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J. Phys. Chem. B 2010, 114, 6056–6064
Molecular Dynamics Modeling of Proton Transport in Nafion and Hyflon Nanostructures Jaanus Karo,† Alvo Aabloo,‡ John O. Thomas,† and Daniel Brandell*,† Department of Materials Chemistry, Uppsala UniVersity, Box 538, SE-751 21 Uppsala, Sweden, and Institute of Technology, Tartu UniVersity, Nooruse 1, 50411 Tartu, Estonia ReceiVed: April 9, 2009; ReVised Manuscript ReceiVed: March 18, 2010
Classical molecular dynamics modeling studies at 363 K are reported of the local atomic-level and macroscopic nanostructures of two well-known perfluorosulfonic acid proton exchange polymer membrane materials: Nafion and Hyflon. The influence of the different side-chain lengths in the two polymers on local structure is relatively small: Hyflon exhibits slightly greater sulfonate-group clustering, while Nafion has more isolated side chains with a higher degree of hydration around the SO3- side-chain ends. This results in shorter mean residence times for water molecules around the end groups in Nafion. Hyflon also displays a lower degree of phase separation than Nafion. The velocities of the water molecules and hydronium ions are seen to increase steadily from the polymer backbone/water interface toward the center of the water channels. Because of its shorter side chains, the number of hydronium ions is ∼50% higher at the center of the water channels in Hyflon, and their velocities are ∼10% higher. The water and H3O+ diffusion coefficients are therefore higher in the shorter side-chain Hyflon system: 6.5 × 10-6 cm2/s and 25.2 × 10-6 cm2/s, respectively; the corresponding values for Nafion are 6.1 × 10-6 cm2/s and 21.3 × 10-6 cm2/s, respectively. These calculated values compare well with experiment: 4 × 10-6 cm2/s for vehicular H3O+ diffusion. 1. Introduction Fuel cells (FCs) are expected to emerge in due course as the most important energy conversion system, capable of supplementing or even totally replacing conventional fossil-fuel technologies.1,2 There already exists today a wide variety of FC concepts, from small portable devices to enormous systems for large-scale power generation. However, the high cost and relatively short lifetimes of the materials currently available mean that FC devices have yet to make a significant mark on our everyday lives. The most common and certainly the most promising FC concept at the lower end of the power scale is the PEMFC (Polymer Electrolyte Membrane Fuel Cell) which, as the name implies, exploits a proton-conducting polymer membrane. The heart of the design is the membrane electrode assembly (MEA), with the polymer electrolyte membrane (PEM) being the most critical component in determining the performance of the entire FC. Such a membrane material must satisfy a number of stringent requirements: high intrinsic proton conductivity, good mechanical properties, chemical and electrochemical stability in a highly acidic and oxidizing environment, and low fuel permeability. Perfluorosulfonic acid (PFSA) based membranes are widely used in such PEM fuel cells and have been studied intensively for several decades.3 Nafion was developed by DuPont in the 1960s and is currently the most common and widely studied PFSA material, but several alternatives have also been developed, e.g., Flemion and Aciplex from Asahi Glass, and the short side-chain (SSC) PFSA membrane originally synthesized by Dow Chemicals but now by Solvay-Solexis under the name Hyflon4–9 (see also Figure 1). These membranes all have the same polytetrafluoroethylene (PTFE) backbone with SO3H* Corresponding author. E-mail:
[email protected]. † Uppsala University. ‡ Tartu University.
Figure 1. Schematics of the Nafion and Hyflon molecular structures. Atom labeling is as introduced in the text.
terminated side chains; they differ only in the length and separation of the side chains, resulting in different equivalent weights (EWs). Hydrated Nafion has long been seen as the PEM membrane of choice for PEMFCs, but better performance has recently been demonstrated for the Hyflon membrane; it is now seen and as a serious competitor for Nafion.5,7,10,11 Among other things, hydrated Hyflon has a higher Tg (165 °C) than Nafion, giving it a higher mechanical stability at elevated temperatures. The overall aim of this study is therefore to endeavor to
10.1021/jp903288y 2010 American Chemical Society Published on Web 04/19/2010
Proton Transport in Nafion & Hyflon Nanostructures understand through molecular dynamics (MD) simulation how the different side-chain character of these two polymer systems influences above all their proton conduction properties when they are hydrated. Although thousands of papers have appeared examining the morphology in PFSA materials, their structures are still widely debated. On the basis of experimental results from small-angle X-ray scattering (SAXS), small-angle neutron scattering (SANS), and wide-angle X-ray diffraction (WAXD), several models have been suggested. There is a general consensus in the literature that, in their hydrated state, the hydrophobic backbone and hydrophilic SO3H-terminated side chains of these polymers result in a phase separation into a polymer host and protonconduction water channels, with the size and shape of these channels strongly dependent on the water content. Perhaps the most widely accepted nanoscale structure model has been suggested by Gierke12 (the “cluster-network model”), where spherical ionic clusters (diameter: 4-5 nm) are interconnected by narrow water channels (diameter: 1 nm; length: 4-5 nm). However, this model has recently been challenged by SchmidtRohr and Chen,13 who claim that elongated parallel but otherwise randomly packed water channels are surrounded by partially hydrophilic side chains to form inverted-micelle cylinders. At 20 vol % water, the water channels are claimed to have an average diameter of 2.4 nm, and elongated semicrystalline regions (∼10 vol %), crucial for the mechanical properties of the Nafion film, are formed parallel to the water channels. In an earlier MD study, we simulated PFSA-based polymer materials with three different side-chain types: Hyflon/Dow, Nafion, and Aciplex.14 The main conclusion was that the highest H3O+-ion diffusion was found for Nafion. However, the limited size of the simulation box made it impossible to address the critical issues of phase-separation and water-channel nanostructure, thus leaving many key questions unanswered. Other groups have also modeled Nafion using classical MD techniques,15–23 and some of these studies have gone so far as to incorporate proton-hopping, either using a two-state empirical valence-bond (EVB) model24 or a self-consistent multistate EVB model25,26 to allow the making and breaking of chemical bonds. In this present work, we return to an in-depth study of the two PFSA materialssHyflon and Nafionsnow using an eight times larger MD box, making this one of the largest all-atom force-field Nafion simulations ever made, though still not including the possibility for proton jumps to occur. The simulation should, nevertheless, still be able to give us new insights into the nanostructure of the polymer/water system formed since the MD box size used is well in excess of distances characteristic of the nanostructural features of interest. In a recent study,27 we showed that using this MD box size can reproduce the key features of an experimental diffraction profile. The temperature has also been increased to 90 °C to correspond more closely to the working temperature in real Nafion-based fuelcell applications. The higher temperature will also greatly improve the statistics of the study. 2. Details of the Simulation In the MD methodology, a number of atoms are placed in a simulation box (the MD box), and all interactions between these atoms are described by classical forces. A repeated solution of Newton’s equations of motion for the atoms in the box generates an atomic-scale “movie” of the material over a limited time interval. Electrons are not treated explicitly but are taken into account in developing the force-field used as input data for the
J. Phys. Chem. B, Vol. 114, No. 18, 2010 6057 simulations. The modified DREIDING force-field used here28 was the same as that used in our previous study.14 Similar force fields have been used in a number of other MD simulations of Nafion.15–17 Two initial cubic MD boxes were constructed with sidelengths of ∼80 Å to contain Nafion and Hyflon, along with ∼20 wt % water molecules and hydronium ions. This was accomplished by duplicating the final configurations in our previous work14 in all three orthogonal directions. The MD box side-lengths shrank to 75 and 73 Å, respectively, during the preliminary relaxation process. The molecular structures of our systems were chosen to achieve Nafion and Hyflon EWs close to 1100 and 928 g · mol-1, respectively, thereby imitating the commonly used Nafion 117 membrane and its Hyflon equivalent. Both MD boxes contained 32 independent oligomers, each with 10 side chains separated by 14 -CF2- monomers and with 4800 H2O molecules and 320 H3O+ ions to make the systems charge neutral. The boxes thus contained a total of 37 504 and 34 304 atoms for Nafion and Hyflon, respectively. The effective level of hydration (λ) was thus 15 in both systems. The Nafion MD-box was first relaxed in an NVT ensemble for 5 ps at 363 K, followed by a 3.5 ns simulation in NPT at the same temperature. Data sampling was performed during the last 3 ns of this time period, during which the system was in equilibrium. The Hyflon system was relaxed for 40 ps in an NVT ensemble, followed by 500 ps in an NPT ensemble at a slightly higher temperature (423 K). This higher annealing temperature accelerated the relaxation of the system. After reaching equilibrium, the final 3 ns data sampling period was made in an NPT ensemble at 363 K. All ensembles used Nose-Hoover thermostats or barostats. The simulations were made using the DL_POLY software,29 where periodic boundary conditions were imposed on our cubic MD box. An Ewald summation routine was used to calculate long-range electrostatic forces with a relative precision of 10-5 in the calculation of forces. Both simulations were run at normal pressure; time steps of 1 fs were used, and data were sampled every 0.5 ps (500 steps). Other simulation details are as follows: • NVT thermostat relaxation time parameter: 1.0 ps • NPT thermostat relaxation time parameter: 0.1 ps • NPT barostat relaxation time parameter: 0.3 ps • Verlet neighbor list cutoff: 20 Å • Verlet neighbor list border width: 0.5 Å • multiple time-step interval: 5 • primary cutoff for multiple time-step algorithm: 6 Å 3. Results and Discussion The densities for the two simulated PFSA systems decrease as the level of hydration and temperature increase. For example, varying the water content from 1.5 to 24 wt % at 300 K changes the density of Nafion (1100 EW) from 2.0 to 1.6 g/cm3.30 Similar results were obtained at 300 K by Venkatnathan et al.19 in their MD simulations. For the water content used in this study (λ ) 15), the experimental density of Nafion (1100 EW) is given as ∼1.75 g/cm3 at 300 K.30,31 Under similar conditions, the density of Nafion fluctuates within the range 1.61-1.69 g/cm3 in different simulation studies.16–19,25 In our simulations, the densities of the equilibrated systems were found to be a little highersaround 1.73 g/cm3 in Nafion and around 1.69 g/cm3 in Hyflon. However, we consider our density values to be quite reliable since the experimental density of Nafion is ∼1.75 g/cm3 at 300 K and a temperature increase of 50 K has earlier been found to result in a density decrease of 0.02-0.04 g/cm3.19
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Figure 3. Radial distribution functions (RDFs; thick lines) and coordination number functions (CNFs; thin lines) for S-OH and S-OW. Note that the CNFs overlap totally.
Figure 2. Typical local water/hydronium clustering: (a) in the H2O/ H3O+ channel; a H9O4+ ion has been circled; (b) around a sulfonate end group; and (c) linking different side chains, with typical interatomic distances taken from the RDFs. Fluorine atoms are omitted, and hydrogen bonds are illustrated as dotted lines.
3.1. Local Structure. Radial distribution functions (RDF) and coordination number (CN) functions are useful means of illustrating general aspects of local structure. All RDFs were here obtained from analyzing 6000 configurations at 0.5 ps intervals for the Nafion and Hyflon systems. As an illustration, typical local geometries found in Nafion are shown in Figure 2, with key distances extracted from the RDF plots (all not shown). Generally, closely overlapping RDF and CN functions for Nafion and Hyflon suggest that the local structures close to the terminal SO3- groups and in the aqueous environment are not strongly dependent on side-chain length. Hence, different side-chain lengths do not appear to result in significant differences in local structure. Only marginal differences are seen in the RDFs for the sulfur atoms: the number of SO3- groups in a cluster differs somewhat, and a slightly higher degree of hydration is seen around the sulfonate groups in Nafion since the longer side chains extend further into the water channels. 3.1.1. Water Molecules and Hydronium Ions. As illustrated in Figure 2a, water molecules form an intermolecular hydrogenbond network and appear at typical H · · · O distances of 1.7-1.9 Å and O-O distances of ∼2.9 Å. Unlike the situation in bulk
water (determined from neutron diffraction32,33), where two different O-O distances are clearly distinguished, water in Nafion and Hyflon has here only one well-defined coordination shell. The reason for this is clearly that the narrow water channels in the perfluorinated membranes compared to bulk water perturb the long-range ordering, leading to several different water environments in the PFSA membranes. This result has also been found in previous simulation studies.19 The H3O+-H2O RDFs show that one H3O+ is generally surrounded by two to three H2O molecules at O-O distances of 2.8 Å, while a second water shell is located at 5.1 Å. In other studies,19 these distances have been 2.6 and 4.6 Å, respectively; these differences are not significant. As shown in Figure 2a, water coordinates to the hydronium ions with a typical H · · · O distance of 1.9 Å. No sharp maxima can be seen in the RDFs for the hydronium oxygens. However, three small RDF maxima, corresponding to preferred hydronium-oxygen distances, are found at 5.1, 7, and 9 Å, reflecting preferred arrangements close to the PFSA side chains. The shorter distance corresponds to a second H3O+ coordination shell. The H3O+-H3O+ CN function shows that only one to two H3O+ neighbors are found up to distances of 7-8 Å, indicating that the hydronium ions are only sparsely distributed within the water channels. These results are similar to those of Devanathan et al.,16 who found an average hydronium-hydronium distance of 7.1 Å at a water concentration (λ) of 13.5. 3.1.2. SO3--H2O/H3O+ Interactions. There are two distinct hydration spheres around the sulfonate groups, almost independent of polymer side-chain length. The first is at an S-OW distance of ∼4 Å, containing five to seven water molecules; the second is at ∼6.3 Å (see Figure 3). The strong H-bonding between sulfonate groups and water molecules means that the probability of finding water close to the side chain increases as we move from the side-chain connecting point to the terminal SO3- group; this is illustrated in Table 1. Although the water molecules are highly mobile, the water-hydrogens near the side chains generally orient toward the oxygens of the SO3- groups at HW-OSO3 hydrogen-bond distances of 1.8 Å, as illustrated in Figure 2b. The S-OH CN plot (Figure 3) indicates on average ∼1 H3O+ ion at ∼4 Å in the first coordination shell around each SO3group and a further H3O+ ion lying on a second coordination sphere at ∼6 Å. The OH-S CN plot (not shown) suggests that there is slightly less than one hydronium ion per sulfonate group in the first coordination shell. The difference between the two
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TABLE 1: Average Distances of H2O and H3O+ in the First Coordination Shell to Side-Chain Atomsa Nafion
Hyflon Ion
side-chain atom
H 2O
H 3 O+
H 2O
H 3O +
S C6 C5 O2 C2 O1 C1
3.6 4.0 4.3 4.6 4.9 5.0 5.2
5.1 5.5 6.3 6.8 7.7 7.8 8.2
3.6 4.0 4.4 4.6 5.0
5.0 5.4 6.2 6.8 7.4
a
Atom numbering given in Fig. 1.
Figure 4. Average distribution of hydrated proton species in Nafion and Hyflon taken over all sampling time steps for two H · · · O hydrogenbond criteria: 1.7 and 1.9 Å.
CN numbers indicates that some SO3- groups share the same hydronium ion, leading to sulfonate end-group clustering. Some hydronium ions thus serve to bridge cluster-forming sulfonate groups. The phenomenon is illustrated in Figure 2c, where two hydronium ions bridge three side-chain ends at a typical OSO3-OH distance of 2.6 Å in a hydrogen-bond network. The bridging ion tends not to lie on a straight line between the SO3groups. The RDF plots between SO3- groups and hydronium ions are consistent with refs. 18 and 19. A picture emerges of terminal SO3- groups surrounded on average by ∼6 water molecules and one hydronium ion, with several side chains held together by hydrogen bonds to the hydronium ions. Such local sulfonate group clusters create hydrophilic nodes with random shape in the overall nanostructure (see Figure 5 and discussion below). 3.1.3. Hydrated Clusters. The H3O+ ions in the two systems typically occur with different degrees of hydration. For example, Figure 2a shows two trihydrated H3O+ ions (Eigen ions: H9O4+). Figure 4 shows the average distribution of such clusters for two different H · · · O length criteria: 1.7 and 1.9 Å. The similar distributions for the two systems are striking. When longer H · · · O distances are included in the analysis, both systems are dominated by H5O2+ and H7O3+ clusters; 75% of all H3O+ ions exist in these cluster types. This leaves the hydronium ions with at least one H-atom free to form hydrogen bonds with the sulfonate groups. Using the shorter H · · · O criterion (1.7 Å), the systems are clearly dominated by H3O+ and H5O2+ ions. The number of H5O2+ ions does not change significantly with H · · · O distance criterion, indicating that H5O2+ ions are relatively frequent occurrences. 3.1.4. Side Chain and Backbone Hydration. The RDFs show that the first water/hydronium coordination shell around the
backbone starts at C-O distances of 4.4 Å. Table 1 gives the average shortest distances between different side-chain atoms and the aqueous environment, as given by RDF- and CN-plots. In both PFSA materials, the distances become gradually shorter close to the ends of side chains. This is due to the hydrophilicity of the side-chain ends, where hydrogen bonds are formed, and hydrophobicity of the backbone. Distances for H2O oxygen to the different side-chain atoms (C, O, and S) vary from 3.6 to 5.2 Å in Nafion and from 3.6 to 5.0 Å in Hyflon. For H3O+ ions, these values range from 5.1 to 8.2 Å and 5.0 to 7.4 Å, respectively. Since the terminal sulfonate group attracts water, and side-chains are longer in Nafion, the water surface is drawn further away from the side-chain connecting points than in Hyflon. 3.1.5. Local Polymer Structure. The RDF plots also show that no side-chain ends approach closer than an S-S distance of 4 Å. This was also found in a previous simulation study.18 The typical side-chain length (S-C1 distance) is 5.4 Å in Hyflon; Nafion has two characteristic values: 5.9 and 7.1 Å. This is because the longer Nafion side chains have a higher degree of rotational freedom, so that several local energy minima can occur in the side-chain conformations. However, the distances between sequential side-chain connecting points (estimated separately from RDFs for each oligomer) are very similar for the two materials: 12.8 Å in Nafion and 12.7 Å in Hyflon. Although the S-S RDF peaks are broad, indicating that the local distances between side-chain ends are not well determined, two S-S distances can still be distinguished at 7.1 and 9.0 Å, both shown in Figure 2c. Interestingly, these distances are relatively similar, irrespective of side-chain length. Notably, these favored distances are not found between adjacent sidechain ends along a single backbone but rather occur within hydrophilic clusters, where side-chains belonging to different oligomers bond together. The typical S-S distance for adjacent side-chains is 16.1 Å in Nafion and 15.1 Å in Hyflon since the end groups of adjacent side chains along a given backbone are generally located on opposite sides of the backbone and the side-chains tend to arrange themselves perpendicular to their backbone and the surrounding water surface (confirming a study by Urata et al.21). Longer side chains thus have longer adjacent S-S separations. 3.1.6. SO3- End-Group Clustering. The S-S RDFs show that most side chains aggregate in three to four SO3- group clusters with S-S distances of 7-9 Å, with each SO3- group exhibiting one shorter S-S distance of 7 Å. By counting side chains which are closer to one another than 8 Å (corresponding to the first minimum of the S-S RDF plot), the average cluster size can be determined: 3.6 SO3- groups per cluster in Nafion and 4.1 in Hyflon. At any time step, an average of 67 sulfonategroup clusters could be found in Nafion, and 61 in Hyflon. Hyflon thus promotes the formation of fewer but larger clusters than Nafion. However, not all side chains participate in cluster formation: 24.6% of all side chains in Nafion and 22.1% in Hyflon are isolated side chains distributed between the SO3- group clusters. The slightly larger number for Nafion could explain the experimental observation that proton diffusion is roughly an order of magnitude higher in Nafion than in short side-chain PFSA polymers at low levels of hydration.10 By gradually decreasing the water content in PFSA materials, the size and connectivity of the water channels also decrease. In Nafion, the
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Figure 5. 5 Å thick projected slice cut through the 76 × 76 Å Nafion MD box. Empty regions represent the polymer backbone, while the colored points represent coordinates for different atom types during the simulation. The hydrophobic/hydrophilic interface is illustrated as a thick black line.
single and separated side chains can help to maintain the connectivity of the remaining water channels at lower water content. 3.2. Nanoscale Structure. Figure 5 shows a 5 Å thick slice through the 76 × 76 Å Nafion simulation box, illustrating the spatial distribution of water, hydronium ions, and sulfonate groups. Other atoms are not shown, so the polymer backbone appears as white regions, and the hydrophobic/hydrophilic interface is illustrated as a thick black line. The elongated yellow clouds are the sulfonate clusters, and the typical width of a water channel is around 10 Å. The SO3- groups are not situated directly on the channel surface but extended somewhat into the aqueous regions. Although H3O+ ions can be found throughout the channel network, they clearly collect around the sulfonate groups. It has been established from experimental scattering data (SAXS, SANS, etc.) that hydrated PFSA membrane polymers contain phase-separated regions of water and hydrated proton networks, and other regions contain the polymer host. The size, topology, and morphology of these regions are still very much a subject of debate, however. Key to improving the proton conductivity is clearly an understanding of the factors controlling the formation and evolution of these hydrophilic and hydrophobic regions. The simulation-box sizes used here (edge length: ca. 75 Å) are not large enough to model totally adequately the nanostructures suggested from the scattering studies (see, for example, the work of Schmidt-Rohr and Chen13) but can still give a reasonable qualitative and quantitative picture of phase separation. 3.2.1. Phase Separation. We have first calculated the occurrence frequency of three components of the system (backbone, side chain, and H2O/H3O+ network) by scanning the content in a subset of 3375 5 × 5 × 5 Å boxes cut out from the full simulation box. The occurrence frequency of combinations of the different species has also been calculated. This analysis gives a picture of the phase separation34 (see Table 2). Phase separation is confirmed between the polymer backbone and water/hydronium network, including the side chains. The occurrence frequency for the water domain is relatively independent of side-chain length, spanning ca. 64% of the entire simulation box. The side-chain frequency is 12% units lower in Hyflon due to the smaller number of side-chain atoms. Interestingly, the backbone component is 4% units higher in Hyflon, indicating that the polymer chain is somewhat more
Karo et al. dispersed. The shorter side chains appear to allow the backbone a higher degree of flexibility. 3.2.2. H2O/H3O+ Distribution. Figure 6 shows histograms (plotted as curves) for H2O and H3O+ distances to their closest polymer backbone atom; this gives an estimate of the topological character of the systems. For both materials, two peaks occur at 4.4 and 6.9 Å. These represent H2O or H3O+ molecules more or less strongly bound to the SO3- groups or close to polymer backbone atoms; the tails of the curves represent the amount of “free” water and hydronium ions occurring far away from the polymer/water interface. The spatial distributions of the H2O/H3O+ species show some noticeable differences. In Hyflon, both water molecules and hydronium ions are more frequent close to the polymer backbone. Considering that the number of water molecules is the same in both systems, this means that the polymer/water interface area is larger for Hyflon. Furthermore, since the number of polymer backbone atoms is the same for both polymers, it can be concluded that the surface-area to volume ratio (SAVR) is higher in Hyflon, which means that the water channel topology is less spherical than in Nafion. The polymer/water interface can be depicted as having a somewhat more tortuous form in Hyflon: this is also consistent with the findings in the above phase separation study: Section 3.2.1. It is clear that H3O+ ions are situated more frequently around the SO3- groups than are water molecules, forming a greater number of hydrogen bonds to the sulfonate groups. This is verified by comparing the ratios of the first and the second peak areas in Figure 6; the first peak is proportionately larger for H3O+ than for H2O, as can also be seen in Figure 5. For comparison, in Hyflon, 23% of the H2O molecules lie
