In the classical MD method, the ion conduction process is normally simulated with the following considerations: (i) A cubic computational domain with particles containing all of the material components needed in the actual operation of the ionic membrane is shown in Figure 1, which can be considered as a unit lattice. (ii) Each atom or atom group within the computational domain is treated as a single particle, and their interactions and motions are governed by Newton’s second law of mechanics. Therefore, the simulation depends on the type and number of the particles within the computational domain, and the forces acting on each particle.

To balance statistical results and computational time within a domain, 10 polymer chains (or backbones, as illustrated by the black solid line in Figure 1) are considered along with the number of the ten repeat units in each backbone. An exact number of water molecules is specified by the hydration parameter λ, denoted as the absorbed water molecules per hydroxide group. Each hydroxide ion corresponds to a quaternary ammonium group of each side chain, resulting in a total of 100 hydroxy groups to maintain electrical neutrality. The size of the cubic domain was determined by the reference density. The total mass was set based on the polymer composition, as described above, and the density was set by adjusting the lattice size. The polymer chains, hydroxide anions, and water molecules were randomly packed within the computational domain in the initial state (Figure 1).

In MD simulation, atom interactions and motions are governed by Newton’s second law of mechanics as given in Eq. 1: F i t = m i a i t (1) where a i t and m i are the acceleration at time t and the mass of atom i, and i = 1, 2 … N. Here, N represents the total number of atoms in the computational domain. The net force acting on the atom i at any instant of time t, F i t , is expressed in terms of the position gradient of the potential energy the atom i has in the multi-atom system, E i t , or F i t = − d E i d r i (2) such that − d E i d r i = m i d 2 r i d t 2 (3) where r _i is the position of the atom i at the instant of time t.

Parameterized complex functional forms, such as off-diagonal cross-coupling terms and high-order force constants, were taken into account by the COMPASS force field. The potential energy is expressed by Equations (S1)‒(S6) in the Supporting Material. Three-dimensional periodic boundary conditions (described in the Supporting Material) were adopted in this study. The initial position and initial velocity of each atom in the computational domain are described by Equation (S7).

The above equations form a conventional mathematical model for MD simulation. The simulation process was to solve the governing Newton’s equations of motion as shown in Equations (S8)‒(S10) and the simulation details are shown in the Supporting Material. Once the threshold reached the convergence tolerances of energy and force of geometry optimization shown in Equations (S15)‒(S16), the system was considered to be equilibrium, then model validation could be carried out as shown in Supplementary Figure S1.

In order to investigate the effect of mechanical stretching (deformation) in a given direction on the transport of ions in the membrane, a uniaxial deformation was applied in the z-direction (shown in Figure 1), after the unit lattice had reached thermodynamic equilibrium. The degree of deformation can be varied to assess the impact of the deformation on the oriented structure, morphology, and ion transport. The deformation in the z-direction was considered as the total atom number remains the same. Therefore, the deformation may be described as: L z 1 = L z 0 + L z 0 × s t r a i n (4) L x 1 = L y 1 = V / L z 1 1 / 2 (5)

Similarly, the deformation for individual atoms have the effect of changing the inter-atom distance in the z, x and y directions such that z i j = z i j , 0 1 + s t r a i n (6) x i j = x i j , 0 L x 1 ;   y i j = y i j , 0 L y 1 (7) where L and V is the side length and volume of the unit lattice, x i j , y i j , and z i j are the distances between the atoms i and j in the x, y and z directions, respectively. The subscript “0” represents the distance before deformation (strain). A series of strains were considered in the z-direction, with the corresponding compression in the other two directions (x and y) in order to maintain a constant density. Clearly, the strain mainly affects potential energy E _i in Eq. 2 through the change in the distance among the atoms in the computational domain, and the stress can be obtained through dividing the force given in Eq. 3 by the area ( L x 1 × L y 1 ).

Poly(2,6-dimethyl-1,4-phenylene oxide) (PPO, M _n = 20,000), N-bromosuccinimide (NBS, 99%), 2-2′-azobisisobutyronitrile (AIBN, 98%), trimethylamine (TMA, 3.2 M solution in ethanol), chlorobenzene and N-methyl-2-pyrrolidone (NMP) were obtained from Sigma-Aldrich and used as received, except AIBN.

Bromination and quaternization reactions were used to prepare trimethylamine functionalized PPO AEMs as shown in Figure 2. PPO was brominated using NBS according to a procedure outlined in the literature (Yang et al., 2018). In summary, NBS and recrystallized AIBN initiator (molar ratio 0.8:1) were added to a PPO solution in chlorobenzene. The mixture was heated and maintained at 135°C for 3 h under a nitrogen atmosphere, and then it was rapidly poured into methanol, resulting in a produce yellow precipitate. After washing with ethanol and drying in a vacuum oven at 30°C for 24 h, clean brominated PPO (BPPO) was obtained, having approximately 20% degree of bromination.

The BPPO polymer and TMA were dissolved in NMP for 1 h at room temperature (RT) under ultrasonication. To ensure the benzyl bromine groups quaternization completely, the molar ratio of N in TMA to the bromobenzyl groups in BPPO was adjusted to 3:1. The solution was poured onto dry Petri plates sized 10 cm × 10 cm, then heated at 70°C to drive off TMA reagent and solvent. To convert the counter ions from bromide ions to hydroxide ions, the membranes were peeled off and submerged in 1 M KOH solution at room temperature for 48 h. The AEMs were then washed with deionized water until they were neutral pH. The synthesized quaternary ammonium membranes (approximately 10 cm × 10 cm, thickness approximately 50 μm) are denoted as PPO-TMA.

The IEC was measured experimentally by the Mohr method (Wang et al., 2019; Xu and Yang, 2001). Dried membranes in the Br⁻ form were immersed into Na₂SO₄ solution to release bromine ions. The released bromide ions were determined by titration with 0.01 M AgNO₃ aqueous solution with the indicator K₂CrO₄ solution. The IEC value was calculated as follows: I E C = 0.01 × V A g N O 3 m d r y (13) where VAgNO₃ is the volume of consumed AgNO₃ aqueous solution and m _dry is the weight of dried membrane.

The ion conductivity (σ, mS cm^-1) was measured in the in-plane direction by the four-electrode AC impedance method. The membrane was clamped in the test device and placed in an environmental chamber (Espec, SH-222) at different relative humidity (RH). The ion conductivity was calculated as follows: σ = L R ∙ A (14) where L is the distance between the two reference electrodes (cm), R is the measured resistance, and A is the cross-sectional area of the membrane (cm²).

WU and λ were calculated from followed formulae: W U = W w e t − W d r y W d r y × 100 (15) λ = W U × 1000 I E C × 18 (16) where W _wet is the weight of the wet membrane; W _dry is the weight of the dry membrane. The dried membrane was immersed in deionized water at a specified temperature for 24 h. After removing it and quickly blotting off the surface water, the weight was measured. Then, the membrane was placed in a vacuum oven at 60°C for 24 h and again weighed.

The membranes were cut into strips (1 cm × 3 cm) and stretched mechanically by a tensile system (Instron, E1000). The loading was static and the stress state was uniaxial stretching. Mechanical stretching was conducted at RT with a constant strain rate (2 mm min⁻¹) to obtain the stress‒strain (SS) correlations and repeated three times.

The surfaces or cross-sections of membrane were characterized by an S4800 field emission scanning electron microscope (Hitachi, Japan) at an accelerating voltage of 5 kV. The observed areas were pre-sputtered with a thin layer of platinum under vacuum.

The two-dimensional SAXS patterns were recorded using the Beijing Synchrotron Radiation Facility (BSRF) 1W2A experimental site using a Cu Kα (λ = 1.54 Å) radiation generator, with a distance of 1.5 m between the membrane sample and detector.

The effect of molecular oriented arrangement on ion transport in PPO-TMA was studied by MD simulation. The results show that the oriented ion transmission pathways improve conduction efficiency. Interestingly, the σ at λ = 5 of oriented-arranged PPO-TMA (inset in Figure 3) was 1.391 mS cm⁻¹ at 300 K, which is 2.4 higher than that of randomly-arranged PPO-TMA (0.405 mS cm⁻¹), suggesting that oriented polymer chains significantly promote ionic transport, which is consistent with the literature (Meng et al., 2019).

The above-mentioned oriented arrangement is an idealized model, because it is difficult to achieve an absolutely oriented arrangement. Here we present that mechanical stretching induces relatively ordered arrangement, which results in improved anion conductivity. The effect of mechanical stretching on PPO-TMA AEMs (such as changes of polymer chain arrangement and water cluster distribution) was investigated by experimental work combined with MD simulation, as shown in Figure 4A. Young’s modulus (initial slope section) and yield stress can be obtained from the stress-strain curves. It should be noted that the experimental conditions and parameters were identical with those used in the MD simulation. For simulation, a linear elastic region is found at a strain of less than 2%, which correlates with the experimental results. The yield stress obtained from the experiment is also in the same order as the simulation results, although there are some slight deviations from the simulation due to statistical errors.

Morphology characteristics were measured using SEM and shown in Figures 4B–E. The polymer chain displays a relatively uniform structure morphology before stretching (Figure 4B), while the cross-sectional SEM image after stretching shows a relatively oriented structure (Figure 4C). The polymer molecular arrangement or aggregation can be described via simulation of the density field calculation, which is presented in Supplementary Figure S2. The color gradient from white to black shown in Supplementary Figure S2A, B corresponds to the increase in density of polymer chains. It is seen that after the tensile stretching simulation, the density value decreases and the polymer morphology tends to be stretched and extended toward the stretched direction. Figures 4D, E shows the surface morphology of un-stretched and stretched PPO-TMA. A relatively smooth surface of un-stretched membrane is observed in Figure 4D. A large number of submicroscopic pores are formed during stretching of PPO-TMA. The elliptical pores formed during this process are oriented with their major axes parallel to the stretching direction and the film surface (Figure 4E). The lengths of the slits are typically in the range from 53 nm to 419 nm. The porous structure provides a continuous configuration necessary for fast ion and water transport (Morehouse et al., 2006; Sarada et al., 1983). Two-dimensional SAXS characterization provides additional evidence for the oriented structure. The isotropic SAXS data show a diffuse outer ring in Figures 4F–H, which has been attributed to scattering from the polymer aggregates (phase-separation of hydrophilic‒hydrophobic domains). As the membrane was stretched, the initially isotropic scattering pattern transforms into a strongly anisotropic scattering pattern, as observed in Figures 4G–I. For the stretched membrane, evident anisotropism is observed in SAXS pattern, indicating oriented morphology. This is attributed to the alignment of elongated polymer aggregates in the direction of uniaxial stretching (van der Heijden et al., 2004).

Structure changes of PPO-TMA by stretching was simulated and is shown in Figure 5. The 10 colors represent 10 polymer chains in Figure 5A. As the membrane is stretched, the backbones become oriented in the direction of stretching, which coincides with the strain effect that has been found in proton exchange membranes (Cable et al., 1995). With the consideration of adsorbed water molecules (λ = 15), a dramatic change in structure due to stretching can also be observed in Figures 5C, D. Water clusters tend to be extended along the stretching direction. The simulation results of the density field of water clusters also shows the same phenomenon (Supplementary Figure S3).

To further verify the increased porosity and connected channels of stretched PPO-TMA, the free volume of the unit lattice was calculated (Supplementary Figure S4). Free volume increased gradually with strains of up to 60% at all levels of water content. A high water content results in higher free volume for the same strain. The rapid increase in the free volume with increasing hydration levels is due to the increase in the number of water molecules in the membrane, causing a plasticizing effect and a larger distance between the polymer chains (Kuo et al., 2018).

In order to probe the detailed changes in the lattice orders in the local structure during PPO-TMA deformation at different water contents, N−N (nitrogen atom in polymer), N−O_w (oxygen atom in water molecule), and N−O_h (oxygen atom in hydroxide ion) RDFs were analyzed (Supplementary Figure S5), followed by calculation of the quantitative coordination numbers (CNs), as shown Figure 6. The CNs of N‒N, N‒O_w, and N‒O_h indicate the interaction strength between TMAs, TMA and water, TMA and OH⁻, respectively.

Supplementary Figure S5A shows the simulated RDFs of N−N linkage. The position of peaks at distances of <12 Å and >12 Å can be assigned to adjacent N−N between two chains as well as the N−N in the same chain, respectively (Dong et al., 2018). The differences among the RDFs at the prophase curves demonstrate the changes in the crystal lattice order of PPO-TMA. As the water content increases, the CNs for the un-stretched membrane decrease from 6.214 to 3.011 (Figure 6 and Supplementary Table S1), indicating that the nitrogen atoms tend to be separated at higher water content (Kuo et al., 2016). When the membrane was stretched, the CNs decrease for low water contents but increase for high water contents. At low water content, quaternary ammonium groups aggregate densely in the local hydrophilic phase, which is not conducive to conformational relaxation for the side chains in response to membrane deformation. Under uniaxial deformation, the side chains tend to align parallel to the stretching direction. At high water content, the quaternary ammonium groups are fully hydrated, resulting in flexible side chains, which allow rearrangement during membrane stretching. In addition, a decrease in the peak intensity at ∼13 Å indicates that the distance between N atoms in the same chain increases with stretching, also inducing a highly orientated polymer chain.

To investigate how the quaternary ammonium groups are solvated by water molecules, the RDFs of nitrogen and oxygen atoms in H₂O for different systems were investigated, as shown in Supplementary Figure S5B. Firstly, the peak intensity and CNs decrease as the water content increases, indicating that water molecules bind weakly with the quaternized groups with increasing water content. However, the peak positions do not change. This indicates that stretching mainly has an effect on the probability of the atoms in proximity with the quaternized groups. There is no significant change in the distribution of water molecules as the density decreases. Secondly, the CNs of water molecules surrounding each quaternary ammonium group are found to decrease with stretching for all water contents. This again confirms that the elongation of water clusters under mechanical stretching results in a decrease in the number of water molecules associated with the quaternized groups.

To investigate the relationship between R₄N⁺ groups and OH⁻, the CNs of the N−O_h were calculated and the results are shown in Figure 6C. At low water content, compared to the un-stretched membranes, the stretched membranes have lower CNs for N‒O_h. Hydroxide ions aggregate densely in the hydrophilic phase. As the water cluster extends due to uniaxial deformation, the number of water molecules and hydroxide ions correlated with the quaternary ammonium groups decreases. Therefore, at high water content, the polymer side chains have greater conformational flexibility and are more likely in a relaxed state when stretching the membrane, and thereby interact with free hydroxide ions. This leads to an increase in CNs and hydroxide ions around the quaternary ammonium group. Similar results have been reported in the literature (Kuo et al., 2017).

To analyze the ion diffusion characteristics, the diffusion coefficients of hydroxide ions were calculated at various water contents and different strain. Supplementary Figure S6 shows the hydroxide ion MSD curves at 300 K. Figure 7 summarizes the diffusion coefficients calculated from the hydroxide ion MSD curves at different water contents. Notably, Supplementary Figure S6 shows the slope of hydroxide ion MSD curves increases apparently with an increase in strain. The slopes increase more significantly with the change in the water contents rather than the strain levels. The diffusion coefficients of hydroxide ion in the un-stretched membrane at different water contents are 0.006 × 10⁻⁵ to 0.286 × 10⁻⁵ cm² s⁻¹, with λ from 5–20, respectively. The corresponding calculated σ values are 0.608, 1.989, 11.75 and 16.63 mS cm⁻¹, respectively.

Compared with the effect of changes in strain, the influence of change in water content is more significant. When the membrane was stretched with different strain, the D values change. For λ = 5 with the strain of 0%–60%, the corresponding D values are in the range of 0.006 × 10⁻⁵ to 0.025 × 10⁻⁵ cm² s⁻¹, respectively. The calculated σ values are 0.608–2.589 mS cm⁻¹ (an increase of 326% compared with un-stretched membrane). At the condition of λ = 15, when the strain changes from 0% to 60%, D increases from 0.172 × 10⁻⁵ to 0.2 × 10⁻⁵ cm² s⁻¹; the corresponding ion conductivity is 11.75 mS cm⁻¹ (reference value 11.25 mS cm^-1 (Yang et al., 2018)) and 14.02 mS cm⁻¹ (an increase of less than 50% than that of the un-stretched membrane), respectively. It has also been reported that the proton conductivity of oriented membranes in the direction of the strain increased compared with un-stretched membranes (Dan et al., 2006).

The ratios of D and σ in stretched and un-stretched membranes are shown in Figure 7 as embedded tables. The stretching effect on σ is not obvious at high water content, which can be explained by the morphology changes. At low water contents, the enhancement in hydroxide transport can be attributed to the stretched membrane with a high orientation of polymer chain and water pathways (Park et al., 2011). For higher water contents of λ = 15 and 20, flexible hydrated side chains are strongly correlated with free hydroxide ions, reducing the increase in D. Thus, the effects of stretching on ion transport are noticeably different at different water contents. The σ reaches the maximum value at λ = 20 and at a strain of 60%. It can be concluded that the orientation of water clusters and polymer chains are extended in the stretching direction by the uniaxial stretching of the membrane. The above analysis also correlates with the analysis of the microscopic morphology diagram shown in Figure 4, resulting in pathways that facilitate hydroxide ion transport.

To further verify the simulation results, experimental conductivity tests were conducted at different RH with the membranes before and after mechanical stretching. From calculations based on experimental values of water uptake (WU) and IEC, λ is obtained, which represents the number of water molecules corresponding to each quaternary ammonium group, consistent with the definition of λ in the MD simulation. Therefore, we observe that when λ = 15.86, σ = 11.33 mS cm⁻², which is in good agreement with the simulation results in Figure 7B (λ = 15, σ = 11.75 mS cm^-2). In addition, the conductivity of membrane at 20% elongation in the stretching direction was also tested. In the stretched z-direction, the σ increased by 3.24, 2.61, 1.61 and 1.57 times with increasing λ (listed in Table 1), respectively. Such results well demonstrate that mechanical stretching has a positive effect on the ion conduction in the tensile direction, which further verifies the conclusion obtained in the above simulation.