Molecular Dynamics Study of the Morphology of Hydrated

Subscriber access provided by CORNELL UNIVERSITY LIBRARY

Article

Molecular Dynamics Study of the Morphology of Hydrated Perfluorosulfonic Acid Polymer Membranes An-Tsung Kuo, Wataru Shinoda, and Susumu Okazaki J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b08015 • Publication Date (Web): 24 Oct 2016 Downloaded from http://pubs.acs.org on October 29, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 39

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

The Journal of Physical Chemistry

Molecular Dynamics Study of the Morphology of Hydrated Perfluorosulfonic Acid Polymer Membranes

An-Tsung Kuo, Wataru Shinoda┼, and Susumu Okazaki┿

Department of Applied Chemistry, Nagoya University, Nagoya 464-8603, Japan

┼

Corresponding author. Tel: (+) 81-52-789-5288. Fax: (+) 81-52-789-5118. Email: [email protected]

┿

Corresponding author. Tel: (+) 81-52-789-5229. Fax: (+) 81-52-789-5118. Email: [email protected] 1

ACS Paragon Plus Environment


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

ABSTRACT Many morphological models have been proposed to describe the water swelling behavior and proton transport mechanism of perfluorosulfonic acid (PFSA) polymer membranes through the experimental and modeling studies. However, the ongoing structural debate has not been completely resolved yet. We here conducted a series of all-atom molecular dynamics simulations of hydrated PFSA membranes to evaluate changes in the membrane morphology at different water contents. We found a similar dependence of the morphology on the water content between PFSA membranes with equivalent weight (EW) of 844 and 1144 g/equiv. That is, the morphology of the aqueous domain changes with increasing water content, from a channel-network structure to a tortuous layered structure, while once attained the tortuous layered structure, water layer just thickened gradually by further increasing water contents. Furthermore, we found more heterogeneous water domains in the higher-EW PFSA membrane, demonstrating the stronger aggregation behavior of the aqueous domains in the high-EW membranes. The variation of the PFSA membrane morphology observed here is useful to understand the proton transport mechanism and design new materials suitable for polymer electrolyte fuel cells in the near future.

2


Page 2 of 39

Page 3 of 39

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. INTRODUCTION Perfluorosulfonic

acid

(PFSA)

ionomers

composed

of

a

hydrophobic

polytetrafluoroethylene (PTFE) backbone with hydrophilic side chains terminated by a sulfonic acid, such as Nafion, Flemion, Aciplex, and Hyflon (Fig. 1), are widely used as proton exchange membranes for polymer electrolyte fuel cells (PEFCs).1 In particular, Nafion, as a standard material for PEFCs, has been studied extensively and found to exhibit good mechanical stability and proton conductivity.1,

2

Hydrated Nafion membranes exhibit

microphase separation between hydrophobic and hydrophilic domains, whose morphology is likely related to the mechanical and dynamical properties of the membrane.1, 2 Understanding the phase-segregated morphology of the Nafion ionomer is thus important for achieving efficient proton transport and for designing new materials for PEFCs.

Figure 1. Schematic illustration of perfluorosulfonic ionomers. Nafion: m =1, n = 2; Flemion: m = 0–1, n = 1–5; Aciplex: m = 0–2, n = 1–4; Hyflon: m = 0, n = 2.1, 3

On the basis of experimental and modeling studies, many different morphological models have been proposed to describe the water swelling behavior and proton transport mechanism of hydrated Nafion membranes.2,

4-10

Hsu and Gierke proposed the first

morphological model of hydrated Nafion membranes, the cluster-network model, involving spherical domains of a water-rich sulfonic acid phase connected by narrow channels.4, 5 In the dry state, the diameter of the spherical water clusters was ~ 2 nm and the clusters were believed to be disconnected from each other. With increasing water content, the size of the water clusters increased to about 4 nm in diameter and narrow channels with length and 3



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

Page 4 of 39

diameter of ~ 1 nm were formed to connect them. Diat and co-workers proposed a fibrillar structure model, according to which the basic entity in the Nafion membrane consists of elongated polymeric aggregates with cylindrical or ribbon-like shape surrounded by ionic groups and water.7, 8 Upon swelling, the hydrated aggregates were dispersed in a colloidal suspension. Schmidt-Rohr and Chen proposed a parallel cylinder model, in which parallel cylindrical ionic water channels were embedded in a locally aligned polymer matrix.9 Kreuer and Portale reported a film-like morphology and suggested that water films acted as a positively charged glue keeping together the negatively charged polymer structures.10 Although many different morphological models of the hydrated Nafion membrane have been proposed on the basis of various experimental studies, no clear consensus has yet been reached on the structure of these systems. A number of computer simulations of model PFSA systems have been carried out to obtain more details on the membrane structure and function.11-13 Ab initio calculations were used to investigate the role of the side chains of PFSA in proton transfer.14, 15 Molecular dynamics (MD) simulations were employed to explore various issues of the PFSA membranes, including the effects of hydration, equivalent weight, side chain length, and distribution along the backbone on structural and transport properties of the hydrated membrane,16-24 gas adsorption and permeation,25 water sorption and permeation,26, mechanical deformation.28,

29

27

and

Empirical valence bond (EVB)30-32 and multistate empirical

valence bond (MS-EVB)33-39 methods were adopted to describe proton hopping. The latter more accurately discusses the full physics of hydrated proton behavior, including the proportion of Eigen to Zundel cations and the mechanism of proton hopping in water. Moreover, coarse-grained (CG) MD and dissipative particle dynamics simulations were used to study the mesoscale morphology and the mechanical properties of the membranes.40-47 In early atomistic MD simulations of the PFSA membrane, the simulation box was too 4


Page 5 of 39

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


small (< 10 nm cubic box length) to enable an accurate determination of the structure and morphology of the segregated hydrophobic and hydrophilic domains.16-18, 22, 26, 30 To date, only two atomistic studies have focused on the morphology of the PFSA membranes employing large-scale MD simulations.21, 23 Knox and Voth used large-scale MD simulations (simulation cubic box length ~ 30 nm, or ~ 2 million atoms) with a 34 ns equilibration run to probe different morphological models of the hydrated Nafion membranes. They concluded that the characteristic scattering peak (ionomer peak) is insensitive to the segregated morphology and the structure factor cannot clearly distinguish the morphological models.21 Komarov et al. conducted MD simulations of large systems representing the hydrated Nafion membrane (~ 36 nm cubic box length, ~ 4 million atoms) starting from an initial configuration generated by replicating equilibrated configurations of smaller size (~ 9 nm cubic length, ~ 65,000 atoms) and suggested a bicontinuous double-diamond structure of the segregated domains.23 However, it should be noted that replicating small models to generate a large initial configuration would result in spurious effects due to the long relaxation time of the glassy polymer chains. Hence, accurately probing the morphology of the PFSA membranes still represents a challenge for atomistic MD simulations. The morphology of the PFSA membranes is related to their water content. However, to the best of our knowledge, no atomistic MD studies have focused on the effect of hydration on the morphology of the PFSA membrane. In order to quantitatively assess the morphological evolution of the membranes at different water contents by MD simulations, integral-geometry morphological image analysis was employed in the present study. This method uses additive image functionals, called Minkowski functionals, to classify the shape and connectivity of patterns formed by the pixels of a 2D or 3D image.48 This approach has been successfully applied to analyze the phase-separated block copolymer systems,49, 50 hence it should be applicable to study the phase-segregated morphology of the PFSA membranes. In 5



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

addition, the ratio of the interfacial area to volume, which provides information on the water distribution within the hydrated membrane, was previously used to characterize the morphology of the Nafion membrane.51 Therefore, the surface-to-volume ratio was also calculated and discussed in the present paper. Furthermore, previous experiments reported that membranes formed by low-equivalent weight (EW) PFSA absorb more water than those composed of high-EW PFSA.52 This may result in a different morphology of low- and high-EW PFSA membranes. For this reason, we simulated two PFSA membranes with different EW (844 and 1144 g/equiv) in an attempt to identify the morphological model that best describes the hydrated PFSA membranes. In the present study, we first conducted small-scale MD simulations (~ 6 nm cubic box length) of the hydrated PFSA membranes to validate the chosen force field, by confirming that it correctly reproduces the experimental density and the structural properties. Then, we carried out MD simulations with a simulation box length of ~ 13 nm to determine the morphological properties of the membrane. Finally, large systems (~ 27 nm cubic box length) with high water contents were simulated. Using the integral-geometry morphological image analysis and the surface-to-volume ratio calculations, we characterized the morphological changes in the membranes at different water contents and examined previously proposed morphological models, concluding that the aqueous domains show a channel-network structure at low water contents, which turns into a tortuous layered structure at high water contents.

2. SIMULATION METHODS 2.1. Details of the simulations In this study, we examined two PFSA ionomers with different EW (844 and 1144 g/equiv) consisting of 10 monomers, representative of Asahi Glass Flemion (EW ~ 910 6


Page 6 of 39

Page 7 of 39

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


g/equiv) and Dupont Nafion (EW ~ 1100 g/equiv), respectively. The repeating unit of the first ionomer with EW 844 g/ equiv is composed of 10 (x = 4, y = 1, see Fig. 1) CF2 groups in the main chain with m = 1, n = 2, and that of the second ionomer with EW 1144 g/equiv is composed of 16 (x =7, y = 1) CF2 groups in the main chain with m = 1, n = 2 (see Fig. 1). The sulfonic groups in the pendant side chains are assumed to be fully ionized to H+ and SO3 at －

all hydration levels, and the resulting protons combine with water to form hydronium ions (H3O+). We used the modified DREIDING force field by Mabuchi and Tokumasu for the PFSA ionomer,24 together with the F3C water model53 and the classical hydronium model.16 Three different system sizes (denoted as “small”, “medium”, and “large” systems) were examined. The small system consisted of 25 polymer chains, 250 hydronium ions, and different numbers of water molecules. Six different hydration levels (λ = 3, 6, 9, 12, 15, and 20, where λ = (H2O, H3O+)/SO3－) were considered. Initial configurations were generated by arranging these molecules randomly in a cubic box with a side length of 20 nm using the Packmol software.54 The medium systems were 8 times larger than the corresponding small systems. Their initial configurations were generated by randomly arranging the molecules in a 40 nm × 40 nm × 40 nm simulation box. The large systems consisted of 1344 polymer chains for the EW 1144 PFSA membrane, and 1600 polymer chains for the EW 844 PFSA membrane. Each large system also contains hydronium ions for charge neutralization and a number of water molecules corresponding to λ = 20. Again, the initial configurations were obtained by randomly arranging the molecules in a 50 nm × 50 nm × 50 nm cubic cell using Packmol. The all-atom MD simulations were carried out using the Gromacs package, version 5.04.55,

56

After energy minimization, each system was thermalized using the annealing

procedure proposed by Mabuchi and Tokumasu.24 First, the simulation cell was gradually compressed to a volume approximately corresponding to the experimental density in an NPT 7



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

(constant number of particles, pressure, and temperature) MD run at T = 800 K and P = 1000 bar, using Lennard-Jones (LJ) potential parameters ε reduced to 1/100 magnitude for all PFSA atoms. Then, additional NPT MD simulations were performed to gradually switch the LJ parameters back to their original values and change the simulation conditions to T = 300 K and P = 1 bar. After that, a constant volume MD run of 1 ns was carried out, during which the temperature was increased to 800 K and decreased to 300 K every 250 ps, followed by an NPT run of 5 ns at T = 300 K and P = 1 bar. The process was repeated four times to confirm that the density had attained a constant value. After the annealing process, a production MD run was carried out in the NPT ensemble at T = 300 K and P = 1 bar for 100–300 ns. The temperature and pressure of the system were controlled using the Nosé-Hoover thermostat57 and the isotropic Parrinello-Rahman barostat,58, 59 respectively. The long-range electrostatic interactions were estimated using the particle-mesh Ewald (PME) method,60 and the LJ pair interactions were evaluated within a cutoff distance of 1.5 nm without a truncation shift function. A time step of 1 fs was used for all MD simulations. The lengths of the MD runs were 300 ns for the small and medium systems and 100 ns for the large systems.

2.2. Simulation analysis 2.2.1 Euler characteristic In the integral-geometry image analysis the morphological information of an image is described through 4 additive image functionals (Minkowski functionals)48: volume V, surface area S, mean curvature B, and Euler characteristic χ. The Minkowski functionals are calculated for binary (black-and-white) images. The 3D image is first mapped onto a cubic lattice filled with black and white pixels, which represent the object, that is, hydrophobic or hydrophilic region of the membrane here, and the background, respectively. Each black pixel is considered as the union of 6 faces, 8 vertices, 12 edges, and the interior of the cube. Then, 8


Page 8 of 39

Page 9 of 39

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


the total numbers of cube interiors (or black pixels) nc, faces nf, vertices nv, and edges ne are calculated by adding black pixels to an initially completely white background. The geometrical and topological descriptors of a 3D object are then calculated as:48 V = nc , S = −6nc + 2n f , 2 B = 3nc − 2n f + ne , χ = −nc + n f − ne + nv

(6)

The Euler characteristic χ is a number that describes the shape or structure of a topological space. In three dimensions, χ is given by the number of connected components minus the number of tunnels (holes), plus the number of cavities.48, 49 For instance, χ = 1 for a solid sphere (a continuous phase), χ = 0 for a torus (a connected circle and a hole), χ = 2 for a hollow sphere (a connected sphere shell and a cavity), and χ = -1 for a double torus (a ∞ shape with two holes).49 The additivity of the Euler characteristic allows defining simple rules for determining the main topology of a structure. In particular, a very positive χ indicates the predominance of isolated structures, such as isolated spherical or parallel cylindrical structures, while a very negative χ can be interpreted as denoting a highly connected structure with numerous tunnels (holes), such as a porous connected structure (Fig. 2).

Figure 2. Schematic illustration of the structures associated to the Euler characteristic indicated in the figure.

2.2.2 Volume and surface area The surface-to-volume ratio is a quantitative parameter used to describe the geometry 9



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

and size of an object. To compute the volume of the aqueous domain (labeled WV) of a configuration, we removed all water molecules and hydronium ions from the structure. Then, a spherical probe with a radius of 0.14 nm was randomly inserted into the simulation box, and the volume fraction of the aqueous domain was determined as the fraction of insertions that did not overlap with any atom.61 An analogous surface area calculation performed using the same probe62 yielded the solvent-accessible surface area (SA) of the polymer exposed to the aqueous phase. It should be noted that, since water molecules are treated as hard spheres, the computed volume and surface area of the aqueous domain might be slightly underestimated. Nevertheless, their ratio should still be representative of the morphology of the water cluster.

2.2.3 Structure factor Experimentally, small angle X-ray scattering (SAXS) spectroscopy has been widely used to study the morphology of hydrated PFSA membranes, including the size and shape of the hydrophobic and hydrophilic domains.1 The ionomer peak position in the SAXS spectrum is associated to the mean distance between clusters (l = 2π/q) and to a characteristic periodic dimension in the membrane. The Cromer-Mann relation was adopted in this study to obtain the X-ray scattering intensity. The structure factor was calculated as: atom

F(q) = ∑ f j exp(ir j ⋅ q)

(2)

j =1

where fi is the atomic scattering factor of the i-th atom. The atomic scattering factor can be obtained from the Cromer-Mann formula: 4

f (sin θ / l) = ∑ ai exp[−bi (sin θ / l) 2 ] + c

(3)

i =1

where l is the radiation wavelength and the 9 (ai, bi, c, i = 1–4) parameters can be found in the literature.63 Finally, the scattering intensity I(q) can be obtained from the structure factor and the polarization factor P: 10


Page 10 of 39

Page 11 of 39

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


2

I (q) = F(q) P

(4)

P = 0.5 1 + cos 2 (2θ ) 

(5)

2.2.4 Radius of gyration The radius of gyration (Rg) of the polymer chain was calculated as :

 ∑ mi ri  Rg =  i mi  ∑  i

1

2

2    

where ri is the position of atom i with respect to the center of mass of the polymer chain, and mi is the mass of atom i.

2.2.5 Diffusion coefficients We determined the diffusion coefficient, D, of the water molecules (DW) and hydronium ions (DH) using the mean square displacement (MSD) to satisfy the Einstein relation: D = lim t →∞

1 2 r (t ) − r (0) 6t

where r(t) is the center of mass position vector of water and hydronium ion at time t.

3. RESULTS AND DISCUSSION 3.1. Validation of the equilibration The density of the simulated systems is plotted as a function of the water content, λ, in Fig. 3, together with the corresponding experimental data. The experimental data plotted in the figure are obtained from the following fitting equation:64

11



ρ=

EW + M 0 λ Vm + λV0

(1)

where EW is the equivalent weight, M0 is the molecular weight of water, and Vm and V0 are the partial molar volume of the dry membrane and water, respectively. The partial molar volumes of the dry membrane and water are calculated as Vm = EW/ρm and V0 = M0/ρ0, respectively, where ρm and ρ0 are the densities of the dry membrane (2.05 g/cm3)65 and water, respectively. The results clearly indicate that the modified DREIDING force field used in our MD simulations accurately reproduces the experimental density for both the low- and high-EW PFSAs.

2.2 Exp-EW 844 Sim-EW 844 Exp-EW 1144 Sim-EW 1144

3

Density, g/cm

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

2.0 1.8 1.6 1.4 0

5

10

15

20

Water content (λ)

Figure 3. Density of the simulated systems and corresponding experimental data.

To confirm that equilibration was achieved, we performed MD simulations of the small systems starting from 10 different initial configurations. The annealing protocol employed in our simulations effectively reproduced the experimental density starting from the different initial configurations, with error bars smaller than the size of the symbols in Fig. 3. We also monitored the sulfur-sulfur radial distribution function (RDF) averaged over different time windows (Fig. 4a). The dependence of the RDF on the starting configuration is small and the 12


Page 12 of 39

Page 13 of 39

height of the first peak gradually increases with increasing simulation time up to 100 ns. No significant further changes in the RDF could be detected after 100 ns. Moreover, the relative error in the diffusion coefficients of water molecules (DW) and H3O+ ions (DH) obtained after 100 ns and from the 10 MD runs started from different initial configurations is less than 10%. Thus, we can confirm that the small system achieves equilibration after 100 ns and that the simulation results are independent of the initial configuration employed. We also evaluated possible system size effects on the structure by comparing the results obtained for the medium and large systems. No changes in density resulted from the different size of the simulation box. A comparison of the S-S RDFs calculated for systems of different size showed no major differences, even though a slightly lower first peak was observed for the small system (Fig. 4b). Furthermore, a comparison of the DW and DH for small and medium systems shows that the relative error is less than 10% (Tables S1 and S2). Thus, we can confirm that the medium and large systems achieved equilibration during the simulation time length specified.

1.5

1.5

(a)

(b)

1.0 0-10 ns 90-100 ns 190-200 ns 290-300 ns

0.5

0.0 0.2

g(r)

1.0

g(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


0.4

0.6

0.8

1.0

0.5

0.0 0.2

1.2

small system medium system large system

0.4

r, nm

0.6

0.8

1.0

1.2

r, nm

Figure 4. (a) S-S RDF for small EW 844 PFSA systems with λ = 20 calculated from various simulation time windows and (b) S-S RDF for small, medium, and large EW 844 PFSA systems with λ = 20 calculated from the last 10 ns of the MD trajectory. 13



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

Page 14 of 39

3.2. Morphologies of the hydrated membranes 3.2.1 MD snapshots of the membrane The upper panels of Fig. 5 show MD snapshots of the medium-size models of EW 844 PFSA membranes at different water contents. The lower panels of Fig. 5 display isosurface representations of the water domains also including the sulfonic groups of the polymer, as created by generating a volumetric Gaussian density map using the VMD package with a spatial resolution of 1.3.66, 67 At λ = 3, the water/sulfonic groups domains are distributed over the simulation box and seem to form random water channels. With increasing water content, the water domain gradually increases in size and phase segregation is clearly discernible.

(a)

(d)

λ=3

(b)

λ = 12

(c)

λ = 20

(f)

(e)

Figure 5. Snapshots from the MD simulations of medium-size models of EW 844 PFSA membranes (upper panels) and isosurface representations of water domains including sulfonic groups (lower panels); (a, d): λ = 3, (b, e): λ = 12, and (c, f): λ = 20. Polymer chains are shown as dark red particles, sulfur atoms are represented as yellow particles, and the water region is drawn as a cyan solid contour. 14


Page 15 of 39

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


The variation of the morphology of the hydrated EW 1144 PFSA membrane with increasing water content is similar to that of the EW 844 one (Fig. S1). In order to elucidate the difference in morphology between these two membranes, we conducted large-scale MD simulations (~ 27 nm cubic box length) at λ = 20. The morphologies of the PFSA membranes obtained from the large-scale simulations are shown in Fig. 6. A more heterogeneous water domain was found to develop in the EW 1144 PFSA membrane. The higher-EW PFSA, which possesses a longer PTFE backbone per sulfonic group, has stronger hydrophobicity and thus tends to form a hydrated membrane with stronger repulsion between the hydrophobic and hydrophilic phases. This leads to the formation of larger water aggregates in the higher-EW PFSA membrane.68

(a) EW 844

(b) EW 1144

Figure 6. Snapshots from MD simulations of large-scale models of the (a) EW 844 and (b) EW 1144 PFSA membranes at λ = 20. Polymer chains are shown as dark red particles and the water region is drawn as a cyan solid contour.

15



3.2.2 Radius distribution function The S-S RDFs of medium EW 844 and EW 1144 PFSA systems are presented in Fig. 7. The first peak of the S-S RDFs in the EW 844 and EW 1144 PFSA membranes was found at r = ~0.45 nm and decreased in height with increasing water content. The general trends in our simulation results are comparable with those reported in the previous studies.18, 22, 24, 69 We further calculate the coordination number of sulfur atoms (shown in Table 1), which is defined as the number of neighboring sulfur atoms within the distance of 0.63 nm, which corresponds to the first minimum of S-S RDFs in Fig. 7. The coordination number of sulfur atoms in both EW 844 and EW 1144 PFSA membranes becomes smaller with increasing water content, indicating that the sulfur atoms tend to stay closer together at low water content and be separated at high water content. Furthermore, the coordination number in the EW 1144 PFSA membrane is higher than that in the EW 844 PFSA membranes at all water contents. This reveals that the sulfonic groups in the higher-EW PFSA tend to aggregate more closely to one another than those in the lower-EW PFSA.

(a) EW 844

(b) EW 1144

8

8

λ=3 λ=6 λ=9 λ = 12 λ = 15 λ = 20

4 2 0 0.2

λ=3 λ=6 λ=9 λ = 12 λ = 15 λ = 20

6 g(r)

6 g(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

Page 16 of 39

4 2

0.4

0.6

0.8

1.0

0 0.2

1.2

0.4

r, nm

0.6

0.8

1.0

1.2

r, nm

Figure 7. S-S RDF for (a) EW 844 and (b) EW 1144 PFSA membranes obtained from the MD simulations of the medium systems.

16


Page 17 of 39

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


Table 1. Coordination number of each sulfur evaluated from the S-S RDF within the distance 0-0.63 nm and from the S-OW RDF within the distance 0-0.47 nm at various water contents

λ. S-S

S-OW

λ EW 844

EW 1144

EW 844

EW 1144

3

2.72

2.79

2.99

2.95

6

1.61

1.67

5.39

5.37

9

1.12

1.19

6.42

6.31

12

0.92

0.94

6.82

6.74

15

0.76

0.84

7.13

6.91

20

0.62

0.76

7.36

7.04

Figure 8 shows the S-OW (water oxygen) RDFs of medium EW 844 and EW 1144 PFSA systems. The heights of the peaks in the RDFs of both EW 844 and EW 1144 PFSA membranes decrease as increasing the water content, demonstrating that the water molecules bind to sulfonic groups less strongly with increasing water content. Similar results were reported in the previous works.18, 22, 24, 69 The hydration number of sulfur atoms was also estimated using the cutoff distance of 0.47 nm (Table 1), which corresponds to the first minimum of S-OW RDFs in Fig. 8. The hydration numbers of sulfur atoms in both EW 844 and EW 1144 PFSA membranes increase as increasing the water content. Moreover, the hydration number in the EW 844 PFSA membrane is higher than that in the EW 1144 PFSA membranes at all water contents. This indicates that low-EW PFSA membrane tends to have more water molecules around the sulfonic group of the polymer.

17



(a) EW 844

(b) EW 1144 λ=3 λ=6 λ=9 λ = 12 λ = 15 λ = 20

8 6 4

10

2 0 0.2

λ=3 λ=6 λ=9 λ = 12 λ = 15 λ = 20

8 g(r)

10

g(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

Page 18 of 39

6 4 2

0.4

0.6

0.8

1.0

0 0.2

1.2

0.4

r, nm

0.6

0.8

1.0

1.2

r, nm

Figure 8. S-OW RDF for (a) EW 844 and (b) EW 1144 PFSA membranes obtained from the MD simulations of the medium systems.

3.2.3 Euler characteristic To quantify the topological properties of the PFSA membranes, the Euler characteristic of the hydrophilic and hydrophobic regions in the membranes (χp and χnp, respectively) were calculated and are listed in Table 2. We define the hydrophilic region as the area occupied by water clusters and the sulfonic groups of the polymer, and the hydrophobic region as the area occupied by the polymer, excluding the sulfonic groups. In the case of the EW 844 PFSA membrane, large negative χp and χnp values are observed for λ = 3, indicating that both hydrophilic and hydrophobic regions have highly connected network structures. With increasing hydration level from λ = 3 to λ = 9, the χp value increases to -181, while the negative χnp turns to a positive value of ~ 1000. In the higher hydration range of λ ≥ 9, the negative χp value gradually increases up to -116 whereas χnp maintains a positive constant value. This indicates that the number of holes in the water cluster network gradually decreases with increasing water content, and isolated structures of the hydrophobic region are 18


Page 19 of 39

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


formed at λ ≥ 9. Thus, the isolated hydrophobic region may be dispersed over the water domain or separated by a water layer. In contrast to the EW 844 PFSA membrane, a positive χnp value was observed for the EW 1144 PFSA membrane at λ = 3, suggesting that the higher-EW PFSA membrane, with a longer PTFE backbone per sulfonic acid, has a higher probability to form the isolated hydrophobic region than the lower-EW PFSA membrane. For higher water contents, the χp and χnp values stay almost constant at a negative value of ~ -110 and a positive value of ~ 2000, respectively. This finding also shows that the isolated hydrophobic regions are separated by water domain for the EW 1144 membrane.

Table 2. Euler characteristics of the hydrophobic and hydrophilic regions (χnp and χnp, respectively) in the medium-size models of the PFSA membranes with different water contents (λ).

EW 844

λ

EW 1144

χp

χnp

χp

χnp

3

-530

-459

-297

952

6

-224

781

-154

1806

9

-181

1059

-119

2027

12

-179

1062

-117

2063

15

-134

1116

-108

2027

20

-116

1026

-106

1993

3.2.4 Surface-to-volume ratio The volume-to-surface ratio (or surface-to-volume ratio) is a quantitative parameter with length (or inverse length) dimensions, useful to describe the geometry and size of an object. A decrease in the volume-to-surface ratio indicates that (1) the size of the object decreases or (2) 19



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

the shape of the object becomes distorted and elongated (less spherical). The ratio can thus be used to compare the morphologies of the water clusters formed in different systems. Moreover, the ratio of the interfacial area (SA) at the water-polymer boundary to the total volume (TV) of the membrane can be employed to describe the distribution of water within the hydrated membrane. A higher SA/TV ratio indicates that water tends to disperse in the membrane rather than aggregate in clusters. The volume and surface area of the aqueous domain, the total volume of the membrane, and the ratio of SA to these volumes are listed in Table 3. The WV/SA ratio was found to increase with increasing water content, indicating that the water clusters (1) have a larger size and/or (2) show higher sphericity. Table 3 also shows that the SA/TV ratio rapidly increases with increasing water content in the range of λ ≤ 9, although it reaches a maximum at around λ = 12–15 (1.31 and 1.06 nm-1 for the EW 844 and EW 1144 PFSA membranes, respectively) and slightly decreases at λ = 20. A similar trend in the variation of the SA/TV ratio as a function of λ was observed in previous experiments,51 even though the experimental values are smaller. The quantitative difference between simulations and experiments may result from the fact that a mixture of PFSAs with much larger molecular weights is used in the experiments and that the experimental SA/TV data are not direct measures, but are estimated from the Porod region of the SAXS curve. The lower SA/TA ratio of the membrane at λ = 3 can be ascribed to the lower number of water molecules. With increasing hydration level from λ = 3 to λ = 9, the SA/TV ratio increases. This is a reasonable result, since the larger number of water molecules in the membrane causes a more pronounced change in the interfacial area at the water-polymer boundary than in the total volume. At high hydration levels (λ ≥ 9), even though the variation in the SA/TV ratio of the membrane is small, the SA and TV values increase with increasing water content. As mentioned in section 3.2.3, polymer aggregates are separated by 20


Page 20 of 39

Page 21 of 39

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


the water domain at high water contents. In the case of the polymer dispersion, SA is not affected by the amount of water present, while it increases with increasing water content if the polymer aggregate is simply separated by the water layer. Therefore, at higher water contents the polymer region is not dispersed over the water domain but separated by the water layer.

Table 3. Volume (WV) and surface area (SA) of the aqueous domain, and total volume (TV) of the membranes obtained from simulations performed using medium-size systems, for different water contents (λ).

Water

Total

Surface

volume

volume

area

(nm3)

(nm3)

(nm2)

3

21

1578

6

104

9

λ

WV/SA SA/WV SA/TV (nm )

(nm )

(nm-1)(Exp.)*

762

0.028

36.27

0.48

1737

1689

0.061

16.30

0.97

231

1911

2346

0.099

10.14

1.23

12

387

2088

2692

0.144

6.96

1.29

15

546

2265

2973

0.184

5.45

1.31

－－－－－

20

828

2563

3211

0.258

3.88

1.25

－

3

23

2089

856

0.027

36.90

0.41

0.47

6

105

2244

1774

0.059

16.86

0.79

0.53

9

236

2417

2372

0.100

10.05

0.98

0.60

12

388

2594

2760

0.140

7.12

1.06

0.52

15

554

2770

2926

0.189

5.29

1.06

0.51

20 838 3069 *Experimental data from ref. 51

3149

0.266

3.76

1.03

0.38

EW 1144

-1

SA/TV

(nm)

EW 844

-1

No significant differences in the WV/SA ratio of the aqueous domain of the EW 844 and EW 1144 PFSA membranes emerge from Table 3. However, the table clearly demonstrates that for each λ the SA/TV ratio of the higher-EW PFSA membranes is smaller than that of the lower-EW ones, indicating that water molecules in the higher-EW PFSA membranes have a 21



higher tendency to form a local aggregated water cluster compared to molecules in the lower-EW membranes. This also reflects the strong aggregation behavior of the aqueous domain in the higher-EW PFSA membranes, as discussed in Section 3.2.1.

3.2.5 Radius of gyration The average Rg for medium EW 844 and EW 1144 PFSA systems is plotted as a function of water content in Fig. 9. At any water contents, Rg in the EW 1144 PFSA membrane is larger than that in the EW 844 PFSA membrane. This is simply due to a longer PTFE backbone per sulfonic group in the higher-EW PFSA. In addition, the Rg in both EW 844 and EW 1144 PFSA membranes slightly increase by ~0.2 nm from λ = 3 to 12 and show an approximate constant value in λ ≥ 12. In the range of λ = 3 to 12, the interfacial area of the water-polymer boundary is pronounced increased, leading to a slight expansion of polymer chain. However, at higher water content, polymer aggregate is already separated by the water layer. Therefore, further increase of water contents does not give rise to any change in Rg.

Radius of gyration, nm

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

2.5 2.0 1.5

EW 844 EW 1144

1.0 0

5

10

15

20

Water content (λ)

Figure 9. Radius of gyration of polymers in EW 844 and EW 1144 PFSA membranes.

22


Page 22 of 39

Page 23 of 39

3.2.6 Structure factor The structure factor, S(q), of the PFSA membranes obtained from the simulations performed with the medium-size simulation boxes are plotted in Fig. 10, and the corresponding mean cluster separations calculated as 2π/q are listed in Table 4. The table clearly shows that, with increasing water content, the ionomer peak position shifts to smaller q values and the corresponding mean cluster separation increases from 1.9 nm to 6.8 nm for the EW 844 PFSA membrane and from 2.5 nm to 4.8 nm for the EW 1144 PFSA membrane, in good agreement with the experimental data of 2.7–5 nm,10 except for the EW 844 membranes with λ = 3 and 20. The higher-EW PFSA membranes also show a larger cluster spacing than the lower-EW ones in the range of λ ≤ 15. This is simply due to the higher hydrophobicity of the higher-EW PFSA membranes.

(a) EW 844

(b) EW 1144

10000

10000

λ=3 λ=6 λ=9 λ = 12 λ = 15 λ = 20

1000 100

Intensity

Intensity

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


λ=3 λ=6 λ=9 λ = 12 λ = 15 λ = 20

1000

10

100 10

1

1 0

1

2

3 q, nm

4

5

6

0

1

-1

2

3 q, nm

4

5

6

-1

Figure 10. Structure factor of the (a) EW 844 and (b) EW 1144 PFSA membranes obtained from the MD simulations of the medium systems.

23



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

Page 24 of 39

Table 4. Cluster separation (nm) in PFSA membranes models of the medium systems. OW denotes oxygen atoms belonging to water molecules or hydronium ions.

EW 844

EW 1144

Group

λ=3

λ=6

λ=9

λ = 12

λ = 15

λ = 20

Total

1.94

3.00

3.10

3.20

4.38

6.84

OW

2.33

3.00

3.10

3.20

4.38

6.84

S

2.33

2.40

2.48

2.56

2.63

2.28

Total

2.56

2.62

3.36

3.44

4.68

4.84

OW

2.56

2.62

3.36

3.44

3.51

4.84

S

2.56

2.62

3.36

3.44

2.81

2.91

We also computed the partial structure factor for sulfur and OW atoms, where OW denotes an oxygen atom belonging to a water molecule or a hydronium ion, and calculated the mean cluster separation corresponding to the S and OW species (Table 4). In the EW 844 PFSA membrane, the separation between sulfur clusters (dS) is smaller than that between water clusters (dOW), except for λ = 3, at which dS = dOW. The difference in cluster spacing between S and OW increases at λ ≥ 15. One may argue that since water clusters are composed of the water molecules and sulfonic groups of the polymer, dS should be close to dOW. However, considering the water layer structure, the mean cluster separation of the sulfonic groups located at the interface between the polymer and the aqueous regions must be smaller than dOW, and the difference in the cluster separation would increase with increasing water content. Hence, the trends of dS and dOW clearly support the layered structure of the aqueous domains, especially at higher water contents. Furthermore, we examined the S(q) obtained for the large systems at λ = 20 in an attempt to probe the so-called “matrix knee” peak at q ~ 0.5 nm-1, which is supposed to represent the crystalline structure by experiments. Except for the ionomer peak at q ~ 1.6 nm-1, another peak at q ~ 0.9 nm-1 is observed (Fig. S2). The corresponding characteristic 24


Page 25 of 39

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


dimension of 6.8 nm is smaller than the characteristic length of 10–20 nm of the crystalline structure in the Nafion membrane.9 This suggests that the 0.9 nm-1 peak is not associated to the matrix knee. The peak would likely merge into the ionomer peak for larger models and longer simulation times.21 The MD simulations of the larger systems (~ 27 nm cubic box length) were carried out for 100 ns. Although the RDFs and density achieved equilibration, S(q) was not fully converged in the small-q range. In addition, the polymer chain in the models, including 10 sulfonic groups, is shorter than the actual polymer chain, which contains ~ 100 sulfonic groups. The characteristic peak at smaller q values, corresponding to the longer characteristic lengths, may thus have some degree of uncertainty. Therefore, a larger MD system composed of longer polymer chains, together with longer simulation times, are required to accurately probe the matrix knee peak and to provide detailed information on the crystalline structure. Because such simulations would require extremely high computational costs, identifying ways to rapidly achieve equilibration is a central issue for these systems. Chemically accurate CG simulations of the PFSA polymer could overcome the drawbacks relative to the high computational costs. A CG modeling study based on the current all-atom MD results is underway, and will be reported in a forthcoming paper.

3.2.7 Morphological model Current morphological models of the PFSA membrane, the cluster-network model5 and the parallel water-channel model9 suggested the presence of isolated spherical water clusters and parallel cylindrical water channels, respectively, in the membrane at low hydration levels. In these cases, the Euler characteristic of the hydrophilic region should be positive. However, the negative χp value obtained here (Table 2) clearly demonstrates that the above models are not suitable. The polymer ribbon and bundle models7, 8 are possible valid models for λ ≥ 6, 25



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

due to the positive χnp value found in this work, which provides evidence of isolated hydrophobic regions. Nevertheless, the minor change in the SA/TV ratio caused by the similar increase in SA and TV at higher water content (Table 3) showed that polymer aggregates were not dispersed as a colloidal suspension, as would be implied by the polymer bundle model. Based on the MD snapshot shown in Fig. 5, we can infer that, at λ = 3, the water molecules and sulfonic groups of the polymer tend to form random water channels in the membrane. In addition, the negative χp value (Table 2) denotes an aqueous domain with a highly connected network structure. The water molecules and sulfonic groups of the polymer thus appear to form aqueous domains with a channel-network structure at λ = 3. As the water content increases from λ = 3 to λ = 9, χnp also increases and turns positive (Table 2), reflecting the formation of an isolated hydrophobic region, separated by the water layer. At higher water contents, the minor change in the SA/TV ratio due the similar increase in SA and TV (Table 3) confirms that the isolated hydrophobic region is not dispersed in the water region, but separated by a water layer. Furthermore, the dS value of the membrane tends to be smaller than dOW (Table 4), especially at high water contents, clearly supporting the layered structure of the aqueous domains. The morphological behavior observed in this study is similar to that of the film-like model.10 However, it should be noted that the MD snapshot of the membrane shows an irregular extended water cluster (Fig. 5). Hence, the shape of the water layer is not flat but tortuous. Based on the simulation results mentioned above, we conclude that the water molecules and the sulfonic groups of the polymer form aqueous domains with a channel-network structure at λ = 3. The channel-network structures gradually expand and turn into tortuous layered structures upon increasing λ to 9. The water layer between the hydrophobic regions then swells and increases in thickness with further increases in water content. A typical structure extracted from the MD trajectory illustrating these 26


Page 26 of 39

Page 27 of 39

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


transformations is shown in Fig. 11.

Figure 11. Schematic illustration of the morphology of the water domains at low and high water contents. The structures are extracted from the MD trajectory for EW 844 PFSA membranes. Water and polymer domains are represented as cyan and pink solid contours, respectively. The size of the box shown in the scheme is 8 nm × 8 nm × 7 nm.

3.3. Dynamics of water molecules and hydronium ions The morphology change of the PFSA membrane with hydration has been examined in the previous sections. The variation in morphology should affect the dynamics of water molecules and hydronium ions in the PFSA membrane. Figure 12 plots the diffusion coefficients of water molecules (DW) and hydronium ions (DH) in the PFSA membranes as a function of the water content. Both DW and DH in the PFSA membranes are enhanced with increasing water content. The DW in the EW 1144 PFSA membranes show good agreement with experimental values of Nafion membrane from nuclear magnetic resonance (NMR)70, 71 and QENS72. However, the DH in the EW 1144 PFSA membranes are smaller than the experimental values of Nafion membranes.72, 73 This is due to the limitation of the simple model employed for hydronium ions; the proton transfer or hopping is not described satisfactorily. Thus, the diffusion coefficient calculated in this work reflects only the simple 27



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

diffusion as a hydronium ion and does not include the proton hopping as described by the Grotthuss mechanism. In the lower water contents of λ ≤ 9, both DW and DH slowly increase. However, in the higher water contents of λ ≥ 9, DW and DH increase almost linearly. This is a plausible consequence of morphology changes of polymer domains with increasing water content, i.e., from the channel-network structure at low water contents to the tortuous layered structure at high water contents. The increase of the free water (not bound) in the latter structure leads to greater variation in both DW and DH at higher water contents. Furthermore, both DW and DH are lower in the EW 1144 PFSA membranes than in the EW 844 PFSA membranes. A similar was also found in the previous study22 and MS-EVB study38. It has been suggested that proton swapping between sulfonic groups is the primary transport mechanism and proton diffusion coefficient is highly correlated with the hydrophobic/hydrophilic surface area when Grotthuss proton hopping is included.38,

39

However, the difference in the surface area

between the EW 844 and 1144 PFSA membranes is small in this study (Table 3). Since the higher-EW PFSA tends to form membranes with local water clusters, the localized water aggregates with a weaker connectivity results in the lower diffusivities of water and hydronium ion in the higher-EW PFSA membranes.22

28


Page 28 of 39

Page 29 of 39

0.9

(a)

EW 844 EW 1144 Nafion-NMR Nafion-QENS

0.6

-5

-5

1.0

(b)

2

2

EW 844 EW 1144 Nafion-NMR Nafion-QENS

DH, 10 cm /s

1.5 DW, 10 cm /s

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


0.5 0.0

0.3 0.0

0

6

12

18

24

0

Water content (λ)

6

12

18

24

Water content (λ)

Figure 12. Diffusion coefficients of (a) water molecules and (b) hydronium ions in hydrated PFSA membranes obtained from the MD simulations of the medium systems. The NMR experimental data were obtained from refs. 70, 71, 73 and the QENS experimental data were obtained from ref. 72.

4. CONCLUSIONS We have carried out a series of MD simulations to investigate the morphology of hydrated PFSA membranes. The Euler characteristics and surface-to-volume ratios obtained from the simulations showed that the aqueous domains form a connected network structure at λ = 3, which transforms into a layered structure separating the hydrophobic regions upon increasing the water content up to λ = 9. The analysis of the structure factor revealed a smaller cluster spacing for sulfonic groups than water molecules, providing evidence in support of the layered structure of the aqueous domains. The extended irregular water clusters observed in the MD snapshots of the membrane suggest the formation of a tortuous water layer structure. Therefore, we concluded that the morphology of the hydrated PFSA membrane changes with increasing hydration level, from a channel-network structure at λ = 3 to a tortuous layered structure at λ = 9, and that the thickness of the tortuous water layer increases at higher water contents. Furthermore, the comparison between the EW 844 and EW 1144 PFSA membranes 29



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

revealed no significant differences in the way their morphologies change with increasing water content. However, the formation of a more heterogeneous water cluster in the higherEW PFSA membranes clearly highlighted the stronger aggregation behavior of the aqueous domains of high-EW PFSA membranes.

5. ACKNOWLEDGMENTS The authors would like to acknowledge Drs. Jun Irisawa and Atsushi Tanaka of the Research Center of Asahi Glass Co. for useful discussions. This research was supported by the Impulsing Paradigm Change through Disruptive Technologies (ImPACT) program. This work was also partly supported by MEXT as a social and scientific priority issue (“Development of New Fundamental Technologies for High-efficiency Energy Creation, Conversion/Storage, and Use”) to be tackled using the post-K computer. The calculations were performed primarily on the Nagoya University supercomputer, and in part on the K-computer hosted at the RIKEN Advanced Institute for Computational Science (Proposal No. hp150249 and hp150275).

6. SUPPORTING INFORMATION MD snapshots and isosurface representation of water/sulfonic groups domains of the EW 1144 PFSA membranes, diffusion coefficients of water molecules and hydronium ions for small and medium PFSA membranes, and structure factors of the large models of the PFSA membranes with λ = 20.

7. REFERENCES (1) Eikerling, M.; Kulikovsky, A., Polymer Electrolyte Fuel Cells: Physical Principles of 30


Page 30 of 39

Page 31 of 39

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


Materials and Operation. CRC Press: 2014. (2) Mauritz, K. A.; Moore, R. B., State of Understanding of Nafion. Chem. Rev. 2004, 104, 4535-4586. (3) Grava, W.; Okada, T.; Kawano, Y., Thermal Characterization of Flemion® Membranes Substituted by Alkali Metal Cations. J. Therm. Anal. Calorim. 2007, 89, 163-168. (4) Hsu, W. Y.; Gierke, T. D., Elastic Theory for Ionic Clustering in Perfluorinated Ionomers. Macromolecules 1982, 15, 101-105. (5) Hsu, W. Y.; Gierke, T. D., Ion Transport and Clustering in Nafion Perfluorinated Membranes. J. Membr. Sci. 1983, 13, 307-326. (6) Kreuer, K. D., On the Development of Proton Conducting Polymer Membranes for Hydrogen and Methanol Fuel Cells. J. Membr. Sci. 2001, 185, 29-39. (7) Rubatat, L.; Rollet, A. L.; Gebel, G.; Diat, O., Evidence of Elongated Polymeric Aggregates in Nafion. Macromolecules 2002, 35, 4050-4055. (8) Rubatat, L.; Gebel, G.; Diat, O., Fibrillar Structure of Nafion: Matching Fourier and Real Space Studies of Corresponding Films and Solutions. Macromolecules 2004, 37, 7772-7783. (9) Schmidt-Rohr, K.; Chen, Q., Parallel Cylindrical Water Nanochannels in Nafion Fuel-Cell Membranes. Nat. Mater. 2008, 7, 75-83. (10) Kreuer, K.-D.; Portale, G., A Critical Revision of the Nano-Morphology of Proton Conducting Ionomers and Polyelectrolytes for Fuel Cell Applications. Adv. Funct. Mater.

2013, 23, 5390-5397. (11) Paddison, S., Proton Conduction Mechanisms at Low Degrees of Hydration in Sulfonic Acid-Based Polymer Electrolyte Membranes. Ann. Rev. Mater. Res. 2003, 33, 289-319. (12) Kreuer, K.-D.; Paddison, S. J.; Spohr, E.; Schuster, M., Transport in Proton Conductors for Fuel-Cell Applications: Simulations, Elementary Reactions, and Phenomenology. Chem. 31



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

Rev. 2004, 104, 4637-4678. (13) Elliott, J. A.; Paddison, S. J., Modelling of Morphology and Proton Transport in PFSA Membranes. Phys. Chem. Chem. Phys. 2007, 9, 2602-2618. (14) Paddison, S. J.; Elliott, J. A., Molecular Modeling of the Short-Side-Chain Perfluorosulfonic Acid Membrane. J. Phys. Chem. A 2005, 109, 7583-7593. (15) Paddison, S. J.; Elliott, J. A., On the Consequences of Side Chain Flexibility and Backbone Conformation on Hydration and Proton Dissociation in Perfluorosulfonic Acid Membranes. Phys. Chem. Chem. Phys. 2006, 8, 2193-2203. (16) Jang, S. S.; Molinero, V.; Çaǧın, T.; Goddard, W. A., Nanophase-Segregation and Transport in Nafion 117 from Molecular Dynamics Simulations: Effect of Monomeric Sequence. J. Phys. Chem. B 2004, 108, 3149-3157. (17) Urata, S.; Irisawa, J.; Takada, A.; Shinoda, W.; Tsuzuki, S.; Mikami, M., Molecular Dynamics Simulation of Swollen Membrane of Perfluorinated Ionomer. J. Phys. Chem. B

2005, 109, 4269-4278. (18) Devanathan, R.; Venkatnathan, A.; Dupuis, M., Atomistic Simulation of Nafion Membrane: I. Effect of Hydration on Membrane Nanostructure. J. Phys. Chem. B 2007, 111, 8069-8079. (19) Devanathan, R.; Venkatnathan, A.; Dupuis, M., Atomistic Simulation of Nafion Membrane. 2. Dynamics of Water Molecules and Hydronium Ions. J. Phys. Chem. B 2007, 111, 13006-13013. (20) Brandell, D.; Karo, J.; Liivat, A.; Thomas, J., Molecular Dynamics Studies of the Nafion®, Dow® and Aciplex® Fuel-Cell Polymer Membrane Systems. J. Mol. Model. 2007, 13, 1039-1046. (21) Knox, C. K.; Voth, G. A., Probing Selected Morphological Models of Hydrated Nafion Using Large-Scale Molecular Dynamics Simulations. J. Phys. Chem. B 2010, 114, 32


Page 32 of 39

Page 33 of 39

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


3205-3218. (22) Liu, J.; Suraweera, N.; Keffer, D. J.; Cui, S.; Paddison, S. J., On the Relationship between Polymer Electrolyte Structure and Hydrated Morphology of Perfluorosulfonic Acid Membranes. J. Phys. Chem. C 2010, 114, 11279-11292. (23) Komarov, P. V.; Khalatur, P. G.; Khokhlov, A. R., Large-Scale Atomistic and Quantum-Mechanical Simulations of a Nafion Membrane: Morphology, Proton Solvation and Charge Transport. Beilstein J. Nanotechnol. 2013, 4, 567-587. (24) Mabuchi, T.; Tokumasu, T., Effect of Bound State of Water on Hydronium Ion Mobility in Hydrated Nafion Using Molecular Dynamics Simulations. J. Chem. Phys. 2014, 141, 104904. (25) Ban, S.; Huang, C.; Yuan, X.-Z.; Wang, H., Molecular Simulation of Gas Adsorption, Diffusion, and Permeation in Hydrated Nafion Membranes. J. Phys. Chem. B 2011, 115, 11352-11358. (26) Daly, K. B.; Benziger, J. B.; Debenedetti, P. G.; Panagiotopoulos, A. Z., Molecular Dynamics Simulations of Water Sorption in a Perfluorosulfonic Acid Membrane. J. Phys. Chem. B 2013, 117, 12649-12660. (27) Daly, K. B.; Benziger, J. B.; Panagiotopoulos, A. Z.; Debenedetti, P. G., Molecular Dynamics Simulations of Water Permeation across Nafion Membrane Interfaces. J. Phys. Chem. B 2014, 118, 8798-8807. (28) Abu-Hakmeh, K.; Sood, P.; Jae Chun, B.; Choi, J.; Jang, S., Effect of Uniaxial Deformation on Structure and Transport in Hydrated Nafion 117: Molecular Dynamics Simulation Study. Mater. Perform. Charact. 2015, 4, 131-147. (29) Xie, J.; Ban, S.; Liu, B.; Zhou, H., A Molecular Simulation Study of Chemical Degradation and Mechanical Deformation of Hydrated Nafion Membranes. Appl. Surf. Sci.

2016, 362, 441-447. 33



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

(30) Seeliger, D.; Hartnig, C.; Spohr, E., Aqueous Pore Structure and Proton Dynamics in Solvated Nafion Membranes. Electrochim. Acta 2005, 50, 4234-4240. (31) Dokmaisrijan, S.; Spohr, E., MD Simulations of Proton Transport Along a Model Nafion Surface Decorated with Sulfonate Groups. J. Mol. Liq. 2006, 129, 92-100. (32) Kawakami, T.; Shigemoto, I., Molecular Dynamics Studies on the Structures of Polymer Electrolyte Membranes and Diffusion Mechanism of Protons and Small Molecules. Polymer

2014, 55, 6309-6319. (33) Petersen, M. K.; Voth, G. A., Characterization of the Solvation and Transport of the Hydrated Proton in the Perfluorosulfonic Acid Membrane Nafion. J. Phys. Chem. C 2006, 110, 18594-18600. (34) Petersen, M. K.; Hatt, A. J.; Voth, G. A., Orientational Dynamics of Water in the Nafion Polymer Electrolyte Membrane and Its Relationship to Proton Transport. J. Phys. Chem. B

2008, 112, 7754-7761. (35) Feng, S.; Voth, G. A., Proton Solvation and Transport in Hydrated Nafion. J. Phys. Chem. B 2011, 115, 5903-5912. (36) Feng, S.; Savage, J.; Voth, G. A., Effects of Polymer Morphology on Proton Solvation and Transport in Proton-Exchange Membranes. J. Phys. Chem. C 2012, 116, 19104-19116. (37) Tse, Y.-L. S.; Herring, A. M.; Kim, K.; Voth, G. A., Molecular Dynamics Simulations of Proton Transport in 3M and Nafion Perfluorosulfonic Acid Membranes. J. Phys. Chem. C

2013, 117, 8079-8091. (38) Savage, J.; Tse, Y.-L. S.; Voth, G. A., Proton Transport Mechanism of Perfluorosulfonic Acid Membranes. J. Phys. Chem. C 2014, 118, 17436-17445. (39) Savage, J.; Voth, G. A., Proton Solvation and Transport in Realistic Proton Exchange Membrane Morphologies. J. Phys. Chem. C 2016, 120, 3176-3186. (40) Yamamoto, S.; Hyodo, S.-a., A Computer Simulation Study of the Mesoscopic Structure 34


Page 34 of 39

Page 35 of 39

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


of the Polyelectrolyte Membrane Nafion. Polym. J. 2003, 35, 519-527. (41) Malek, K.; Eikerling, M.; Wang, Q.; Liu, Z.; Otsuka, S.; Akizuki, K.; Abe, M., Nanophase segregation and water dynamics in hydrated Nafion: Molecular modeling and experimental validation. J. Chem. Phys. 2008, 129, 204702. (42) Wu, D.; Paddison, S. J.; Elliott, J. A., A Comparative Study of the Hydrated Morphologies of Perfluorosulfonic Acid Fuel Cell Membranes with Mesoscopic Simulations. Energy Environ. Sci. 2008, 1, 284-293. (43) Jorn, R.; Voth, G. A., Mesoscale Simulation of Proton Transport in Proton Exchange Membranes. J. Phys. Chem. C 2012, 116, 10476-10489. (44) Morohoshi, K.; Hayashi, T., Modeling and Simulation for Fuel Cell Polymer Electrolyte Membrane. Polymers 2013, 5, 56. (45) Vishnyakov, A.; Neimark, A. V., Self-Assembly in Nafion Membranes upon Hydration: Water Mobility and Adsorption Isotherms. J. Phys. Chem. B 2014, 118, 11353-11364. (46) Liu, S.; Savage, J.; Voth, G. A., Mesoscale Study of Proton Transport in Proton Exchange Membranes: Role of Morphology. J. Phys. Chem. C 2015, 119, 1753-1762. (47) Ghelichi, M.; Malek, K.; Eikerling, M. H., Ionomer Self-Assembly in Dilute Solution Studied by Coarse-Grained Molecular Dynamics. Macromolecules 2016, 49, 1479-1489. (48) Michielsen, K.; De Raedt, H., Integral-Geometry Morphological Image Analysis. Phys. Rep. 2001, 347, 461-538. (49) Sevink, G. J. A.; Zvelindovsky, A. V., Kinetic Pathways of Sheared Block Copolymer Systems Derived from Minkowski Functionals. J. Chem. Phys. 2004, 121, 3864-3873. (50) Rehse, S.; Mecke, K.; Magerle, R., Characterization of the Dynamics of Block Copolymer Microdomains with Local Morphological Measures. Phys. Rev. E 2008, 77, 051805. (51) Kong, X.; Schmidt-Rohr, K., Water–Polymer Interfacial Area in Nafion: Comparison 35



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

with Structural Models. Polymer 2011, 52, 1971-1974. (52) Jalani, N. H.; Datta, R., The Effect of Equivalent Weight, Temperature, Cationic Forms, Sorbates, and Nanoinorganic Additives on the Sorption Behavior of Nafion®. J. Membr. Sci.

2005, 264, 167-175. (53) Levitt, M.; Hirshberg, M.; Sharon, R.; Laidig, K. E.; Daggett, V., Calibration and Testing of a Water Model for Simulation of the Molecular Dynamics of Proteins and Nucleic Acids in Solution. J. Phys. Chem. B 1997, 101, 5051-5061. (54) Martinez, L.; Andrade, R.; Birgin, E. G.; Martinez, J. M., PACKMOL: a Package for Building Initial Configurations for Molecular Dynamics Simulations. J. Comput. Chem. 2009, 30, 2157-64. (55) Pronk, S.; Páll, S.; Schulz, R.; Larsson, P.; Bjelkmar, P.; Apostolov, R.; Shirts, M. R.; Smith, J. C.; Kasson, P. M.; van der Spoel, D.; Hess, B.; Lindahl, E., GROMACS 4.5: A High-Throughput and Highly Parallel Open Source Molecular Simulation Toolkit. Bioinformatics 2013, 29, 845-854. (56) Abraham, M. J.; Murtola, T.; Schulz, R.; Páll, S.; Smith, J. C.; Hess, B.; Lindahl, E., GROMACS: High Performance Molecular Simulations Through Multi-Level Parallelism from Laptops to Supercomputers. SoftwareX 2015, 1–2, 19-25. (57) Martyna, G. J.; Klein, M. L.; Tuckerman, M., Nose-Hoover Chains: the Canonical Ensemble Via Continuous Dynamics J. Chem. Phys. 1992, 97, 2635-2643. (58) Parrinello, M.; Rahman, A., Polymorphic Transitions in Single Crystals: A New Molecular Dynamics Method. J. Appl. Phys. 1981, 52, 7182-7190. (59) Martyna, G. J.; Tobias, D. J.; Klein, M. L., Constant Pressure Molecular Dynamics Algorithms. J. Chem. Phys. 1994, 101, 4177-4189. (60) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G., A Smooth Particle Mesh Ewald Method. J. Chem. Phys. 1995, 103, 8577-8593. 36


Page 36 of 39

Page 37 of 39

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


(61) Lourenço, T. C.; Coelho, M. F. C.; Ramalho, T. C.; van der Spoel, D.; Costa, L. T., Insights

on

the

Solubility

of

CO2

in

1-Ethyl-3-methylimidazolium

Bis(trifluoromethylsulfonyl)imide from the Microscopic Point of View. Environ. Sci. Technol.

2013, 47, 7421-7429. (62) Eisenhaber, F.; Lijnzaad, P.; Argos, P.; Sander, C.; Scharf, M., The Double Cubic Lattice Method: Efficient Approaches to Numerical Integration of Surface Area and Volume and to Dot Surface Contouring of Molecular Assemblies. J. Comput. Chem. 1995, 16, 273-284. (63) Cromer, D. T.; Mann, J. B., X-ray Scattering Factors Computed from Numerical Hartree-Fock Wave Functions. Acta Crystall. A 1968, 24, 321-324. (64) Weber, A. Z.; Newman, J., Transport in Polymer-Electrolyte Membranes: II. Mathematical Model. J. Electrochem. Soc. 2004, 151, A311-A325. (65) Morris, D. R.; Sun, X., Water-Sorption and Transport Properties of Nafion 117 H. J. Appl. Polym. Sci. 1993, 50, 1445-1452. (66) Humphrey, W.; Dalke, A.; Schulten, K., VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33-38. (67) Krone, M.; Stone, J. E.; Ertl, T.; Schulten, K., Fast Visualization of Gaussian Density Surfaces for Molecular Dynamics and Particle System Trajectories. EuroVis-Short Papers

2012, 1, 67-71. (68) Wu, D.; Paddison, S. J.; Elliott, J. A.; Hamrock, S. J., Mesoscale Modeling of Hydrated Morphologies of 3M Perfluorosulfonic Acid-Based Fuel Cell Electrolytes. Langmuir 2010, 26, 14308-14315. (69) Cui, S.; Liu, J.; Selvan, M. E.; Keffer, D. J.; Edwards, B. J.; Steele, W. V., A Molecular Dynamics Study of a Nafion Polyelectrolyte Membrane and the Aqueous Phase Structure for Proton Transport. J. Phys. Chem. B 2007, 111, 2208-2218. (70) Zawodzinski, T. A.; Neeman, M.; Sillerud, L. O.; Gottesfeld, S., Determination of Water 37



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

Diffusion Coefficients in Perfluorosulfonate Ionomeric Membranes. J. Phys. Chem. 1991, 95, 6040-6044. (71) Ohkubo, T.; Kidena, K.; Takimoto, N.; Ohira, A., Molecular Dynamics Simulations of Nafion and Sulfonated Poly Ether Sulfone Membranes II. Dynamic Properties of Water and Hydronium. J. Mol. Model. 2012, 18, 533-540. (72) Perrin, J.-C.; Lyonnard, S.; Volino, F., Quasielastic Neutron Scattering Study of Water Dynamics in Hydrated Nafion Membranes. J. Phys. Chem. C 2007, 111, 3393-3404. (73) Ochi, S.; Kamishima, O.; Mizusaki, J.; Kawamura, J., Investigation of Proton Diffusion in Nafion®117 Membrane by Electrical Conductivity and NMR. Solid State Ionics 2009, 180, 580-584.

38


Page 38 of 39

Page 39 of 39

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


TOC Graphic

for Table of Contents use only

Title : Molecular Dynamics Study of the Morphology of Hydrated Perfluorosulfonic Acid Polymer Membranes ┼

┿

Authors: An-Tsung Kuo, Wataru Shinoda┼, and Susumu Okazaki┿

39


Molecular Dynamics Study of the Morphology of Hydrated

Recommend Documents