Atomistic insights into structure–morphology relationships in hydrated poly(benzimidazolium) and poly(bis-arylimidazolium) ionene membranes

Abstract

Ease of preparation and the alkaline stability characteristics have spurred immense interest in polyelectrolytes composed of poly(benzimidazolium) (HMT-PMBI) and poly(bis-arylimidazolium) (PAImMM) ionene anion exchange membranes. The present work emphasises the structure and morphological traits of hydrated structures based on ionene membranes using molecular dynamics simulations. The influence of the benzimidazolium group and the bis-arylimidazolium group on the hydrated structure of the membrane is analysed through the radial distribution function and structure factor at 300 and 333 K. A notable difference is seen in the spatial density maps with an increase in temperature for HMT-PMBI, where a more dense and enhanced distribution of water molecules is shown compared to 300 K. Angular autocorrelation (torsional and rotational) decays relative faster for PAImMM compared to HMT-PMBI. Water clusters around the skewed and extended configurations show a similar hydration pattern for both membranes. The mobility of the hydroxide ion is found to be relatively faster in HMT-PMBI compared to PAImMM. This work provides valuable atomistic insights that can inform the rational design of future ionene derivatives with enhanced ionic conductivity and structural robustness for electrochemical energy applications.

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Design, System, Application

Anion exchange membranes (AEMs) represent a rapidly emerging field due to their ability to facilitate efficient hydroxide (OH⁻) ion transport, offering a more environmentally friendly alternative to traditional proton exchange membranes (PEMs). One of the key factors influencing AEM performance is the choice of membrane material and functional groups. In this work, we present a molecular dynamics simulation study of poly(benzimidazolium) and poly(bis-arylimidazolium) ionene membranes, with a focus on cost-effective anion exchange membranes (AEMs) for alkaline fuel cell devices. Our key findings include an in-depth analysis of the comparison between the benzimidazolium ionomer and bis-arylimidazolium, in hydrated form. We demonstrate that subtle variations in polymer backbone flexibility and functional group chemistry profoundly influence hydration shell organization, ion transport efficiency, and water channel architecture. HMT-PMBI supports more ordered hydration networks and faster hydroxide mobility, whereas PAImMM exhibits steric hindrance that limits ion conduction.

1. Introduction

Ion exchange membranes (IEMs) facilitate the selective transport of ionic species and are fundamental components in modern electrochemical energy conversion devices. The proton exchange membranes (PEMs) have dominated both research and commercial activity due to their high efficiency. However, PEMs suffer from several critical limitations, including high cost, reliance on perfluorinated polymers with associated environmental concerns, high fuel crossover, and sluggish reaction kinetics.^1–3 Over the past decade, there has been a growing shift toward anion exchange membranes (AEMs) as a promising alternative to PEMs.^4–7 AEMs support the conduction of hydroxide ions, enabling the use of non-precious metal catalysts in place of costly platinum-group metals, and allowing for the design of fluorine-free, environmentally benign membranes.^8–10 In addition, hydroxide conduction in alkaline media provides intrinsic advantages such as enhanced oxygen reduction reaction (ORR) kinetics and improved electrochemical oxidation performance, especially under elevated temperature conditions and long-term caustic media.^11–17

To be viable for applications in anion exchange membrane fuel cells (AEMFCs), the next-generation AEMs must simultaneously achieve high ionic conductivity, thermal, mechanical and alkaline stability, and prolonged operation durability under strongly alkaline and high-temperature environments. The fundamental challenge of the early generations of AEMs was to achieve a balance of these critical requirements, specifically alkaline stability. For instance, among the most widely studied materials, AEMs functionalized with quaternary ammonium (QA) cations have received considerable attention. Despite their ease of synthesis, structural tunability, and widespread use, QA groups exhibit poor chemical stability in alkaline environments, as they are prone to nucleophilic substitution (S_N2) and can undergo Hofmann or E2 elimination reactions.¹⁸ Other systems, such as pyridinium-functionalized AEMs, have also been investigated, but researchers have noted their inherently low hydroxide conductivity and chemical vulnerability. Under elevated temperatures, the pyridinium ring can be irreversibly transformed into an inactive pyridone species.¹⁹ A continued effort involving strategic structural manipulation and molecular engineering of cationic groups and backbones is progressively yielding more chemically robust AEM candidates capable of addressing long-standing stability and performance concerns.^14,20–22

To address the challenges for a sustainable AEM, there has been a growing consideration of poly(arylimidazolium) and poly(arylbenzimidazolium)-based AEMs.^23–31 These materials incorporate imidazolium or benzimidazolium based functional groups and have demonstrated remarkable ionic conductivity, high ion-exchange capacity (IEC), and promising alkaline stability. These emerging AEM candidates often lack the conventional phase-separated morphologies with long-range order as typically observed in high-performance AEMs via structural factor analysis.^32–35 However, the presence of nano-phase separation into hydrophobic and hydrophilic regions is critical for water channels in the membrane matrix. These membranes show efficient ion transport, which is attributed to their reduced swelling behavior and the formation of sub-nanometer water channels. Such confined hydration environments are believed to enhance the Grotthuss mechanism, offering higher ionic mobility.^33,36–39 Derivatives of these membranes have attained significant recognition, where some formulations demonstrate superior performance in AEMFCs technology compared to conventional QA-based membranes. Over the past few years, a variety of imidazolium and benzimidazolium-functionalized AEMs have been developed, exhibiting a broad range of physicochemical and electrochemical performance.

Wright et al.⁴⁰ introduced hexamethyl-p-terphenyl poly(benzimidazolium) (HMT-PMBI), a highly methylated derivative of polybenzimidazole (PBI), which resulted in significant improvements in ion exchange capacity (IEC), hydroxide ion conductivity, and chemical robustness of previously vulnerable structural motifs.^26,31,41 Additionally, some studies have reported that incorporating functional imidazolium groups into the polymer backbone, as in HMT-PMBI, significantly improves ion transport properties. HMT-PMBI exhibited a significantly higher hydroxide ion conductivity of 80 mS cm⁻¹ at 40 °C under 90% relative humidity (RH), compared to 19 mS cm⁻¹ for poly(phenylene oxide) (PPO) functionalized with pendant imidazole groups (PPO-Im).⁴¹ Fan et al.⁴² synthesized a series of poly(arylimidazolium)-based AEMs featuring targeted substitutions at the C2 and N1/N3 positions of the imidazolium ring. These structural modifications were designed to suppress chemical degradation under caustic conditions. Supported by DFT calculations, they demonstrated that longer alkyl substituents at these positions increase steric hindrance and electrostatic potential, effectively inhibiting degradation pathways such as ring-opening and dealkylation. The resulting membranes exhibited exceptional chemical stability, minimal swelling, and excellent hydroxide ion conductivity, reaching 82 mS cm⁻¹ at 80 °C under 95% RH. Further studies was reported by Sana et al.,⁴³ who developed polybenzimidazole (PBI) derivatives incorporating both pyridinium and imidazolium functional groups. Their work highlighted the synergistic role of electronic and steric effects in determining membrane properties. Among the synthesized derivatives, the pyridine-bridged PBI with a butyl-substituted imidazolium exhibited the best balance of stability and performance, achieving a high IEC of 3.37 meq g⁻¹ and a remarkable hydroxide conductivity of 128.6 mS cm⁻¹ at 80 °C. More recently, Tao et al.⁴⁴ introduced a new class of ether-free poly(aryl piperidinium) (PAP) derivatives containing imidazolium-functionalized side chains. Other classes of AEMs, poly(oxindole biphenylene),⁴⁵ poly(arylene piperidinium)^46,47 and polyarylmethylpiperidinium (PAMP),⁴⁸ and quaternary ammonium ionene membranes^49,50 have also been explored and showed prolonged alkaline stability with a good water uptake. Among these, PAP-Im-3 stood out due to its exceptional alkaline durability, robust mechanical properties, and enhanced phase-separated morphology, culminating in a hydroxide conductivity of 165 mS cm⁻¹ at 80 °C. These advancements collectively underscore the importance of rational molecular design, particularly the choice and positioning of cationic functional groups, backbone rigidity, and side-chain engineering in developing next-generation AEMs.^{27,32,33,41,51–53}

Notably, comprehensive theoretical studies on solvation structures and transport mechanisms have gained significant momentum in advancing our understanding of ion transport.^34,54–56 Using atomistic ab initio molecular dynamics (AIMD) simulations, Zelovich et al.⁵⁷ demonstrated the influence of different cationic functional groups such as trimethyl alkyl ammonium (TMA) and imidazolium (IMI) on hydroxide and water mobility under nanoconfined and low-hydration conditions. Their study revealed that TMA-functionalized systems exhibit higher diffusivity of both hydroxide and water at room temperature. At elevated temperatures, the IMI-functionalized system outperforms TMA due to its enhanced rotational mobility, making it more chaotropic and better suited for facilitating ion transport through narrow bottleneck regions in the membrane. Dong et al.³⁴ investigated the mechanisms of ion transport in polymer matrices and found that narrow constraints can impede ion movement and result in vehicular diffusion being thermodynamically unfavourable. Under such nanoconfined conditions, the Grotthuss mechanism becomes the dominant transport pathway by enabling hydroxide conduction through sub-nanometer water channels. Zhang et al.⁵⁸ employed classical MD simulations to investigate changes in the hydration structure around imidazolium groups in imidazolium-grafted poly(2,6-dimethyl-1,4-phenylene oxide) membranes. Their findings showed that increasing water uptake leads to the expansion of hydration shells and reduces the electrostatic attraction between hydroxide ions and cationic sites. Furthermore, the formation of percolated and well-connected water channels was observed at moderate hydration levels (λ ∼ 12). At higher hydration, an excessive matrix swelling leads to over-expanded channels and potentially compromises the mechanical integrity of the membrane. Tipp et al.⁵⁹ employed quantum calculations and experimental validation to explore structure–reactivity relationships in benzimidazolium-based AEMs. The authors established that the Gibbs free energy of hydroxide attack at the C-2 position serves as a more predictive and powerful computational descriptor for chemical stability than the traditionally used LUMO energy. This insight offers a valuable criterion for screening and designing stable membrane materials.

Despite extensive experimental studies and advancements in theoretical approaches, a prominent gap remains in molecular-scale investigations of ionene-based membranes. A molecular approach to examine the structural and transport characteristics of backbone-functionalized AEMs is essential to get deeper insight into membrane architecture and ion transport. This understanding is critical for the rational design and development of next-generation polymer membranes with enhanced efficiency and stability. Apart from ionic conductivity, it is important to explore the solvation environment of the anions and the water uptake capacity as a function of membrane structure, composition, and the nature of the cationic moieties.^41,57,58,60

In this work, we present a relative molecular analysis of two hydrated poly(arylbenzimidazolium) and poly(bisarylimidazolium) ionene membrane derivatives, HMT-PMBI^61,62 and PAImMM, at 300 K and 333 K.⁴² These are functionalized with benzimidazolium and bis-arylimidazolium groups, respectively. The obtained experimental value was 2.5 mmol g⁻¹ for HMT-PMBI and 2.86 mmol g⁻¹ for PAImMM. To ensure meaningful comparison, we normalized the hydration level to λ = 8 in our simulations to reflect equivalent water per cationic site as observed in experiments.^40,42 The chemical structures of the two membranes are shown in Fig. 1. The complete simulation details are provided in the methodology section. We explored the temperature-dependent structural and dynamical behaviour of these membranes using MD simulations. The present work and simulation results are limited to one hydration level only. Bulk structural properties are characterized through the analysis of radial distribution functions (RDFs), spatial distribution functions (SDFs), radius of gyration, end-to-end distance, structure factors, void size distribution, and water cluster analysis. Dynamical properties are evaluated using time correlation functions (including torsional and ring-plane normal autocorrelations), diffusion coefficients to map vehicular diffusion in classical simulations and residence times. The summary of important results concludes the work and the results are within the scope of classical MD simulations at the chosen hydration level.

Fig. 1 Left panel: chemical structure and snapshot of the decamer geometry. Right panel: representative snapshot of the cubic simulation box after a 40 ns NVT production run at 300 K for (a) HMT-PMBI and (b) PAImMM [color scheme: (1) HMT-PMBI polymer chain: licorice (C – orange, H – white), CPK (N – blue, C – orange), polyhedra (methyl groups – orange), and paper chain (ring plane – orange-yellow); (2) PAImMM polymer chain: licorice (C – melon, H – white), CPK (N – blue, C – melon), polyhedra (methyl groups – melon), and paper chain (ring plane – melon-green); (3) hydroxide ions: CPK (O – red, H – white); (4) water molecules: cyan surface].

2. Simulation methodology

Force field parameters

The monomer structures of HMT-PMBI and PAImMM were constructed using GaussView⁶³ and subsequently optimized at the MP2/6-31G(d,p) level of theory in Gaussian 16⁶⁴ software. The optimized geometries were used to calculate atomic partial charges via the CHELPG⁶⁵ method, and the resulting values are presented in Fig. S1. Bonded (bond, angle, dihedral, improper) and non-bonded (Lennard-Jones and Coulombic) interaction parameters for both membranes were derived from the OPLS-AA (Optimized Potentials for Liquid Simulations All Atom) force field.⁶⁶ The MS-RMD hydroxide model and the aSPC/Fw water model, as developed by Chen⁶⁷ and Park et al.,⁶⁸ were employed to represent hydroxide and water interactions, respectively.

System setup and simulation protocol

All MD simulations were carried out using GROMACS 2023.4⁶⁹ software. A single decamer chain for each polymer was built using the .rtp file of GROMACS by assigning atom types, bonds, and link residues for three residue types as (i) head unit, (ii) middle repeat-unit segment, and (iii) tail unit. The decamer chain was replicated using the Packmol⁷⁰ program to generate the 27 replicated decamer chains and optimized to get the best fit of the simulation box. Energy minimization was performed for the obtained configuration via the steepest descent⁷¹ algorithm. The chemical structure of the monomer and the energy-minimized decamer chain are shown in Fig. 1(left panel). A configuration consisting of 27 replicated decamer chains for both systems was used to carry out simulated annealing for 28 ns with four cycles. Each cycle lasted 7 ns with a 1 fs timestep, where the system temperature was ramped from 300 K to 1000 K and then cooled back to 300 K. The annealed temperature and density fluctuation profiles for both HMT-PMBI and PAImMM are shown in Fig. 2, and representative snapshots of the replicated and annealed configurations are provided in Fig. S2.

Fig. 2 Fluctuations in temperature and density were observed during simulated annealing: (a) HMT-PMBI and (b) PAImMM over a 28 ns trajectory.

Following annealing, 540 hydroxide ions (to ensure overall charge neutrality) and 4320 water molecules (λ = 8, corresponding to moderate hydration level) were added to both membrane systems using Packmol.⁷⁰ Long-range electrostatics were treated using the Particle Mesh Ewald (PME)⁷² method with a real-space cutoff of 1.2 nm. After energy minimization, each system underwent a 2 ns pre-equilibration run at 300 K and 333 K. The pre-equilibrated configurations were then subjected to a 20 ns NPT (isobaric–isothermal) equilibration run, followed by a 40 ns NVT (isochoric–isothermal) production run (to avoid position rescaling due to barostat)⁷³ at both 300 K and 333 K, the final configurations are illustrated in Fig. 1(right panel). During the NPT phase, pressure was maintained at 1 bar using the C-rescale⁷⁴ barostat (compressibility = 4.5 × 10⁻⁵ bar⁻¹, coupling time constant = 1 ps). Temperature control was achieved using a Nosé–Hoover⁷⁵ thermostat with a coupling time of 0.2 ps. Detailed system composition, cubic simulation box length, and calculated densities are provided in Table 1. HMT-PMBI and PAImMM are commercially available as Aemion™ and Aemion+™ ionomers, respectively, supplied by Ionomr Innovations Inc. and have an approximate density of 1.2 g cm⁻³, which is within the range of computed density values in this study. MD simulations at ambient conditions yield a system density in good agreement with available experimental/reference values (6.6% deviation), with deviations within typical OPLS accuracy (5%). These results confirm that the charge model is compatible with OPLS and adequate for describing intermolecular electrostatic interactions in the present system. The simulation protocol may be implemented for other similar AEMs including piperidinium-based and quaternary-ammonium AEMs. Trajectories were recorded at 0.5 ps intervals during the production run and were used for all subsequent structural and dynamical analyses discussed in the Results and discussion section.

Table 1 System size details, cubic box length, and calculated density from MD simulations of hydrated HMT-PMBI and PAImMM at 300 and 333 K

Polyelectrolyte	Total no. of atoms	No. of hydroxide ions	No. of water molecules	Temperature (K)	Cubic box length (Å)	Density (g cm^−3)
HMT-PMBI	37 845	540	4320	300	71.819	1.116
				333	72.575	1.056
PAImMM	38 394	540	4320	300	72.481	1.116
				333	73.093	1.085

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3. Results and discussion

Radial distributions

The interfacial interactions between the ionene, water, and hydroxide ions play a critical role in defining the physicochemical characteristics of the polymer matrix. To elucidate these interactions, radial distribution functions⁷⁶ (RDFs) were calculated (Fig. 3) at 300 K and 333 K, represented by solid and dashed lines, respectively. The corresponding coordination numbers, obtained by integrating the first solvation shell of the RDFs, are provided in Table S1. The interactions between the ammonium functional groups on the polymer backbone and surrounding water and hydroxide molecules were analyzed using RDFs between the nitrogen atoms (N) of the ionene and the oxygen atoms of hydroxide (O_h) and water (O_w), as shown in Fig. 3a and b. The broad and low-intensity peaks observed in these RDFs suggest weak interactions and the presence of a broad solvation shell. With increasing temperature from 300 K to 333 K, no significant changes were observed in the overall RDF profiles. However, the oxygen atoms of both hydroxide and water exhibit slightly weaker interactions with the nitrogen site (N_B) of PAImMM compared to the nitrogen site (N_I1/N_I2) of HMT-PMBI, a similar trend also reflected in the corresponding coordination numbers.

Fig. 3 Radial distribution functions (RDFs) calculated from a 40 ns NVT production run at 300 K (solid line) and 333 K (dashed line) for: (a) ionene–hydroxide ion interactions (N–O_HYD); (b) ionene–water interactions (N–O_SOL); (c) hydroxide ion–water interactions (O_HYD–O_SOL); (d) ionene–ionene interactions (N–N); (e) hydroxide ion–hydroxide ion interactions (O_HYD–O_HYD); and (f) water–water interactions (O_SOL–O_SOL).

The presence of consistent hydrogen bonding interactions were evidenced by quantitatively and qualitatively identical, intense peaks in the RDFs between the oxygen atoms of O_h–O_w and O_w–O_w, observed at 2.7 Å and 2.9 Å, respectively (see Fig. 3c and f). While a slightly reduced interaction with increasing temperature is observed in the oxygen–oxygen peak profile at 4.3 Å in the O_h–O_h RDF (see Fig. 3e). Structural illustration of the polymer chains was obtained by examining ionene–ionene interactions through nitrogen–nitrogen (N–N) RDFs. In Fig. 3d, the calculated N_I1–N_I1/N_I2–N_I2, and N_B–N_B RDFs represent the ammonium functional groups’ nitrogen–nitrogen atoms’ correlations in HMT-PMBI and PAImMM, respectively, intramolecular interactions within the benzimidazolium ring (PAImMM) are excluded. N_I1 and N_I2 refer to non-equivalent nitrogen atoms present in the polymer backbone of the HMT-PMBI ionomer which exhibit distinct peak profiles. The N–N RDFs show peaks at 8.6 Å (N_I1–N_I1), 7.6 Å (N_I2–N_I2), and 7.5 Å (N_B–N_B), corresponding to intramolecular interactions between nitrogen atoms of imidazolium and benzimidazolium rings of adjacent monomer units along the polymer chain. Among the nitrogen–nitrogen RDFs, the N_I1–N_I1 and N_I2–N_I2 profiles exhibit lower peak intensities with broad bases, indicating a more dispersed or random distribution of nitrogen atoms of imidazolium rings within the monomer. Moreover, the N_B–N_B RDF exhibits a sharp and well-defined peak at 6.6 Å, indicating a highly ordered and consistent spatial arrangement of nitrogen atoms of benzimidazolium rings within the monomer.

Spatial distributions

The spatial distribution functions (SDFs) were calculated to map the 3D arrangement of hydroxide and water molecules around the monomer units of the polymer chains in HMT-PMBI and PAImMM at 300 K and 333 K (see Fig. 4). The distributions of oxygen atoms of hydroxide and water molecules are predominantly localized around the imidazolium and benzimidazolium rings, reflecting their hydrophilic nature. Moreover, negligible distribution is observed around the benzene rings in the backbone (in HMT-PMBI) and phenyl substituents (in PAImMM), highlighting their hydrophobic character.

Fig. 4 Spatial distribution functions (SDFs) calculated from a 40 ns NVT production run showing the density distribution of oxygen (O) atoms of hydroxide ions around the monomer unit of HMT-PMBI at (a) 300 K and (b) 333 K, and PAImMM at (c) 300 K and (d) 333 K, respectively [color scheme: (1) HMT-PMBI monomer unit: licorice (C – orange, H – white), CPK (N – blue, C – orange, H – white), polyhedra (methyl groups – orange), and paper chain (ring plane – orange-yellow); (2) PAImMM monomer unit: licorice (C – melon, H – white), CPK (N – blue, C – melon, H – white), polyhedra (methyl groups – melon), and paper chain (ring plane – melon-green); (3) oxygen (O) atoms of hydroxide ions: isosurface (yellow) at an isovalue of 0.036 Å⁻³; (4) oxygen (O) atoms of water molecules: isosurface (cyan) at an isovalue of 0.020 Å⁻³].

Among the observed distributions, the oxygen atoms from water and hydroxide show a more concentrated and dominant distribution near the imidazolium rings, while their presence is more scattered and less pronounced around the benzimidazolium moieties. These findings reinforce the trends observed in the N–O_w and N–O_h RDFs peak profiles and coordination numbers. Moreover, the oxygen atoms of water and hydroxide do not exhibit spatial overlap. Water molecules are found to localize closer to the polymer chain, while hydroxide ions appear slightly offset or behind; this spatial separation suggests stronger hydration interactions. Interestingly, the SDFs also exhibit significant temperature-dependent changes. Notably, with increasing temperature from 300 K to 333 K, the spatial distribution of oxygen atoms (water and hydroxide) expands in the case of HMT-PMBI (see Fig. 4a and b), while it contracts in the case of PAImMM (see Fig. 4c and d). To gain deeper insight into this behavior, time correlation functions were analysed, which are discussed in the following section.

Angular autocorrelations

The presence of semi-flexible behavior and actively induced motions in IEMs significantly influences their efficiency.⁶⁷ In this study, to better characterize the structural aspects of the polymer chains, along with the notable temperature-dependent distribution trends observed above, we carefully examined these features by calculating both torsional (TACF) and rotational (RACF) autocorrelation functions for torsion angle and ring plane normal, respectively.

The distinct autocorrelation functions (TACFs and RACFs) calculated at 300 K and 333 K for HMT-PMBI and PAImMM are shown in Fig. 5 and 6, respectively. In HMT-PMBI, we observed a steep rate of decay (brown) in the torsional correlation function that corresponds to the torsion angle between the benzimidazolium rings (see Fig. 5a), without any significant differences in the ring plane rotational motions (Fig. 6a). In contrast, PAImMM exhibited a faster rate of decay (green) in the torsional correlation function of the torsion angle between the imidazolium ring and the phenyl substituent (Fig. 5b), along with a notable change in the rate of rotational motion (green) of the phenyl substituent planes (Fig. 6b). This suggests a greater degree of correlation due to increased angular motion of the phenyl group in PAImMM compared to HMT-PMBI. These observations clearly indicate the presence of a sort of freedom of rotational motions in both polymer membranes. Due to structural differences, the membrane properties are affected in contrasting ways. In HMT-PMBI, the temperature-dependent accelerated conformational correlation within the backbone enables the dispersion of hydroxide and water molecules with increasing temperature. On the other hand, in PAImMM, the significant substituent-associated motions hinder the localization of hydroxide ions near the functional groups. These findings demonstrate that variations in polymer chain architecture can significantly influence the structural properties in ionene-based membranes, which in turn affect the chemical characteristics.^77–79

Fig. 5 Torsional autocorrelation functions (TACF) calculated for different torsion angles present in (a) HMT-PMBI and (b) PAImMM at 300 K (solid line) and 333 K (dashed line).

Fig. 6 Rotational autocorrelation functions (RACF) calculated for different ring plane normals in (a) HMT-PMBI and (b) PAImMM at 300 K (solid line) and 333 K (dashed line) [color of graphs is as per color of ring presented].

Scattering profiles

To correlate the spatial correlations with the phase morphology in the HMT-PMBI and PAImMM membrane matrix, we calculated the Fourier-transformed pair correlations. These Fourier-transformed pair correlations also considered partial structure factors for certain atom pairs. We have performed Fourier transforms of the RDFs⁸⁰ for ionene–ionene (N–N), ionene–water (N–O_w), and water–water (O_w–O_w) interactions, as shown in Fig. 7. The partial structure factors were calculated using the TRAVIS program.⁸¹ The g(r) between atom types were computed up to a maximum sampled distance of r_max = 3.6 nm with a resolution of 7200 bins. A Lorch-type window function was applied to minimize truncation artifacts. Structure factors were evaluated up to a maximum wave-vector modulus of q_max = 200 nm⁻¹ with a resolution of 2000 points. No separation between intramolecular and intermolecular correlations was performed. Therefore, bonded and non-bonded pair contributions are both included. The total structure factor needs to be analysed by the sum of all partial functions to map with experiments.⁸² However, we presented partial structure factors of specific atom pairs only. In Fig. 7a, the partial structure factor corresponding to ionene–ionene (N–N) interactions exhibits a broad peak centered around 0.5–1.0 Å⁻¹, indicative of short-range ordering among backbone nitrogen atoms. This corresponds to a real-space correlation length of approximately 6–12 Å (calculated as 2π/q), which falls within the range reported in previous studies (6–20 Å).⁸³ The ionene–water (N–O_w) partial structure factor, shown in Fig. 7b, displays sharp and intense peaks at 0.45 Å⁻¹ for HMT-PMBI and 0.47 Å⁻¹ for PAImMM, signifying the presence of well-defined, stable hydration shells around the cationic sites. The higher intensity of the peak in HMT-PMBI suggests a stronger and more structured hydration environment compared to PAImMM. Similarly, the water–water (O_w–O_w) partial structure factor shown in Fig. 7c presents sharp peaks at 0.47 Å⁻¹ and 0.5 Å⁻¹ for HMT-PMBI and PAImMM, respectively. These are consistent with the formation of hydrogen-bonded water networks. The higher peak intensity in HMT-PMBI indicates more confined and ordered water domains, further highlighting its superior water structuring capacity relative to PAImMM. Despite the absence of phase segregation and long-range order, as evidenced by the low intensity of the ionene–ionene partial structure factor in the MD simulations, the prominent peaks in the N–O_w and O_w–O_w partial structure factors indicate the temperature-independent formation of well-connected, interpenetrating water channels in both HMT-PMBI and PAImMM. These channels are likely to facilitate efficient ion conduction. Such features are close to previous experimental⁸⁴ observations and theoretical studies on similar membrane systems, supporting the presence of robust water domains even in the absence of classical phase-separated morphologies.^34,83,85,86

Fig. 7 Partial structural factors calculated at 300 K (solid line) and 333 K (dashed line) for: (a) N–N, (b) N–O_SOL, and (c) O_SOL–O_SOL correlations. Panels (d) and (e) display representative snapshots of hydrated ionene membranes for HMT-PMBI and PAImMM, respectively, along with their corresponding water channel width distribution histograms [color scheme: (1) HMT-PMBI polymer chain: licorice (C – orange), CPK (N – blue, C – orange, H – white), polyhedra (methyl groups – orange), and paper chain (ring plane – orange-yellow); (2) PAImMM polymer chain: licorice (C – melon), CPK (N – blue, C – melon, H – white), polyhedra (methyl groups – melon), and paper chain (ring plane – melon-green); (3) hydroxide ions: CPK (O – red, H – white); (4) water molecules: CPK (O/H – cyan)].

Void size distribution

The formation of water channels is clearly observed in the snapshots shown in Fig. 7d and e for HMT-PMBI and PAImMM, respectively, where the cyan-colored regions represent the spatial distribution of water channels. To estimate the cross-sectional dimensions of the water channels, we computed the pore size distribution across the polymer matrix, as illustrated in the subfigures of Fig. 7d and e. Pore-size analysis was performed using PoreBlazer 4.0,⁸⁷ which calculates the accessible space inside the material using a probe molecule. For this analysis, the last 10 000 frames of the trajectory were used, sampled at 0.5 ps intervals. A porous structure was obtained by removing water and hydroxide molecules, and the pore-size distribution was calculated using a 2.8 Å probe diameter and 0.02 Å grid spacing.

It was observed that the majority of water channels exhibit diameters around ∼7 Å, regardless of the polymer matrix and temperature. The cross-sectional dimensions identified in this study are consistent in scale with those reported by Dong et al., with ∼6 Å channels observed in PPO-derived polymer systems^34,35 and by Frischknecht et al. for hydroxide-conducting polymers.⁸⁸

Structural integrity

Furthermore, to understand the structural characteristics of the polymer matrix, we calculated the radius of gyration and end-to-end distance⁸⁹ for each of the 27 polymer chains at 300 K and 333 K, as shown in Fig. 8 and 9, respectively. Fluctuations are represented by error bars. The average radius of gyration values at 300 K and 333 K were calculated to be 29.2 ± 0.6 Å and 29.9 ± 0.6 Å for HMT-PMBI, and 30.9 ± 0.2 Å and 31.5 ± 0.5 Å for PAImMM, respectively. Likewise, the average end-to-end distances at 300 K and 333 K were found to be 34.8 ± 1.2 Å and 34.3 ± 1.7 Å for HMT-PMBI, and 33.1 ± 1.3 Å and 34.4 ± 1.1 Å for PAImMM, respectively. The minimal changes in radius of gyration and end-to-end distance upon escalating temperature indicate that the polymer membranes maintain their structural integrity and polymer chain stability.

Fig. 8 Radius of gyration (R_g) calculated for 27 polymer chains over a 40 ns NVT production run for (a) HMT-PMBI and (b) PAImMM at 300 K (purple line) and 333 K (orange line). Error bars represent the standard deviation from the time-averaged.

Fig. 9 End-to-end distance (R_E-E) calculated for 27 polymer chains over a 40 ns NVT production run for (a) HMT-PMBI and (b) PAImMM at 300 K (purple line) and 333 K (orange line). Error bars represent the standard deviation from the time-averaged values.

Water cluster

According to the study by Ziv et al.,⁴¹ regardless of the type of anion, membrane morphology and water cluster size^90,91 can significantly impact water uptake, which in turn affects anion conductivity. To gain insight into the solvation environment of the polymer chains, we examined the local hydration structure by analyzing water clustering around decamer polymer chains. The skewed and extended chain configurations are identified based on their minimum and maximum end-to-end distances and are selected for this analysis. The average water cluster structures surrounding the skewed and extended configurations of HMT-PMBI and PAImMM at 300 K are illustrated in Fig. 10. In HMT-PMBI, the number of water molecules forming clusters around the skewed configuration was found to be 151 ± 8 at 300 K and 141 ± 12 at 333 K, while for the extended configuration, the corresponding values were 158 ± 5 and 147 ± 9, respectively. Similarly, in PAImMM, the number of clustered water molecules around the skewed configuration was 155 ± 9 at 300 K and 143 ± 6 at 333 K, whereas for the extended configuration, it was 159 ± 10 and 144 ± 8, respectively. Despite the structural and correlational differences discussed earlier (Angular autocorrelations section), both polymers exhibit a comparable number of water clusters surrounding their chains. Upon increasing the temperature by 30 °C, the average number of associated water molecules in both systems subtly decreased by ∼10–15, indicating a slight loss in hydration. In contrast, the change in configuration from skewed to extended resulted in only a minimal difference of ∼1–7 water molecules.

Fig. 10 Representative snapshots of skewed and extended polymer chain conformations surrounded by water clusters at 300 K. Panels (a) and (b) show the skewed and extended configurations of HMT-PMBI, respectively, while panels (c) and (d) depict the corresponding configurations for PAImMM [color scheme: (1) HMT-PMBI polymer chain: licorice (C – orange, H – white), CPK (N – blue, C – orange), polyhedra (methyl groups – orange), and paper chain (ring plane – orange-yellow); (2) PAImMM polymer chain: licorice (C – melon), CPK (N – blue, C – melon, H – white), polyhedra (methyl groups – melon), and paper chain (ring plane – melon-green); (3) water molecules: CPK (O/H – cyan)].

Transport dynamics

The effect of interfacial interactions among ionene–hydroxide, ionene–water, and hydroxide–water pairs was further explored by examining the mobility of hydroxide and water molecules within the hydrated HMT-PMBI and PAImMM polymer matrix. To characterize molecular mobilities, the mean square displacement (MSD) was computed as a function of time and log–log scaling plots (see Fig. S4 and S5 in the SI, respectively). The fundamental dynamical quantity, self-diffusion coefficients (D_c) are calculated from the linear regime of the MSD versus time curves using the Einstein relation.⁷⁶ The resulting diffusion coefficients are tabulated in Table S2 in the SI.

At 300 K, the molecular mobilities of hydroxide and water in HMT-PMBI are measured as 0.093 × 10⁻⁵ cm² s⁻¹ and 0.6513 × 10⁻⁵ cm² s⁻¹, respectively. For PAImMM, the corresponding mobilities are 0.0545 × 10⁻⁵ cm² s⁻¹ for hydroxide and 0.5577 × 10⁻⁵ cm² s⁻¹ for water. As expected, an overall increase in diffusivity for both species was observed with increasing temperature. Specifically, increasing the temperature from 300 K to 333 K (ΔT = 33 K) led to an increase in the hydroxide D_c by a factor of 2.5 in HMT-PMBI and 2.7 in PAImMM, whereas the water diffusion coefficient increased by a factor of 2.0 in both systems. This analysis highlights a stronger temperature dependence for hydroxide mobility compared to water, particularly in PAImMM, which can be attributed to the weaker interactions between hydroxide/water molecules and the ionene backbone.

Ion residence behavior

Further, the hydroxide transport via vehicular mechanisms is examined using the residence time (t_r) of hydroxide ions in the vicinity of the cationic ammonium nitrogen functional sites to understand the role of ion–polymer interactions in transport. The t_r was evaluated through the time autocorrelation function approach.^92,93 The t_r of hydroxide molecules is calculated within the first solvation shell of the nitrogen atoms at the polymer's functional sites, within the first solvation shell cutoff of the N–O_h RDFs. The calculated residence time autocorrelation function (C_r) for both polymer systems at 300 K and 333 K is shown in Fig. S6. The average t_r is calculated as the integral of the residence time autocorrelation function and found to be 279.3 ps and 218.8 ps for HMT-PMBI at 300 K and 333 K, respectively. For PAImMM, the corresponding values are 271.6 ps and 225.3 ps, respectively.

At 300 K, the t_r for HMT-PMBI and PAImMM (279.3 and 271.6 ps, respectively) do not fully align with the trend observed in the MSD-based diffusion coefficients, while the t_r at 333 K (218.8 ps for HMT-PMBI and 225.3 ps for PAImMM) are consistent with the MSD trends. These findings indicate that at lower temperatures (300 K), hydroxide ions tend to remain less frequently in the vicinity of the cationic functional sites. In contrast, at higher temperatures (333 K), the increased thermal energy enhances the ionic mobility which allows a greater number of hydroxide ions to randomly engage with the polymer backbone. For instance, Dong et al.³⁴ observed significantly shorter hydroxide t_r (∼19 ps) in fully reactive ReaxFF simulations for poly(p-phenylene oxide) (PPO)-based systems, while their non-reactive ReaxFF simulations yielded longer t_r (∼350 ps). Moreover, Dubey et al.⁹⁴ reported an average hydroxide t_r of ∼232 ps in poly(vinyl benzyl trimethylammonium) polymer systems using classical MD simulations.

4. Conclusion

A comprehensive MD simulation study to compare the structural and transport properties of two hydrated ionene AEMs, HMT-PMBI and PAImMM, under alkaline conditions was undertaken. Our results provide a molecular understanding of the hydrated polymer structure, the role of functional groups, and how morphology governs ion transport and membrane behavior at the single hydration level i.e. (λ = 8). HMT-PMBI showed a more structured hydration shell, enhanced hydroxide and water diffusivity, and stronger intermolecular ordering compared to PAImMM. The torsional and rotational autocorrelation analyses (TACF and RACF) revealed increased conformational flexibility in the HMT-PMBI backbone compared to PAImMM, enabling more dispersed and extended distributions of hydroxide and water molecules. In contrast, PAImMM exhibited more localized dynamics, primarily associated with the phenyl substituents. This behavior is attributed to steric hindrance from the phenyl rings, which limits solvent accessibility, leading to constrained hydration and slightly reduced ion mobility.

Water cluster analysis revealed that both systems maintain a consistent hydration structure at both temperatures. However, HMT-PMBI exhibited slightly lower hydroxide residence times at elevated temperatures, indicating more dynamic ion–polymer interactions (the trend aligns well with the observed diffusion coefficients). The chain configuration assessed through radius of gyration and end-to-end distance confirmed that both membranes retain structural integrity with minimal thermal deformation. The study demonstrates that the variations in morphological traits and temperature-induced conformational dynamics behavior can significantly influence the ion transport in ionene-based AEMs. The contribution of structural diffusion needs to be examined in the future for these membranes to get deep insights into the ion transport. Our study highlights the importance of backbone architecture, functional group selection, and conformational freedom in designing next-generation membranes for AEMFCs, but was restricted to one hydration level due to limited experimental data. It must be noted that the results are based on a selective hydration λ = 8 which is close to experimental PAImMM water uptake. The influence of water uptake at varying hydration levels and inclusion of structural diffusion may produce more deeper insights for the molecular designs of these AEMs.

Author contributions

SD performed all the calculations and carried out formal analysis. APS administered the project and helped in the funding acquisition, formal analysis and investigation. SD and APS contributed in writing and review – editing.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI).

Supplementary information: calculated CHELPG charges for (a) HMT-PMBI and (b) PAImMM in Fig. S1. Typical snapshots of the simulation box showing the replicated and simulated annealed geometries for HMT-PMBI in panels (a) and (b), and for PAImMM in panels (c) and (d), respectively in Fig. S2. Density fluctuations during a 20 ns NPT equilibration run of the hydrated polymer matrices: (a) HMT-PMBI and (b) PAImMM at 300 K and 333 K in Fig. S3. Coordination numbers calculated from a 40 ns NVT production run at 300 and 333 K for HMT-PMBI and PAImMM for various atom–atom interactions in Table S1. MSD and log–log plots of mean square displacement (MSD) versus time for (a) hydroxide ions and (b) water molecules, obtained from a 40 ns NVT production run at 300 K (solid filled symbols) and 333 K (unfilled symbols) in Fig. S4 and S5 respectively. Diffusion coefficients (D × 10⁻⁵ cm² s⁻¹) of hydroxide ions and water molecules calculated from the 40 ns NVT production run. Values in parentheses represent standard deviations in Table S2. Time correlation functions calculated from a 40 ns NVT production run for hydroxide ions located in the first solvation shell of the nitrogen atom at the functional active site of the polymer chain for (a) HMT-PMBI and (b) PAImMM at 300 K (solid line) and 333 K (dashed line) in Fig. S4. See DOI: https://doi.org/10.1039/d5me00224a.

Acknowledgements

SD thanks the Anusandhan National Research Foundation (ANRF), New Delhi for financial support. APS acknowledges the ‘Anusandhan National Research Foundation (ANRF)’, Govt. of India for SERB – CRG/2022/001938 Grant.

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