Atomistic Simulations of Perfluoro Phosphonic and Phosphinic Acid

ARTICLE pubs.acs.org/JPCB

Atomistic Simulations of Perfluoro Phosphonic and Phosphinic Acid Membranes and Comparisons to Nafion Nagesh Idupulapati,* Ram Devanathan, and Michel Dupuis Chemical and Materials Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States ABSTRACT: We used classical molecular dynamics simulations to investigate the morphology and proton transport properties of perfluoro phosphonic (FPA) and phosphinic acid (FPA-I) membranes that have potential applications in lowtemperature fuel cells. We systematically investigated these properties as a function of the hydration level. We examined changes in structure, transport dynamics of water and hydronium ions, and water network percolation relative to those in Nafion membrane to examine the effect of functional group acidity on these properties. Phosphonic and phosphinic acid moieties in FPA and FPA-I have lower acidity than sulfonic acid in Nafion, yet the diffusion of water was faster in FPA and FPA-I than in Nafion, particularly at low hydration levels. However this did not give rise to notable differences in hydronium ion diffusion and water network percolation for these membranes over Nafion. These results, along with similar findings from our recent study of perfluorosulfonyl imide membranes carrying stronger superacids than the sulfonic acid of Nafion, suggest that there is no strong correlation between the acidity of the functional groups and the dynamics of water and hydronium ions in hydrated polymer electrolyte membranes with similar fluorocarbon backbones and side chains.

1. INTRODUCTION Polymer electrolyte membrane (PEM) fuel cells (PEMFCs) have attracted strong recent scientific interest because of their potential applications in transportation, distributed power, and portable power for electronic devices.1,2 PEMs are important components of PEMFCs, as they allow selective proton conduction from anode to cathode.1,3 Nafion, a perfluorinated sulfonic acid (PFSA) membrane is one of the best known and most widely used PEMs.1,3 However, Nafion suffers from thermal and chemical stability limitations that make the quest for improved PEMs pressing. For example, it is desirable to operate fuel cells above the boiling point of water to increase the kinetics of the electrode reactions and decrease CO poisoning of the electrode catalysts. Such operating conditions would reduce cathode flooding and the need for water management and improve overall cell performance.1-3 However, Nafion shows poor proton conductivity at temperatures above 80 °C and under low relative humidity.1-3 Nafion can also undergo desulfonation, that is, the loss of sulfonic acid unit by hydrolysis.4 Physical and chemical degradation especially under low humidity is also a performancelimiting factor in PFSA membranes.5,6 These limitations have been the main driver for the search of PEMs with improved physical and chemical properties, including high proton conductivity, chemical and thermal stability under low humidity, and higher operating temperatures.4,5 Previous work on PEMs has proposed a correlation between the acidity of the side chain functional groups, such as SO3-, and proton conductivity.7 Our previous work tested this hypothesis by employing electronic structure calculations8 to characterize acidity and compare acidic dissociation under low hydration r 2011 American Chemical Society

conditions for selected PEMs such as perfluoro sulfonyl imide (PFSI) and Nafion. The acidic moieties for these PEMs required only three water molecules for spontaneous proton dissociation, but sulfonyl imide showed slightly higher acidity when measured by the ease of solvent separation of the hydronium ion and its pKa value.8 In an effort to examine the effect of higher acidity on the structure of the hydrophilic domain, water percolation, and the diffusion of water molecules and hydronium ions, we carried out classical molecular dynamics (MD) studies9 on PFSI membranes having a similar structure as Nafion, but carrying a higher acidic sulfonyl imide acid group than the sulfonic acid group in Nafion. This higher acidity resulted in a larger fraction of free hydronium ions, that is, hydronium ions not bound to an acidic group, at low hydration levels in PFSI when compared to Nafion. However, the calculated diffusion coefficients of the H3Oþ ions and H2O molecules as a function of the hydration level were found to be comparable to corresponding values in Nafion.9 To further test the hypothesis about the role of acidity on transport properties in hydrated membranes, our current work examines the effect of weaker acidic groups on the membrane structure, and hydronium and water transport dynamics in PEMs similar to Nafion. Phosphonic and phosphinic acids were believed to be less acidic than the sulfonic acid group in Nafion.10-12 Recent experimental4,10,13-28 and computational modeling work11,12,27,29,30 in phosphonic and phosphinic acid PEMs has examined membrane stability, water retention, and Received: December 16, 2010 Revised: January 27, 2011 Published: March 10, 2011 2959

dx.doi.org/10.1021/jp111972h | J. Phys. Chem. B 2011, 115, 2959–2969

The Journal of Physical Chemistry B

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Figure 1. (a) Chemical structure of the three perfluoro membranes investigated with different terminal acid groups; (b) terminal acid group in Nafion; (c) terminal acid group in FPA; (d) terminal acid group in FPA-I.

proton conductivity. Phosphonic acid membranes have higher chemical and thermal stabilities than sulfonic acid membranes.4,18,28 Their higher thermal stabilities were attributed to the strong carbon-phosphorus bond that permits higher operating temperatures.19,27 Indeed, Paddison et al.29 investigated the chemical degradation of PFSA membrane side chains with ab initio calculations. These authors showed that the degradation of side chain fragment holding the sulfonic acid group starts with the cleavage of the carbon-sulfur bond.29 With regard to humidifying conditions, phosphonic acidbased membranes are known to have a greater ability to retain water, a critical property when it comes to maintaining high conductivity at elevated temperatures.4,16,20 Experimental measurements by Schuster et al.31 suggested that the phosphonic acid-based PEMs display high conductivity and high stability. In contrast, imidazole-based PEMs are severely vulnerable to oxidation under low humidity and high-temperature conditions. Through their theoretical studies, Paddison et al.30 showed that water binds more strongly to alkyl phosphonic acid molecules than to imidazole and sulfonic acid functionalized alkanes. Paddison et al.27 also showed that among methyl, phenyl, benzyl, trifluoromethyl, and phenyldifluoro phosphonic acids, the fluorinated molecules exhibit slightly stronger water binding affinity than the nonfluorinated molecules. The results from these authors also indicated that the weaker acidity of phosphonic acid can be improved by using fluorinated segments closer to the -H2PO3 group.27 Recently, Herath et al.10 characterized the proton conductivity, viscosity, and acidity of trifluoromethyl phosphonic, sulfonic, carboxylic, and bis-trifluoromethyl phosphinic acid moieties. Phosphonic and phosphinic acids exhibited the highest proton conductivity and viscosity under anhydrous conditions, even though their acidity is lower than sulfonic acid.10 These authors suggested that membranes containing perfluoro phosphonic and phosphinic acids could have high conductivity at high temperature and under low water content conditions.10 Borodin et al.11,12,15 carried out electronic structure calculations about the proton dissociation of trifluoromethyl phosphonic and bis-trifluoromethyl

phosphinic acid moieties under low-humidity conditions (λ = 1-6 where λ is number of water molecules/acid group). At λ = 3, a preferred configuration of the acid-cluster complex has the acidic proton shared between the acid and one water molecule and spontaneous proton dissociation is observed at λ = 4 for phosphonic acid.11,12,15 For phosphinic acid, at λ=3, the configuration with the proton shared between the acid and a water molecule is ∼1 kcal/mol more stable than configurations with the deprotonated acid.11,12,15 In comparison, Paddison et al.32 had shown that the trifluoromethyl sulfonic acid group requires only three water molecules for spontaneous proton dissociation. These findings about proton dissociation are consistent with the experimentally measured acidities of Herath et al.10 Kotov et al.18 synthesized and characterized membranes made of perfluorinated phosphonic acid that have a structure similar to the one of Nafion. These membranes showed promising electrochemical properties such as proton conductivity comparable to Nafion at 300-350 K.18 Several other phosphonic-acid functionalized PEMs such as perfluorvinylethers,18,23 polyphosphazenes,13,14 polysulfones,21,22 and polyphenylsulfones17,33 were also synthesized, but they exhibited low proton conductivity due to low concentration of phosphonic acid groups in the membrane. Steininger et al.25,26 suggested that fluorination of polymeric segments next to the phosphonic acid group may lead to higher conductivities as a consequence of higher water uptake and ease of acidic dissociation under hydrous conditions. Recently, Creager et al.15 reported the synthesis of several promising perfluorinated membranes containing fluoroalkyl phosphonic (FPA) and phosphinic acid (FPA-I) functional groups. However, conductivity at 100% relative humidity and water uptake of these membranes were found to be lower than in Nafion. Possible factors suggested for the poor conductivity were low acid content, too much/too little cross-linking of the ionomers, and large variations in equivalent weight during ionomer synthesis.15 To the best of our knowledge, the influence of the weaker acidity of perfluorinated phosphonic and phosphinic acids (as characterized by Herath et al.10 and Creager et al.11,12,15) on the transport dynamics of water and hydronium ions in FPA and in 2960

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The Journal of Physical Chemistry B FPA-I and on the water network percolation in these membranes has not been investigated in detail. This is the subject of this paper. To this end, we followed the approach from previous studies11,12,15,25-27 of replacing the sulfonic acid groups in Nafion side chains with phosphonic and phosphinic acid moieties as shown in Figure 1. Namely, molecular dynamics simulations were used to investigate the structure and the proton and water transport under different hydration conditions in membrane models containing FPA and FPA-I acid groups. We report here the results of these MD simulations and compare them with those obtained for Nafion from our previous classical MD work.34-37 The merit and limitations of all-atom MD simulations of the type used here have been pointed out in some detail in our previous classical MD studies.9 Proton-hopping dynamics and membrane pore morphology dynamics occur on very different length and time scales, and no single simulation method to date can encompass both phenomena. Our approach occupies a niche between the molecular level proton hopping models explored by ab initio molecular dynamics studies38,39 and restricted to very small time and length scales on one hand, and dissipative particle dynamics studies40,41 of pore morphology that coarse-grain the atomistic details of PEMs dynamics on the other hand. Similar classical MD simulations of Nafion34-37,42-45 showed excellent accord with many experimental data reported in the literature,46-48 including water diffusion and vehicular diffusion of hydronium ions. The goal of the present work is to compare structural and transport details in hydrated FPA and FPA-I membranes with those from previous Nafion simulations34-37 of comparable system size and duration taken as a baseline. The paper is organized as follows: in Section 2, we give the details of the simulations; in Section 3, we discuss the effect of level of hydration on the membrane structure, the dynamics of water and hydroniums, and on the water network percolation. We summarize our findings in Section 4.

2. COMPUTATIONAL METHODOLOGY We performed classical molecular dynamics simulations of hydrated models of FPA and FPA-I membranes including water and hydronium ions using all-atom force fields. The chemical structures of the membranes simulated in this work, along with the structure of the benchmark Nafion membrane, are displayed in Figure 1. We maintained the same fluorocarbon backbone and side chain for all three membranes while varying the terminal acid groups to isolate the effect of acidity. Each simulation cell contained eight chains with ten hydrophilic acid pendants (m = 10 in Figure 1a) in each chain spaced evenly by seven nonpolar -CF2-CF2- monomers (n = 7 in Figure 1a) as the hydrophobic backbone (for a total of 692 and 712 atoms in each chain of FPA and FPA-I, respectively). We assumed all the acid groups to be ionized for both FPA and FPA-I on the basis of prior electronic structure calculations of Borodin et al.11,12,15 for λ g 3. The equivalent weights (EW) of the membrane models generated were 1147 and 1198 g mol-1 of acid group for FPA and FPA-I, respectively. A total of eighty hydronium ions were added to ensure charge neutrality and the membranes were solvated by adding water molecules corresponding to λ values of 3, 5, 7, 9, 11, and 20, respectively. We did not impose any geometry distribution of the water molecules or any predetermined density. We used the DL_POLY 2.20 code,49 the DREIDING force field50 for the polymer, and the F3C force field51 for water and

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Table 1. Density of FPA and FPA-I As a Function of λ Used in the Simulations density (g/cm3) λ

FPA

FPA-I

3

1.81

1.80

5

1.82

1.82

7 9

1.83 1.79

1.79 1.78

11

1.76

1.76

20

1.66

1.64

hydronium. We used the smooth particle-mesh Ewald method52 to calculate the electrostatic interactions with a cutoff distance of 8 Å and a Ewald sum precision of 10-6. The energy of each system containing eight FPA and FPA-I chains, 80 H3Oþ, and from 240 up to 1600 H2O were minimized separately using the steepest descent algorithm.53 After the minimization step, we used the method of “shrinking box54-56 and annealing” to generate systems of varying density from low-density initial configurations in the following five step process: (1) NPT MD simulation for 100 ps at 300 K, where the pressure was increased from 1 to 100 atm; (2) NVT MD simulation for 50 ps, where the temperature was raised from 300 to 800 K; (3) NPT MD simulation for 100 ps at 800 K, where the pressure was raised from 100 to 150 atm while retaining only the repulsive nonbonded potentials to avoid clustering and strain in dihedrals; (4) NVT MD simulation for 50 ps, where the temperature was lowered from 800 to 300 K; (5) NPT MD simulation for 100 ps at 300 K, where the pressure was maintained at 150 atm with all interaction potentials turned on. This five step process was repeated three times and the final structure attained was used as a starting configuration for an NPT MD equilibration for 2 ns at 300 K, where the pressure was maintained at 1 atm. The resulting system densities after equilibration are listed in Table 1. Following the equilibration, NVT MD simulations for 2 ns at 300 K (with 1 fs integration time step) were performed for each λ and the configurations were saved at regular intervals for subsequent analysis of the structural and dynamical properties.

3. RESULTS AND DISCUSSION The hydrated membrane morphologies of FPA and FPA-I were characterized by extracting selected structural properties such as radial distribution functions and coordination numbers, by analyzing selected hydronium and water configurations and the water network percolation behavior, as well as by determining dynamical properties such as diffusion of water and hydronium ions. The results obtained for both types of membranes were compared with previous simulation data for Nafion. 3.1. Effect of Hydration on Membrane Morphology. The phosphorus-phosphorus radial distribution functions (gP-P(r)) for FPA and FPA-I respectively are shown in panels a and b of Figure 2 for various levels of hydration (λ = 3 to 20). The first peak occurs at ∼5.2 Å for FPA at λ = 3 and the peak becomes broader and less intense as the hydration level increases, albeit without much change in its position. For FPA-I, the position of the peak shifts from 6.0 Å at λ = 3 to 6.8 Å at λ = 20 suggesting that the phosphonate groups move apart from each other as the hydration level increases. In the case of Nafion too, the first peak shifted from 5.3 Å at λ = 3 to 6.7 Å at λ = 20, indicative of a similar 2961



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Figure 2. Radial distribution functions gP-P(r) at various hydration levels for (a) phosphorus-phosphorus in FPA (b) phosphorus-phosphorus in FPA-I (c) The table shows the distances at which the P- (or S-) coordination number equals 1.0 based on the RDFs for FPA, FPA-I, and Nafion.

Figure 3. Radial distribution functions gP-Oh(r) at various hydration levels (λ indicated by the legend) for phosphorus-hydronium oxygen in (a) FPA and (b) FPA-I.

behavior, namely increased separation between acidic groups upon increasing hydration level.34 Integrating the gP-P(r) RDF between zero and r gives the average number of phosphorus atoms nP-P(r) within a sphere of radius r around a reference phosphorus atom. We call such a number as the phosphorusphosphorus coordination number. In the table of Figure 2, we listed the values of r for which the phosphorus-phosphorus coordination number, nP-P(r) equals 1.0 along with the corresponding values of r where nS-S(r) = 1.0 in Nafion.34 Compared to Nafion, these r values for FPA are almost the same at low hydration levels (λ e 5) and slightly smaller at higher hydration levels, indicating that the phosphonate groups are linked slightly more strongly than the sulfonate groups in Nafion. For FPA-I, the r values are always larger than in Nafion at all hydration levels implying that the acid groups are further apart from each other and the membranes show less structure. The changes in the phosphorus-hydronium oxygen interaction in the form of gP-Oh(r) RDFs for FPA and FPA-I respectively

are depicted in Figure 3 panels a and b with increasing λ. Both RDFs display a dominant peak between 3.8 and 3.9 Å. As λ increases from 3 to 20, the area under the first peak (up to 4.4 Å, the range for the first hydration shell) decreases drastically while the area under the second peak increases. This is an indication that the hydronium ions move away from the first hydration shell into the second shell of any phosphorus atom (between 4.4 to 6.8 Å) with increasing λ. In Table 2, the coordination number of hydronium ions (NP-Oh) to the phosphorus atoms, based on a neighbor cutoff distance of 4.4 Å, is listed for both membranes and compared with the corresponding hydronium ion coordination numbers to the sulfur atoms in Nafion (NS-Oh).34 With increasing hydration, we see the coordination numbers taking values less than unity indicating that the hydronium ions move further away from the acid groups into the aqueous phase. At low hydration levels (λ e 5), the coordination number of hydronium ions to the acid group is lower for FPA than for Nafion. At higher hydration levels, the coordination number is slightly higher for 2962



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FPA than Nafion. At all hydration levels, the coordination number of hydronium ions to the acid groups in FPA-I is lower compared to that in FPA and in Nafion. Figure 4 provides a snapshot of the geometry near the acid groups in the three membranes explored at the lowest hydration level (λ = 3). Hydronium ions are coordinated by multiple acid groups and form bridges between them, which hinders their diffusion from the end of the acid pendant. The percentages of H3Oþ that are “bound” to one acid group (have at least one acid neighbor) or “bridging” at least two acid groups (coordinated to multiple acid groups) or “free” (not coordinated to an acid group) as a function of λ are shown in Figure 5. Lines have been drawn through the data points to guide the eye. The percentages of “bound” and “bridging” hydronium ions decrease and the percentages of “free” hydronium ions increase almost linearly with λ for all three membranes. The percentages of hydronium ions are almost the same for Nafion and FPA with small differences at all hydration levels. For FPA-I, hydronium ions appear more “free” and less “bound” and “bridging” compared to FPA and Nafion, particularly at low and medium hydration levels (λ e 9) . The acid groups being further apart from each other in FPA-I compared to FPA and Nafion as shown in Figure 2 is a likely reason for the fewer “bridging” hydroniums in this membrane. A small increase in hydronium ion diffusion was observed in FPA-I, which can be related to the smaller percentages of “bound” and “bridging” hydronium ions compared to Nafion (see Section 3.3). Table 2. Average Coordination Numbers of Hydronium Ions NP-Oh (NS-Oh) around Any Phosphorus Atom for FPA and FPA-I (Sulfur Atom for Nafion) and of Water Molecules NP-Ow (NS-Ow for Nafion) As a Function of the Hydration Level λa NP(S)-Oh

a

NP(S)-Ow

λ

FPA

FPA-I

Nafion

FPA

FPA-I

Nafion

3

1.75

1.56

2.05

1.82

0.96

2.23

5

1.37

1.10

1.59

2.77

2.06

3.65

7

1.27

0.82

1.14

3.23

2.70

4.26

9

1.07

0.61

0.97

3.9

3.24

4.81

11

0.87

0.63

0.77

4.34

3.11

5.34

20

0.58

0.39

0.49

4.99

3.67

5.79

Values for Nafion are taken from ref 34.

The phosphorus-water oxygen interactions are depicted in the form of gP-Ow(r) RDFs of FPA and FPA-I in panels a and b of Figure 6, respectively. It can be readily noted that both RDFs show a first peak at 3.9 Å and that the P-Ow RDF for FPA-I has a much more structured second peak than FPA. As λ increases from 3 to 20, the height of the first peak decreases for both RDFs. The second peak occurs around 5.0-5.2 Å for both RDFs and the decrease in the height of this peak with increasing hydration is more dominant in FPA-I. The solvation numbers of the sulfur (Nafion)34 and phosphorus atoms, that is, the number of water molecules within the first solvation shell of these atoms (4.4 Å according to Figure 6), are listed in Table 2 for the various hydration levels. The solvation numbers are larger for Nafion and smaller for FPA-I at all hydration levels. We take the changes in shapes of the RDFs and in solvation numbers of sulfur and phosphorus as an indication that the water molecules are less tightly bound to the acidic group in FPA-I than in FPA and in Nafion as the water content increases. The RDFs between the oxygen atoms of hydronium ions and the oxygen atoms of water molecules (gOh-Ow(r)) for FPA and FPA-I are shown in panels a and b of Figure 7. For both systems, the first peak occurs around 2.6 Å and its height decreases with increasing λ, while the second peak appears between 4.6 and 4.8 Å and its height also decreases with increasing λ. From the RDFs, we extracted the number of water molecules coordinated to a hydronium ion within a distance of 3.5 Å. They are listed in Table 3 along with the same quantities obtained for Nafion.34 The average coordination numbers of water molecules around a hydronium ion are slightly larger for FPA-I compared to those in the other two membranes. Fluctuations of these coordination numbers for FPA and Nafion34 are somewhat irregular with increasing hydration level. The water oxygen-water oxygen RDFs for FPA and FPA-I, respectively are shown in Figure 8a,b. The first peak occurs around 2.8 Å and the second peak around 4.0 Å, the height of which decreases with increasing λ. It essentially disappears for very large λ. The numbers of water molecules within the first hydration shell (3.5 Å) of H2O for the three membranes at various λ are tabulated in Table 3. The increase in the water coordination number with increasing hydration level is more pronounced for FPA and FPA-I compared to Nafion. Figure 9 shows the percentage of “bound”, “weakly bound”, and “free” water molecules as a function of λ for all three membranes. Bound water are water molecules within 4.4 Å of

Figure 4. Snapshots of water and hydronium nearest to the acid groups for (a) FPA, (b) FPA-I, and (c) Nafion. H3Oþ and H2O molecules are represented in red and white atoms, respectively; acid groups are represented by PO3H-, PO2-, and SO3- groups only for FPA, FPA-I, and Nafion, respectively; backbone and side chain attached to the acid groups were not shown for clarity. 2963



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Figure 5. Percentages of bound, bridging, and free hydronium ions as a function of the hydration level in FPA, FPA-I, and Nafion. Data is obtained from 2000 configurations at 1 ps intervals.

Figure 6. Radial distribution functions gP-Ow(r) at various hydration levels (λ indicated by the legend) for phosphorus-water oxygen in (a) FPA and (b) FPA-I.

Figure 7. Radial distribution functions gOh-Ow(r) at various hydration levels (λ indicated by the legend) for hydronium oxygen-water oxygen in (a) FPA and (b) FPA-I. 2964



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Table 3. Average Coordination Numbers of Water Molecules around a Hydronium Ion (Nhw) and Water Molecules around a Water Molecule (Nww) As a Function of Hydration Level for the Three Membranesa Nhw

a

Nww

λ

FPA

FPA-I

Nafion

FPA

FPA-I

Nafion

3

1.61

1.6

1.49

0.98

0.7

1.01

5

2.23

2.43

2.26

2.24

1.78

1.8

7

2.54

2.93

2.73

2.71

2.62

2.18

9

2.99

3.42

3.08

3.19

3.12

2.53

11

3.31

3.44

3.37

3.5

3.32

2.75

20

3.97

4.06

3.83

4.25

4.15

3.43

Values for Nafion were taken from ref 34.

a phosphorus (sulfur) atom. Water molecules with four other neighboring water molecules (within 3.5 Å as in bulk water) are classified as free water molecules, and the remaining water molecules are classified as weakly bound.34 As λ increases, the percentage of bound and weakly bound water molecules decreases and the percentage of free water molecules increases monotonically for all three membranes. At all hydration levels, the percentage of bound water is smaller for FPA and notably smaller for FPA-I compared to Nafion.34 This is consistent with the increase in weakly bound and free water molecules for FPA and FPA-I. Particularly at low hydration conditions (λ e 7), the probability of finding a water molecule as “weakly bound” is high for FPA-I compared to FPA and Nafion. This higher availability of “weakly bound” water showed a characteristic upward change in the diffusion of water in FPA and FPA-I compared to Nafion, which will be discussed in the corresponding Section 3.3.

Figure 8. Radial distribution functions gOw-Ow(r) at various hydration levels (λ indicated by the legend) for water oxygen-water oxygen in (a) FPA and (b) FPA-I.

Figure 9. Percentages of bound, weakly bound, and free water molecules as a function of the hydration level for FPA, FPA-I, and Nafion. Data is obtained from 2000 configurations at 1 ps intervals. 2965



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Figure 10. (a-c) Snapshots of a FPA membrane under hydration levels of 3, 9, and 20; (d-f) snapshots of a FPA-I membrane under hydration levels of 3, 9, and 20. H3Oþ ions and H2O molecules are shown in van der Waals (red, oxygen; white, hydrogen), the acid groups are shown as large beads (purple and yellow for FPA and FPA-I, respectively) and the rests of the side chains and backbones are shown as ball and stick (green).

3.2. Water Percolation Analysis. The spatial distribution of water molecules and hydronium ions in FPA (panels a-c) and FPA-I membranes (panels d-f) at various hydration levels (λ = 3, 9, 20) are depicted from the snapshots of the final MD configurations in Figure 10. At low water content, we observe isolated small clusters. As the water content increases, the spatial extent of the clusters grows and we see the formation of more continuous water clusters for both membranes. The phase separation between hydrophobic and hydrophilic components is seen with the hydrophilic acid groups extending into the water channels and away from the rest of the hydrophobic core of the membrane. We carried out detailed percolation analyses following the methodology described in our previous work36 to obtain more quantitative information about the change in water network as the hydration level increases. H3Oþ and H2O were considered to be part of the same cluster if the oxygen atoms were separated by less than 3.5 Å. This separation distance corresponds to the first hydration shell of water molecules and hydronium ions on the basis of the waterwater and water-hydronium RDFs (Figures 7 and 8). The time-averaged cluster size distribution of H3Oþ and H2O as a function of the hydration level for FPA (panels a and b) and FPA-I (panels c and d) are plotted in Figure 11. The cluster size was declared “small” for sizes between 0 and 100 molecules or “large” for sizes above 400 molecules. With increasing hydration levels, the number of clusters of size less than 100 decreases while the number of clusters greater than 400 increases. This behavior is the same for both the FPA and FPA-I membranes. For λ = 3 and 5, the maximum peak occurs at cluster size 3 and 4 respectively,

consistent with the higher occurrence of small clusters for both membranes. Water molecules belonging to large clusters (greater than 400 molecules) were observed only for λ greater than 7. For λ = 9, the first peak occurred at almost the same cluster size (∼680) for both FPA and FPA-I, indicative of the formation of a large spanning cluster in both cases. At λ g 11, the majority of the water molecules belong to large clusters, and the behavior is almost the same for FPA and FPA-I with regard to the change in the peak height. From the analysis of cluster size distribution, we can say that the percolation transition or threshold (λp),36,57-60 that is, the threshold at which a consistent spanning water network starts to develop in the membrane, occurs between λ = 3 and 7 for both FPA and FPA-I. The range of the percolation threshold attained for Nafion was also the same from our previous calculations.36 To locate exactly the onset of λp for both membranes, we examined the probability of finding H3Oþ or H2O in small and large clusters. The sum of probabilities of finding a H2O or H3Oþ species in small clusters (size S ranging from 0 to 100, blue curve) and in large clusters (S > 400, red curve) is shown in Figure 12. At λ = 3, the total probability of finding a H2O or H3Oþ species in the small clusters is 1.0, indicating that small clusters only get formed for both FPA and FPA-I. At λ = 5, some intermediate sized clusters are formed at the expense of small clusters for both membranes. For λ g 7, the probability of finding larger clusters dominates for both membranes. The total probability of finding a H2O or H3Oþ species in a large cluster is almost 1.0 for λ g 11 for both membranes. From Figure 12a,b, the crossover between 2966



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Figure 11. (a,b) The distribution of water/hydronium cluster sizes for FPA; (c,d) the same distribution for FPA-I based on cutoff distance of 3.5 Å.

Figure 12. Probability of finding water and hydronium in small (blue line) and large (red line) clusters as a function of the hydration level for (a) FPA and (b) FPA-I.

Table 4. Percolation (Pp) and Spanning Probabilities (Ps) As a Function of Hydration Level for the FPA, FPA-I, and Nafion (from Reference 36) FPA

FPA-I

Nafion

λ

Pp

Ps

Pp

Ps

Pp

Ps

3 5

0 0.20

0 0.32

0 0.10

0 0.12

0 0.62

0 0.84

7

0.73

0.96

0.79

0.98

0.88

0.99

9

0.92

0.98

0.81

0.96

0.99

1

11

0.99

1

0.98

1

1

1

20

0.99

1

0.99

1

1

1

the two probability curves for both membranes occurs between λ = 6 and 7, which indicates the onset of percolation transition. As other measure of λp, spanning (Ps) and percolation probabilities (Pp) of the water clusters in FPA and FPA-I were determined following percolation theory57-60 (Table 4). These probabilities indicate the existence of persistent percolating and

spanning water network formation in PEMs. For λ = 3, both Pp and Ps are zero for both membranes. At λ = 5, for both FPA and FPA-I there is a small probability of a percolating water network and of a spanning cluster formation. For λ g 9, Pp and Ps lies between 0.9 and 1.0 for both membranes indicating a persistent water network formation. Brovechenko et al.57-60 indicated that the λ value at which Ps exceeds 0.95 can be taken as the upper bound of λp. From our percolation calculations, spanning probability exceeds 0.95 at λ = 7 for both membranes, which is consistent with the estimate of percolation transition discussed above. Similar percolation characteristics were observed, albeit with small differences, when we compare the above results with those reported for Nafion in our recent study.36 For Nafion, large clusters containing water or hydronium were also formed for λ g 7. A percolation transition was observed to occur between λ = 5 and 6.36 Only at λ = 5 were the percolation and spanning probabilities observed to be higher in Nafion compared to FPA and FPA-I (Table 4). For λ g 7, these probabilities look almost the same for all the three membranes. 3.3. Diffusion Coefficients of H2O and H3Oþ. The diffusion coefficients for water molecules and hydronium ions as a function of 2967



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Table 5. Diffusion Coefficientsa of (a) Hydronium Ion (b) Water for FPA, FPA-I, and Nafion (from Reference 35) λ

FPA

3

FPA-I

Nafion

0.007

0.008

0.005

5 7

0.02 0.03

0.02 0.05

0.01 0.04

9

0.05

0.09

0.08

11

0.10

0.12

0.06

20

0.28

0.30

0.29

λ

FPA

FPA-I

Nafion

3

0.06

0.07

0.04

5

0.17

0.19

0.08

7 9

0.25 0.35

0.31 0.36

0.13 0.32

11

0.51

0.55

0.33

20

1.02

1.12

0.72

(a)

(b)

a

Calculated from mean square displacements. All values 10-5 cm2 s-1.

the hydration level are tabulated in Tables 5a,b for FPA, FPA-I, and Nafion.35 The mean square displacement of the hydronium ions and the water molecules were evaluated at 0.2 ps intervals, and the corresponding diffusion coefficients were determined over the simulation time. Overall, the diffusion coefficients were seen to increase with increasing hydration levels, a result that can be attributed to the growth of aqueous phase clusters, which enhances the mobility of water molecules and hydronium ions. Table 5a shows the vehicular diffusion coefficients of H3Oþ (recall that the method of classical molecular dynamics used here does not capture the structural diffusion) at various levels of hydration for the three membranes. There was almost an order of magnitude increase in DH3Oþ as λ increases from 3 to 5 for all the systems. For λ g 7, there was a steady increase of the diffusion of hydronium ions. This finding was consistent with the increase in the percentage of free hydronium ions with increasing hydration level (Figure 5). As discussed earlier, the hydronium ion coordination to the acid group was slightly smaller and the hydronium ion solvation number slightly higher for FPA-I compared to FPA and Nafion at all hydration levels. Also, there was a decrease in bridging H3Oþ formation and slight increase in free hydronium ions in FPA-I, particularly at low hydration levels with respect to the other two membranes. All these characteristics resulted in a very small increase in hydronium ion diffusion coefficients for FPA-I compared to FPA and Nafion. Table 5b shows the diffusion coefficients (DH2O) of H2O molecules for the three membranes. Diffusion of water was found to be faster in both FPA and FPA-I compared to Nafion35 at all hydration levels. The larger number of weakly bound and free water molecules for FPA and FPA-I with respect to Nafion were responsible for the increased water diffusion coefficients for these membranes. Particularly, at λ = 5 and 7 the water diffusion coefficient for FPA and FPA-I compared to Nafion was increased by over 50%. At λ = 20, the water diffusion coefficient was almost one-half that of the bulk water diffusion coefficient51 for both FPA and FPA-I.

4. CONCLUSIONS We used atomistic simulations to study the variations in membrane structure, water network percolation, and H3Oþ and H2O diffusion in fluoroalkyl phosphonic FPA and phosphinic acid FPA-I membranes as a function of the hydration level. The results were compared with those from previous classical MD studies on Nafion.34-37 Under low hydration conditions (λ e 7), an increased population of free hydronium ions was observed in FPA-I along with a decrease in bound and bridging H3Oþ compared to Nafion and FPA. As well, the probability of finding weakly bound or free water molecules is higher for FPA-I compared to FPA and Nafion at all hydration levels. Using percolation analysis, the percolation transition was determined to occur at a slightly higher hydration level for FPA and FPA-I (between λ = 6 and 7) compared to Nafion (between λ = 5 and 6). At λ = 3, no spanning cluster or percolating water network was detected for the three membranes. At λ = 5, spanning and percolation starts to occur and for λ g 7, the formation of a continuous water network was observed for all membranes. These similar percolation characteristics could be because the three membranes have the same fluorocarbon backbone and side chain carrying respective acid groups. The diffusion of hydronium ions was calculated to be similar for all three membranes at all hydration levels. However, diffusion of water was slightly faster in FPA and FPA-I compared to Nafion. At low hydration levels (λ = 5 and 7), the diffusion of water for FPA and FPA-I was more than doubled compared to Nafion.35 An increase in the percentage of weakly bound and free water for these membranes is consistent with the improved water diffusion. The lower acidities of the perfluoro phosphonic and phosphinic acid groups in the FPA and FPA-I membranes, respectively, (compared to perfluoro sulfonic acid of Nafion) determined experimentally by Herath et al.10 and confirmed by calculations11,12,15 were found to have no significant effects on water network percolation and on diffusion of water and hydronium ions. Under low hydration levels, these properties were at least as good or better in FPA and FPA-I, compared to Nafion. Also from our previous MD studies on PFSI membranes,9 we indicated that the higher acidity of sulfonyl imide acid groups in PFSI compared to Nafion did not translate into higher hydronium and water diffusion or water network percolation. Thus, from the type of classical MD studies used here, it appears that there is no significant direct correlation between acidity of the functional acid groups and their influence on dynamics of water molecules and hydronium ions in PEMs with similar fluorocarbon backbone. This study also corroborates previous experimental and computational work that FPA and FPA-I membranes exhibit transport properties that are comparable to those of Nafion and could be considered for further development for operation in low-temperature PEM fuel cells. Work is in progress to assess whether the similar backbone used with all acid groups is responsible for the overall properties of the PEMs and what other factors might lead to higher diffusion. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by the U.S. Department of Energy’s (DOE) Office of Basic Energy Sciences, Chemical Sciences, 2968


The Journal of Physical Chemistry B Geosciences and Biosciences Division under Contract DE-AC05-76RL01830. It was performed in part using the Molecular Science Computing Facility (MSCF) in the EMSL, a national scientific user facility sponsored by DOE’s Office of Biological and Environmental Research located at Pacific Northwest National Laboratory (PNNL). PNNL is operated by Battelle for DOE. This work benefited also from resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of DOE under Contract No. DE-AC02-05CH1123.

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Atomistic Simulations of Perfluoro Phosphonic and Phosphinic Acid

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