Synthesis of cPIMs
To an AO-PIM-1 solution (2âwt% in dimethyl sulfoxide) was added an anhydride in one portion (5âmol eq. relative to the repeating unit of AO-PIM-1). After full dissolution of the anhydride, the mixture was stirred at 30â°C for a further 4âh; then, potassium ethoxide was added (13âmol eq. relative to the repeating unit of AO-PIM-1). The mixture was vigorously stirred at room temperature for 1âh and then poured into 400âml water. Hydrochloric acid was added dropwise to the solution until the pH reached 1â2. The precipitate was filtered, suspended in 0.5âM aqueous H2SO4 and heated to reflux for 4âh. The powder was collected by filtration, washed with deionized water and acetone, and briefly dried in air at 110â°C for 1âh 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 4â10âwt% and centrifuged at 12,000ârpm for 10âmin 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 60â°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 1âM 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 6âh. 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 3âwt% in an autoclave at 160â°C for 2âh. The solutions were dried over anhydrous MgSO4 and centrifuged at 12,000ârpm for 10âmin 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 1âM KOH solution (H2O/EtOH, 1:1 by volume) for 1â2âh at 40â°C before use. TFC membranes were prepared by spin-coating 1âml 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 70â100ânm for 0.5âwt% polymer solutions at 1,000ârpm and around 1âµm for 3âwt% polymer solutions at 500ârpm. The thickness of the selective layer was characterized by atomic force microscopy and scanning electron microscopy. TFC membranes fabricated with 0.5âwt% polymer solutions were used for pressure-driven water permeation tests, whereas those with 3âwt% cPIM-Ph solutions were used for cross-over tests. Before use, TFC membranes were pretreated in 1âM 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 6âh.
Gravimetric uptake and dimensional swelling ratio
Membrane samples were dried at 110â°C under vacuum for 12âh, 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 24âh. 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):
$$\text{uptake}\,=\,\left[\frac{{W}_{{\rm{hydrated}}}}{{W}_{{\rm{dry}}}}-1\right]\times 100 \% $$
(1)
where Whydrated and Wdry 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 (lhydrated) and dry (ldry) free-standing membranes, measured using a micrometer, and was calculated according to equation (2):
$$\text{swelling ratio}\,=\,\left[\frac{{l}_{{\rm{hydrated}}}}{{l}_{{\rm{dry}}}}-1\right]\times 100 \% $$
(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 1,653ânm 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 600ânm. All ellipsometry data were analysed with Semilab SEA software, using the TaucâLorentz 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):
$$\text{swelling ratio}\,=\,\left(\sqrt[3]{\frac{{V}_{{\rm{hydrated}}}}{{V}_{{\rm{dry}}}}}-1\right)\times 100 \% $$
(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 10âmV and a frequency range of 0.2âMHz to 10âHz. Membrane samples were pretreated in 1âM aqueous KOH to fully deprotonate carboxylic acid groups and then soaked in 1âM aqueous KCl three times, with each immersion time lasting at least 6âh. 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 2âΩâcm2 (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 measurements35,36. 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 2âΩâcm2 (cPIM-BP and as-received Nafion), the ionic conductivity was calculated on the basis of a single measurement according to the following equation:
$$\sigma =\frac{L}{({R}_{{\rm{m}}}-{R}_{0})\times A}$$
(4)
where Rm is the apparent resistance measured from Nyquist plots, L is the membrane thickness, A is the active membrane area (2.00âcm2) and Rm represents resistance from contact and electrode resistance (0.2âΩâcm2) measured from a shorted cell without membrane and verified by the stacking method.
Apparent ion transference number
VâI curves were measured in an H-shaped cell using two Ag/AgCl electrodes (3.0âM 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:
$${V}_{0}=\left[\frac{{t}_{+}}{{z}_{+}}-\frac{{t}_{-}}{{z}_{-}}\right]\,\left[\frac{{k}_{{\rm{B}}}T}{e}\right]\,{\rm{l}}{\rm{n}}\,\left[\Delta C\frac{{\gamma }_{{\rm{h}}{\rm{i}}{\rm{g}}{\rm{h}}}}{{\gamma }_{{\rm{l}}{\rm{o}}{\rm{w}}}}\right]$$
(5)
where kB is the Boltzmann constant, z is the ion charge number, T is the Kelvin temperature, e is the elementary charge, ÎC is the ratio of high concentration to low concentration (ÎCâ=â10), and γhigh and γlow 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 1.54âcm2. Feed and permeate solutions were 0.1âM redox-active molecules dissolved in 1âM aqueous KCl (or KOH) solution and 1âM 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 0.1âml aliquots to 9.9âml 2âwt% 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 ultravioletâvisible spectroscopy analysis and recycled back to the permeate solution. The permeation rate (flux) of ions and redox molecules across the membrane follows Fickâs first law:
$$J=\frac{V}{A}\left[\frac{\partial C}{\partial t}\right]$$
(6)
where J is the permeation rate (molâcmâ2âsâ1), V is the solution volume (ml), A is the effective membrane area (1.54âcm2), C is the concentration of the permeate solution (molâcmâ3) and t is the diffusion time (s). As C2ââªâC1 (hence C1âââC2âââC1), under the assumption that boundary resistances next to the membrane are negligible, Fickâs first law can be simplified as:
$$J=\frac{p({C}_{1}-{C}_{2})}{l}=\frac{p{C}_{1}}{l}$$
(7)
where p is the permeability (cm2âsâ1), C1 is the concentration of the feed solution (molâcmâ3) and l is the membrane thickness (cm).
Free-standing membrane samples were used for cross-over tests with a typical membrane thickness of around 50âµm, except for cPIM-Et, which had a thickness of 120âµm. 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 0.28âmmolâlâ1âhâ1, 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 1â9âbar. The effective membrane area of the dead-end cell was 12.56âcm2. Before measurement of water flux under different pressures, a pressure of 20âbar was applied for at least 6âh 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 7.0âT superconducting magnet operating at a 1H frequency of 300.13âMHz and at a sample temperature of 302.5â±â0.3âK unless stated otherwise. 1H pulsed gradient stimulated echo (PGSTE) NMR was performed using a 5âmm 1H radiofrequency coil and 7Li PGSTE NMR using a 10âmm 7Li radio-frequency coil, both in a Bruker diff30 probe with a maximum gradient strength of 17.7âTâmâ1. 1H NMR spectra were acquired for each hydrated cPIM sample with a 10âkHz spectral width, four signal averages and a repetition time of 5âs. Chemical shifts were referenced externally to the water peak in a spectrum of 1âM 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 1âM aqueous LiOH overnight, followed by washing and immersion in 1âM aqueous LiCl more than three times, for at least 6âh each time. Fully hydrated polymer samples were quickly rolled up and placed into NMR glass tubes (Norell, 5âmm) 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, SG, against the gradient strength, G, using the StejskalâTanner equation:
$${S}_{{\rm{G}}}={S}_{0}{{\rm{e}}}^{-{\gamma }^{2}{\delta }^{2}{G}^{2}D\left(\varDelta -\frac{\delta }{3}\right)}$$
(8)
where S0 is the signal intensity when Gâ=â0, γ is the gyromagnetic ratio, δ is the gradient pulse length and Î is the observation time between gradient pulses.
Typical parameters for 1H PGSTE NMR experiments were 16 gradient steps, spectral width (SWH)â=â10,000âHz, δâ=â0.57âms and a minimum of 28 signal averages. Typical 90° pulse lengths fell in the range 7.5â9.0âμs. Experiments were carried out over a range of observation times, Îâ=â5.9, 6.5, 7.0, 7.5, 8.0, 10, 15, 20 and 30âms. Typical parameters for 7Li PGSTE NMR experiments were eight gradient steps, SWHâ=â20,000âHz and δâ=â1âms, with a minimum of 256 signal averages. Typical 90° pulse lengths were around 17.5âμs. Experiments were carried out at observation times of Îâ=â8, 10, 12, 15, 20, 30, 50, 75, 100 and 120âms. Maximum gradient strengths, Gmax, were chosen to minimize SG/S0. Error bars were determined from the average standard deviation of three repeats of experiments in which Îâ=â10 and 50âms. 7Li PGSTE NMR experiments were also performed on cPIM-Et and cPIM-Ph at temperatures 289.5, 293.5, 298.0, 302.5 and 306.5â±â0.3âK. Eight gradient steps were used with δâ=â1.5âms, Îâ=â30âms and Gmaxâ=â17âTâmâ1, with SWHâ=â20,000âHz and 256 signal averages.
To assess the presence of restricted diffusion, the MSD over time, â¨[râ²(t)âââr(0)]2â©, was determined from the measured diffusion coefficient, D, using the Einstein definition40
$$\langle {[{{\bf{r}}}^{{\prime} }(t)-{\bf{r}}(0)]}^{2}\rangle =2D\varDelta $$
(9)
and was plotted as a function of the observation time, Î.
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 model42,43. Water bonds and angles were restrained using the SHAKE algorithm44. A short-range cutoff of 12âà was used for non-bonded interactions, and long-range coulombic interactions were implemented with the particleâparticle particleâmesh technique. A timestep of 1.0âfs 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 data45,46. 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 1âns over a total 20âns 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 1âà probe and 60,000 Monte Carlo samples. The specific volume occupied by the polymer chains (VvdW) 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 (Vbox) and VvdW using the following equation48:
$$\text{fractional free volume}\,=\,1-1.3\frac{{V}_{{\rm{vdW}}}}{{V}_{{\rm{box}}}}$$
(10)
Degree of percolation
Water network characterization used the average of five independent models across 20âns of molecular dynamics simulation sampled every 1âns, 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 3.5âà . This distance was chosen to encompass the entire first peak in the oxygenâoxygen 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, gab(r) between two groups of atoms, a and b, within the polymer models were calculated using the MDAnalysis package over trajectories of 20âns with frames every 10âps.
$${g}_{{\rm{ab}}}(r)={({N}_{\text{a}}{N}_{\text{b}})}^{-1}\mathop{\sum }\limits_{i=1}^{{N}_{\text{a}}}\mathop{\sum }\limits_{j=1}^{{N}_{\text{b}}}\langle \delta (| {r}_{i}-{r}_{j}| -r)\rangle $$
(11)
We also calculated the radial number density distribution function (nab(r)) for a more direct comparison between systems with different numbers of atoms, where Ï is the number density of observed atoms:
$${n}_{{\rm{ab}}}(r)=\rho {g}_{{\rm{ab}}}(r)$$
(12)
Self-diffusion coefficient
Mean square displacement (MSD) was plotted every 10âps over a trajectory of 20âns. Self-diffusion coefficients (Dself) 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:
$${D}_{{\rm{self}}}=\frac{1}{2d}\frac{\text{d}}{\text{d}t}\text{MSD}$$
(13)
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-à probe, and the Euclidean distances between pore spheres and polymer atoms were calculated. Atoms located within 1âà 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 333âK at a heating rate of 0.13âKâminâ1. The scattering signal was integrated at either ÎEâ=â0 (elastic; EFWS) or around an arbitrarily chosen energy range (inelastic; IFWS) with an integration width equivalent to Eres.
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 (Tââ¤â100âK, for which the DebyeâWaller approximation is valid), EFWS is also effective for calculating the temperature dependence of the MSD, â¨u2â©, of hydrogen atoms:
$$\frac{{I}_{{{\rm{inc}}}_{{\rm{elastic}}}}(Q,T)}{{I}_{{{\rm{inc}}}_{{\rm{elastic}}}}(Q,{T}_{\min })}=\exp \left[-\frac{1}{3}{Q}^{2}(\langle {u}^{2}\rangle {\langle {u}^{2}\rangle }_{{T}_{\min }})\right]$$
(14)
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.
$${I}_{{\omega }_{{\rm{o}}{\rm{f}}{\rm{f}}}}^{{\rm{I}}{\rm{F}}{\rm{W}}{\rm{S}}}(T)\propto \frac{B}{{\rm{\pi }}}[1-{A}_{0}(Q)]\frac{\tau (T)}{1+{\omega }_{{\rm{o}}{\rm{f}}{\rm{f}}}^{2}\tau {(T)}^{2}}$$
(15)
$$\tau (T)\,={\tau }_{0}\exp \,\left[-\frac{{E}_{\text{A}}}{{k}_{{\rm{B}}}T}\right]$$
(16)
where B is a constant accounting for the resolution function, Ïoff is the energy offset, Ï is the relaxation time (with Ï0 the high T limit), A0 is the elastic incoherent structure factor, kB is the Boltzmann constant and EA 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 Eres of 3âμeV, covering the nanosecond timescale (~0.02â<âÏâ<â2âns); and (2) LET (ISIS, UK)51 to explore picosecond relaxation dynamics. The repetition rate multiplication method used with LET enabled simultaneous recording at three Eres values (14.6, 32.8 and 91.3âeV) with incident neutron energies of 1.03, 1.77 and 3.70âmeV, respectively, covering the timescale range of ~1.5â<âÏâ<â200âps. 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 17.5âμeV and covered the momentum transfer range of 0.56ââ¤âQââ¤â1.84âà â1, probing motions within the timescale range of 5â<âÏâ<â100âps. 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, Ï), 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 (Scoh) and the spatiotemporal correlation between identical nuclei (Sinc). The latter includes contributions from vibrational (Sv), translational and/or diffusional (St) and rotational/reorientation (Sr) motions:
$${S}_{{\rm{inc}}}(Q,\omega )={S}_{{\rm{v}}}(Q,\omega ){\bigotimes S}_{{\rm{t}}}(Q,\omega )\bigotimes {S}_{{\rm{r}}}(Q,\omega )\bigotimes R$$
(17)
where R is the resolution function and is experimentally determined using a vanadium standard or sample at a base temperature of approximately 10âK 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, Sv becomes equal to \({{\rm{e}}}^{-\frac{1}{3}{Q}^{2}\langle {u}^{2}\rangle }\), where â¨u2â© 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 (Î, 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 âimmobileâ protons) incorporated within the elastic scattering signal [δ(Ï)].
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 (Dloc and Dlr) in cPIM membranes were quantified on the basis of the following Gaussian model:
$${I}_{{\rm{F}}}(Q,t)=\exp \,\left[-{Q}^{2}{\sigma }^{2}(1-\exp \left(-\frac{{D}_{{\rm{l}}{\rm{o}}{\rm{c}}}t}{{\sigma }^{2}(1+2{D}_{{\rm{l}}{\rm{o}}{\rm{c}}}{Q}^{2}\tau )}\right))\right]\times \exp (\,-{D}_{{\rm{l}}{\rm{r}}}{Q}^{2}t)$$
(18)
where Ï is the characteristic time of the local jump diffusion, and Ï 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 (4âcmâÃâ5âcm). The aluminium cell, with an inner thickness of 0.5âmm, achieved around 90% neutron transmission. Indium was used to seal the cell. Scattering profiles were acquired between 200 and 333âK, covering a Q range of 0.3 to 2.1âà â1. For normalization, complementary scattering profiles for the vanadium standard, an empty aluminium cell and samples at 5âK were also obtained. Data analysis was carried out on the S(Q, Ï) 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 7âcm2, 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 40âmlâminâ1 through a Cole-Parmer peristaltic pump. All measurements were conducted in an argon-filled glovebox.
Carbon papers were pretreated by baking at 400â°C in the air for 24âh. Nafion 212 was pretreated following an established protocol57. Before full cell tests, membranes were soaked in 1âM aqueous KCl for 24âh. Membrane thicknesses were 45, 55 and 50âµm for cPIM-PA, Nafion 212 and sPEEK membranes, respectively, as measured in the hydrated state by a micrometer. The catholyte was prepared by dissolving 5âmmol K4Fe(CN)6 and 5âmmol Na4Fe(CN)6 in 6.7âml deionized water. The anolyte was prepared by dissolving 5.05âmmol 2,6-D2PEAQ, 5.05âmmol KOH and 5.05âmmol NaOH in 5âml mixed supporting electrolyte of 0.5âM KCl and 0.5âM NaCl. A trace amount of 1âM aqueous KOH was added to catholyte and anolyte solutions to adjust the pH to 7.0.
Galvanostatic cycling was performed at 40â°C with a constant current density of 80âmAâcmâ2, using cutoff voltages of 0.5 and 1.3âV. To access 100% depth of discharge and ensure accurate evaluation of decay rates, potentiostatic steps were added to each galvanostatic half cycle58,59, with a current cutoff of 2âmAâcmâ2. 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 studies32,60,61, 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 1.5âV at 40â°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 200âmAâsâ1 from â6,000 to 6,000âmA at 40â°C. The corresponding power density at specific states of charge (20%, 50% and approximately 100%) was derived from the currentâvoltage curve. EIS was performed using a Biologic SP-150 potentiostat with an a.c. bias of 10âmV and a frequency range of 1âMHz to 100âHz. 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 pKa 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 1.5âΩâcm2 to ensure economical viability of flow battery systems. This resistance corresponds to a conductivity of 3.3âmSâcmâ1 assuming a membrane thickness of 50âμm. 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.