Molecular Dynamics Analysis of Hydroxide Ion Transport Mechanism in Anion Exchange Membrane

EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244121 A0804 Page 1/10 A0804 Molecular Dynamics Analysis of Hydroxide Ion Transport Mechanism in Anion Exchange Membrane Ryusei Ono* (1,2), Hiroto Suzuki (1,2), Kenji Miyatake (3), Takashi Tokumasu (2) (1) Graduate School of Engineering, Tohoku University, Sendai/Miyagi/Japan; (2) Institute of Fluid Science, Tohoku University, Sendai/Miyagi/Japan; (3) Clean Energy Research Center, University of Yamanashi, Kofu/Yamanashi/Japan; *Contact corresponding authors: www.EFCF.com/ContactRequest Abstract In order to address global climate change, clean energy sources that reduce CO2 emissions must be urgently developed. Hydrogen has emerged as a promising energy carrier due to its high energy density and environmentally friendly combustion, producing only water. Among hydrogen production technologies, green hydrogen, which is produced via water electrolysis powered by renewable electricity, is a key solution for decarbonization. In particular, anion exchange membrane water electrolysis is considered a cost-effective alternative because it allows the use of non-precious metal catalysts and offers the potential for operation with pure water. However, the relatively low conductivity of hydroxide ions in anion exchange membrane (AEM) is a major challenge in improving system performance. To investigate hydroxide ion transport mechanisms at the molecular scale, this study employs classical molecular dynamics (MD) simulations using QPAF-4, an AEM containing pendant trimethylammonium groups. Focusing on the vehicle mechanism, we explore how changes in water contents (λ) affect hydroxide ion diffusion. Our MD simulation reveals that the diffusion coefficient of hydroxide ion increases rapidly with water content at low λ, particularly between λ = 6 and 9, but shows a more gradual rise at higher λ values. This behavior is considered to be influenced by structural changes in the solvation structure around the trimethylammonium groups. We defined a “solvation number” to quantify the number of first solvation shells surrounding each hydroxide ion and categorized the local structures accordingly. At low λ, hydroxide ions were predominantly trapped in overlapped areas with strong electrostatic interactions, whereas at high λ, they mainly resided in isolated areas or the second solvation shell, exhibiting higher mobility. These results suggest that increased water content increases the distance between trimethylammonium groups and decreases the overlap of solvation shells, thus weakening ion trapping and promoting diffusion. Our results provide basic insights into the relationship between solvation structure and ion transport. These insights offer guidelines for the rational design of high-performance AEM materials for next-generation water electrolysis systems. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244121 A0804 Page 2/10 Introduction In response to the Paris Agreement, many countries have accelerated decarbonization efforts, setting goals such as carbon neutrality by 2050 and emission reductions by 2030. Major economies, including the EU and the U.S., regard renewable energy and green hydrogen as essential to sustainable growth. Hydrogen, with its high energy density and zero CO₂ emissions upon combustion, has attracted attention as a next-generation energy carrier [1]. However, most current hydrogen production methods rely on fossil fuels or biomass, resulting in CO₂ emissions. In contrast, green hydrogen produced by water electrolysis powered by renewable electricity is a key technology for realizing a decarbonized society [2]. Electrolyzers not only utilize surplus renewable electricity but also function as effective energy storage devices [3], [4], [5]. Electrolyzers are classified by membrane type into proton exchange membrane water electrolysis (PEMWE) and anion exchange membrane water electrolysis (AEMWE). PEMWE enables high-purity hydrogen production and rapid dynamic response. However, it operates under acidic conditions, which require the use of expensive precious metal catalysts. This substantially increases the overall system cost. AEMWE, in contrast, operates under alkaline conditions, enabling the use of non-precious metals and significant cost reduction [6]. Additionally, AEMWE can be operated with low-concentration alkaline solutions and is expected to enable pure-water operation, improving both safety and costeffectiveness. Consequently, AEMWE is considered to be a promising technology for nextgeneration water electrolysis [7], [8]. A typical water electrolyzer consists of a stack of unit cells, each containing a membrane electrode assembly (MEA) comprising an anion exchange membrane (AEM), catalyst layers, and gas diffusion layers [3]. In AEMWE, water is reduced at the cathode to produce hydrogen and hydroxide ions (Eq. 1). The generated hydroxide ions migrate through the AEM to the anode, where they are oxidized to form oxygen, water, and electrons (Eq. 2). The overall water-splitting reaction is summarized as follows (Eq. 3): cathode：4H2O+4e−→2H2+4OH−(1) anode：4OH−→O2+2H2O+4e−(2) total：2H2O→2H2+O2(3) The efficiency of hydrogen production in AEMWE is directly governed by hydroxide ion transport through the AEM. Therefore, high hydroxide ion conductivity is a critical requirement for membrane development. The ionic conductivity of AEMs is strongly dependent on internal water content. Although hydration enhances conductivity, electro-osmotic drag often leads to dehydration near the cathode. Over-hydration can compromise mechanical strength, while insufficient hydration lowers ion transport performance. Thus, optimal water management is essential. Operating conditions such as temperature and pressure also significantly influence water distribution in the membrane. Molecular dynamics (MD) simulations have been widely employed to investigate such internal water dynamics. Despite recent advances, hydroxide ion conductivity in AEM remains lower than proton conductivity in proton exchange membrane (PEM). For example, Nafion® PEM exhibits about 100 mS/cm at 25 °C when fully hydrated in water, whereas Tokuyama A201 AEM shows about 46 mS/cm at 22 °C under similarly fully hydrated conditions in water [9], [10]. All-atom MD simulations have been conducted to compare the diffusion coefficients of ions in polymer systems sharing the same backbone, but with different ion-exchange groups— sulfonic acid (PEM) and quaternary ammonium (AEM). These simulations showed that hydroxide ion diffusion in AEMs corresponds to only 6–11% of the hydronium ion diffusion in PEMs [11], [12]. These findings highlight that enhancing ion transport efficiency within AEMs is a key challenge for improving the overall performance of AEMWE. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244121 A0804 Page 3/10 Although AEM has been actively studied, the relationship between hydroxide ion transport mechanisms and membrane structure remains insufficiently understood [13]. Two main transport mechanisms have been proposed: the vehicle mechanism, involving the physical migration of hydroxide ions, and the Grotthuss mechanism, involving proton hopping through hydrogen-bonded networks [14], [15]. Previous studies have demonstrated that water content critically affects the dominant mechanism. Ab initio simulations by Tamar et al. showed that the vehicle mechanism prevails under low hydration (λ = 2–4), while insufficient hydration suppresses ion mobility [16]. In contrast, multiscale reactive molecular dynamics simulations by Chen et al. indicated that at high hydration (λ = 14), overlapping solvation shells facilitate vehicle-type transport via continuous water channels [17]. Foglia et al., using neutron scattering, found a transition from Grotthuss to vehicle mechanism with increasing hydration [18]. These findings suggest that hydroxide ion transport is strongly governed by both water content and membrane morphology. In this study, we focus primarily on the vehicle mechanism to elucidate the underlying ion transport behavior within AEMs. Direct observation of such nanoscale transport phenomena remains challenging with conventional experimental techniques. While quantum chemical methods offer high accuracy, they are computationally costly and impractical for large polymer systems. Classical MD simulations, in contrast, provide an efficient means of analyzing structural and dynamical properties of membranes across various conditions. By applying MD simulations to a model AEM system, this study aims to reveal the structural factors governing hydroxide ion mobility. The obtained insights will support the rational design of AEM materials with improved performance for sustainable hydrogen production. 1. Simulation methods 1.1 Simulation Details In this study, we conducted classical MD simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) to investigate the transport behaviours of hydroxide ions in AEM, with a particular focus on the vehicle mechanism. As the membrane model, we adopted the QPAF-4 polymer, which contains trimethylammonium functional groups and exhibits high hydroxide conductivity, excellent mechanical strength, and stability under alkaline conditions (Figure 1) [19], [20], [21]. The polymer structure and charge assignment were based on quantum chemical calculations. We set the degree of polymerization to m = 25 and n = 15, corresponding to an ion exchange capacity of 1.47 meq/g. This composition showed optimal hydroxide conductivity (47.8 mS/cm) and moderate water uptake (105%) in experiments [19]. The simulation system comprised seven QPAF-4 chains randomly placed in a periodic cubic box (600 × 600 × 600 ų). Each chain contained 30 trimethylammonium groups, resulting in Figure 1: Molecular structure of the QPAF-4 polymer [20] EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244121 A0804 Page 4/10 a total of 210 groups, and the same number of hydroxide ions was added for charge neutrality. Water molecules were introduced to achieve water contents of λ = 3, 6, 9, 12, 15, and 18, where λ is defined as the ratio of the total number of water molecules and hydroxide ions to the number of trimethylammonium groups. The system performed a series of thermal annealing treatments to remove artificial metastable states resulting from the complex polymer structure and random initial configurations. First, we performed energy minimization, followed by high-temperature NPT compression at 800 K and 200 bar, which we gradually reduced to 300 K and 1 bar. Then, we conducted 10 cycles of the following two steps to further equilibrate the system: (1) NVT simulation at 800 K for 100 ps, and (2) NPT simulation with cooling from 800 K to 300 K under 1 bar for 100 ps. This process enabled the system to overcome local energy minima and stabilize. We then performed a 5 ns equilibrium simulation under the NPT ensemble at 300 K and 1 bar. We used the resulting structure to perform production runs under the NVT ensemble at 300 K with a 1 fs timestep, saving snapshots every 1 ps over a total of 10 ns. 1.2 Analysis Details To evaluate the local structure, we used the radial distribution function (RDF), which gives the probability of finding a type B particle at a distance r from a reference type A particle: 𝑔𝐴−𝐵(𝑟)=(𝑛𝐵 4𝜋𝑟2𝛥𝑟) (𝑁𝐵 𝑉)(4) Here, nB is the number of B-type particles found within a spherical shell of thickness Δr at radius r, NB is the total number of B-type particles in the system, and V is the system volume. The coordination number (CN), representing the number of surrounding particles within a specific interaction range, was computed as: 𝐶𝑁=∫ 𝑔 A-B (𝑟)𝑑𝑟 𝑟𝑣 0(5) In this equation, rv represents the radial distance corresponding to the first minimum following the RDF peak. Furthermore, the diffusion coefficient D of hydroxide ions was calculated based on the slope of the mean squared displacement (MSD) as a function of time, using the following Einstein relation: 𝐷=1 6𝑑 𝑑𝑡⟨|𝑟(𝑡)−𝑟(0)|2⟩ (6) Here, the MSD was averaged over all hydroxide ions and multiple time origins, and the slope was extracted from the linear region of the MSD curve to determine the diffusion coefficient. To evaluate the dynamic retention of hydroxide ions in specific areas, the residence time distribution was analyzed using the approach proposed by Bruun et al [22]. The distribution function rtd(τk) is defined by the following time correlation function: 𝑟𝑡𝑑(𝜏𝑘)= ∑∑ 1 𝑀−𝑘𝜈𝑖(𝑡𝑗) 𝑁 𝑘=1 𝑀−𝑘 𝑗=1 𝜈𝑖(𝑡𝑗+𝜏𝑘),𝜏𝑘=𝑘∆𝑡,𝑘=0,1,2,…,(𝑀−1)(7) Here, N is the number of hydroxide ions, νi(tj) is an indicator function that equals 1 when ion i resides within the defined area at time tj , and 0 otherwise. Δt is the sampling interval (1 ps), and M is the total number of sampled time frames. The average residence time τrt was then extracted by fitting the decay of rtd(τ) with an exponential function using the following relation: 𝑙𝑛(𝑟𝑡𝑑(𝜏) 𝑟𝑡𝑑(𝜏𝑚𝑖𝑛))=−𝜏𝑟𝑡 −1𝜏(8) This method was applied to determine the mean residence times of hydroxide ions in various areas within the membrane. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244121 A0804 Page 5/10 2. Results 2.1 Analysis of Hydroxide Ion Diffusion Coefficients Figure 2 presents the diffusion coefficients of hydroxide ions at different water content conditions. As λ increases, the diffusion coefficient shows a rise, attributed to the growing number of water molecules surrounding the trimethylammonium groups. This hydration reduces electrostatic interactions, allowing free hydroxide ion movement within the membrane. Notably, the increase is nonlinear for λ ≤ 9 and becomes linear at higher λ, suggesting a transition in transport behavior. This shift likely reflects structural changes such as the reorganization of hydration shells and the formation of continuous water channels, which influence the hydroxide ion transport mechanism depending on the water content. Although similar trends have been observed in other AEMs, the direct correlation between polymer structure and diffusion enhancement remains insufficiently understood. To clarify the molecular basis of this water content dependence, the solvation structures specific to QPAF-4 is analyzed in the next section. By examining how these configurations affect hydroxide mobility, we aim to identify key transport mechanisms and potential limiting factors underlying the observed trend. 2.2 Molecular Structure Around Trimethylammonium Groups This study examined the molecular environment surrounding the trimethylammonium groups in QPAF-4. At each water content, RDFs were calculated between nitrogen atoms of the trimethylammonium groups and the oxygen atoms of water and hydroxide ions. From the RDFs, we defined the spatial ranges of the first and second solvation shells: the first solvation shells were defined from the start to the end of the first RDF peak, and the second from the end of the first RDF peak to the end of the second RDF peak. These definitions enabled a quantitative assessment of how the electrostatic field of the trimethylammonium groups influences local water and hydroxide ion distributions. We also analyzed RDFs between nitrogen atoms (N–N) of different trimethylammonium groups under varying water content. Based on these, we defined the overlapped area as Figure 2: Water content dependence of hydroxide ion diffusion coefficients in QPAF-4 membranes EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244121 A0804 Page 6/10 where first solvation shells of multiple trimethylammonium groups intersect, and the isolated area as where shells exist independently without overlap (Figure 3). As water content increased, more water molecules entered between the trimethylammonium groups, expanding their separation and decreasing the overlapped volume. Hydroxide ions in overlapped and isolated areas of the first solvation shell, and in the second solvation shell, experience distinct electrostatic environments. Consequently, their diffusion behavior is expected to differ. The transport characteristics associated with each area will be discussed in the following section. 2.3 Residence Time Analysis of Hydroxide Ions in Each Solvation Area We analyzed the preferential localization of hydroxide ions in different solvation areas under varying water content. To quantify this, we defined the solvation number (SN) as the number of first solvation shells from trimethylammonium groups that surround each hydroxide ion. A hydroxide ion with SN = 0 is located outside all first solvation shells, SN = 1 corresponds to an isolated area influenced by a single shell, and SN = 2 or 3 indicates overlapped areas where the hydroxide ion is simultaneously affected by two or three overlapping shells, respectively. These classifications are illustrated in Figure 4. For simplicity, we focused on water content at λ = 3, 9, and 15 and calculated the percentage of hydroxide ions present at each SN (Figure 5). SN ≥ 5 occurred rarely (e.g., 0.009% at λ = 3) and were excluded. At λ = 3, 52.0% of hydroxide ions were in SN = 3 and 16.4% in SN = 4. At λ = 15, SN = 0 and 1 were dominant, accounting for 22.9% and 48.6%, respectively, Figure 3: Schematic of first and second solvation shells around trimethylammonium groups (λ = 15), illustrating overlapped and isolated areas within the first shell Figure 4: Schematic illustration of solvation environments categorized by solvation number within the first solvation shell EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244121 A0804 Page 7/10 while SN = 4 dropped to 0.08%. We also evaluated residence times by solvation area (Figure 6). Due to the extremely low presence of ions with SN = 0 and 1 at λ = 3, and SN = 0 at λ = 6 (each below 1%), these cases were excluded from the analysis in Figure 6 due to insufficient statistical reliability. At low water content (λ = 3, 6), hydroxide ions resided mostly in highly coordinated structures (SN = 3, 4), where strong electrostatic trapping in overlapped areas resulted in long residence times. In contrast, at high water content (λ = 15, 18), reduced SN in overlapped areas led to shorter residence times due to weakened trapping. Residence times in isolated areas (SN = 1) were relatively stable across water content, likely due to consistent one-to-one electrostatic interactions. A slight increase in Figure 5: Presence ratio of hydroxide ions as a function of solvation number within the first solvation shell under different water contents Figure 6: Mean residence time of hydroxide ions in each area of the first and second solvation shells as a function of water content EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244121 A0804 Page 8/10 residence time from λ = 6 to 12 may reflect expanded isolated area volume, as suggested by increased N–N distance. Beyond λ = 12, the N–N distance stabilized (about 8.90 Å), and residence times remained unchanged. 2.4 Transport Characteristics in Each Solvation Area We evaluated the trapping strength of hydroxide ions at each SN using presence ratio (Figure 5) and the volume fraction (Figure 7). At low water content (λ = 3), SN = 3 and 4 areas accounted for only 5.70% and 1.09% of the total volume, respectively, yet contained 52.0% and 16.4% of the hydroxide ions. This imbalance indicates strong trapping within overlapped areas. At λ = 15, the volume of SN = 2 decreased to 9.91%, while SN = 3 and 4 dropped below 1%, reflecting reduced overlap due to increased N–N distance. This shift increased the volume and occupancy of SN = 1, as well as the presence of ions in SN = 0. These changes suggest weaker trapping at high water content, allowing more mobile hydroxide ion behavior and supporting the linear increase in diffusion coefficient observed in Section 2.1. Furthermore, the trends observed in the presence ratio (Figure 5) and volume fraction (Figure 7) indicate that higher SN structures correspond to stronger ion confinement. Overall, at low water content, hydroxide ions are strongly trapped in overlapped areas, resulting in longer residence times and restricted mobility. In contrast, at high water content, reductions in both SN and overlapped volume weaken trapping strength, enhance diffusivity, and directly contribute to improved hydroxide ion conductivity. 3. Conclusion In this study, classical molecular dynamics simulations were performed to elucidate the water content-dependent transport behavior of hydroxide ions in AEM, focusing on the vehicle mechanism. By employing QPAF-4, an AEM material with trimethylammonium groups, we systematically analyzed how water content affects solvation structure, residence time, and hydroxide ion diffusivity. The diffusion coefficient increased nonlinearly at low λ and linearly at high λ, indicating a structural transition. At low λ, hydroxide ions were mainly confined in overlapped areas Figure 7: Volume fraction of each solvation number region λ = 3, 9, and 15 EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244121 A0804 Page 9/10 formed by multiple first solvation shells, resulting in strong electrostatic trapping and limited mobility. As λ increased, expanded spacing between trimethylammonium groups reduced overlap, shifting ion localization toward isolated areas and second solvation shells, where mobility was higher. We introduced the SN to quantify the number of overlapping shells per hydroxide ion and confirmed its correlation with confinement strength. Higher SNs indicated stronger electrostatic trapping and limited mobility. These results offer molecular-level insight into the role of solvation structure in water content-dependent hydroxide ion transport, providing a foundation for designing AEMs with enhanced hydroxide ion conductivity for efficient and durable AEMWE applications. Acknowledgements This work was supported by the GteX Program Japan (Grant Number JPMJGX23H2) and the JSPS Core-to-Core Program (Grant Number JPJSCCA20210005). The computations were performed using the next-generation integrated research system at the Institute of Fluid Science, Tohoku University. We would like to express our deepest gratitude to all individuals and supporters involved in this research. References [1] Agency for Natural Resources and Energy, Clean Energy Strategy: Interim Summary. Proceedings of the Ministry of Economy, Trade and Industry Report, Tokyo, Japan, May 2022. https://www.enecho.meti.go.jp/committee/council/basic_policy_subcommittee/carbon_ neutral/report_20220519_01.pdf [2] Naiying Du et al., Anion-Exchange Membrane Water Electrolyzers. Proceedings of the American Chemical Society Chemical Reviews, Canada, April 2022. [3] Altech Co., Ltd., What Is a Water Electrolyzer? Objectives, Research, and Manufacturing Trends. 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