Molecular Analysis of the Relationship between Water Clusters and Proton Diffusion Properties inside a Polymer Electrolyte Membrane in PEFC under Subzero Conditions

EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244131 A1110 Page 1/9 A1110 Molecular Analysis of the Relationship between Water Clusters and Proton Diffusion Properties inside a Polymer Electrolyte Membrane in PEFC under Subzero Conditions Hiroki Nishizawa* (1,2), Takuya Mabuchi (1), Takashi Tokumasu (1) (1) Institute of Fluid Science, Tohoku University, Sendai/Miyagi/Japan; (2) Graduate School of Engineering, Tohoku University, Sendai/Miyagi/Japan; *Contact corresponding authors: www.EFCF.com/ContactRequest Abstract Polymer Electrolyte Fuel Cells (PEFCs) play a crucial role in achieving carbon neutrality and the Sustainable Development Goals (SDGs). PEFCs face several challenges, including diffusion polarization, material transport efficiency, and durability. Our research focuses particularly on the operation of PEFCs under the harsh conditions of subzero temperatures. Many regions worldwide experience cold climates, making the resolution of these issues vital for the further popularization of PEFCs. In such environments, the transport efficiency of materials within the polymer electrolyte membrane (PEM), including protons crucial for fuel cell operation, decreases due to the potential freezing of water molecules and a significant reduction in kinetic energy. Nevertheless, previous research[1] elucidated that proton hopping contributes proton diffusion in ice. Therefore, this phenomenon is critical to the context of this research. In this study, we conducted a detailed analysis of the relationship between changes in water clusters and proton diffusion properties within PEM. We performed ReaxFF[2] MD simulations, which can treat proton hopping. The parameter set, which comprehensively defines the empirical coefficients, was modified from the one developed by D. Fantauzzi et al.[3] This modification includes adjusting the ionization degree to theoretical value and preventing the abnormal bond which occurred in Nafion chains. Based on the transport analysis, both water and hydronium ions reduced diffusion coefficients under subzero conditions, with the decrease in water, which is more pronounced at higher water contents. In contrast, the diffusion coefficient of hydronium ions decreased less significantly. To investigate this discrepancy, proton transport by proton hopping was analyzed, revealing that proton hopping increased under subzero conditions. This increase likely mitigated the reduction in hydronium ion diffusivity compared to water. Structural analysis further indicated that the hydrogen-bonding network among water molecules becomes more enhanced under subzero conditions, leading to the formation of larger water clusters around sulfonic acid groups. This structural change is presumed to have facilitated additional proton hopping pathways, thereby enhancing proton transport. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244131 A1110 Page 2/9 Introduction Fuel cells are being increasingly deployed as part of initiatives aimed at achieving carbon neutrality and the sustainable development goals (SDGs). Among various types, polymer electrolyte fuel cells (PEFCs) have attracted significant attention owing to their capability for room temperature start-up and their potential for miniaturization and lightweight design. These characteristics have facilitated their application in residential stationary power systems and fuel cell vehicles. PEFCs face persistent challenges, including the enhancement of mass transport efficiency[4], [5], [6], reduction of precious metal loading[7], [8], and stable operation under harsh environmental conditions[9], [10], [11]. This study focuses on the operation of PEFCs under subzero conditions. Under such environments, several critical issues emerge: transport impediments due to water freezing within the catalyst layer (CL)[9], marked deterioration of mass transport within the polymer electrolyte membrane (PEM), and mechanical delamination between the PEM and CL[9] arising from volumetric expansion of frozen water during shutdown phases[9]. Furthermore, even under conditions of fully hydrated state, partial freezing of water within the PEM has been reported[11]. Conversely, proton diffusion mediated by the Grotthuss mechanism[12], [13] may be enhanced. These phenomena have primarily been investigated through experimental approaches, while the specific mechanisms and nanoscale structural changes involved remain largely unexplored. Based on these considerations, this study specifically targets the investigation of mass transport properties and the internal state of the PEM under subzero conditions. Proton transport in the PEM is generally governed by two principal mechanisms: Vehicle mechanism and Grotthuss mechanism[12], [13]. In Vehicle mechanism, hydronium ions diffuse by physical migration. In contrast, the Grotthuss mechanism involves the reorganization of hydrogen bonds and covalent bonds between water molecules and hydronium ions, facilitating proton hopping. Under subzero conditions, a pronounced decrease in kinetic energy is expected to significantly hinder proton transport via Vehicle mechanism. Meanwhile, Uritski et al.[14] reported that proton diffusion in ice increase by Grotthuss mechanism. Thus, considering the contribution of Grotthuss mechanism is necessary when analyzing proton transport behavior under subzero conditions. Water clusters, aggregates of water molecules formed around the hydrophilic functional groups of the PEM, play an essential role in facilitating Grotthuss mechanism. Because hydronium ions tend to localize within these clusters[15], [16], larger clusters provide more extensive hydrogen-bond networks, thereby promoting proton hopping. Accordingly, both the presence and size of water clusters are critical factors influencing proton transport within the PEM. The final objective of this research is to provide fundamental insights that may guide the development of PEM materials with improved resistance to performance degradation under subzero conditions, through a detailed investigation of proton transport properties and internal structural states. In particular, this study focuses on elucidating the relationship between the characteristics of water clusters within the PEM and proton diffusion behavior, which are deemed critical factors governing PEM performance. Proton transport properties within PEM and internal structure of PEM have been extensively investigated not only by experimental methodologies but also via numerical simulations. Previous studies have employed classical molecular dynamics (MD) simulations[4], [17], [18], density functional theory (DFT) calculations[19], [20], and ab initio calculations[21]. As previously noted, consideration of Grotthuss mechanism is indispensable for an accurate understanding of proton transport under subzero conditions. While DFT and ab initio MD EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244131 A1110 Page 3/9 simulations can capture Grotthuss mechanism, their application is constrained by the limited ability to address dynamics processes over extended time scales. Accordingly, in this study, numerical simulations utilizing reactive force field molecular dynamics (ReaxFF MD)[2] were conducted, a method capable of simultaneously accounting for both chemical reactions and dynamics behavior. 1. Methods 1.1 Simulation details ReaxFF MD simulations were performed to evaluate the relationship between water clusters and proton diffusivity in PEM under subzero conditions. The parameter set used in ReaxFF MD defines a comprehensive collection of empirical coefficients that govern interatomic interactions. The parameter set is defined for specific molecules and atoms, so constructing an appropriate one is crucial for performing accurate simulations. In this study, a parameter set originally developed by D. Fantauzzi et al.[3] was employed, with modifications to address issues related to ionization degree and the formation of anomalous bonds within the PEM. Nafion with EW=1100, a material widely used in previous studies of polymer membranes, was selected as the material of PEM. All simulations were performed with large-scale atomic/molecular massively parallel simulator (LAMMPS)[22]. The system configuration included 10 Nafion chains, 100 hydronium ions, and 200, 600 or 900 water molecules, corresponding to water contents of 3, 7, 10, respectively. A time step of 0.25 fs and a sampling interval of 250 fs were adopted, with three-dimensional periodic boundary conditions. For the annealing process, classical MD simulations were first conducted using the DREIDING force field[23]. As in prior studies, structural relaxation was achieved through repeated application of NVT and NPT ensembles[23]. Following this, the force field was transitioned from DREIDING force field to ReaxFF, accompanied by additional short relaxation steps using NVT and NPT ensembles. Sampling calculations were conducted for 10 ns, and the resulting data were used for analysis. Six simulation conditions were investigated in total, combining two temperatures (300 K and 200 K) with three water contents (3,7 and 10). 1.2 Analysis details The self-diffusion coefficient is a widely used metric in numerical simulations that quantitatively evaluates the ease with which molecules diffuse. In this study, self-diffusion coefficients were calculated from the slope of the linear region of the mean square displacement (MSD) curve. Equation (1) was used for the calculation, where 𝐷 is the diffusion coefficient, 𝑡 is the sampling time, and 𝑅𝑖(𝑡) denotes the position vector of each atom at time 𝑡. In this equation, the time average is calculated by varying the initial time 𝑡0, which helps eliminate sample dependence arising from the initial conditions. 𝐷= lim 𝑡→∞ 1 6𝑡〈|𝑅(𝑡+𝑡0)−𝑅(𝑡0)|2〉 (1) The radial distribution function (RDF) is a method that allows the evaluation of the local structure formed by molecules in the system. In this study, RDF was computed using equation (2), which describes the probability of finding a particle B at a distance 𝑟 from particle A. Here, 𝑛𝐵 is the number of particles B within a spherical shell of thickness Δ𝑟 at distance 𝑟 from particle A, 𝑁𝐵 is the total number of particles B in the system, and 𝑉 denotes the volume of the simulation cell. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244131 A1110 Page 4/9 𝑔𝐴−𝐵(𝑟)=(𝑛𝐵 4𝜋𝑟2Δ𝑟) (𝑁𝐵 𝑉) (2) The coordination number is also analyzed by equation (3). In this analysis, the coordination number was calculated by integrating the RDF results. 𝑐(𝑟) denotes the coordination number. 𝑐(𝑟)=∫ 𝑔𝐴−𝐵(𝑟)𝑑𝑟 𝑟 0(3) To analyze diffusion via Grotthuss mechanism, both the number of proton hopping events and rattling[24] behavior were examined. The number of hopping events was counted using the scheme illustrated in Fig. 1(a), enabling a consistent count regardless of sampling duration. Rattling, as shown in Fig. 1(b), refers to repeated proton hopping between the same hydronium ions and water molecule, a process that does not contribute to proton diffusion. Therefore, the proportion of non-rattling events was calculated to assess the effective contribution of proton hopping to diffusion. The non-rattling rate was evaluated using equation (4). 𝑅𝑛𝑜𝑛−𝑟𝑎𝑡𝑡𝑙𝑖𝑛𝑔 =1− 𝑁𝑟𝑎𝑡𝑡𝑙𝑖𝑛𝑔 𝑁𝑡𝑜𝑡𝑎𝑙 ℎ𝑜𝑝𝑝𝑖𝑛𝑔 (4) For the analysis of water clusters, the focus was placed on both the number and size of clusters. In this study, water molecules forming hydrogen bonds were defined as belonging to the same cluster. Since hydrogen-bonded water molecules tend to gather within a specific range, the end point of the first peak in the RDF between water molecules was adopted as the cutoff distance for identifying water clusters. The analysis of cluster size included both the maximum and average cluster sizes. Given that a single water cluster can occasionally contain a disproportionately large number of water molecules compared to other clusters, including the largest cluster in the average is statistically inappropriate. Accordingly, the average size was calculated by excluding the largest cluster from the analysis. Fig. 1. (a) Analysis of the number of proton hopping events. In the upper diagram, the number of proton hopping events is counted as one; in the lower diagram, it is counted as two. (b) Schematic illustration of rattling behaviour. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244131 A1110 Page 5/9 2. Results and discussion 2.1 Diffusion properties Diffusion coefficients of water molecules and hydronium ions were evaluated. Fig. 2 presents the calculated diffusion coefficients for water and hydronium ions. The qualitative trend of water and hydronium ion diffusion coefficients with respect to water content is consistent with previous studies[23], [25]. These results reveal that both species exhibit a significant decrease in diffusion coefficients at 200 K. While the quantitative values of hydronium ion diffusion coefficients vary depending on the water content, their qualitative trend remains consistent across conditions. In contrast, the temperature-dependent trends of water diffusion coefficients showed both quantitative and qualitative differences with water content. Notably, under the water content of 10, the diffusion coefficient decreased much more significantly than under other conditions. To investigate these differences in diffusion behavior, proton hopping characteristics were analyzed. Table. 1 summarizes the number of proton hopping events per picosecond and the corresponding non-rattling rate. The analysis indicates that at 200 K, the frequency of proton hopping increases, with a higher increase observed at greater water contents. Furthermore, the non-rattling rate was also found to be higher at 200 K. These findings suggest that proton transport via Grotthuss mechanism becomes more prominent at 200 K, especially at higher water contents. Consequently, although water molecule diffusivity sharply decreases as water contents, the hydronium ion diffusivity remains relatively less affected due to the enhanced contribution of proton hopping. 2.2 Structure analysis To analyze the structural properties, the RDF between water molecules and sulfonic groups was analyzed for each condition, as shown in Fig. 3. The position of the first peak of RDF is consistent with previous studies[26], [27], indicating that the characteristic interaction distance between water molecules and sulfonic groups is accurately captured. The RDF results indicate that the coordination number increases at 200 K, suggesting that water molecules tend to cluster more densely around sulfonic groups under subzero conditions. To further investigate these structural changes, the RDF between water molecules was also analyzed. As shown in Fig. 4, the peak intensity of RDF is consistently higher at 200 K across all water contents. The first peak of RDF is consistent with previous studies[28]. The first peak in water-water RDF corresponds to hydrogen-bonded water molecules[29], indicating that a stronger hydrogen-bonding network forms at 200 K. (a) (b) Fig. 2. (a) Diffusion coefficients of water molecules. (b) Diffusion coefficients of hydronium ions. Both figures show temperature-dependent trends. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244131 A1110 Page 6/9 Table. 1. The number of proton hopping and non-rattling rate. 𝑁hopping [/ps] 𝑅Non−rattling [%] 𝜆=3,300 K 0.213 1.42 𝜆=3,200 K 0.212 1.65 𝜆=7,300 K 0.306 3.87 𝜆=7,200 K 0.410 6.18 𝜆=10,300 K 0.355 5.11 𝜆=10,200 K 0.429 6.09 Additional analysis was conducted on the size of water clusters, as presented in Fig. 5. The results show a general trend of decreased average cluster size at 200 K for all water contents. Moreover, the total number of clusters tends to decrease at 200 K. The observed relationship between the average cluster size and the number of water clusters is consistent with previous studies[15]. The hydrogen-bonding network becomes more robust at 200 K. This enhanced network likely promotes the formation of larger water clusters while reducing their overall number. These findings collectively indicate that, the hydrogen-bonding network among water molecules within the PEM becomes more rigid, leading to the formation of larger water clusters around sulfonic acid groups. The results of the aforementioned analyses indicate that, under subzero conditions, the hydrogen-bonding network formed by water molecules becomes more strongly developed, leading to the formation of larger water clusters surrounding sulfonic acid groups. This structural tendency is increasingly pronounced with higher water contents. Such structural (a) (b) (c) Fig. 3. The results of RDF between sulfonic acid groups and water molecules. The solid lines show the results of RDF and the dashed lines show the results of coordination number. The coordination number corresponds to the right axis. (a), (b) and (c) show the results for water contents of 3, 7 and 10, respectively. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17244131 A1110 Page 7/9 changes are presumed to enhance the availability of proton hopping pathways for hydronium ions, thereby increasing both the number of hopping events and the non-rattling rate. As a result, proton transport via Grotthuss mechanism is facilitated, which is likely responsible for the observed divergence in transport characteristics between water molecules and hydronium ions. 3. Conclusion This study focused on elucidating the transport properties and internal structure of PEM under subzero conditions through molecular-level analysis using ReaxFF MD simulations. Structural analyses revealed that, compared to room temperature, the hydrogen-bonding network formed by water molecules within the PEM becomes more enhanced under subzero conditions. Consequently, larger water clusters tend to form around sulfonic acid groups. This structural change is considered to enhance the availability of proton transport pathways, thereby increasing transport via Grotthuss mechanism. As a result, the diffusion behavior of water molecules and hydronium ions diverges under these conditions. (a) (b) (c) Fig. 4. The results of RDF between water molecules. (a), (b) and (c) show the results for water contents of 3, 7 and 10, respectively. (a) (b) Fig. 5. The results of water cluster properties. 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