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Assembled Structures of Perfluorosulfonic Acid Ionomers Investigated by Anisotropic Modelling and Simulations Wenduo Chen, Fengchao Cui, Lunyang Liu, and Yunqi Li J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b06412 • Publication Date (Web): 25 Sep 2017 Downloaded from http://pubs.acs.org on September 27, 2017

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The Journal of Physical Chemistry

Assembled Structures of Perfluorosulfonic Acid Ionomers Investigated by Anisotropic Modelling and Simulations Wenduo Chen1, Fengchao Cui1, Lunyang Liu1,2, Yunqi Li*,1 1 Key Laboratory of Synthetic Rubber, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 5625 Renmin Street, Changchun, PR China, 130022 2 University of Chinese Academy of Sciences, Beijing, PR China, 100049

1

ACS Paragon Plus Environment


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Abstract: Nafion®, a classic of perfluorosulfonic acid ionomers, has broad applications in proton conduction, attributed from the unique structures. However, a satisfactory structure model from theoretical calculation and simulation that can match with the well-known experimental observations is still absent. We performed GPU-accelerated molecular dynamics simulations to investigate the assembled structures of Nafion at different water contents based on an anisotropic coarse-grained model equipped with Gay-Berne potential. Accurate parameters for the coarse-grained model are collected by matching energy profiles based on density functional theory calculations. The results show that the hydrophilic phase in Nafion assemblies undergoes a crossover from isolated spherical clusters to interconnected cluster/channel networks with the increase of water content. We found the crystalline domains in polymer matrix and they are suppressed at elevated water content. These microphase separated structures achieve quantitative agreement with existing experimental observations, including morphologies from electron microscopy and intensity profiles from scattering experiments. This work suggests that accurate consideration of the anisotropy is a key to reveal the formation of unique assembled structures of perfluorosulfonic acid ionomers at different water contents.

2


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I. INTRODUCTION Nafion®, the first commercial perfluorosulfonic acid (PFSA) ionomer, has broad applications in proton exchange, catalysis, separation and electrochemical sensing, benefiting from its high conductivity, thermal, mechanical and chemical stabilities, which are attributed from the unique structure swollen by water1-3. Nafion has a relatively straight backbone composed of helical poly(tetrafluoroethylene) (PTFE) units and flexible pendant side chains terminated with PFSA groups, as shown in Fig. 1. The phase-separated morphologies become obvious during the swelling process, under the balance of the entropic contribution from hydrophilic groups, the electrostatic interactions between hydrated protons and sulfonate groups, as well as the deformation energy from hydrophobic polymer matrix2. A unified model that can provide a unanimous description for the self-assembly structure of Nafion at different water contents is still in debate4-6. The major disputes are over the shape and connectivity of ionic clusters, the orientation and distribution of PTFE backbones (polymer matrix), and the distribution of hydrated protons in confined domains. In order to propose a unified model, a possible solution is simulating Nafion structures based on an accurate modeling and validating the structures according to solid experimental observations. Solid experimental observations associating with the structure of Nafion assemblies have five characteristics, including i) the morphologies of microphase separation captured by electron microscope (EM)6-8, ii) the matrix knee of 10-25nm9-10, iii) the ionic/ionomer peak of 2-6nm 4, 11-13 revealed by small angle neutron (SANS) and X-ray scattering (SAXS), iv) the persistence length of 3~5nm for PTFE backbone obtained by nuclear magnetic resonance (NMR) spectra14-15, as well as v) the presence of crystallite in hydrophobic matrix with the size of 0.24-0.41 nm and the crystalline degree of 7%-20% by wide angle X-ray scattering (WAXS)16 or differential scanning calorimetry13. Mainly based on experimental observations, especially the intensity profiles from scattering experiments, a number of structure models have been proposed, such as the cluster-network model17-18, the bicontinuous network model19, the parallel cylindrical channel model4, the elongated polymer aggregates with water pools10, and a locally flat morphology20. 3



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These models are mainly under the frame introduced by Eisenberg21, in which the size, shape, orientation, connectivity and distribution of ionic and hydrophobic domains are adaptive to minimize the total free energy. Hitherto, these models are limited to provide clear and unique understandings at the molecular level, because they are not definitive and one scattering intensity profile may correspond to variant 3D structures2. A model is more convincing when it not only provides a good match with experimental observations, but also the dependence on some factors, which significantly affect the structure of Nafion assemblies. Water content is the most important factor. The distribution of water satisfies the Brunauer–Emmett–Teller (BET) equation analogue to small molecules dispersed in porous material at the macro-scale22 , and in the forms of hydronium ions, Zundel cations, Eigen cations and free water at the micro-scale23. Along the elevation of water contents, water experiences an adsorbed state where water molecules are bound to sulfonic group, a cluster state (weak bound) where water and sulfonic groups form hydrophilic domains, and a free state in the bulk-like domains2. Allen et al. found two typical structures of hydrophilic phase domains by using analytical TEM and cryogenic TEM tomography: the spherical clusters for the dry membranes, and the channel-network model at the maximum water contents6. However, the evolution of the structures from the dry state to the maximum water content hardly can be soundly interpreted by current known models. The aforementioned models with high symmetry provide physical simplicity, but the detailed characteristics need the validations from computer simulations. Typical ordered structures possibly appearing in Nafion assemblies have been reported from large-scale simulations19,

24-27

. A

bicontinuous network structure of water cluster was observed through a set of dissipative particle dynamics (DPD) simulations coupled with Flory-Huggins interaction parameters19,

28-31

. A

sponge-like morphology with roughly spherical clusters was presented by molecular dynamics (MD) simulations, and the sizes of hydrophilic domains increase from 1 to 3nm27 , smaller than the typical 2-6nm ionomer cluster in Nafion assemblies4,

32

. Kuo et al reported the ordered

structures change from a channel-network to a tortuous layer at elevated water content using MD simulations25. Interestingly, Knox and Voth found that the ionomer peak can not be the only characteristic to explain scattering profiles because it appears insensitive of six different 4


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simulation structures26. These simulation efforts largely facilitate our understanding in the structural evolution for Nafion assemblies at different water contents, while an accurate model that can be quantitatively consistent with the five experimental characteristics is still absent. Particularly, the presence of crystalline regions in hydrophobic matrix, which allow the high thermal, mechanical and chemical stability for Nafion products, has been rarely illustrated from simulations. The major reason is that, for previous simulation works, molecules were modeled by spherical particles based on CG models and the anisotropic feature is disregarded. Consequently, a clear and reliable description for the structures of Nafion assemble needs both accurately anisotropic modeling and robust simulation structure validation.

II. COARSE-GRAINED MODELLING AND SIMULATION METHOD We construct an anisotropic coarse-grained model equipped with Gay-Berne (GB)

33-34

and

Lennard-Jones (LJ) potentials to describe the Nafion and water molecules, as shown in Fig. S1 of Supporting Information S1. Each monomer of Nafion is represented by four CG particles. The PTFE backbone segments of Nafion are described by GB ellipsoidal potential, which can precisely model the rigidity and anisotropic orientation of the backbone. The rest flexible side chain, sulfonic acid group, and water molecules are modeled by spherical particles. As illustrated in Fig. 1, the backbone has two uniaxial ellipsoidal particles (A and A’), and each represents chemical unit of C8F16 in reference to Nafion117. Two spherical particles C (-OCF2C(CF3)FOCF2- group) and D (-CF2SO3H group) are used to model the pendant side-chain. A CG particle W standing for a cluster of 4 water molecules is also explicitly considered. The sizes, location and interaction parameters of these CG particles are determined based on quantum chemical calculations according to the optimized atomic structures. The optimized structures of 3 sequential monomers and 4 water molecules are computed using a density functional theory (DFT) with the B3LYP/6-31G(d,p) basis set implanted in Gaussian0935. In the optimized structure, side chains are uniformly distributed along relatively straight helical backbone (Fig. 1(III)), which is consistent with NMR observations4. A number of protons (H+) are randomly integrated into particle W to keep charge neutrality with fully disassociated sulfonate groups (D).

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Fig. 1. Illustration of the accurately anisotropic modeling for Nafion117, (I) the chemical structure, (II) the optimized atomic structure, the corresponding CG particles for a monomer, and a cluster of 4 water molecules, (III) a view of the optimized structure of 3 sequential monomers along the backbone.

Based on the CG model, the energy function to guide the GPU-accelerated MD simulation is written as

U total =U LJ + U GB + U GB/LJ + U bond + U angle + U q Here, ULJ, UGB and UGB/LJ are non-bond interactions. The harmonic bond potential Ubond and Uangle are used to model the connectivity of neighboring particles and the rigidity of polymer chains. The electrostatic interactions Uq between charged particles are described by Coulombic interactions36. GPU-accelerated MD simulations37 are performed to investigate the structures of Nafion assemblies at different water contents, and more simulation details can be found in Supporting Information S1 and S2.

III. RESULTS AND DISCUSSION Accurately Modelling. To improve the accuracy of CG model and keep the potency for CG to atomistic relocation, we introduce anisotropic CG model with exact geometry and potential calculated from optimized atomistic structures. The atomic energy profiles for the interactions 6


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between any two particles are calculated using DFT with M062X/6-31++G(d,p) basis set, in which the energy is averaged over 729 (ULJ/LJ), 288 (UGB/GB) or 324 (UGB/LJ) configurations from the Boltzmann distribution at various separation distances and orientation angles, as shown in cartoon of Supporting Information. Such accurately modelling strategy has been validated by the interaction of two CH4 molecules (see Fig. S3 of Supporting Information S3). The GB potential, simplified into LJ potential, well matches the energy profile from quantum chemical calculations with Pearson correlation coefficient R2=0.998, as shown in Supporting Information S3. Accordingly, the non-bond energy profiles for different pairs of particles are shown in Fig. 2. Interacted pairs at the side, end and cross locations have different energy profiles where the minimum indicates the equilibrium separation distance, e.g. for A-A pair, there are four orientations including side-by-side, cross, side-to-end and end-to-end, as shown in Fig. S1 of Supporting Information S1. For all interacted pairs, the GB curves show satisfactory agreement with the profiles by quantum chemical calculations. The final GB parameters for all CG particles, the correlation coefficients (R2) and the root-mean-square error (RMSE) are listed in Table 1. The CG parameters of bond and angle potentials are shown in Supporting Information S4. So far, this anisotropic CG model provides the highest conservation of atomistic details, which is expected to offer new insight for the structure of Nafion assembly in CG-based simulation.

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Fig. 2. Energy profiles from DFT calculations (dash lines) for the interactions between (I) A-A, (II) A-C, (III) A-D, (IV) A-W, (V) W-W, (VI) C-C, (VII) D-D, (VIII) C-D, (IX) C-W, (X) D-W particles. The solid lines represent coarse-grained Gay-Berne or Lenard-Jones potentials.

Table.1 Interaction parameters for CG particles, Pearson correlation coefficients R2 and the root-mean-square error RMSE from the best-fitting of GB potential to the atomic energy profiles by quantum chemical calculations. Gay-Berne σ0 ε0 particles (Å) (kCal/mol)

κ

κ'

ν

µ

R2

RMSE

(kCal/mol)

8


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A-A’

5.20

0.80

2.69 4.55 0.70 1.08 0.82

0.20

A-C

4.75

0.90

2.43 1.89 1.00 0.05 0.94

0.09

A-D

4.50

0.78

2.58 1.60 1.00 1.00 0.96

0.11

A-W

5.90

1.00

2.20 2.50 1.00 0.20 0.94

0.15

C-C

4.60

1.25

-

-

-

-

0.93

0.17

C-D

4.55

1.12

-

-

-

-

0.94

0.14

C-W

4.68

2.52

-

-

-

-

0.89

0.26

D-D

4.20

4.25

-

-

-

-

0.92

0.43

D-W

4.24

3.86

-

-

-

-

0.87

1.06

W-W

3.97

6.60

-

-

-

-

0.95

0.75

Structures and Morphologies of Nafion Assemblies at Different Water Contents. The simulation configurations of Nafion assemblies at different water contents λ are shown in Fig. 3a. The coexistence of hydrophobic and hydrophilic domains becomes prominent with water content elevating. For Nafion assemblies at low water content (λ = 0 and 4), the shape of hydrophilic domains are nearly spherical and isolated with only weak connections. When the water content up to λ = 8, the hydrophilic domains is percolated, and the structure is consistent with the cluster-network model38. At high water content λ = 20, hydrophilic domains form cluster/channel network structure, as shown in Fig. 3 and Fig. S4 of Supporting Information S5. The water domains seem more like elongated and interconnected clusters, which is confirmed similar to the stable 3D structure image in hydrated Nafion assemblies using cryo-TEM tomography by Allen et al6. Further, sulfonic groups together with side chains locate in the interface between PTFE backbone and water clusters to minimize the free energy, analogue to typical emulsions. Unsurprisingly, protons also form an enriched layer around the sulfonic acid groups, and a small portion of protons are dispersed in bulk water (see Fig. S5 in Supporting Information S5). 9



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Fig. 3. (a) Simulation configurations for Nafion assemblies at different water contents. PTFE backbones A and A’ are presented in purple, side chain C in green, sulfonic acid groups D in yellow and water clusters W in blue. (b) The distribution of hydrophilic domains including water and sulfonic groups are presented in grey. The largest domain is highlighted in cyan. (c) Two-dimensional projections of the distribution of hydrophilic domains (dark region), the corresponding scattering patterns in reciprocal space, and the size of the images is 84nm×84nm (9 periodic images).

To highlight the evolution of hydrophilic domains, their 3D distribution, the largest domains, the corresponding 2D projection of these domains and the scattering patterns are presented in Fig. 3b and 3c, respectively. Hydrophilic domains, composed of sulfonic group D, water clusters W and protons P, are isolated and nearly spherical at dry state, and the largest domain becomes percolated at around λ = 8. It agrees with the reported by Chen et al., where percolation appears when λ is up to 7.3 and the water volume fraction reaches about 20%4. At high water content (λ = 20 and volume fraction about 41%5), a predominant majority of water and sulfonic groups form elongated and penetrated clusters or channels. Further projection of hydrophilic domains onto 2D morphology is highly consistent with the images captured by TEM/SEM6, 8.

10


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Distribution of Phase Domains at Different Water Contents. The microstructures of hydrophilic and hydrophobic domains are characterized by the radial distribution function (RDF) g(r) (see Supporting Information S5 for definition). The value of g(r) = 1 indicates random distribution, larger value for enrichment, and less than 1 for the depletion of particles at given separation range. The RDFs of the water particles for different water contents are shown in Fig. 4a. Cluster radius is determined at the distance where radial distribution function g(r) passes the value 1 for the first time30-31. The average separation distance of two neighboring clusters is derived from the position of the 2nd maximum (the dashed line)30. The average radii of water clusters can be obtained, which is 1.8~4.0 nm, consistent with the results from experiments39. The average radii and separation distance of water clusters, as well as the intensity of these peaks increase with λ. The separation distance of peaks is the average sizes of CG particles in insert of Fig. 4a. Besides the increased correlation of hydrophilic domains with Nafion, the enrichment of protons in the hydration layer also can be seen from g(r) for the distribution of side chains C, sulfonic groups D, water clusters W and protons P, as shown in Fig. S6 of Supporting Information S5. The fraction of disassociated protons from hydrated layer to bulk water linearly increases with λ beyond the percolation of hydrophilic domain, and around 45% of all protons are distributed in bulk water at λ = 20 (see Fig. S7 of Supporting Information S5).

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Fig. 4. Properties calculated from simulation configurations at different water contents λ. (a) The radial distribution functions g(r) of water, in which the dashed arrow show the average separation distance of two neighboring clusters. (b) The average radii and separation distance of water clusters, ■ are cluster distances in our work and ● from Dorenbos30; □ is Bragg spacing in our work, △ is for preboiled Nafion and ◊ for as-received Nafion at 25oC from Kusoglu et al.12, ☆ from Mochizuki et al.8 at 80oC, and ▽ from Dorenbos30, ○ is cluster diameter from Gierke et al.40 for comparison; ✳ is water cluster radii and × from Dorenbos. (c) The distribution of hydrophilic domain sizes. (d) Scattering intensity profiles for Nafion assemblies.

The average radii, separation distances of water clusters, and Bragg maxima (2π/qmax with qmax is the location of ionomer peak) of hydrophilic domainsas a function of water content λ are shown in Fig. 4b. The former is a measurement of the size for hydrophilic domains and the latter shows the size of hydrophobic matrix. The average radii and separation distances are consistent with the simulation results from Dorenbos30. The Bragg maxima of hydrophilic domains are consistent with the reported measurements by Kusoglu et al.12 for the preboiled Nafion at λ ≥ 10.0, 12


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and Gierke et al.40 at 12.0 ≥ λ ≥ 3.0. Linear relationship appears, where d (λ ) = d 0 + sd / λ λ with the slope sd/λ is from 0.125 to 0.135, and d0 is about 2.7 nm for Nafion at the dry state according to a recent review2. The slope sd/λ is 0.20 and d0 is about 2.08 nm in this work. The larger d0 from experiments is attributed to the residual water for Nafion at dry state. The average separation distance of hydrophilic clusters is 5.4 nm for λ = 7.3, slightly larger than the characteristic size 5.0 nm at water volume fraction 20 Vol% (λ = 7.3)18, and the slope sd/λ is 0.25 with d0 = 2.2 nm for the average separation distance of hydrophilic domains. Further, the distribution of hydrophilic domains at different λ is presented using our previous method41 in Fig. 4c. The hydrophilic domain size is the volume fraction of all particles in a percolated hydrophilic domain against the whole hydrophilic domain, and the volume fraction in Z axis is that for all hydrophilic domains against the system volume averaged from 100 parallel configurations. Neighboring hydrophilic beads separated less than a cutoff of 1.2nm are regarded in the same domain, according to ionic groups is about 0.6-1.2nm in the interconnected channels42. Hydrophilic domains have wide distribution in sizes, and gradually shift to large domains with elevating water contents. Beyond the percolation of hydrophilic domains at λ = 7.3, more than 60Vol% of all water molecules are enclosed in the largest domain. At λ = 20, the distribution of hydrophilic domains narrows down at large domains, and almost all water molecules are in one percolated and fully expanded hydrophilic domain. The elongated and penetrated clusters with interconnected channels provide the continuous channel to transport protons and water, a contributor for the high water diffusion constants in experimental observation for water in Nafion membranes. The small angle scattering intensity profiles computed from the scattering pattern (Fig. 3c) are presented in Fig. 4d. The details for the calculation and the comparison on the different projections can be found in Supporting Information S6. The scattering intensity profiles show a strong ionomer peak at 2.0 nm and greater. With λ increasing, the peak moves to larger values (smaller q), consistent with the results from scattering experiments8, 39. The matrix knee in SAXS scattering is the spacing distance between crystalline domains of PTFE matrix2. The plateau of matrix knees in our work is not obvious and its location is almost independent on water contents (see Fig. 4d). The strength of the matrix knees is strongly dependent on the membrane fabrication processes. For example, the matrix knee is not obvious for the preboiled Nafion 13



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membranes, while it becomes evident after thermal annealing2. The position of matrix knee is around 15.7 nm, which is in the range of 10~25nm from the experiment observation2.

Polymer Matrix. The crystallites of PTFE backbone can be identified from the orientation of anisotropic backbone particles A/A’. The radial distribution function of backbone g(r) and the second-rank orientation correlation function g2(r)34 of PTFE backbone are presented in Fig. 5a and 5b. The value of g2(r) equals to 1 means that orientation within the intra-layers is aligned, while the value 0 means the isotropic phase. All systems show an obvious first correlation peak around 0.5 nm which represents the side-by-side packing of particles A. The second peaks for g2(r) are two times the separation distance of the first peak, corresponding to the cross-sections of crystallites around (1.5nm)2. It is close to the size proposed by Gebel et al.9, in which the elongated polymeric aggregates into cylindrical or ribbon-like shape with cross-section of (1nm)2. The third and forth peaks for g2(r), which is not obvious for g(r), are mainly contributed from the end-to-end packing with the correlation length 1.4nm and 2.8nm, respectively.

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Fig. 5. (a) Radial distribution function g(r) and (b) orientation correlation functions g2(r) of Nafion backbones (A/A’) at different water contents λ. (c) The distribution of orientation angle among backbone ellipsoidal particles, and insert is a configuration with crystallites (yellow ‘rod’) at λ=8. (d) The volume fraction of the local semicrystallines χc as a function of λ.

The distribution of orientation angle (θ = arccos(ui·uj) with the principal axis ui of an ellipsoidal particle i, and a simulation configuration with highlighted crystallites are shown in Fig. 5c. Accordingly, the degree of crystalline is proportional to the probability χc to count the preference of local ordering with separation distance less than 2.8 nm and θ > θc. Here cosθc is a cutoff that filters particles with high alignment to be crystal, and larger values require that particles are more aligned (cosθc>0.9). From Fig. 5d, in reference to either all particles or all backbone particles, χc slightly decreases, suggests that the increase of water contents can suppress 15



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the crystalline in Nafion assemblies. Such decrease in crystalline is consistent with the decrease of polymer bundles in the process of water sorption4. The range of the degree of crystalline is estimated at 8~20%, in agreement with 7~17% for Nafion 117 characterized using WAXS2, 40. Further, we revealed that the crystallites do not show long-range order and the orientation of crystallites are randomly distributed in polymer matrix, probably confined from irregular orientation of hydrophilic domains.

Correlation of Simulation Structures with Experimental Observations. A number of simulation works have been carried out to address the structures of Nafion assemblies. We summarized the representative ones and the correlation of simulated structures with experimental observations in Table 2. There are five solid experimental proofs as stated in introduction that can validate simulation structures, including: i) morphology, ii) matrix knee, iii) hydrophilic domain, iv) persistence length, and v) crystalline in polymer matrix. All simulations show the characteristic lengths of ionomer peaks and the consensus in the increase of the size of hydrophilic domains with water contents. Comparing with other simulations, we employ an anisotropic CG simulation method to study the structures of hydrophilic and hydrophobic domains with a wide range of water contents: from dry Nafion (λ=0) to the maximum water content (λ=24). The Bragg maxima of water cluster and the crystallites of PTFE backbone are consistent quantitatively with scattering and EM experiments. The average radii and separation distances of water clusters are consistent with DPD simulation30 with higher accuracy, mainly attributed to the consideration of explicit charges and anisotropic potentials for the backbone beads34.

Table 2. Summary of simulation structures for Nafion assemblies from different simulation reports. Label √ represents the quantitative agreement with experiments, ○ represents the qualitative agreement with experiments, and - represents without this characteristics. Structure Simulation method

Simulation structure

Water Cluster Size (nm)

characteristic

λ

16


i

ii iii iv v

Reference

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Atomistic MD Simulation

from isolated small water

cluster radii

clusters to a single cluster

≥ 2.5

a bicontinuous double-diamond structure from a channel-network structure to a tortuous layered structure from roughly spherical

MD

domains to elongated cylindrical shapes

channels

Simulation

DPD

clusters to bicontinuous domains

Bragg spacing 2.5 ~ 4.8

cluster radii 1~3

cluster radii 1.7 ~ 2.5 cluster radii 1.6~ 2.6

from isolated spherical SCMF domains to elliptical and barbell domains

○

√

-

5, 10, 20

○

-

○

√

-

3 ~ 20

○

-

○

√

-

2 ~ 15

○

-

○

-

-

5 ~ 16

√

-

√

-

-

2.7~10.3

○

-

○

-

-

2.7~10.3

○

-

○

-

-

2 ~ 16

○

-

○

-

-

0 ~ 20

√ ○

√

√

√

2.55, 3.96, 5.01

2~6 CG

-

size of water

Bragg spacing from the isolated water

3.4 ~ 11.8 ○

Bragg spacing 2.5 ~ 4.2

Cui, et al, 2007 43 Komarov, et al, 2013 24

Kuo, et al, 2016 25

Malek, et al, 2008 27 Wu, et al, 201119, 28 Dorenbos, et al, 2009 30 Yamamoto, et al, 2003 29 Wescott, et al, 2006 44

from isolated spherical Anisotropic

clusters to the

cluster radii

CG-MD simulation

interconnected

1.8~ 4.0

This work

cluster/channel network

IV. CONCLUSION We present an anisotropic CG simulation method to study the structure of dry and hydrated Nafion assemblies. Nafion assemblies present microphase separation between the hydrophobic matrix and hydrophilic ionic domains. As the water content elevates, Nafion structures change from isolated spherical clusters to a cluster/channel network model embedded in the polymer matrix with crystallites. The poly(tetrafluoroethylene) backbones show the local order and the volume fraction of Nafion crystallites decreases with water content increasing. The morphologies are highly consistent with electron microscopy. The characteristic lengths of phase domains and the scattering intensity profiles get convincing agreement with small angle scattering. This anisotropic model reproduces both the local structure and the chain dimensions properly. The stringent and accurate simulation parameters and the experimentally accessible signals employed in this work 17



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present a robust way for molecular simulation to study advanced materials with complex structures. We also prospect that the anisotropic modeling provides the advantage to exactly remap the coarse grained systems to atomistic simulation structures, which is still undergoing.

ASSOCIATED CONTENT Supporting Information. Figures: Figure S1. interaction profiles of GB potential; Figure S2. evolution of temperature and cluster radius as a function of time; Figure S3. Gay-Berne interactions between two interacted CH4 molecules; Figure S4. snapshot of hydrophilic domains for Nafion assemblies; Figure S5. distribution of sulfonic groups, protons, and bulk water in hydrophilic domains; Figure S6. radial distribution function of side chain groups, sulfonic groups, hydrated protons, and water particles; Figure S7. fraction of all protons distributed in bulk water; Figure S8. scattering patterns of the 2D gray morphologies. Tables: Table1. number of oligomers, neutral water particles, charged particles, and mass densities for simulation systems. Table. S2 Coarse-grained parameters of the bond and angle potentials. Cartoons: Cartoon S1 (Nafion A-A side-by-side configuration), Cartoon S2 (Nafion C-C configuration), Cartoon S3 (Nafion A-W configuration), and Cartoon S4 (Nafion D-W configuration).

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]. Phone: +86 (0)431 85262535

ACKNOWLEDGMENTS The authors are grateful for Dr Youliang Zhu and Professor Zhaoyan Sun for GALAMOST 18


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software assistant. This work was supported by National Natural Science Foundation of China (21374117, 21404105 and 21774128), Major State Basic Research Development Program (2015CB655302), Key Research Program of Frontier Sciences (QYZDY-SSW-SLH027) and One Hundred Person Project of the Chinese Academy of Sciences. We are also grateful to Computing Center of Jilin Province for essential support.

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TOC Graphic Assembled Structures of Perfluorosulfonic Acid Ionomers Investigated by Anisotropic Modelling and Simulations Wenduo Chen1, Fengchao Cui1, Lunyang Liu1,2, Yunqi Li*,1

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Assembled Structures of Perfluorosulfonic Acid ... - ACS Publications

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