Molecular Model and Structural Stability Study of a Nafion Ionomer-Based Membrane Electrode Assembly

One of the most important parts of a polymer electrolyte membrane fuel cell (PEMFC) is the membrane electrode assembly (MEA). However, the delamination between the membrane and electrode layers, induced by uneven distribution of internal stress and stress concentration due to the inconsistent water and thermal expansion properties, greatly reduces the PEMFC durability. Based on the data from the literature or use of commercial products, this work established the molecular model of membrane and electrode layers, and aimed to find the stable structure of MEA. Nafion ionomer and its composite with graphite-supported platinum were considered as a proton exchange membrane and catalyst electrode layer materials, respectively. Molecular dynamics simulations were employed to investigate the coefficients of thermal and water expansion of membrane and electrode layers. The structural stability of a three-layer MEA model (anode-membrane-cathode) was discussed by exerting various external pressures and calculating the binding energies between layers and between graphene and platinum. The results showed that very high pressures squeeze the internal molecules excessively, resulting in the platinum particles detaching from their support material, while lower pressure weakens the binding between layers.


Introduction
In recent years, environmental pollution has been the focus of much research, and practical applications of clean energy technologies have undergone rapid development, particularly the fabrication of proton exchange membrane fuel cells (PEMFCs).Although PEMFC products have been put into production, low durability still limits their full development.A three-layer membrane electrode assembly (MEA) without a gas diffusion layer, generally fabricated using the catalyst-coated membrane (CCM) technique, is the core part of a PEMFC, and its properties directly determine PEMFC durability. 1 In a MEA system, the electron-, proton-, and water-transfer processes in the wet-heat cyclic loading easily cause internal mechanical damage.Although chemical interactions are a direct threat to PEMFC durability, the effects of internal mechanical damage cannot be ignored. 2[8] With the complexity of preparation processes and the work environment, it is difficult to accurately measure MEA properties using conventional macroscopic techniques and methods.It is well known that to great extent microstructures determine the properties of macroscopic material.Therefore, microstructure analysis of the performance of membranes and CLs has become significant.Molecular dynamics (MD) simulation is currently a popular research method for analysing the physical properties of nanoscale materials. In this work, we selected Nafion as a membrane material, and a compound of Nafion and graphene-supported platinum (GN/Pt) as a CL material.1] In addition, an ion polymer solution in a CL plays the role of a bonding and transmission medium, 22 and generally has a similar chemical composition as membrane material.Thus, Nafion is also considered to play the role of a bond in CLs.The purpose of this work is to devise a method of designing a MEA molecular model with excellent structural stability.

Membrane model
The chemical formula of the selected Nafion membrane is shown in Fig. 1(a); it has a similar molar mass (1143 g mol −1 ) as repeating units of Nafion 117 (≈1100 g mol −1 ).Five monomers are included in a single chain, and 16 single chains form a Nafion oligomer.They were constructed in a tetragonal lattice, and then subjected to geometric optimization under an external pressure of 0.1 GPa.Fig. 1(b) shows the optimized structure with a density of 1.7 g cm −3 .; thus, the system remains electroneutral.The increase in water levels would increase proton conductivity, but at the same time reduce the mechanical properties.We considered four different humidity lev-els for Nafion molecular structures, and the corresponding hydration levels are λ = 0, 4, 9, 13 and 17 among , where N is the number of particles.Hydration levels higher than 17 is considered as the relative humidity above 95 %.

CL model
Commercial catalysts have Pt particle diameters ranging from 1 to 3 nm and show good performance, e.g., Pt/carbon black (Hispec 3000, Johnson Matthey Co.).Two different diameters of Pt particles, 1.2 and 1.6 nm, are considered in our model.Anode and cathode models are differentiated by layer thickness and Pt content.In experiments, catalysts in an anode generally show an excellent catalytic efficiency with a lower mass fraction of Pt than in a cathode.Thus, here we consider a Pt mass fraction of ≈ 20 % in the anode CL, and ≈ 30 % in the cathode CL.Four-layer graphene is used for supporting the Pt cluster.

MEA model
The CCM-MEA preparation is implemented by means of hot packaging of the proton exchange membrane and electrode layers to achieve close contact.In our initial MEA model, we construct a layer-by-layer structure along the z direction (thickness direction) according to the equilibrium structures of the membrane and electrode layers after MD simulation, like a sandwich model, in which the membrane is in the middle, with the two sides being the anode and cathode layers.

Computational details
The MD simulations are carried out using Materials Studio commercial software.In Nafion systems, we use the Dreiding force field 23 to describe the interaction between atoms.5] In the CL system, the universal force field (UFF) 26 is applied to describe the interaction of all atoms, including the interaction of Pt atoms, carbon atoms, and the atoms of the Nafion oligomers.8][29] For the initial system constructed, we first conducted a geometric optimization, with ultrafine precision.
After geometric optimization, a 60 ps annealing simulation, with a time step of 1 fs and using a constant pressure and temperature (NPT) ensemble, is performed in each system, where temperature and pressure are maintained, respectively, by a Nose thermostat and a Berendsen barostat, at a pressure of 0.1 GPa, an initial temperature of 300 K, a middle cycle temperature of 500 K, and cycle times of 30.
Then, for the last equilibrium structures with minimum potential energy, we continued 100 ps MD simulations at various temperatures, and recorded the last 20 ps of structures for collecting data such as the energy, density, and volume; we then averaged these values for further analysis.
Finally, we construct a three-layer MEA model according to the above equilibrium structures, and then geometrically optimize it.A quench MD simulation with a 200 ps simulation time and 1 fs time step was performed in succession to globally determine the equilibrium structure with the lowest energy.The NPT ensemble with 298 K temperature was exploited.Then for each model, we analysed the equilibrium structures and calculated the binding energy between the layers, the GN and the Pt cluster.

Coefficient of thermal expansion
The coefficient of thermal expansion (CTE) can characterize the physical quality of a body, and here we mainly focus on the volume expansion.At a certain pressure, when a body's temperature increases by 1 K, the CTE is expressed by the ratio of its volume change to its corresponding volume at 298 K (25 °C), as a function of temperature, where V 0 denotes the volume of the system at 298 K, ∆V the volume change, and ∆T the temperature change.

Coefficient of moisture expansion
Letting M be the humidity (water content), V 0 the system volume at room temperature (298 K) in a dry state, the coefficient of moisture expansion (CME) can be expressed by ΔM is humidity change.

Results and Discussion
We investigated the coefficients of thermal and moisture expansion according to the PEMFC working temperature (298 -358 K) and humidity (hydration), respectively.

Coefficient of thermal expansion
The composition and the corresponding content of membrane and CLs are listed in Table 1.Five different temperatures were considered, i.e., 298, 313, 328, 343, and 358 K, to study the relationship between the CTE and temperature, as shown in Fig. 3.It is seen that the CTE appears to change nonlinearly, and in the earlier period of temperature change, it is much higher, and then upon increasing temperature, the CTE of each layer will reach a similar value, 343 K (45 °C), i.e., ≈ 2 • 10 −4 K −1 .This value is similar to that of pure water.The CTE for a Nafion membrane gradually decreases with the temperature, while for anode and cathode CLs, the CTE decreases from 313 to 343 K, then increases slightly.This inconsistent expansion process easily results in an uneven distribution of internal stress and stress concentration.This deference is mainly caused by the addition of Pt and GN, which provides an increase trend in CTE-temperature curve at the range from 343 to 358 K.Moreover, the CTE of cathode CL is much larger than that of anode CL.It demonstrates that the Pt content has also an important influence on CTE, the larger the Pt content, the smaller the CTE will be.

Coefficient of moisture expansion
Various water contents were examined for each MEA layer, and the corresponding parameters -the number of particles and hydration level (λ) -are listed in Table 2.When the water content reaches 21 % of mass in the hydrated membrane, there will exist a continuous water channel where protons can smoothly migrate from the anode to cathode layer using SO 3 − as a carrier.Compared to the membrane working environment and its performance, the mass fraction of water in CLs is much lower; In this work, we determined an upper limit of 17 % for the anode CL and 10.2 % for the cathode CL.Owing to the Pt cluster having a larger number of atoms (139) in the cathode layer, its binding force with GN will become weaker when the water content is higher under a pressure of 0.1 GPa, i.e., the increase in the number of water molecules and hydronium ions will greatly reduce the interaction between the Pt cluster and GN.In our simulation, when the mass fraction of water reaches 16 % in the cathode layer, the Pt cluster totally detaches from the graphene.
According to Eq. ( 2), we can obtain the CME of each MEA layer under different levels of moisture, as shown in Fig. 4. It is observed that the CME of the membrane increases slowly with increasing temperature, while there is a decline in the CL.As reported by He et al., 30 Pt nanoparticle had a stronger attraction to water molecules than sulfonic acid group and hydronium ion, thus the introduction of Pt nanoparticle can produce a large CME, particularly in the initial stage of moisture.Furthermore, as Pt content increases, CME of CL system has also a significant growth.In addition, all three layers exhibit a rapid change in volume at the initial stage of moisture adsorption, which corresponds to a much larger CME value; then, with an increase in the number of water molecules, i.e., in the late stage of adsorption, although the volume still swells, the CME changes negligibly, reaching a constant value.

Structural stability
Five external pressures (0.1, 0.2, 0.5, 1, and 2 GPa) were used to investigate the structural stability of MEA models according to binding-energy calculations.The equilibrium structure of a MEA with the lowest potential energy was chosen for further analysis, and the potential energies of each individual component were calculated, i.e., that of the membrane and anode layer, membrane and cathode layer, GN and Pt, membrane, anode layer, cathode layer, GN, and Pt cluster.The binding energy between two systems is defined as the total energy of the compound system minus the energies of each system.Table 3 lists the potential energy of the MEA structure (E MEA ) and the binding energies between the membrane and anode layer (E B/M-A ), the membrane and cathode layer (E B/M-C ), GN and Pt clusters in the anode (E B/GN-Pt/A ) and cathode layers (E B/GN-Pt/C ) under various pressures.It was observed that the energy of the MEA structure had the lowest value under a pressure of 0.2 GPa; thus it is an energetically stable structure [see Fig. 5(a)].In addition, the results of the binding energies show that the larger the external pressure is, the larger the binding energy between layers will be; whereas, this conclusion is not valid for GN and the Pt cluster.When the pressure is 1 GPa, we find the lowest binding energy (−6.67 kcal mol −1 ) for GN and the Pt cluster in the cathode layer, and it can be seen from Fig. 5(b) that the Pt cluster almost detaches from graphene.
Because GN and the Pt cluster interact quite weakly (van der Waals interactions), this part of MEA deforms easily when subjected to elevated pressure.

Conclusions
A three-layer MEA molecular model was established in this work comprising organic-inorganic composite Nafion oligomer, graphene, and Pt Thermal and expansion properties of volume were investigated for each MEA layer.It is found that the CTE of the Nafion membrane decreases with increasing temperature and finally becomes flat, while for CLs, the CTE decreases in an initial period and then slightly increases  with increasing temperature.In order to reduce the difference of CTE between CLs and membrane, two methods may be valid.One is to choose other high-efficiency catalysts that contribute a similar CTE-temperature curve with membrane; the other is to improve the working temperature range of PEMFC, such as 45 - 80 °C.The CME for Nafion gradually increases, while for the CL, it decreases with increasing moisture.The increase in Pt content makes CME become greater, thus, decreasing the Pt content can reduce the CME difference between MEA layers.Finally, we investigated the effect of pressure on the stability of the MEA structure.Our results show that, under a pressure of 0.2 GPa, the molecular structure of a MEA exhibits the lowest potential energy and a greater binding energy of GN and the Pt cluster; thus, it is a more stable structure.
This work may provide a model reference for designing MEA materials in real engineering.

Table 1 -
Composition of each layer of the MEA

Table 2 -
Water content and number of particles in membrane and electrode layers Tablica 2 -Vlažnost i broj čestica u mebrani i elektrodnim slojevima