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First-Principles Molecular Dynamics Study of a Hydrocarbon Copolymer for Use in Polymer Electrolyte Membrane Fuel Cells Yuan-yuan Zhao, Eiji Tsuchida, Yoong-Kee Choe, Tamio Ikeshoji, Tatsuya Oshima, Masahiro Rikukawa, and Akihiro Ohira J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b04030 • Publication Date (Web): 07 Jun 2016 Downloaded from http://pubs.acs.org on June 11, 2016

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The Journal of Physical Chemistry

First-principles Molecular Dynamics Study of a Hydrocarbon Copolymer for use in Polymer Electrolyte Membrane Fuel Cells Yuan-yuan Zhao,∗,† Eiji Tsuchida,‡ Yoong-Kee Choe,‡ Tamio Ikeshoji,†,‡ Tatsuya Oshima,¶ Masahiro Rikukawa,¶ and Akihiro Ohira†,§ †Fuel Cell Cutting-Edge Research Center Technology Research Association (FC-Cubic), AIST Tokyo Waterfront Main Building, 2-3-26 Aomi, Koto-ku, Tokyo 135-0064, Japan ‡Research Center for Computational Design of Advanced Functional Materials, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 2, Umezono 1-1-1, Tsukuba 305-8568, Japan ¶Department of Chemistry, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan §Research Institute of Electrochemical Energy, National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31 Midorigaoka, Ikeda, Osaka 563-8577, Japan E-mail: [email protected] Phone: +81 (0)29 861 2314

Abstract The structural and dynamic properties of a brush-type hydrocarbon copolymer are investigated using first-principles molecular dynamics simulations. Two model compounds, one with mainly hydrophilic domains and one with mainly hydrophobic domains, were selected and used in the simulations. A series of radial distribution

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functions of different groups, such as water-water, sulfonic group-hydrogen, and etherhydrogen, is obtained to investigate the structure of the whole systems. The radial distribution functions of sulfonic groups, gS−S (r), and the structure of water clusters indicate the formation of a well-developed water channel in the studied copolymer. Analysis of proton dissociation reveals that the protons in both systems are not completely dissociated when the number of water molecules per sulfonic group is equal to 4. The low dissociation nature of this copolymer compared with that of Nafion is explained by its intrinsic acid strength and the presence of ineffective hydrogen bonds in the system, where ineffective hydrogen bonds indicate hydrogen bonds that do not contribute strongly to proton transport. The proton conductivity of this copolymer is comparable to that of Nafion, which is ascribed to the formation of good water channels. In addition, the calculated electrical conductivity of the two model compounds shows good agreement with the measured proton conductivity of this copolymer.

Introduction Polymer electrolyte fuel cells (PEFCs) are environmentally friendly energy devices that convert the chemical energy of fuels to electric power through electrochemical reactions. 1 PEFCs are expected to be useful in vehicles and portable devices. In 2015, Toyota began to sell vehicles using PEFCs as their energy source to the mass market. However, there is still much room to improve the efficiency and production cost of PEFCs, to promote their extensive commercial application. 2 A polymer electrolyte membrane (PEM) is one of the crucial components of PEFCs and directly affects the efficiency and cost of the whole fuel cell. 3 It is, on one hand, used to separate the electrodes, and on the other hand, to form a membrane electrode assembly with the electrodes. For both of these applications, high proton conductivity, low water uptake, and good stability are desirable properties for the PEMs used in PEFCs. Nafion is currently a major electrolyte used in PEFCs because of its excellent properties such as good

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stability and high proton conductivity. 4,5 However, its high production cost and environmental inadaptability push researchers to find alternatives to Nafion with good performance and low cost. 6 Aromatic polymer electrolytes have received much attention because of their promise in PEFCs. 7,8 Over the past years, the structures and proton transport of many types of copolymers, including perfluorocarbon and aromatic polymers, have been simulated extensively using various techniques. 9–15 Choe et al. reported the proton dynamics in Nafion and sulfonated polyethersulfone determined from first-principles molecular dynamics (FPMD) simulations. 16–18 Jorn et al. used the multistate empirical valence bond model to investigate the proton conductivity of Nafion using classical molecular dynamics (MD) and coarse-grained descriptions. 9 Mahajan and Ganesan compared the structure and transport properties of solvated sulfonated poly(ether ether ketone) (SPEEK) membranes and Nafion using all-atom MD simulations. 19 There are many types of aromatic polymer electrolytes including random copolymers and block copolymers. Each type of copolymer has a characteristic structure and corresponding morphology, and such structural aspects strongly affect its proton conductivity when used in PEFCs. Therefore, many experimental and theoretical investigations have been performed on the synthetic technology and the relationship between the structure and properties of copolymers. 20–22 Peckham and Holdcroft emphasized that it is essential to understand the structure–morphology–property relationships of PEMs and highlighted a series of interesting studies that illustrate factors affecting proton conduction, such as water content and morphology. 23 Thus, understanding the fundamental properties of PEMs, including their microstructures, proton transport mechanisms, and water clusters, is crucial to improve the parameters that influence their PEFC performance, such as stability and proton conductivity. Rikukawa and colleagues synthesized a novel brush-type hydrophilic–hydrophobic block copolymer, SP1-P2(m-n), where m:n denotes the ratio of the hydrophilic to hydrophobic domains, starting from poly(p-phenylene)s via successive catalyst-transfer polymerization.

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This copolymer showed high proton conductivity, comparable to that of Nafion, with a small humidity dependence when the molecular weight and polydispersity index of the diblock copolymers were precisely controlled. 24,25 Although much effort has been devoted to studying various copolymers, the structures and proton transport of such brush-type copolymers have seldom been investigated at the atomistic level, which leads us to investigate the fundamental properties of SP1-P2 systematically to understand the origin of its good performance found in the experiments. We have already investigated the chemical stability of this copolymer by simulating its degradation mechanisms caused by radicals and identified the weak sites in its structure. 26 We report here the dynamic properties of the hydrated copolymer obtained from large-scale FPMD simulations. The rest of this paper is organized as follows. The theoretical methods used in this study are introduced in the Method section. The structure of the whole system (polymer and water), and the dynamic properties and proton conductivity of SP1-P2(m-n) are presented in the Results and Discussion. In the last section, the conclusions are given.

Methods The newly synthesized copolymer SP1-P2(m-n) was used as our target system. The chemical structure of SP1-P2(m-n) is shown in Figure 1(a). Figure 1(b) and (c) display the two model compounds for this copolymer, M1 and M2, respectively, used in the simulations. M1 consists of only hydrophilic domains with (m,n)=(4,0), and M2 consists mainly of hydrophobic domains with (m,n)=(1,4). For both systems, referred to as S1 (M1+water) and S2 (M2+water), the hydration level is λ (H2 O/SO3 H) = 4. System S1 is composed of three M1 molecules (Npolymer ) and 96 water molecules (Nwater ), with 990 atoms (Natom ) in total. For S2, the number of polymer molecules, water molecules, and atoms is Npolymer =4, Nwater =32 and Natom =1104, respectively. The compositions of the systems and their densities are summarized in Table 1. The densities of the two systems were obtained based on

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the extrapolation of experimental results for different values of m and n. First we carried out classical MD simulations to construct the initial configurations for FPMD. For classical MD simulations of both systems, we used the Forcite module of Materials Studio 7.0. The NVT ensemble was generated at 600K using the Nos´e thermostat. The condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field 27 was used, and proton dissociation was not allowed in these simulations. The simulations lasted for 1 ns using a time step of 1 fs. O(CH2)l

OC6H13

SO3H

m HO3S

n

(H2C)l O

l=3 or 4

C6H13O

(a)

O(CH2)3

SO3H

O(CH2)3

SO3H

H

H

H

4

4

(H2C)3O

HO3S

OC6H13

HO3S

(H2C)3O

C6H13O

(c )

(b )

Figure 1: Chemical structures of (a) SP1-P2(m-n), (b) hydrophilic model compound M1, and (c) hydrophobic model compound M2.

Table 1: Parameters used in the simulations. System S1 S2

m 4 1

n 0 4

Npolymer 3 4

Nwater 96 32

Natom 990 1104

Density (g/cm3 ) 1.249 1.142

Cell size (˚ A) 21.80 21.70

Starting from the initial structures obtained from classical MD simulations, FPMD simulations were carried out using our own code, finite element method based total energy calculation kit (FEMTECK ). 28,29 The Perdew–Burke–Ernzerhof exchange-correlation functional was employed, 30 and the norm-conserving pseudopotentials were used for the inner core electrons. 31,32 Adaptive finite elements with an average cutoff energy of 54 Ryd were used as the basis set. The first 40 ps of each simulation was used to reach equilibrium, 5



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and the following 100 ps was used for the data analysis using a time step of 0.6 fs with the temperature controlled at 353.15 K. During the simulations, the electronic structures were quenched to the Born–Oppenheimer surface at every time step. Snapshots for the two systems are presented in Figure 2. y

y

x

x

(a)

(b)

Figure 2: Snapshots of the two simulated systems with periodic mirror image, (a) S1 and (b) S2. Green, red, yellow, and white spheres represent C, O, S, and H atoms, respectively.

Results and Discussion Structure of the systems Generally, the dynamic properties of hydrated polymers are influenced by their structural features. We first investigated the structures of both model systems with an emphasis on the configurations of the systems arising from the distribution of sulfonic groups and water clusters. We denoted some atoms of the systems as follows: hydrogen atoms in sulfonic groups as Hp , hydrogen atoms in water molecules and hydronium ions as Hw , oxygen atoms in sulfonic groups as Os , oxygen atoms in water molecules and hydronium ions as Ow , and oxygen atoms in ether groups as Oe . The radial distribution functions (RDFs) for an atomic pair S-S, gS−S (r), and the RDFs of Ow -Ow atoms, gOw−Ow (r), were calculated and are 6


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presented in Figure 3(a) and 3(b), respectively. As illustrated in Figure 3(a), gS−S (r) of S1 has two clear peaks. The first peak of S1 is located at around 4.6 ˚ A, which corresponds to the formation of Os1 -Hp -Os2 , namely, one proton shared by two sulfonic groups. According to the analysis of the trajectory, one proton remains trapped in one of these complexes throughout the whole simulation (100 ps), and the two sulfonic groups in this complex accept no other protons during this period, which has a negative effect on the proton conductivity in S1. The other peak is located at around 6.0 ˚ A and corresponds to a distribution of sulfonic groups connected by one water molecule. In contrast, only one peak is observed at around 6.0 ˚ A for S2. The absence of the peak at around 4.6 ˚ A suggests that the Os1 -Hp -Os2 structure is not formed in S2, which is attributed to the relatively low sulfonic group concentration in S2. These results suggest that when the sulfonic group concentration is high, protons are localized through the formation of Os1 -Hp -Os2 . Meanwhile, a small number of sulfonic groups in the polymer leads to poor water sorption, which decreases proton conductivity. Therefore, an appropriate sulfonic group concentration is desirable for use of copolymer in a PEM. We also note that the relatively broad distribution of S-S in this copolymer is similar to that in Nafion, 33 while a more structured S-S distribution was observed for phenylated sulfonated poly (ether ether ketone ketone) membranes at similar hydration levels. 34 A broad S-S distribution indicates high mobility of sulfonic groups, which is considered beneficial for proton conduction in a PEM. 35 As shown in Figure 3(b), two strong peaks are visible in the Ow -Ow RDFs at 2.7 and 4.2 ˚ A, indicating that two main water shells are formed in the system. Moreover, the water distributions around the sulfonic groups and hydrocarbon chains were calculated to investigate the interfacial structures between water clusters and hydrophilic/hydrophobic domains. The RDFs of S-Ow and C-Ow for both systems are depicted in Figure 4 (only the closest carbon atoms to each water molecule are considered). Three peaks appear in the S-Ow RDFs of both systems, which indicates that water molecules surrounding S atoms are well structured, particularly in S1. In contrast, no intense peak was observed in the C-Ow

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4

16

3.5

S1 S2

3

12 10

gOw-Ow (r)

gS-S(r)

S1 S2

14

2.5 2

1.5

8 6

1

4

0.5

2

0 4

4.5

5

5.5

6

6.5

7

7.5

8

0

2

3

4

5

6

r/Å

r/Å

(a)

(b)

7

8

Figure 3: Radial distribution functions of (a) S-S and (b) Ow -Ow .

RDFs, which is typical of the hydrophobic hydration of a hydrocarbon polymer in water. 8

3.5

7

S-Ow C-Ow

3

S-Ow C-Ow

6

gX-Ow(r)

2.5

gX-Ow(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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2 1.5

5 4 3

1

2

0.5 0

1 2

3

4

5

6

7

0

8

2

3

4

5

r/Å

r/Å

(a)

(b)

6

7

8

Figure 4: Radial distribution functions of S-Ow and C-Ow for (a) S1 and (b) S2.

The size of water clusters is another important factor that affects the proton transport of copolymers. Consequently, the probability distribution for different sizes of water clusters in S1 and S2 was calculated, as shown in Figure 5. Any O-H pair was considered to be connected if the distance between them was shorter than 2.2 ˚ A. Several small water clusters of less than ten water molecules and one large water cluster, involving about 85 water molecules, were observed for S1. In contrast, for S2, the size of water clusters was diverse, 8


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S1 S2

0.2

Probability

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.1

0

0

10

20

30 40 50 60 70 Size of water clusters

80

90

100

Figure 5: Calculated size of water clusters in S1 and S2.

which is manifested by many small peaks in the figure. Therefore, S1 has a high probability of forming one large water cluster and a well-connected hydrogen-bond network, while several disconnected clusters are formed in S2. The smaller number of water molecules and lower ratio of hydrophilic to hydrophobic domains in S2 are considered responsible for the scattered distribution of water molecules in it. The high probability of forming a large water cluster in S1 is consistent with the high proton conductivity of this copolymer.

Proton dynamic properties The dynamic properties of protons include proton dissociation and proton transport, both of which are known to directly affect the proton conductivity of PEMs. First we calculated the RDFs for an atomic pair of Os and H(p+w) for both systems to understand their proton dissociation behavior, as depicted in Figure 6. As shown in the figure, peak locations in the RDFs for S1 and S2 are similar. The first peak is located at 1.0 ˚ A, corresponding to an atomic pair of associated Os atoms and H atoms, and the second peak is located at 9



1.8 ˚ A, indicating the distribution of H(p+w) in the first hydration shell. The peak at 1.0 ˚ A reveals that the protons in the copolymer are not completely dissociated at the current hydration level. To understand the probability of proton dissociation for both systems, the integration of this peak was calculated, as illustrated in the inset of Figure 6. About 24% of the protons are undissociated in the case of hydrophilic system S1 and about 48% are undissociated in hydrophobic system S2 when λ=4.

36

These values are higher than that of

Nafion, which shows complete dissociation at λ=4.25, 18 while other common hydrocarbon membranes show proton dissociation properties similar to those of this brush-type copolymer. 13,17 Hydrophobic system S2 shows a lower proton dissociation probability than that of S1, partly because of the small amount of water molecules in this system resulting from the low ratio of hydrophilic domains (only eight protons are associated with S2). 10

8

6

0.2 Coordination number

S1 S2

gOs-H (r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.15 0.1 0.05 0

0.6 0.8

1

1.2 1.4 1.6 1.8 2

r/Å 4

2

0 1

2

3

4

5

6

r/Å Figure 6: Radial distribution functions of Os -H(p+w) for S1 and S2. The inset shows the running coordination numbers.

Besides the intrinsic acid strength, other possible factors affecting the proton dissociation in the copolymer were also studied. We calculated the number of water molecules in the first 10


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hydration shell around the sulfonic group, as shown in Figure 7(a). The results reveal that for S1, the average number of water molecules per sulfonic group is about 4.4, which is slightly higher than the given hydration condition of λ=4. This is mainly because two sulfonic groups often share one (or more) water molecule(s). For S2, the average number of water molecules per sulfonic group is only 3.2, which is less than λ=4. This is another important factor leading to the lower proton dissociation probability in S2 than S1. We then investigated the distribution of other water molecules. Visual inspection of the trajectories revealed that several hydrogen bonds are formed between hydrogen atoms in water (or sulfonic groups) and oxygen atoms of ether groups. Thus, we calculated the RDFs and corresponding coordination numbers for an atomic pair between Oe atoms and H(p+w) atoms, gOe −H (r), for S1 and S2; the results are provided in Figure 7(b). The peak at around 1.6–1.8 ˚ A corresponds to the hydrogen bonds between Oe and Hp (or Hw ) atoms in both systems. This peak indicates that Oe atoms interact with some hydrogen atoms or protons to a certain degree, which affects the water distribution and also proton dissociation in S1 and S2, while in Nafion, several researchers reported that the vicinity of the ether group is hydrophobic. 12,33 In addition, there is another possibility for interacting with hydrogen, which is referred to as the πhydrogen bond. This bond is usually formed between a hydrogen atom of water molecules and a phenyl ring. 37–39 The hydrocarbon copolymer investigated here includes many phenyl groups. Therefore, the possible interaction between Hp (or Hw ) and phenyl groups was considered through the calculation of RDFs of H(p+w) and the center of phenyl groups (those connected to S and O atoms were treated separately). The results are shown in Figure 8. For both S1 and S2, the peak shape between different phenyl groups, namely phenyl on S and phenyl on O, shows remarkably different, which is mainly because of the hydrophilicity of side chain and the hydrophobicity of main chain. However, there is one peak observed at around 2.5 ˚ A for both systems, indicating the formation of π-hydrogen bonds. Although this peak is weak, it still shows that it is possible for phenyl groups to interact with some water molecules in our studied copolymer. Therefore, both the ether and phenyl groups

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attract some water molecules, with the former effect being more pronounced. Moreover, these groups often appear in the middle of hydrophobic domains, and thus are likely to disturb the formation of water channels that enable the Grtthuss proton shuttling. 20,40 8

5 4

S1 S2

3

3.5

4

4.5

Coordination number

6

7 6 5 4 3 2 1 0

0.8

gOe-H (r)

Coordination number

1

7

gS-Ow (r)

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5

0.6

0.6

'

S1 S2

0.4 0.2 0 1

2

3

4

5

0.4

3 2

0.2

1 0

0

3

4

5

6

7

8

1

1.5

2

r/Å

2.5

3

3.5

4

4.5

5

r/Å

(a)

(b)

Figure 7: Radial distribution functions of (a) S-Ow and (b) Oe -H(p+w) . Insets show corresponding running coordination numbers.

Electrical conductivity Proton conductivity is an important property of PEMs, and directly reflects their performance. Takeoka et al. 25 measured the proton conductivity of the brush-type copolymer SP1-P2(m-n) with different ratios of m:n experimentally at different humidity and 80 ◦ C. For comparison, we calculated the electrical conductivity of the two model systems based on the Green–Kubo formula. 41 As shown in equation (1) and (2) , the electrical conductivity σ is given by a time integral over a current–current autocorrelation function: 1 σ= 3V kB T

Z

∞

hJ(t) · J(0)i dt, 0

12


(1)

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2 3

Phenyl on S Phenyl on O

gphenyl-Hw(r)

1.6 gphenyl-Hw(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.2 0.8

Phenyl on S Phenyl on O

2

1 0.4 0

0 2

2.5 3

3.5 4 4.5 5 r/Å

5.5 6

2

2.5 3

(a)

3.5 4 4.5 5 r/Å

5.5 6

(b)

Figure 8: Radial distribution functions of Hw with the center phenyl rings for (a) S1 and (b) S2.

where V is the unit cell volume and kB T is the thermal energy. J(t) is the total electric current of the system at time t:

J(t) =

NX atom dP = Zi v i , dt i=1

(2)

where P is the total dipole moment of the cell, vi is the velocity of the i-th atom, and Zi denotes the Born effective charge of the i-th atom. Unfortunately, the calculation of Born charges is much more expensive than the ground state calculations, so Eq.(2) was not used for the present system. Instead, we rely on an alternative expression for the electrical conductivity based on the Einstein-Helfand relation:

σ=

1 |P(t) − P(0)|2 lim , 6V kB T t→∞ t

(3)

which allows us to bypass the calculation of Born charges. In the limit of long times, these equations give the same values for electrical conductivity. Equation (3) has been used by several authors for classical MD simulations. 42–44 In this work, we calculate P(t) at each FPMD step using the Berry phase approach, 45 with an overhead of 15 %. The corresponding

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mean square displacements of the cell dipole moment, < |P(t) − P(0)|2 >, for S1 and S2 are shown as a function of t in the Supporting Information. The calculated electrical conductivity for each direction and their average values for the two systems are listed in Table 2. The proton conductivity measured for a family of SP1-P2 ionomers at a similar hydration level 25 lies in the range of 1.0 to 8.0 S·m−1 . Good quantitative agreement between the theoretical and experimental values was observed, demonstrating the reliability of our simulations of the selected model compounds. The calculated electrical conductivity of S1 is much larger than that of S2, which is explained by the relatively small amount of sulfonic groups and water molecules in S2. This result is also consistent with the above observations of well-developed water channels and better proton dissociation properties of S1. The calculated electrical conductivity strongly depends on the x, y, and z directions of the cell. Both systems possess a large value in the x direction, an intermediate value in the y direction, and a small value in the z direction, , as shown in Table 2. To understand the origin of this anisotropy intuitively, snapshots showing only the sulfonic groups and water molecules are provided in Figure 9. The distributions of sulfonic groups and water molecules for both systems on the x-y plane are presented in Figure 9(a) and (c), respectively, and those for the x-z plane are illustrated in Figure 9(b) and (d), respectively. The sulfonic groups and water molecules, which form the water channels, show a strong connection in S1 in both x and y directions, while they have a relatively weak connection in the z direction. This is consistent with the obtained values of electrical conductivity for different directions. For S2, although no strong connection of sulfonic groups and water molecules is formed in any direction, we still notice that the connection in the x direction is more developed than those in other directions, in agreement with the calculated values. The weaker connection in S2 than S1 also explains the smaller calculated values of electrical conductivity of S2 than those of S1. The strong anisotropy of the calculated electrical conductivity and the obtained structure of sulfonic groups and water molecules suggests that a two-dimensional (S1) or one-dimensional network (S2) of proton transport channels is preferred at this hydration

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level, although the time and length scales of our simulations are not large enough to be conclusive. We also note that the formation of low-dimensional lamellar-like and gyroid-like structures was observed in experiments. 25 Table 2: Calculated electrical conductivity in S · m−1 . system S1 S2

σx 5.97 2.94

σy 3.51 0.76

σz 2.22 0.31

σave 3.90 1.33

Effective and ineffective hydrogen bonds Systematic calculations were performed on the structural and dynamic properties of the brush-type hydrocarbon copolymer that possesses good proton conductivity. Its well-developed water channels explain the high proton conductivity of this copolymer. Nevertheless, some negative factors for proton conductivity are also observed, such as unfavorable water distribution and protons interacted with ether groups. Obviously, the hydrogen bond network plays an important role in these phenomena. A continuous hydrogen bond network is beneficial for proton transport. Based on these observations, we summarize several types of hydrogen bonds observed in the system, which are classified into effective and ineffective ones in terms of proton transport, as shown in Figure 10. Effective hydrogen bonds include Eigen, Zundel, and Os -H-Ow complexes, while ineffective hydrogen bonds include Hw -Oe , Hp -Oe , and Os1 Hp -Os2 , as well as π-hydrogen bonds. Ether groups are abundant in the structures of PEMs such as Nafion and SPEEK, and play important roles in polymer synthesis and system flexibility. However, they negatively affect the chemical stability of copolymers to some extent 26 and also lower the efficiency of proton transport by attracting some water molecules and protons through the formation of Hw -Oe and Hp -Oe bonds, which causes the scattered distribution of water molecules. Another type of ineffective bond, Os1 -Hp -Os2 , which is formed between two sulfonic groups, is readily produced in these compounds at a high sulfonic group concentration. Meanwhile, π-hydrogen bonds are formed in all hydrocarbon PEMs including 15



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z

y

x

x

(a)

(b) z

y

x

(c)

(d)

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Figure 9: Snapshots of water molecules and sulfonic groups for the (a) x-y plane of S1, (b) x-z plane of S1, (c) x-y plane of S2, and (d) x-z plane of S2. White, red, and yellow spheres represent H, O, and S atoms, respectively.

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ability of the studied hydrocarbon copolymer is weaker than that of Nafion at this hydration level. About 76% protons were dissociated when λ = 4 in S1, similar to other hydrocarbon PEMs, while 100% protons are dissociated in Nafion when λ = 4.25. 18 Therefore, even if the proton dissociation ability or acid strength of a polymer compound plays an important role in its proton conductivity, the structure of the system and water channel are also important for the performance of PEMs. In addition, the calculated electrical conductivity for the copolymer shows good agreement with the experimentally measured proton conductivity, demonstrating the reliability of our simulations of the selected model compounds. The anisotropy of the simulated electrical conductivities for x, y, and z directions is consistent with the distribution of channels formed by sulfonic groups and water molecules. In this work, we discussed the electrical conductivity of the whole system at only one hydration level, without going into the details of proton dynamics, e.g. the Grotthuss mechanism. Therefore, we are planning to perform FPMD simulations of the present system at different hydration levels as well as Nafion using a large cell comparable to the present model, which will allow us to compare the morphology and proton dynamics in these systems on an equal footing. According to the analysis of the trajectories, we classified the hydrogen bonds into effective and ineffective ones for proton transport. Effective hydrogen bonds include Eigen, Zundel, and Os -H-Ow complexes, while ineffective bonds include Hw -Oe , Hp -Oe , Os1 -Hp -Os2 and π-hydrogen bonds. These ineffective hydrogen bonds are able to interact with some water molecules or protons, thus limiting the proton transport in the copolymer. Therefore, the proton conductivity of this copolymer, as well as other PEMs, will be further improved by modifying their structures to minimize the number of ineffective hydrogen bonds. These insights on the structural and dynamic properties of this copolymer will be helpful for experimentalists synthesizing new PEMs with improved performance.

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Acknowledgments We gratefully acknowledge financial support from the New Energy and Industrial Technology Development Organization. Part of the calculations was carried out using the computer facilities at the Research Institute for Information Technology, Kyushu University.

Notes and References (1) Kordesch, K. V.; Simader, G. R. Chem. Rev. 1995, 95, 191–207. (2) Steele, B. C. H.; Heinzel, A. Nature 2001, 414, 345–352. (3) Zhang, H.; Shen, P. K. Chem. Rev. 2012, 112, 2780–2832. (4) Mauritz, K. A.; Moore, R. B. Chem. Rev. 2004, 104, 4535–4585. (5) Elliott, J. A.; Paddison, S. J. Phys. Chem. Chem. Phys. 2007, 9, 2602–2618. (6) Hickner, M. A.; Ghassemi, H.; Kim, Y. S.; Einsla, B. R.; McGrath, J. E. Chem. Rev. 2004, 104, 4587–4612. (7) Higashihara, T.; Matsumoto, K.; Ueda, M. Polymer 2009, 50, 5341–5357. (8) Rikukawa, M.; Sanui, K. Prog. Polym. Sci. 2000, 25, 1463–1502. (9) Jorn, R.; Savage, J.; Voth, G. A. Acc. Chem. Res. 2012, 45, 2002–2010. (10) Feng, S.; Savage, J.; Voth, G. A. J. Phys. Chem. C 2012, 116, 19104–19116. (11) Hofmann, D.; Kuleshova, L.; D’Aguanno, B. J. Power Sources 2010, 195, 7743–7750. (12) Devanathan, R.; Venkatnathan, A.; Dupuis, M. J. Phys. Chem. B 2007, 111, 8069– 8079. (13) Zhao, Y.; Tsuchida, E.; Choe, Y.-K.; Ikeshoji, T.; Barique, M. A.; Ohira, A. Phys. Chem. Chem. Phys. 2014, 16, 1041–1049. 19



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Sadrabadi, M. M. Int. J. Hydrogen Energy 2012, 27, 10256–10264. (16) Choe, Y.-K.; Tsuchida, E.; Ikeshoji, T.; Yamakawa, S.; Hyodo, S. J. Phys. Chem. B 2008, 112, 11586–11594. (17) Choe, Y.-K.; Tsuchida, E.; Ikeshoji, T.; Ohira, A.; Kidena, K. J. Phys. Chem. B 2010, 114, 2411–2421. (18) Choe, Y.-K.; Tsuchida, E.; Ikeshoji, T.; Yamakawa, S.; Hyodo, S. Phys. Chem. Chem. Phys. 2009, 11, 3892–3899. (19) Mahajan, C. V.; Ganesan, V. J. Phys. Chem. B 2010, 114, 8367–8373. (20) Kreuer, K.-D.; Paddison, S. J.; Spohr, E.; Schuster, M. Chem. Rev. 2004, 104, 4637– 4678. (21) Park, C. H.; Lee, C. H.; Guivera, M. D.; Lee, Y. M. Prog. Polym. Sci. 2011, 36, 1443–1498. (22) Li, N.; Guiver, M. D. Macromolecules 2014, 47, 2175–2198. (23) Peckham, T. J.; Holdcroft, S. Adv. Mater. 2010, 22, 4667–4690. (24) Umezawa, K.; Oshima, T.; Yoshizawa-Fujita, M.; Takeoka, Y.; Rikukawa, M. ACS Macro Lett. 2012, 1, 969–972. (25) Takeoka, Y.; Umezawa, K.; Oshima, T.; Yoshida, M.; Yoshizawa-Fujita, M.; Rikukawa, M. Polym. Chem. 2014, 5, 4132–4140. (26) Zhao, Y.; Tsuchida, E.; Choe, Y.-K.; Wang, J.; Ikeshoji, T.; Ohira, A. J. Membr. Sci. 2015, 487, 229–239. 20


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(27) Sun, H. J. Phys. Chem. B 1998, 102, 7338–7364. (28) Tsuchida, E.; Tsukada, M. J. Phys. Soc. Jpn. 1998, 67, 3844–3858. (29) Tsuchida, E.; Choe, Y.-K.; Ohkubo, T. Phys. Chem. Chem. Phys. 2015, 17, 31444– 31452. (30) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865–3868. (31) Goedecker, S.; Teter, M.; Hutter, J. Phys. Rev. B 1996, 54, 1703–1710. (32) Hartwigsen, C.; Goedecker, S.; Hutter, J. Phys. Rev. B 1998, 58, 3641–3662. (33) Urata, S.; Irisawa, J.; Takada, A.; Shinoda, W.; Tsuzuki, S.; Mikami, M. J. Phys. Chem. B 2005, 109, 4269–4278. (34) Lins, R. D.; Devanathan, R.; Dupuis, M. J. Phys. Chem. B 2011, 115, 1817–1824. (35) Hristov, I. H.; Paddison, S. J.; Paul, R. J. Phys. Chem. B 2008, 112, 2937–2949. (36) These values were obtained by multiplying the coordination number by the number of Os atoms in each sulfonic group (=3). (37) Suzuki, S.; Green, P. G.; Bumgarner, R. E.; Dasgupta, S.; IlI, W. A. G.; Blake, G. A. Science 1992, 257, 942–945. (38) Allesch, M.; Lightstone, F. C.; Schwegler, E.; Galli, G. J. Chem. Phys. 2008, 128, 014501/1–014501/9. (39) Li, S.; Cooper, V. R.; Thonhauser, T.; Puzder, A.; Langreth, D. C. J. Phys. Chem. A 2008, 112, 9031–9036. (40) Marx, D. Chem. Phys. Chem. 2006, 7, 1848–1870. (41) French, M.; Hamel, S.; Redmer, R. Phys. Rev. Lett. 2011, 107, 185901/1–185901/4.

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(42) Hokazono, M.; Ueda, A.; Hiwatari, Y. Solid State Ionics 1984, 13, 151–155. (43) Schrder, C.; Haberler, M.; Steinhauser, O. J. Chem. Phys. 2008, 128, 134501/1– 134501/10. (44) Dommert, F.; Schmidt, J.; Qiao, B.; Zhao, Y.; Krekeler, C.; Site, L. D.; Berger, R.; Holm, C. J. Chem. Phys. 2008, 129, 224501/1–224501/10. (45) Resta, R. Rev. Mod. Phys. 1994, 66, 899–915.

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Table of Contents graphic y

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First-Principles Molecular Dynamics Study of a ... - ACS Publications

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