## Introduction

Anion exchange membranes (AEMs) are important materials for environmental and energy technologies and are widely used in electrochemical applications, such as electrodeionization, water electrolysis, and polymer electrolyte fuel cells (PEFCs) [1,2,3]. AEMs are composed of a hydrocarbon backbone covalently bonded to positively charged side chains, such as ammonium, aromatic, or nonnitrogenous cations [4,5,6,7,8,9]. For AEM-based PEFCs, hydroxide (OH) is used as a mobile ion, and OH conductivity is an essential parameter determining efficiency [10]. However, the ion conductivities of AEMs remain lower than those of proton exchange membranes (e.g., 180 mS cm–1 at 100 °C in water for Nafion®) owing to the inherently lower mobility of OH compared with that of a proton. Thus, several studies have been performed to improve the conductivities of AEMs [11,12,13,14].

Ion conductivity is expressed as the product of the Faraday constant, ion mobility, and ion concentration [15]. The general approach for increasing the ion conductivity of an AEM involves increasing the concentration of ions in the AEM, i.e., the ion-exchange capacity (IEC), by introducing ionic groups [16, 17]. However, introduction of a considerable number of hydrophilic ionic moieties into the polymer generally causes large water uptake in the operating environment, a subsequent decrease in the ion concentration and membrane rupture [18]. Therefore, design of a polymer that can increase the ion conductivity of an AEM without increasing the IEC is essential [19].

Thus, improvement of the ion conductivity by increasing the ion mobility has become a target of research. One of the strategies used to increase ion mobility is to weaken the electrostatic interaction of the ion pair [15]. Weiber et al. [20] and Sun et al. [21] successfully improved ion conductivity by using imidazolium and guanidinium cations, respectively, for which delocalization of the cation charge weakened the electrostatic interactions between OH and cations. Superior conduction by delocalized ions was also observed for Li+ conduction with the superdelocalized anion poly[(4-styrenesulfonyl)(trifluoromethanesulfonyl)imide] [22]. This weakening of the electrostatic interactions between delocalized ions and counterions can be understood with the Pearson Hard Soft Acid Base (HSAB) principle [23, 24]. Moreover, it is also pointed out that AEMs containing ammonium cations suffered from low concentrations of OH due to the low dissociation constant of ammonium [25]. Therefore, higher dissociation of the ion pair is expected to increase the ion concentration and, consequently, increase the ion conductivity [26].

To capitalize on these advantages of delocalized ions, we previously introduced fused expanded pyridiniums (FEPs) with highly delocalized positive charges in their broad π-planes as cationic moieties in an AEM for the first time [27]. In that study, a vinyl monomer equipped with a FEP unit was copolymerized with n-butyl methacrylate (BMA) to fabricate a polymer for the AEM. The resulting AEM exhibited a high ion conductivity of 55.2 mS cm–1 (OH form; 80% relative humidity (RH) and 80 °C), but the IEC was extremely low (0.045 mmol g–1). We explained that the soft acid nature of the FEP originating from delocalization of the positive charge was the cause of the high conductivity seen with the hard base, i.e., OH [27]. However, the softness of the FEP was not compared with the softness of other cations. In addition, the FEP content was limited to 1 mol% because of the poor solubility of the FEP.

In this study, we incorporated a FEP unit via postmodification of a polymer to increase the FEP content, and the softness of FEP was compared with those of other cations with DFT calculations. A styrene-based polymer containing an azide group was used as the host polymer, and the FEP featuring ethynyl groups was incorporated through copper-catalyzed alkyne-azide cycloaddition (CuAAC, Scheme 1) [28]. High FEP contents of up to 10.5 mol% were obtained, and the AEM containing 10.5 mol% FEP exhibited an improved ion conductivity of 123 mS cm–1 under 80% RH at 80 °C, although the IEC was only 0.77 mmol g–1. DFT calculations showed that the FEP cation is much softer than the other cations.

## Experimental

### Materials

N-Methylpyrrolidone (NMP), deuterium oxide (D2O, D, 99.9%), 18-crown-6-ether, tetrabutylammonium hexafluorophosphate and 40 wt.% sodium deuteroxide solution in D2O (D, 99.5%) were purchased from Sigma‒Aldrich Co. LLC (St. Louis, MO, USA). Ethanol, acetonitrile, methanol, tetrakis(triphenylphosphine)palladium(0), N,N-dimethylformamide (DMF), superdehydrated DMF, acetone, dimethylsulfoxide, sodium chloride (NaCl), sodium sulfate, potassium carbonate, chlorobenzene, sodium azide, N,N,N’,N”,N”-pentamethyldiethylenetriamine (PMDETA), silver nitrate, potassium chromate, and potassium hydroxide (KOH) were purchased from FUJIFILM Wako Pure Chemical, Ltd. (Osaka, Japan). Dichloromethane and azobisisobutyronitrile (AIBN) were acquired from Kishida Chemistry Co., Inc. (Osaka, Japan). Diethyl ether and hexane were purchased from Kanto Chemical Co., Inc. (Tokyo, Japan). CDCl3 containing tetramethylsilane (TMS) and dimethylsulfoxide-d6 (DMSO-d6) containing TMS were obtained from Merck & Co. (Darmstadt, Germany). Tributyl(trimethylsilyl)ethynyltin, diethylene glycol bis(2-propynyl) ether, and 4-chloromethylstyrene (>90.0%, stabilized with 4-tert-butylcatechol, 2-nitrobenzenesulfenyl chloride, and 2-nitro-p-cresol) were purchased from Tokyo Chemical Industry Co., Ltd. (Tokyo, Japan). Copper bromide (CuBr) was purchased from Nacalai Tesque Inc. (Kyoto, Japan). The Tokuyama A201 membrane was kindly supplied by Tokuyama Co. (Yamaguchi, Japan). It was immersed in a 1 M potassium hydroxide solution and subsequently placed in N2-purged Milli-Q water for 24 h prior to use. 4-Chloromethylstyrene was used after treatment with neutral alumina. Br-FEP and FEP were prepared according to previous reports [27].

### Characterization

1H, 13C, and 19F-NMR measurements were performed with a JEOL (Tokyo, Japan) JNM-ECZ400 spectrometer (400 MHz). The chemical shifts of the protons are reported in parts per million (ppm; δ scale) downfield from the TMS peak, with the solvent protons used as a reference (CHCl3: 1H(δ) = 7.26 ppm; DMSO: 1H(δ) = 2.50 ppm). The chemical shifts of the carbons are reported in ppm (δ scale) downfield from the TMS peak, with the NMR shifts of solvent carbons used as references (DMSO-d6: 13C(δ) = 39.4 ppm). The data are presented as follows: chemical shift, multiplicity (s = singlet, d = doublet, t = triplet, m = multiplet, br = broad), coupling constant (Hz), and integration. Mass spectrometry was performed with a Bruker (Billerica, MA, USA) MicroTOF-QIII electrospray ionization time-of-flight mass spectrometer (ESI-TOF-MS). Fourier transform infrared (FT-IR) measurements were performed using a Spectrum 65 FT-IR (Perkin-Elmer, Waltham, MA, USA) spectrometer equipped with an attenuated total reflection (ATR) apparatus. Molecular weights were determined via gel permeation chromatography using a Jasco LC-2000 Plus series (RI detector: RI-2031) instrument equipped with a Shodex KD-806 M (SHOWA DENKO, Tokyo, Japan) column (MW = 1000–40,000,000) using 50 mM LiBr in NMP solution as the eluent. The molecular weight was calibrated with standard polystyrene samples [PStQuick E & F (TOSOH Co., Tokyo, Japan) with a MW range of 266–427,000; 11 samples]. Thermogravimetric analyses (TGA) were performed with an EXSTAR TG/DTA7300 Analyzer (Hitachi High-Technologies Corp., Tokyo, Japan) with a heating rate of 20 °C min−1 under an air flow of 200 mL min−1. X-ray photoelectron spectroscopy (XPS) data were obtained with an AXIS-ULTRA (Shimadzu, Kyoto, Japan) instrument. The binding energies were calibrated with the C 1s peak at 284.5 eV. DFT calculations were performed on cationic species containing –1, 0, and +1 electrons with Gaussian 09 software at the B3LYP/6-311+G(d,p) level, and they were visualized with GaussView software [29].

### Synthesis of 2-(4-((trimethylsilyl)ethynyl)phenyl)benzo[1,2]quinolizino[3,4,5,6-def]phenanthridinium tetrafluoroborate (TMSethynyl-FEP) [30, 31]

Br-FEP (201 mg, 0.368 mmol), tetrakis(triphenylphosphine)palladium(0) (24.0 mg, 0.0208 mmol), and tributyl(trimethylsilyl)ethynyltin (434 mg, 1.12 mmol) were added to DMF (superdehydrated, 8 mL), and the solution was stirred at 50 °C under N2 for 24 h. Next, the solution was added to diethyl ether. The crude solid was dissolved in a 1:1 mixture of dichloromethane and acetonitrile, passed through a neutral alumina column, and evaporated to yield a concentrated solution. Subsequently, diethyl ether was added, and the resulting precipitate was collected via filtration through a membrane filter. The filtrate was washed with hexane and evaporated to obtain an 89% yield of the black solid TMSethynyl-FEP, which contained 20% of the deprotected compound (185 mg, 0.33 mmol). 1H NMR (400 MHz, DMSO-d6): δ (ppm) 9.77 (s, 2H), 9.44 (d, J = 8.2 Hz, 2H), 9.25 (d, J = 8.2 Hz, 2H), 9.02 (d, J = 8.2 Hz, 2H), 8.63–8.66 (m, 2H), 8.34 (t, J = 8.0 Hz, 1H), 8.16 (t, J = 7.5 Hz, 2H), 8.03 (t, J = 7.5 Hz, 2H), 7.83–7.88 (m, 2H), 4.57 (s, 0.2H), 0.31 (s, 6.4H). 13C NMR (101 MHz, DMSO-d6): δ (ppm) 148.03, 143.15, 134.52, 133.03, 131.07, 130.33, 129.75, 129.22, 128.39, 128.16, 128.02, 126.04, 125.07, 124.56, 124.07, 118.61, 104.91, 98.40, 0.41. ESI-MS m/z: calcd. for C34H26NSi: 476.67; found: 476.18 [M-BF4]+. FT-IR (ATR): ν (cm−1) = 1629 (C=C, C=N), 1054 (B-F).

### Synthesis of 2-(4-ethynylphenyl)benzo[1,2]quinolizino[3,4,5,6-def]phenanthridinium tetrafluoroborate (ethynyl-FEP) [30, 31]

TMSethynyl-FEP (142 mg, 0.252 mmol) and potassium carbonate (69.6 mg, 0.504 mmol) were added to a 1:1 mixture of DMF and methanol (12 mL), and the solution was stirred at 25 °C under N2 for 15 h. The solution was added to dichloromethane and washed with water. The organic layer was dried over anhydrous Na2SO4 and added to diethyl ether. The resulting precipitate was collected via filtration through a membrane filter, and the filtrate was washed with hexane and evaporated to obtain a black solid (124 mg, 0.19 mmol) in 74% yield. 1H NMR (400 MHz, DMSO-d6): δ (ppm) 9.78 (s, 2H), 9.44 (d, J = 8.2 Hz, 2H), 9.25 (d, J = 7.8 Hz, 2H), 9.02 (d, J = 8.2 Hz, 2H), 8.63 (d, J = 8.7 Hz, 2H), 8.35 (t, J = 8.0 Hz, 1H), 8.16 (t, J = 7.8 Hz, 2H), 8.03 (t, J = 7.5 Hz, 2H), 7.87 (d, J = 8.7 Hz, 2H), 4.56 (s, 1H). 13C NMR (101 MHz, DMSO-d6): δ (ppm) 148.27, 143.34, 134.54, 132.97, 131.61, 131.09, 130.38, 129.38, 128.64, 128.07, 126.53, 125.21, 124.62, 124.14, 118.75, 114.50, 110.22. ESI-MS m/z: calcd. for C31H18N: 404.14; found: 404.15 [M-BF4]+. FT-IR (ATR): ν (cm−1) = 3423 (≡C-H), 1629 (C=C, C=N), 1054 (B-F).

### Synthesis of poly(4-chloromethylstyrene) (poly-CMS) [32]

4-Chloromethylstyrene (3.00 g, 19.9 mmol) and AIBN (4.1 mg, 0.025 mmol) were dissolved in 2 mL of chlorobenzene. The solution was degassed by freeze-pump-thaw cycling and heated at 60 °C for 18 h. The reaction mixture was added to ethanol to yield a white precipitate, which was subsequently collected via filtration through a membrane filter. The filtrate was washed with ethanol and evaporated to obtain a white powder (1.10 g) in 36% yield. The average molecular weight of the obtained polymer was Mn = 6.3 × 104, and the molecular weight distribution Mw/Mn was 2.6.

### Synthesis of poly(4-azidomethylstyrene) (poly-Azide) [32]

Poly-CMS (1.00 g, 6.55 mmol) and sodium azide (426 mg, 6.55 mmol) were dissolved in 20 mL of DMF and heated at 60 °C for 24 h. The reaction mixture was added to a mixed solution of Milli-Q water and methanol (1:3, vol:vol) to yield a white precipitate, which was subsequently collected via filtration through a membrane filter. The filtrate was washed with Milli-Q water and methanol and evaporated to obtain a white powder (0.91 g) in 87% yield. FT-IR (ATR): ν (cm−1) = 2097 (-N3).

### Synthesis of poly(2-(4-(1-(4-vinylbenzyl)-1H-1,2,3-triazol-4-yl)phenyl)benzo[1,2]quinolizino [3,4,5,6-def]phenanthridin-15-ium tetrafluoroborate)-co-poly(4-azidomethylstyrene) (poly-FEPx) [33, 34]

Poly-Azide, ethynyl-FEP, CuBr, and PMDETA were dissolved in 10 mL of NMP. The solution was degassed by freeze-pump-thaw cycling and heated at 50 °C for 48 h. The reaction mixture was added to Milli-Q water to yield a brown precipitate, which was subsequently collected via filtration through a membrane filter and redissolved in NMP. Next, the solution was added to methanol. The resulting brown precipitate was collected via filtration through a membrane filter, and the filtrate was washed with methanol and evaporated to obtain a brown solid. Detailed experimental conditions are listed in Table 1.

### Preparation of anion exchange membranes

A 10 mL NMP solution containing 100 mg of poly-FEPx and 17.2 mg of ethylene glycol bis(2-propynyl) ether as a cross-linker was added to a Teflon Petri dish and heated at 80 °C for 48 h. The resulting membranes were immersed in 1.0 M aqueous KOH for 24 h to exchange to the OH form and subsequently submerged in N2-purged Milli-Q water for 24 h to remove excess salts [35].

### Determination of the FEP content in poly-FEPx

A 1.0 mL DMSO-d6 solution containing 5.0 mg of poly-FEPx and 50.0 μg (0.31 μmol) of ammonium hexafluorophosphate as an internal standard was added to an NMR tube, and the 19F-NMR spectrum was measured. The FEP content was determined from the integrated area of BF4 calibrated with that for PF6.

### Calculation of the ion-exchange capacity

The experimental IECs (IECe) of poly-FEPx were measured via the Mohr titration method. The poly-FEPx membranes were ion-exchanged to a Cl form by immersing them in a 1 M NaCl aqueous solution at 25 °C for 24 h. Subsequently, they were rinsed and equilibrated in a 0.5 M NaCl aqueous solution at 25 °C for 24 h to release Cl. This solution was titrated using a 0.01 M AgNO3 aqueous solution until the K2CrO4 endpoint. The IECes were calculated with the following equation:

$${{{{{{{\mathrm{IEC}}}}}}}}_e = \frac{{V_{{{{{{{{\mathrm{AgNO}}}}}}}}_3} \ast C_{{{{{{{{\mathrm{AgNO}}}}}}}}_3}}}{{W_{{{{{{\mathrm{dry}}}}}}}}},$$

where $$V_{{{{{{{{\mathrm{AgNO}}}}}}}}_3}$$ is the titrated volume and $$C_{{{{{{{{\mathrm{AgNO}}}}}}}}_3}$$ is the concentration of the AgNO3 aqueous solution [36].

### Estimation of water uptake (WU), hydration number (λ), and swelling ratio (SR)

The water uptake (WU) values were calculated with the following equation:

$${{{{{{{\mathrm{WU}}}}}}}} = \left( {{{W}}_{{{{{{{{\mathrm{wet}}}}}}}}}-{{W}}_{{{{{{{{\mathrm{dry}}}}}}}}}} \right)/{{W}}_{{{dry}}} \times 100,$$

where Wwet and Wdry are the weights of the membranes after Milli-Q water immersion for 24 h and after drying at 60 °C for 24 h, respectively [36]. The hydration numbers (λ) were calculated with the following equation [36]:

$$\lambda = 10 \times {{{{{{{\mathrm{WU}}}}}}}}/\left( {18.05 \times {{{{{{{\mathrm{IEC}}}}}}}}} \right).$$

The SR values were calculated with the following equation:

$${{{{{{{\mathrm{SR}}}}}}}} = \left( {{{l}}_{{{{{{{{\mathrm{wet}}}}}}}}}-{{l}}_{{{{{{{{\mathrm{dry}}}}}}}}}} \right)/{{l}}_{{{{{{{{\mathrm{dry}}}}}}}}} \times 100,$$

where lwet and ldry are the lengths of the membranes after Milli-Q water immersion for 24 h and after drying at 60 °C for 24 h, respectively [36].

### Calculation of OH‒ conductivity

Impedance measurements were performed in a temperature- and humidity-controlled N2-flow chamber over the frequency range 1–10 MHz. The through-plane conductivity σ (S cm‒1) was calculated as

$$\sigma = {{L}}/\left( {{{R}} \times {{A}}} \right),$$

where L is the film thickness (cm), R is the resistance (Ω), and A is the measured cross-sectional area (0.45 cm2). All of the membranes were submerged in a 1.0 M KOH solution for 24 h and subsequently immersed in N2-purged Milli-Q water for 24 h before use [37]. The conductivity measurements were performed immediately after drying to prevent CO2 adsorption.

### Alkaline stability tests of the poly-FEP10 membrane and unsubstituted FEP

The poly-FEP10 membrane was immersed in a 1.0 M KOH solution, heated at 80 °C for 500 h and subsequently immersed in N2-purged Milli-Q water for 24 h before use [38]. To measure the stability of the FEP unit, unsubstituted FEP (28 mg, 60 μmol) was dissolved in 3 mL of DMSO-d6, and 2.4 mL of deuterium oxide, 0.6 mL of sodium deuteroxide solution (40 wt.%), and 6 drops of an 18-crown-6-ether solution (0.45 M in D2O) were added. The solution was heated at 80 °C under N2 for 3 h [39, 40].

## Results and discussion

### Preparation and properties of the polymers

4-Chloromethylstyrene was polymerized via radical polymerization with AIBN as the initiator, and the obtained polymer (Mn = 6.3 × 104, Mw/Mn = 2.6) was treated with sodium azide to convert the chloromethyl groups into azidomethyl groups and afford the poly-Azide. FEPs containing ethynyl groups (ethynyl-FEP) were introduced into the poly-Azide via CuAAC to prepare cationic polymers (poly-FEPx) (x denotes the feed ratio of the FEP), as shown in Scheme 1. In this study, polymers with x = 1, 5, and 10 mol% of FEP were synthesized. Polymers with feed ratios greater than 10 mol% were difficult to synthesize due to the limited solubility of ethynyl-FEP. Figure 1a depicts the 1H NMR spectra of the poly-Azide and poly-FEPx. The absence of an ethynyl peak at 4.5 ppm and the presence of FEP aromatic protons between 7.8 and 9.7 ppm indicate successful incorporation of FEP units into the poly-FEPx. Owing to the weak signal for FEP in poly-FEP1, FEP incorporation ratios were determined based on 19F-NMR by using the BF4 peak as an internal standard (see Experimental), and the FEP contents of poly-FEP1, -FEP5, and -FEP10 were determined to be 1.0, 5.2, and 10.5 mol%, respectively (Supplementary Fig. S1); this suggested that FEP incorporation is controllable based on the feed ratio. In a previous report, a FEP containing a vinyl group was used as a monomer and copolymerized with BMA to prepare FEP-based random copolymers (FEP-BMA) [27, 41]. In that approach, the poor solubility of the FEP units limited incorporation of the FEP units to a maximum of 1 mol%. Thus, the strategy presented herein for postmodification of the FEPs shows promise for increasing the FEP content. In the FT-IR spectrum, the intensity of the peak at 2097 cm–1 for the azide stretching vibration decreased, and the intensities of the peaks at 1685 cm–1 for C=C and C=N double bond stretching vibrations increased with increasing FEP feed ratio (Fig. 1b). A TGA of poly-FEPx was conducted under flowing air, and the results are displayed in Fig. 1c. As the feed ratio of FEP was increased, the weight drop near 240 °C for decomposition of the azide group decreased [32]. These results clearly demonstrated that the FEP content increased with increasing feed ratio, consistent with the controlled FEP incorporation method. Incorporation of FEP was also indicated by the N 1s XPS data. In this region, the peaks corresponding to azide (–N=N±=N), azide (–N=N+=N), FEP N+, and triazole (–N–N=N–) appeared at 405.3, 401.5, 402.7, and 399.4 eV, respectively (Supplementary Fig. S2) [42].

### AEM characterization

Poly-FEPx showed good solubility in organic solvents, such as NMP, DMSO, and DMF, and the membranes were prepared by casting a solution of poly-FEPx (10 wt.%) into NMP. To passivate the residual azide groups, ethylene glycol bis(2-propynyl) ether was added to the casting solution and formed cross-linked poly-FEPx membranes. The reactions of the azide groups with the cross-linkers were indicated by the TGA curves, which showed a decrease in the abrupt drop seen at 240 °C and attributed to the azide group (Supplementary Fig. S3), and by a decrease in the azide peak intensity (2097 cm–1) in the FT-IR spectrum (Supplementary Fig. S4) of the poly-FEPx membranes. Thus, free-standing poly-FEPx membranes with good flexibility were successfully prepared (Supplementary Fig. S5). The IECs of the poly-FEPx membranes were measured by Mohr titration (denoted IECe). Although the IECe of poly-FEP1 was difficult to determine, probably due to the low Cl concentration, the IECe values of poly-FEP5 and poly-FEP10 were determined to be 0.42 and 0.77 mmol g–1, respectively (Table 2). These values were well supported by the theoretical IEC values (IECt) calculated from the FEP content, as listed in Table 2. Notably, IECe was larger than IECt, probably because the excess uptake of Cl before titration was due to the cation-dipole interactions between the ether groups in the cross-linker and the Cl [43] that was not removed by washing. The water uptake (WU) values for the poly-FEPx membranes were measured by immersing the membranes into Milli-Q water for 24 h. The WU values of poly-FEP1, -FEP5, and -FEP10 were 7.1%, 7.1%, and 9.0%, respectively (Table 2). These values were significantly lower than those of conventional polystyrene-based AEM systems, which are typically greater than 30 [32]. Such low WU values might be ascribed to the low IEC values of poly-FEPx (<0.77 mmol g–1), which are significantly lower than those of conventional AEMs (usually greater than 1.0 mmol g–1) [44]. In addition, the SR values for poly-FEP1, -FEP5, and -FEP10 were 2.8%, 2.1%, and 4.7%, respectively (Table 2), and were much lower than those of other systems (9–34%) [32]. The low IEC values for poly-FEPx combined with the rigidity and hydrophobicity of the FEP units may have contributed to the low SR value, which in turn prevents softening of the membranes under operating conditions. The λ values of poly-FEP5 and -FEP10 were 9 and 7, respectively (Table 2). The values are similar to those of our previous FEP copolymer (FEP-BMA) with a λ value of 5 but lower than those of other pyridinium-grafted AEMs, which are typically greater than 10 [45, 46]. The relatively low λ value might be attributed to the hydrophobicity of FEP.

The ion conductivities of the poly-FEPx membranes were determined over the frequency range 1–10 MHz via through-plane impedance measurements using the four-terminal electrode method with temperature and humidity control in a N2-flow chamber. Figure 2a displays the temperature dependences of the ion conductivities for poly-FEPx and commercial AEMs at 80% RH. The conductivities of the commercial AEM ranged from 13.3 (±0.4) to 19.7 (±2.2) mS cm−1 as the temperature was increased from 50 to 80 °C [37], confirming the validity of the through-plane conductivity measurements. With increasing FEP incorporation from poly-FEP1 to poly-FEP10, the ion conductivity increased significantly, and poly-FEP10 exhibited a value of 123.4 (±13.3) mS cm–1 at 80 °C. This value was higher than that previously reported for FEP-BMA featuring an FEP content of 1 mol% (55.2 mS cm–1) [27]. Moreover, the obtained value is among the highest values reported for materials with IECs lower than 1.0 mmol g–1 [36]. We attributed this increase in ion conductivity at a low IEC level to weak interactions between the FEP moieties and OH ions. In addition, the large molecular sizes of the FEP units may increase the cationic volume of the film and form OH conductive channels [47]. According to Arrhenius plots, the activation energy for ion conduction was 21 kJ/mol, which was similar to those of conventional polystyrene-based AEMs, suggesting that ion conduction was dominated by the Grotthuss mechanism (Supplementary Fig. S6) [48,49,50].

An alkaline stability analysis of poly-FEP10 was performed according to the literature by immersing the membranes in a 1.0 M KOH solution at 80 °C for 500 h [38]. Although the membrane displayed no clear damage (inset in Fig. 2b), the conductivity at 80 °C (80% RH) decreased by 47% after the test (Fig. 2b), and this decrease was similar to those observed for AEMs containing heteroaromatic cations [51, 52]. In the FT-IR spectrum, the intensity of the C=C and C=N stretching vibrational peak at 1685 cm–1 decreased relative to that of the azide stretching vibration peak at 2097 cm–1, which suggested degradation of the FEP units (Supplementary Fig. S7).

To investigate the mechanism for degradation of the FEP unit, an alkaline stability test was also conducted with unsubstituted FEP in a 1.0 M NaOD DMSO-d6/D2O solution containing 18-crown-6-ether at 80 °C (Fig. 3a) used as the control experiment [39, 40]. In the 1H NMR spectrum, the peak at 9.3 ppm assigned to the proton at C-1 (Ha shown in Fig. 3b) almost disappeared after testing. This result clearly suggested that the FEP units were cleaved via nucleophilic addition and keto–enol tautomerism [53].

### DFT calculations

To gain an in-depth understanding of the reasons for the remarkable ion conductivity of the poly-FEPs, the interaction between the FEP cations and OH ions was estimated based on the HSAB principle [24]. Since OHis a known hard base, evaluation of the FEP as a “soft acid” provided insight into the interaction between FEP and OH. We estimated the absolute electronegativity χ and hardness η of the ions, which represent Lewis acidity and “hardness” in the HSAB formulation, respectively, using the following equations:

$$\chi = \frac{{I + A}}{2},$$
$$\eta = \frac{{I - A}}{2},$$

where I and A are the ionization energy and electron affinity, respectively [54], and are calculated via the following equations using DFT calculations:

$$I = E\left( {X^{1 + }} \right) - E\left( {X^0} \right),$$
$$A = E\left( {X^0} \right) - E\left( {X^{1-}} \right),$$

where E(X0) is the total energy of the cationic species, and E(X1–) and E(X1+) are the total energies of cationic species possessing –1 and +1 electrons, respectively [54]. Several representative cations were used for the AEMs, including tetramethylammonium (TMA), tetraethylammonium (TEA), 1,3-dimethylimidazolium (MIm), and 1-methylpyridinium (MPy), and were also estimated for comparison. The optimized structures of the cations are displayed in Fig. 4, and the calculation results are summarized in Table 3.

Notably, the FEP exhibited a η value significantly lower than those of the other cations, indicating that it is the weakest Lewis acid among the cations studied. In addition, FEP exhibited the highest η value, indicating that it is the softest acid. The combination of significantly “softer” Lewis acid cations and “harder” Lewis base anions improves salt dissociation [54]. Therefore, the FEP has weaker interactions with harder bases (OH), which accounts for the high ion conductivity of the poly-FEPs.

## Conclusion

We designed and synthesized a polystyrene-based polymer containing FEP units as side chains (poly-FEP) via postmodification of an ethynyl-FEP into a poly(4-azidomethylstyrene) using click chemistry. The poly-FEP membrane containing 10.5 mol% FEP exhibited an excellent ion conductivity of 123.4 (±13.3) mS cm–1, which was the highest value among those reported thus far for AEMs with a low IEC value (<1.0 mmol g–1). By estimating the hardness of FEP via DFT calculations, we revealed that it is a weaker and softer acid than conventional cations used in AEMs. This unique feature of FEP accounted for the weak interactions between FEP units and OH ions and enabled excellent ion conductivity of the poly-FEP.