵¹ to explore picosecond relaxation dynamics. The repetition rate multiplication method used with LET enabled simultaneous recording at three E_res values (14.6, 32.8 and 91.3 eV) with incident neutron energies of 1.03, 1.77 and 3.70 meV, respectively, covering the timescale range of ~1.5 < τ < 200 ps. By combining these timescales, a comprehensive relaxation profile was constructed to fully characterize the sample dynamics.

For cPIM-BP, QENS profiles were acquired on the IRIS spectrometer (ISIS, UK) using the PG002 analyser crystal set-up, which provided an energy resolution of 17.5 μeV and covered the momentum transfer range of 0.56 ≤ Q ≤ 1.84 Å^−1, probing motions within the timescale range of 5 < τ < 100 ps. To ensure consistency across different instruments, QENS profiles of cPIM-Ph were also measured under similar conditions using IRIS, allowing for direct comparison with the BASIS and LET results.

The QENS signal appears as broadening in the energy transfer function due to relaxational and/or diffusional dynamics. Analysis of the scattering function, S(Q, ω), which reflects the time Fourier transform of the intermediate scattering function, I(Q, t), provides information on the static and dynamic correlations of different nuclei (S_coh) and the spatiotemporal correlation between identical nuclei (S_inc). The latter includes contributions from vibrational (S_v), translational and/or diffusional (S_t) and rotational/reorientation (S_r) motions:

where R is the resolution function and is experimentally determined using a vanadium standard or sample at a base temperature of approximately 10 K on the assumption that dynamics are not detectable as all protons are in a quasistatic configuration and therefore contribute only to the elastic component. In isotropic cases, S_v becomes equal to \({{\rm{e}}}^{-\frac{1}{3}{Q}^{2}\langle {u}^{2}\rangle }\), where ⟨u²âŸ© is the MSD accounting for vibrational excitations and proton delocalization occurring on timescales faster than the spectroscopical window.

Relaxation dynamics in QENS data are typically described by distinct Lorentzian functions and classified as accessible or non-accessible within a certain spectroscopic window. For accessible dynamics, translational and rotational components can be discriminated by the dispersive or non-dispersive behaviour, respectively, of the Lorentzian line width (Γ, half-width at half-maximum) as a function of Q². Dynamics that exceed the instrument resolutions are classified as: (1) extremely fast dynamics, which produce an extraordinarily broad signal approximated by a relatively flat background function, B(Q); or (2) extremely slow dynamics (such as ‘immobile’ protons) incorporated within the elastic scattering signal [δ(ω)].

The Gaussian model describes molecular motion in a restricted geometry with ill-defined boundaries⁵² and is well suited to analysis of translational water diffusion within membrane hydrated pores. This model has been widely used in systems such as Nafion⁵³ and polyamide⁵⁴. Localized and long-range water diffusion coefficients (D_loc and D_lr) in cPIM membranes were quantified on the basis of the following Gaussian model:

where τ is the characteristic time of the local jump diffusion, and σ is the confinement domain size.

Sample preparation

Two isotopic contrasts, D₂O and H₂O, were used to disentangle water and polymer dynamics by fully hydrating membrane samples with each. In D₂O-hydrated samples, only localized motions associated with polymer matrix dynamics were visible, enabling capture of polymer dynamics in the swollen state. Of note, for cPIM-Et, the high D₂O content meant polymer dynamics acquired at high temperatures may also reflect D₂O dynamics. In H₂O-hydrated samples, both polymer dynamics and translational water dynamics were captured. Potassium-exchanged membranes were fully hydrated, pad-dried to remove surface water, and then stacked in four sheets. These sheets were quickly wrapped in aluminium foil and loaded into aluminium flat cells (4 cm × 5 cm). The aluminium cell, with an inner thickness of 0.5 mm, achieved around 90% neutron transmission. Indium was used to seal the cell. Scattering profiles were acquired between 200 and 333 K, covering a Q range of 0.3 to 2.1 Å^−1. For normalization, complementary scattering profiles for the vanadium standard, an empty aluminium cell and samples at 5 K were also obtained. Data analysis was carried out on the S(Q, ω) spectra using Mantid⁵⁵ and DAVE⁵⁶. Data in the energy domain were analysed at fixed energy resolution, Fourier transformed to the time domain, scaled to obtain a unique relaxation profile, and analysed at fixed Q and temperature.

Flow battery tests

Cell hardware (Scribner Associates) with POCO single serpentine pattern graphite plates was used to assemble the flow cells. A piece of membrane was sandwiched between electrodes with an effective geometric area of 7 cm², comprising a stack of three sheets of carbon paper (Sigracet SGL 39AA). The remaining space between graphite plates was sealed with Viton gaskets. Electrolytes were fed into the cell at a flow rate of 40 ml min^−1 through a Cole-Parmer peristaltic pump. All measurements were conducted in an argon-filled glovebox.

Carbon papers were pretreated by baking at 400 °C in the air for 24 h. Nafion 212 was pretreated following an established protocol⁵⁷. Before full cell tests, membranes were soaked in 1 M aqueous KCl for 24 h. Membrane thicknesses were 45, 55 and 50 µm for cPIM-PA, Nafion 212 and sPEEK membranes, respectively, as measured in the hydrated state by a micrometer. The catholyte was prepared by dissolving 5 mmol K₄Fe(CN)₆ and 5 mmol Na₄Fe(CN)₆ in 6.7 ml deionized water. The anolyte was prepared by dissolving 5.05 mmol 2,6-D2PEAQ, 5.05 mmol KOH and 5.05 mmol NaOH in 5 ml mixed supporting electrolyte of 0.5 M KCl and 0.5 M NaCl. A trace amount of 1 M aqueous KOH was added to catholyte and anolyte solutions to adjust the pH to 7.0.

Galvanostatic cycling was performed at 40 °C with a constant current density of 80 mA cm^−2, using cutoff voltages of 0.5 and 1.3 V. To access 100% depth of discharge and ensure accurate evaluation of decay rates, potentiostatic steps were added to each galvanostatic half cycle^58,59, with a current cutoff of 2 mA cm^−2. Data were recorded using a Biologic SP-150 potentiostat. After cycling, electrolyte aliquots were taken to quantify ferrocyanide cross-over, the capacity-limiting side, using ICP-MS. The degradation of redox-active molecules during cycling, which has been thoroughly investigated in previous studies^32,60,61, was not explored in this work.

To evaluate rating performance, galvanostatic cycling was performed at varied current densities with cutoff voltages of 0.5 and 1.5 V at 40 °C. Electrochemical polarization curves were obtained by charging the cell to a desired state of charge and then polarizing using a linear galvanic sweep method at a rate of 200 mA s^−1 from −6,000 to 6,000 mA at 40 °C. The corresponding power density at specific states of charge (20%, 50% and approximately 100%) was derived from the current–voltage curve. EIS was performed using a Biologic SP-150 potentiostat with an a.c. bias of 10 mV and a frequency range of 1 MHz to 100 Hz. Data were recorded using a Biologic VSP 300 potentiostat.

Suitability of cPIMs for acidic RFB systems

No tests in conventional acidic vanadium flow batteries were conducted in this work. The high pK_a of carboxylates (approximately 4) in cPIM membranes causes the loss of polymer charges in acidic environments, leading to excessive shrinkage of the designed pores, regardless of pendant group structures. This shrinkage falls outside the scope of our pore-size-tuning process. Although the resulting small pore size could enhance vanadium selectivity, the accompanying low proton conductivity represents a significant limitation of charge-neutral PIMs⁶².

Membrane resistance requirements

A previous techno-economic analysis⁶³ suggested that membrane resistance needs to be below 1.5 Ω cm² to ensure economical viability of flow battery systems. This resistance corresponds to a conductivity of 3.3 mS cm^−1 assuming a membrane thickness of 50 μm. Consequently, pretreated Nafion membranes are predominantly used for flow batteries, including in this work to facilitate fair performance comparison and benchmarking (Supplementary Fig. 23). For the same reason, despite its potential for high selectivity, cPIM-BP is not suitable for RFB applications.