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proton dynamics in hydrated environments
Fluid Phase Equilibria 504 (2020) 112340
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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Charge delocalization effects on Nafion structure and water /proton dynamics in hydrated environments Rakesh Pant a, Soumyadipta Sengupta b, Alexey V. Lyulin b, 1, **, Arun Venkatnathan a, * a Department of Chemistry and Centre for Energy Science, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune, 411008, Maharashtra, India b Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, Eindhoven, 5600 MB, the Netherlands
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Article history: Received 1 May 2019 Received in revised form 30 September 2019 Accepted 1 October 2019 Available online 2 October 2019
In this work, using molecular dynamics simulations, we examine the effect of atomic charge delocalization on the pendant side chain of Nafion membrane on the structural and dynamical properties in various hydrated environments. The sulfur-sulfur radial distribution functions suggest that the sulfonate groups of the pendant side chain have closer geometric proximity with an increase in charge delocalization. However, the interactions of the sulfonate groups with water molecules/hydronium ions show a slight change with the charge delocalization. The average water cluster size decreases significantly with charge delocalization, though the diffusion coefficients of water molecules (at medium and higher water concentration) increase initially and then decreases slightly with excessive charge delocalization. The diffusion coefficients of hydronium ions do not follow any particular trend with charge delocalization. A complex interplay between sulfur-sulfur, sulfur-water/hydronium interactions, and water cluster distribution plays an essential role in the magnitude of the diffusion coefficient of water molecules and hydronium ions. © 2019 Elsevier B.V. All rights reserved.
Keywords: Molecular dynamics Nafion Charge delocalization Cluster distribution Diffusion coefficient
1. Introduction Polymer electrolyte membrane (PEM) fuel cells have been widely explored for several stationary and transportation applications [1,2]. Perfluorosufonic acid (PFSA) membranes (e.g. Nafion) have been extensively studied [2e5] using a wide range of experimental techniques and theoretical methods and continues to be preferred choice due to their properties like high proton conductivity and chemical stability. Experimental investigations on hydrated Nafion from spectroscopy, microscopy, X-ray, and neutron scattering studies have mainly focused on morphological changes which occur with varying humidification and temperature [5]. The conductivity of Nafion depends on the extent of hydration which further influences the membrane morphology and the transport dynamics of protons and water molecules. The transport of protons is governed by a vehicular mechanism [6] (e.g. proton attached to
water molecule) and structural diffusion [7] where protons can hop among water molecules. Several theoretical investigations using quantum chemistry calculations and computer simulations [4] (classical/reactive/ coarse-grained/ab initio molecular dynamics (MD) simulations) have also provided a wealth of data on membrane morphology, mechanism of proton transport, and diffusion coefficients in hydrated Nafion environments. Paddison [8] reported that the ether oxygen atoms present in the pendant side chains of Nafion were not hydrophilic and attributed the same to the strong electronwithdrawing effect of the neighboring CF2 groups. In another study, Paddison [9] examined hydrated model polymers and concluded that the excess electron density on the sulfonate group (due to the dissociation of a proton from the sulfonic acid group) is delocalized by the neighboring electron-withdrawing CF2 groups on pendant side-chain Nafion.
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (A.V. Lyulin), [email protected] (A. Venkatnathan). 1 Center for Computational Energy Research, Department of Applied Physics, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands. https://doi.org/10.1016/j.fluid.2019.112340 0378-3812/© 2019 Elsevier B.V. All rights reserved.
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Eikerling et al. [10] investigated hydrated sulfonyl imide moieties and reported that the microscopic details of charge separation due to dissociation of proton and charge delocalization are essential for the understanding of proton/water mobility. Mikami et al. [11], examined the intermolecular hydrogen bonding interactions between CF3O(CF2)2SO 3 and water and showed that the interaction of water is stronger with the oxygen atom of sulfonate group as compared to ether oxygen atoms. Vishnyakov and coworkers [12] showed that CF2 groups and ether oxygen atoms closest to the sulfonate groups in the pendant side-chain possess a substantial negative charge. Urata et al. [13,14] showed that the hydrophobic behavior of ether oxygen atoms is due to the electron-withdrawing effect of fluorination. Urata et al. [15], observed that water molecules have a preferential binding with the sulfonate groups of the Nafion pendant side chain. Spohr et al. [16] investigated the effects on the proton diffusion of the charge delocalization on the sulfonate groups, the motion of the sulfonate groups and the side chains using the empirical valence bond model. The authors employed side chains attached to the cylindrical walls and excluded the hydrophobic backbone of the membrane in their study. The authors proposed that the charge delocalization within the side chain of the Nafion membrane is one of the critical factors which affect proton conduction. However, there have been no MD simulation study on the PFSA membrane or other functionalized membranes under hydrated conditions to understand the effects of the charge delocalization (on the pendant side chain) on structural and dynamical properties. This is important since the hydrophobic parts of PFSA membranes form a continuous phase separate from the water phase and, hence, affect the morphology of water domains. Under varying charge delocalization, this hydrophobic phase could change morphology and in turn, impact the water cluster morphology. In this study, we performed classical MD simulations (T ¼ 353 K) on hydrated Nafion with varying delocalization on its pendant side chain. We calculate i) intermolecular radial distribution functions (RDF), ii) the clustering of water molecules and iii) the diffusion coefficients of water molecules and hydronium ions. Since classical MD simulations cannot account for proton hopping mechanism, only the vehicular diffusion of proton (hydronium ions) is calculated. The remaining part of the paper is organized as follows: Section 2 describes the computational details required to examine charge delocalization in hydrated Nafion. Section 3 presents the effects of the charge delocalization on RDFs, water clusters and
diffusion coefficients. A summary of key findings concludes this paper. 2. Computational details The chemical structure of a Nafion monomer is shown in Fig. 1a. GROMACS 4.6.7 [17] software was used to perform classical MD simulations. The force-field parameters for the Nafion backbone were taken from the OPLS-AA force-field database [18]. The charge delocalization is modeled by using the unscaled charges on the pendant side-chain of Nafion (obtained from the work of Sunda and Venkatnathan [19]). For example, q ¼ 0.70q0 is obtained using q0 ¼ 0.75 (q0 is denoted as unscaled charge and is the total charge on the sulfonate group). Similarly, other charge models such as q ¼ 0.63q0, 0.50q0, 0.38q0 and 0.25q0 were also employed. Depending on the charge model (q), the remaining charge was distributed equally on the remaining pendant side-chain atoms of Nafion. The input configurations are obtained as follows: A single decamer chain of Nafion along with 10 hydronium ions was energy minimized and replicated 48 times. The equivalent weight (EW) of the membrane is 1100 which is defined as the weight of the polymer divided by the number of sulfonate groups. The resultant configuration, containing 48 Nafion chains and 480 hydronium ions, was used as a subsequent input for simulated annealing by warming from (at 50 K/250 ps) T ¼ 353 K to T ¼ 1000 K and cooled back (at the same rate) to T ¼ 353 K, with a total simulation time of 8.25 ns. The final system obtained from the simulated annealing procedure was solvated with a) 1440 water molecules corresponding to the hydration value of l ¼ 3, where l denotes the number of water molecules per sulfonate group, b) 4320 water molecules, which corresponds to l ¼ 9 and c) 7200 water molecules corresponding to l ¼ 15. A snapshot of a configuration of a hydrated Nafion is shown in Fig. 1b. The hydrated configurations were energy minimized further using the steepest descent algorithm. The cutoff for the non-bonded interactions was set to 1.2 nm. The particle mesh Ewald [20] method was used for the calculation of the long-range electrostatic interactions. The leapfrog algorithm was used to integrate the equations of motion with a time step of 1 fs. The hydrated Nafion configurations were equilibrated for 20 ns and T ¼ 353 K using the NPT ensemble. The Berendsen [21] barostat was used to maintain 1 bar isotropic pressure. The velocity-rescale thermostat, with a coupling time of 0.1 ps, was used to keep a fixed temperature. The simulated densities (calculated from
Fig. 1. (a) The molecular structure of the Nafion decamer (EW ¼ 1100) simulated in the present study. 48 Nafion chains have been placed with 480 hydronium ions and different amounts of water molecules. (b) A snapshot (l ¼ 15) illustrating Nafion (green color) with sulfonate groups shown in red color, the blue color represents water, and hydronium ions are shown in white.
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equilibration) at l ¼ 3, 9 and 15 are 1.75, 1.68 and 1.59 g/cm3 respectively are found to be in good agreement with results of Devanathan and co-workers [22,23]. The simulated densities (see Fig. 2) show insignificant change with charge delocalization. The equilibration was followed by a 35 ns production at T ¼ 353 K using the NVT ensemble where the temperature was controlled by the eHoover [24] thermostat. The trajectories were recorded Nose every 5 ps to analyze the structural and dynamical properties of all hydrated Nafion configurations.
3. Results and discussion 3.1. Radial distribution functions Devanathan [2], reported that the width of the water channel and the proton conductivity of hydrated Nafion membranes is closely related to the distribution of the sulfonate groups. This distribution can be characterized by sulfur-sulfur (SeS) RDF [25]. Fig. 3 shows the SeS RDF at T ¼ 353 K and with charge delocalization (decreasing charge on the sulfonate group). At l ¼ 3 (q0) the peak maximum in SeS RDFs appears at 6.0 Å, and further decreases to 5.2 Å (0.25q0). At l ¼ 9 (q0) the peak maximum appears at 6.2 Å and shifts to 5.0 Å (0.25q0). Similarly, at l ¼ 15 (q0) the peak maximum at 6.4 Å shifts to 5.0 Å (0.25q0) with an increase in charge delocalization. The peak maximum at l ¼ 15 (q0) is in agreement with previously reported results [15,22,26,27]. The SeS RDFs suggest that increasing charge delocalization (corresponding to decreasing charge on sulfonate groups) leads to a very pronounced shift of the first maximum to the smaller distances. The shift in peak maximum is observed for all simulated water concentrations. Hence, increased charge delocalization leads to reduced repulsion between the sulfonate groups. Paddison and coworkers [28] have shown that proton dissociation occurs at lower hydration and with lower energy barriers if the separation between side chains is reduced. Hence, we conclude that the charge delocalization could influence proton transfer due to the decreased separation between the sulfonate groups. To characterize the interactions between the sulfonate groups and water/hydronium molecules, the corresponding RDFs between the sulfur (S) and the water oxygens (OW)/hydronium oxygens (OH) were calculated (see Figs. S1 and S2 of Supporting Information). The position of the peak maximum for S-OW RDFs (see Fig. S1 of Supporting Information) shifts slightly towards larger distances
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with increasing charge delocalization which implies a slight decrease in S-OW interactions leading to the larger separations. The peak maximum in S-OW RDFs is observed at 3.9 Å (q0), which is in agreement with the work of Venkatnathan et al. [22]. The value of peak maximum shifts to 4.3 Å (0.25q0), with an increase in charge delocalization. Similarly, the peak maximum for SeOH (sulfur and hydronium) RDF (see Fig. S2 of Supporting Information), shifts slightly to larger distances with increasing charge delocalization. To understand the interactions of the water molecules with pendant side-chain oxygen atom (labeled as OE and OS in Fig. 1a) of Nafion, OE-OW and OS-OW RDFs were also calculated (Fig. S3 of Supporting Information). These RDFs suggest that at the highest charge delocalization (0.25q0) the interactions of water molecules with the pendant side-chain oxygen atoms are significantly increased as compared to the lowest charge delocalization (q0). 3.2. Water cluster distribution The Nafion side chains are hydrophilic due to the presence of the sulfonate groups. In hydrated environments, this results in phase separation and leads to the formation of the water clusters, which is important for proton conduction [29]. Prior studies [30e33] have reported a change in the cluster size distribution with varying hydration, from isolated water molecules (at lower water concentration) to larger water domains (for higher water concentration). The formed water clusters facilitate proton conduction. Hence, it is important to understand the effect of the charge delocalization on the clustering of water molecules. In the present study, the water molecules were considered to be part of a cluster if the minimum distance between water molecules (oxygen atoms) was less than 3.6 Å (distance is close to the first solvation shell) [34]. The average cluster size is calculated as
Pn NCs Avg ¼ Ps¼1 n s¼1 Cs where N is the number of clusters of a particular size, Cs is the size of a cluster of water molecules and n is the total number of clusters. Fig. 4 shows the average water cluster size with charge delocalization at different hydration levels. As seen, water cluster sizes decrease monotonically with the increase in charge delocalization, which implies decreasing phase separation. The largest water cluster is observed for the charge q0; the size of the largest cluster decreases with an increase in the charge delocalization. At lower hydration (l ¼ 3), water clusters could not be observed in this study and is consistent with the findings of Devanathan et al. [35]. 3.3. Diffusion coefficients of water and hydronium ions The translational diffusion coefficients of water molecules and hydronium ions were calculated from the mean square displacements (MSD) using the Einstein relationship [36],
Fig. 2. The simulated densities for hydrated Nafion mixtures at T ¼ 353 K, for different charge delocalization and hydration.
where ri denotes the position of the atoms of water molecules/ hydronium ions and DA is the corresponding diffusion coefficient obtained from the linear regime of the MSD (Fig. S4 of Supporting Information). Fig. 5 shows the diffusion coefficients of a) water and b) hydronium. At l ¼ 15 (q0) the calculated diffusion coefficient of water molecules and hydronium ions is 1.34 105 cm2/s and 0.39 105 cm2/s respectively. These values are in a good agreement with the work of Venkatnathan et al. [22] (1.37 105 cm2/s
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Fig. 3. SeS RDFs, at (a) l ¼ 3 (b) l ¼ 9 and (c) l ¼ 15, with varying charge (q0, 0.70q0, 0.63q0, 0.50q0, 0.38q0, and 0.25q0) on the sulfonate group. The position of the RDF peak maximum is shown within the graphs.
Fig. 4. The average cluster size of the water molecules at a cut-off of 3.6 Å and T ¼ 353 K.
(water) and 0.22 105 cm2/s (hydronium ions)) and Jang et al. [26] (1.43 105 cm2/s (water) and 0.29 105 cm2/s (hydronium ions)). The increase in charge delocalization leads to reduced electrostatic interactions between the sulfonate group and water molecules and is expected to show increased diffusion coefficient of
water molecules. However, we observed strongly non-monotonic dependence of diffusion coefficients of water molecules (see Fig. 5); the water diffusion increases initially with charge delocalization (on reducing the charge on sulfonate group from q0 to 0.50q0) and decreases further with excessive charge delocalization (0.63q0 to 0.25q0). A comparison of diffusion coefficients of hydronium ions (from this study) with experiments and previous simulations is shown in Fig. S5 of Supporting Information. As observed, the vehicular diffusion coefficients from our work are in qualitative agreement with trends observed from experimental, ab initio MD, MS-EVB studies and are in excellent agreement with previously reported results from classical MD simulations. Earlier studies on Nafion [31], SPEEK [37], and PFIA [38] membranes have shown that water diffusion increases with increasing water cluster sizes. In contrast, we find the diffusion coefficients of water molecules increases at l ¼ 15 from 1.34 105 cm2/s (q0) to 1.68 105 cm2/s (0.50q0), though a four-fold decrease in average water cluster sizes (see Fig. 4) is observed. Similar trends are observed at l ¼ 9, with insignificant changes seen at l ¼ 3. This effect could be explained in the following manner. For charge delocalization from q0 to 0.50q0 water molecules experience less electrostatic attraction from the sulfonate groups, which results in a higher diffusivity (though there is a decrease in water cluster sizes). However, when charge delocalization is relatively higher (0.38q0 and 0.25q0), the water cluster size decreases significantly and negates the effects due to the smaller electrostatic attraction between the sulfonate groups and water molecules thus reducing diffusivity. It is also possible that the water molecules are trapped along the side
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Fig. 5. The diffusion coefficients of (a) water molecules and (b) hydronium ions vs charge (q) on the sulfonate group at l ¼ 3, l ¼ 9 and l ¼ 15.
chains at higher charge delocalization, due to the larger negative charge being distributed on the pendant side-chain atoms, which leads to reduced diffusivity of water molecules. This trapping effect can be elucidated by stronger interactions between water molecules and pendant side-chain oxygen atoms, at very high charge delocalization as compared to those at lower charge delocalization as suggested by the RDFs (Fig. S3 of Supporting Information). 4. Conclusions Using classical MD simulations, we have explored the effect of the sulfonate group charge delocalization of hydrated Nafion polymer membrane on its structural and dynamical properties. The sulfur-sulfur RDFs suggest that the repulsion between the sulfonate groups decreases with an increase in charge delocalization. The RDFs suggest that sulfonate-water and sulfonate-hydronium interactions decrease slightly with charge delocalization. The average water cluster size decreases significantly with an increase in charge delocalization. With small amounts of delocalization, the diffusion of water molecules increases because the charge is not concentrated on the sulfonate group alone which allows the water molecules to not be trapped in the vicinity of the sulfonate group. However, with increasing delocalization the water diffusion decreases due to a large decrease in the water cluster sizes. Hence, it can be concluded that the diffusion coefficients of water molecules can be increased slightly by suitably adjusting the amount of charge delocalization. This effect can be useful for reverse osmosis where PEMs are used and water diffusion is critical. The results from this work can be applied to examine other functionalized polymer membranes with sulfonic, phosphoric or carboxylic acid groups which can offer high proton conductivity in hydrated environments. Acknowledgments RP thanks Indian Institute of Science Education and Research, Pune for graduate fellowship and Group Theory of Polymers and Soft Matter at the Technische Universiteit Eindhoven for the hospitality during his stay there. Dr. Arun Venkatnathan is thankful to DST Nanomission Thematic Unit (SR/NM/TP-13/2016) and SERB, DST Grant No: CRG/2018/001536 for financial support towards this work. RP, SS, and AVL acknowledge the funding from 15CSER13 project in the NWO-Shell CSER research program. Appendix A. Supplementary data Supplementary data to this article can be found online at
https://doi.org/10.1016/j.fluid.2019.112340.
References [1] B.C.H. Steele, A. Heinzel, Materials for fuel-cell technologies, Mater. Sustain. Energy 414 (2010) 224e231, https://doi.org/10.1142/9789814317665_0031. [2] R. Devanathan, Recent developments in proton exchange membranes for fuel cells, Energy Environ. Sci. 1 (2008) 101e119, https://doi.org/10.1039/ b808149m. [3] H. Zhang, P.K. Shen, Recent development of polymer electrolyte membranes for fuel cells, Chem. Rev. 112 (2012) 2780e2832, https://doi.org/10.1021/ cr200035s. [4] A. Kusoglu, A.Z. Weber, New insights into perfluorinated sulfonic-acid ionomers, Chem. Rev. 117 (2017), https://doi.org/10.1021/acs.chemrev.6b00159, 987e1104. [5] K.A. Mauritz, R.B. Moore, State of understanding of nafion, Chem. Rev. 104 (2004) 4535e4585, https://doi.org/10.1021/cr0207123. [6] K.D. Kreuer, A. Rabenau, W. Weppner, Vehicle mechanism, a new model for the interpretation of the conductivity of fast proton conductors, Angew. Chem. Int. Ed. Engl. 21 (1982) 208e209, https://doi.org/10.1002/anie.198202082. [7] N. Agmon, The Grotthuss mechanism, Chem. Phys. Lett. 244 (1995) 456e462, https://doi.org/10.1016/0009-2614(95)00905-J. [8] S.J. Paddison, Molecular modeling of the pendant chain in Nafion®, Solid State Ion. 113e115 (1998) 333e340, https://doi.org/10.1016/S0167-2738(98) 00298-7. [9] S.J. Paddison, The modeling of molecular structure and ion transport in sulfonic acid based ionomer membranes, J. New Mater. Electrochem. Syst. 4 (2001) 197e207. [10] M. Eikerling, S.J. Paddison, T.A. Zawodzinski, Molecular orbital calculations of proton dissociation and hydration of various acidic moieties for fuel cell polymers, J. New Mater. Electrochem. Syst. 5 (2002) 15e23. [11] M. Mikami, S. Urata, S. Tsuzuki, W. Shinoda, A. Takada, J. Irisawa, Intermolecular interaction between the pendant chain of perfluorinated ionomer and water, Phys. Chem. Chem. Phys. 6 (2004) 3325e3332, https://doi.org/10.1039/ b316395d. [12] A. Vishnyakov, A.V. Neimark, Molecular dynamics simulation of nafion oligomer solvation in equimolar methanol-water mixture, J. Phys. Chem. B 105 (2001) 7830e7834, https://doi.org/10.1021/jp004082p. [13] S. Urata, S. Tsuzuki, M. Mikami, A. Takada, T. Uchimaru, A. Sekiya, Analysis of the intermolecular interaction between CH3OCH3, CF3OCH3, CF3OCF3, and CH4: high level ab initio calculations, J. Comput. Chem. 23 (2002) 1472e1479, https://doi.org/10.1002/jcc.10118. [14] S. Urata, S. Tsuzuki, A. Takada, M. Mikami, T. Uchimaru, A. Sekiya, Analysis of the intermolecular interactions between CH3OCH3, CF3OCH3,CF3OCF3, and CH2F2, CHF3, J. Comput. Chem. 25 (2004) 447e459, https://doi.org/10.1002/ jcc.10395. [15] S. Urata, J. Irisawa, A. Takada, W. Shinoda, S. Tsuzuki, M. Mikami, Molecular dynamics simulation of swollen membrane of perfluorinated ionomer, J. Phys. Chem. B 109 (2005) 4269e4278, https://doi.org/10.1021/jp046434o. [16] E. Spohr, P. Commer, A.A. Kornyshev, Enhancing proton mobility in polymer electrolyte membranes: lessons from molecular dynamics simulations, J. Phys. Chem. B 106 (2002) 10560e10569, https://doi.org/10.1021/jp020209u. [17] B. Hess, C. Kutzner, D. van der Spoel, E. Lindahl, GROMACS 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation, J. Chem. Theory Comput. 4 (2008) 435e447, https://doi.org/10.1021/ct700301q. [18] W.L. Jorgensen, D.S. Maxwell, J. Tirado-Rives, Development and testing of the OLPS all-atom force field on conformational energetics and properties of organic liquids, J. Am. Chem. Soc. 118 (1996) 11225e11236, https://doi.org/ 10.1021/ja9621760. [19] A.P. Sunda, A. Venkatnathan, Molecular dynamics simulations of side chain
6
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
R. Pant et al. / Fluid Phase Equilibria 504 (2020) 112340 pendants of perfluorosulfonic acid polymer electrolyte membranes, J. Mater. Chem. A. 1 (2013) 557e569, https://doi.org/10.1039/c2ta00390b. T. Darden, D. York, L. Pedersen, Particle mesh Ewald: an N$log(N) method for Ewald sums in large systems, J. Chem. Phys. 98 (1993) 10089e10092, https:// doi.org/10.1063/1.464397. H.J.C. Berendsen, J.P.M. Postma, W.F. Van Gunsteren, A. Dinola, J.R. Haak, Molecular dynamics with coupling to an external bath, J. Chem. Phys. 81 (1984) 3684e3690, https://doi.org/10.1063/1.448118. A. Venkatnathan, R. Devanathan, M. Dupuis, Atomistic simulations of hydrated nafion and temperature effects on hydronium ion mobility, J. Phys. Chem. B 25 (2007) 7234e7244, https://doi.org/10.1021/jp0700276. A.J. Wise, J.K. Grey, R. Devanathan, M. Dupuis, Insight from molecular modelling : does the polymer side chain length matter for transport properties of perfluorosulfonic acid membranes? Phys. Chem. Chem. Phys. 14 (2012) 11281e11295, https://doi.org/10.1039/c2cp24132c. , A molecular dynamics method for simulations in the canonical S. Nose ensemble, Mol. Phys. 52 (1984) 255e268, https://doi.org/10.1080/ 00268978400101201. A.P. Sunda, Venkatnathan, Atomistic simulations of structure and dynamics of hydrated Aciplex polymer electrolyte membrane, Soft Matter 8 (2012) 10827e10836, https://doi.org/10.1039/c2sm26561c. S.S. Jang, V. Molinero, C. Tahir, W.A. Goddard III, Nanophase-Segregation and transport in nafion 117 from molecular dynamics Simulations : effect of monomeric sequence, J. Phys. Chem. B 108 (2004) 3149e3157, https://doi.org/ 10.1021/jp036842c. C.K. Knox, G.A. Voth, Probing selected morphological models of hydrated nafion using large-scale molecular dynamics simulations, J. Phys. Chem. B 114 (2010) 3205e3218, https://doi.org/10.1021/jp9112409. J.K. Clark, S.J. Paddison, S.J. Hamrock, The effect of hydrogen bond reorganization and equivalent weight on proton transfer in 3M perfluorosulfonic acid ionomers, Phys. Chem. Chem. Phys. 14 (2012) 16349e16359, https://doi.org/ 10.1039/c2cp42678a. K.D. Kreuer, On the development of proton conducting polymer membranes for hydrogen and methanol fuel cells, J. Membr. Sci. 185 (2001) 29e39,
https://doi.org/10.1016/S0376-7388(00)00632-3. [30] K. Malek, M. Eikerling, Q. Wang, Z. Liu, S. Otsuka, K. Akizuki, M. Abe, Nanophase segregation and water dynamics in hydrated Nafion: molecular modeling and experimental validation, J. Chem. Phys. 129 (2008) 204702e204710, https://doi.org/10.1063/1.3000641. [31] S. Cui, J. Liu, M.E. Selvan, D.J. Keffer, B.J. Edwards, W.V. Steele, A molecular dynamics study of a nafion polyelectrolyte membrane and the aqueous phase structure for proton transport, J. Phys. Chem. B 111 (2007) 2208e2218, https://doi.org/10.1021/jp066388n. [32] A. Vishnyakov, A.V. Neimark, Molecular dynamics simulation of microstructure and molecular mobilities in swollen nation membranes, J. Phys. Chem. B 105 (2001) 9586e9594, https://doi.org/10.1021/jp0102567. [33] S. Cui, J. Liu, M.E. Selvan, S.J. Paddison, D.J. Keffer, B.J. Edwards, Comparison of the hydration and diffusion of protons in perfluorosulfonic acid membranes with molecular dynamics simulations, J. Phys. Chem. B 112 (2008) 13273e13284, https://doi.org/10.1021/jp8039803. [34] S. Sengupta, A.V. Lyulin, Molecular dynamics simulations of substrate hydrophilicity and confinement effects in capped nafion films, J. Phys. Chem. B 122 (2018) 6107e6119, https://doi.org/10.1021/acs.jpcb.8b03257. [35] R. Devanathan, A. Venkatnathan, R. Rousseau, M. Dupuis, T. Frigato, W. Gu, V. Helms, Atomistic simulation of water percolation and proton hopping in Nafion fuel cell membrane, J. Phys. Chem. B 114 (2010) 13681e13690, https:// doi.org/10.1021/jp103398b. [36] D.J. Allen, M.P. Tildesley, Computer Simulation of Liquids, Oxford Science Publications, New York, 1987. [37] M. Tripathy, P.B.S. Kumar, A.P. Deshpande, Molecular structuring and percolation transition in hydrated sulfonated poly(ether ether ketone) membranes, J. Phys. Chem. B 121 (2017) 4873e4884, https://doi.org/10.1021/ acs.jpcb.7b01045. [38] S. Sengupta, R. Pant, P. Komarov, A. Venkatnathan, A.V. Lyulin, Atomistic simulation study of the hydrated structure and transport dynamics of a novel multi acid side chain polyelectrolyte membrane, Int. J. Hydrogen Energy 42 (2017), https://doi.org/10.1016/j.ijhydene.2017.09.078, 7254e27268.
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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Charge delocalization effects on Nafion structure and water /proton dynamics in hydrated environments Rakesh Pant a, Soumyadipta Sengupta b, Alexey V. Lyulin b, 1, **, Arun Venkatnathan a, * a Department of Chemistry and Centre for Energy Science, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune, 411008, Maharashtra, India b Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, Eindhoven, 5600 MB, the Netherlands
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 May 2019 Received in revised form 30 September 2019 Accepted 1 October 2019 Available online 2 October 2019
In this work, using molecular dynamics simulations, we examine the effect of atomic charge delocalization on the pendant side chain of Nafion membrane on the structural and dynamical properties in various hydrated environments. The sulfur-sulfur radial distribution functions suggest that the sulfonate groups of the pendant side chain have closer geometric proximity with an increase in charge delocalization. However, the interactions of the sulfonate groups with water molecules/hydronium ions show a slight change with the charge delocalization. The average water cluster size decreases significantly with charge delocalization, though the diffusion coefficients of water molecules (at medium and higher water concentration) increase initially and then decreases slightly with excessive charge delocalization. The diffusion coefficients of hydronium ions do not follow any particular trend with charge delocalization. A complex interplay between sulfur-sulfur, sulfur-water/hydronium interactions, and water cluster distribution plays an essential role in the magnitude of the diffusion coefficient of water molecules and hydronium ions. © 2019 Elsevier B.V. All rights reserved.
Keywords: Molecular dynamics Nafion Charge delocalization Cluster distribution Diffusion coefficient
1. Introduction Polymer electrolyte membrane (PEM) fuel cells have been widely explored for several stationary and transportation applications [1,2]. Perfluorosufonic acid (PFSA) membranes (e.g. Nafion) have been extensively studied [2e5] using a wide range of experimental techniques and theoretical methods and continues to be preferred choice due to their properties like high proton conductivity and chemical stability. Experimental investigations on hydrated Nafion from spectroscopy, microscopy, X-ray, and neutron scattering studies have mainly focused on morphological changes which occur with varying humidification and temperature [5]. The conductivity of Nafion depends on the extent of hydration which further influences the membrane morphology and the transport dynamics of protons and water molecules. The transport of protons is governed by a vehicular mechanism [6] (e.g. proton attached to
water molecule) and structural diffusion [7] where protons can hop among water molecules. Several theoretical investigations using quantum chemistry calculations and computer simulations [4] (classical/reactive/ coarse-grained/ab initio molecular dynamics (MD) simulations) have also provided a wealth of data on membrane morphology, mechanism of proton transport, and diffusion coefficients in hydrated Nafion environments. Paddison [8] reported that the ether oxygen atoms present in the pendant side chains of Nafion were not hydrophilic and attributed the same to the strong electronwithdrawing effect of the neighboring CF2 groups. In another study, Paddison [9] examined hydrated model polymers and concluded that the excess electron density on the sulfonate group (due to the dissociation of a proton from the sulfonic acid group) is delocalized by the neighboring electron-withdrawing CF2 groups on pendant side-chain Nafion.
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (A.V. Lyulin), [email protected] (A. Venkatnathan). 1 Center for Computational Energy Research, Department of Applied Physics, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands. https://doi.org/10.1016/j.fluid.2019.112340 0378-3812/© 2019 Elsevier B.V. All rights reserved.
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Eikerling et al. [10] investigated hydrated sulfonyl imide moieties and reported that the microscopic details of charge separation due to dissociation of proton and charge delocalization are essential for the understanding of proton/water mobility. Mikami et al. [11], examined the intermolecular hydrogen bonding interactions between CF3O(CF2)2SO 3 and water and showed that the interaction of water is stronger with the oxygen atom of sulfonate group as compared to ether oxygen atoms. Vishnyakov and coworkers [12] showed that CF2 groups and ether oxygen atoms closest to the sulfonate groups in the pendant side-chain possess a substantial negative charge. Urata et al. [13,14] showed that the hydrophobic behavior of ether oxygen atoms is due to the electron-withdrawing effect of fluorination. Urata et al. [15], observed that water molecules have a preferential binding with the sulfonate groups of the Nafion pendant side chain. Spohr et al. [16] investigated the effects on the proton diffusion of the charge delocalization on the sulfonate groups, the motion of the sulfonate groups and the side chains using the empirical valence bond model. The authors employed side chains attached to the cylindrical walls and excluded the hydrophobic backbone of the membrane in their study. The authors proposed that the charge delocalization within the side chain of the Nafion membrane is one of the critical factors which affect proton conduction. However, there have been no MD simulation study on the PFSA membrane or other functionalized membranes under hydrated conditions to understand the effects of the charge delocalization (on the pendant side chain) on structural and dynamical properties. This is important since the hydrophobic parts of PFSA membranes form a continuous phase separate from the water phase and, hence, affect the morphology of water domains. Under varying charge delocalization, this hydrophobic phase could change morphology and in turn, impact the water cluster morphology. In this study, we performed classical MD simulations (T ¼ 353 K) on hydrated Nafion with varying delocalization on its pendant side chain. We calculate i) intermolecular radial distribution functions (RDF), ii) the clustering of water molecules and iii) the diffusion coefficients of water molecules and hydronium ions. Since classical MD simulations cannot account for proton hopping mechanism, only the vehicular diffusion of proton (hydronium ions) is calculated. The remaining part of the paper is organized as follows: Section 2 describes the computational details required to examine charge delocalization in hydrated Nafion. Section 3 presents the effects of the charge delocalization on RDFs, water clusters and
diffusion coefficients. A summary of key findings concludes this paper. 2. Computational details The chemical structure of a Nafion monomer is shown in Fig. 1a. GROMACS 4.6.7 [17] software was used to perform classical MD simulations. The force-field parameters for the Nafion backbone were taken from the OPLS-AA force-field database [18]. The charge delocalization is modeled by using the unscaled charges on the pendant side-chain of Nafion (obtained from the work of Sunda and Venkatnathan [19]). For example, q ¼ 0.70q0 is obtained using q0 ¼ 0.75 (q0 is denoted as unscaled charge and is the total charge on the sulfonate group). Similarly, other charge models such as q ¼ 0.63q0, 0.50q0, 0.38q0 and 0.25q0 were also employed. Depending on the charge model (q), the remaining charge was distributed equally on the remaining pendant side-chain atoms of Nafion. The input configurations are obtained as follows: A single decamer chain of Nafion along with 10 hydronium ions was energy minimized and replicated 48 times. The equivalent weight (EW) of the membrane is 1100 which is defined as the weight of the polymer divided by the number of sulfonate groups. The resultant configuration, containing 48 Nafion chains and 480 hydronium ions, was used as a subsequent input for simulated annealing by warming from (at 50 K/250 ps) T ¼ 353 K to T ¼ 1000 K and cooled back (at the same rate) to T ¼ 353 K, with a total simulation time of 8.25 ns. The final system obtained from the simulated annealing procedure was solvated with a) 1440 water molecules corresponding to the hydration value of l ¼ 3, where l denotes the number of water molecules per sulfonate group, b) 4320 water molecules, which corresponds to l ¼ 9 and c) 7200 water molecules corresponding to l ¼ 15. A snapshot of a configuration of a hydrated Nafion is shown in Fig. 1b. The hydrated configurations were energy minimized further using the steepest descent algorithm. The cutoff for the non-bonded interactions was set to 1.2 nm. The particle mesh Ewald [20] method was used for the calculation of the long-range electrostatic interactions. The leapfrog algorithm was used to integrate the equations of motion with a time step of 1 fs. The hydrated Nafion configurations were equilibrated for 20 ns and T ¼ 353 K using the NPT ensemble. The Berendsen [21] barostat was used to maintain 1 bar isotropic pressure. The velocity-rescale thermostat, with a coupling time of 0.1 ps, was used to keep a fixed temperature. The simulated densities (calculated from
Fig. 1. (a) The molecular structure of the Nafion decamer (EW ¼ 1100) simulated in the present study. 48 Nafion chains have been placed with 480 hydronium ions and different amounts of water molecules. (b) A snapshot (l ¼ 15) illustrating Nafion (green color) with sulfonate groups shown in red color, the blue color represents water, and hydronium ions are shown in white.
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equilibration) at l ¼ 3, 9 and 15 are 1.75, 1.68 and 1.59 g/cm3 respectively are found to be in good agreement with results of Devanathan and co-workers [22,23]. The simulated densities (see Fig. 2) show insignificant change with charge delocalization. The equilibration was followed by a 35 ns production at T ¼ 353 K using the NVT ensemble where the temperature was controlled by the eHoover [24] thermostat. The trajectories were recorded Nose every 5 ps to analyze the structural and dynamical properties of all hydrated Nafion configurations.
3. Results and discussion 3.1. Radial distribution functions Devanathan [2], reported that the width of the water channel and the proton conductivity of hydrated Nafion membranes is closely related to the distribution of the sulfonate groups. This distribution can be characterized by sulfur-sulfur (SeS) RDF [25]. Fig. 3 shows the SeS RDF at T ¼ 353 K and with charge delocalization (decreasing charge on the sulfonate group). At l ¼ 3 (q0) the peak maximum in SeS RDFs appears at 6.0 Å, and further decreases to 5.2 Å (0.25q0). At l ¼ 9 (q0) the peak maximum appears at 6.2 Å and shifts to 5.0 Å (0.25q0). Similarly, at l ¼ 15 (q0) the peak maximum at 6.4 Å shifts to 5.0 Å (0.25q0) with an increase in charge delocalization. The peak maximum at l ¼ 15 (q0) is in agreement with previously reported results [15,22,26,27]. The SeS RDFs suggest that increasing charge delocalization (corresponding to decreasing charge on sulfonate groups) leads to a very pronounced shift of the first maximum to the smaller distances. The shift in peak maximum is observed for all simulated water concentrations. Hence, increased charge delocalization leads to reduced repulsion between the sulfonate groups. Paddison and coworkers [28] have shown that proton dissociation occurs at lower hydration and with lower energy barriers if the separation between side chains is reduced. Hence, we conclude that the charge delocalization could influence proton transfer due to the decreased separation between the sulfonate groups. To characterize the interactions between the sulfonate groups and water/hydronium molecules, the corresponding RDFs between the sulfur (S) and the water oxygens (OW)/hydronium oxygens (OH) were calculated (see Figs. S1 and S2 of Supporting Information). The position of the peak maximum for S-OW RDFs (see Fig. S1 of Supporting Information) shifts slightly towards larger distances
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with increasing charge delocalization which implies a slight decrease in S-OW interactions leading to the larger separations. The peak maximum in S-OW RDFs is observed at 3.9 Å (q0), which is in agreement with the work of Venkatnathan et al. [22]. The value of peak maximum shifts to 4.3 Å (0.25q0), with an increase in charge delocalization. Similarly, the peak maximum for SeOH (sulfur and hydronium) RDF (see Fig. S2 of Supporting Information), shifts slightly to larger distances with increasing charge delocalization. To understand the interactions of the water molecules with pendant side-chain oxygen atom (labeled as OE and OS in Fig. 1a) of Nafion, OE-OW and OS-OW RDFs were also calculated (Fig. S3 of Supporting Information). These RDFs suggest that at the highest charge delocalization (0.25q0) the interactions of water molecules with the pendant side-chain oxygen atoms are significantly increased as compared to the lowest charge delocalization (q0). 3.2. Water cluster distribution The Nafion side chains are hydrophilic due to the presence of the sulfonate groups. In hydrated environments, this results in phase separation and leads to the formation of the water clusters, which is important for proton conduction [29]. Prior studies [30e33] have reported a change in the cluster size distribution with varying hydration, from isolated water molecules (at lower water concentration) to larger water domains (for higher water concentration). The formed water clusters facilitate proton conduction. Hence, it is important to understand the effect of the charge delocalization on the clustering of water molecules. In the present study, the water molecules were considered to be part of a cluster if the minimum distance between water molecules (oxygen atoms) was less than 3.6 Å (distance is close to the first solvation shell) [34]. The average cluster size is calculated as
Pn NCs Avg ¼ Ps¼1 n s¼1 Cs where N is the number of clusters of a particular size, Cs is the size of a cluster of water molecules and n is the total number of clusters. Fig. 4 shows the average water cluster size with charge delocalization at different hydration levels. As seen, water cluster sizes decrease monotonically with the increase in charge delocalization, which implies decreasing phase separation. The largest water cluster is observed for the charge q0; the size of the largest cluster decreases with an increase in the charge delocalization. At lower hydration (l ¼ 3), water clusters could not be observed in this study and is consistent with the findings of Devanathan et al. [35]. 3.3. Diffusion coefficients of water and hydronium ions The translational diffusion coefficients of water molecules and hydronium ions were calculated from the mean square displacements (MSD) using the Einstein relationship [36],
Fig. 2. The simulated densities for hydrated Nafion mixtures at T ¼ 353 K, for different charge delocalization and hydration.
where ri denotes the position of the atoms of water molecules/ hydronium ions and DA is the corresponding diffusion coefficient obtained from the linear regime of the MSD (Fig. S4 of Supporting Information). Fig. 5 shows the diffusion coefficients of a) water and b) hydronium. At l ¼ 15 (q0) the calculated diffusion coefficient of water molecules and hydronium ions is 1.34 105 cm2/s and 0.39 105 cm2/s respectively. These values are in a good agreement with the work of Venkatnathan et al. [22] (1.37 105 cm2/s
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Fig. 3. SeS RDFs, at (a) l ¼ 3 (b) l ¼ 9 and (c) l ¼ 15, with varying charge (q0, 0.70q0, 0.63q0, 0.50q0, 0.38q0, and 0.25q0) on the sulfonate group. The position of the RDF peak maximum is shown within the graphs.
Fig. 4. The average cluster size of the water molecules at a cut-off of 3.6 Å and T ¼ 353 K.
(water) and 0.22 105 cm2/s (hydronium ions)) and Jang et al. [26] (1.43 105 cm2/s (water) and 0.29 105 cm2/s (hydronium ions)). The increase in charge delocalization leads to reduced electrostatic interactions between the sulfonate group and water molecules and is expected to show increased diffusion coefficient of
water molecules. However, we observed strongly non-monotonic dependence of diffusion coefficients of water molecules (see Fig. 5); the water diffusion increases initially with charge delocalization (on reducing the charge on sulfonate group from q0 to 0.50q0) and decreases further with excessive charge delocalization (0.63q0 to 0.25q0). A comparison of diffusion coefficients of hydronium ions (from this study) with experiments and previous simulations is shown in Fig. S5 of Supporting Information. As observed, the vehicular diffusion coefficients from our work are in qualitative agreement with trends observed from experimental, ab initio MD, MS-EVB studies and are in excellent agreement with previously reported results from classical MD simulations. Earlier studies on Nafion [31], SPEEK [37], and PFIA [38] membranes have shown that water diffusion increases with increasing water cluster sizes. In contrast, we find the diffusion coefficients of water molecules increases at l ¼ 15 from 1.34 105 cm2/s (q0) to 1.68 105 cm2/s (0.50q0), though a four-fold decrease in average water cluster sizes (see Fig. 4) is observed. Similar trends are observed at l ¼ 9, with insignificant changes seen at l ¼ 3. This effect could be explained in the following manner. For charge delocalization from q0 to 0.50q0 water molecules experience less electrostatic attraction from the sulfonate groups, which results in a higher diffusivity (though there is a decrease in water cluster sizes). However, when charge delocalization is relatively higher (0.38q0 and 0.25q0), the water cluster size decreases significantly and negates the effects due to the smaller electrostatic attraction between the sulfonate groups and water molecules thus reducing diffusivity. It is also possible that the water molecules are trapped along the side
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Fig. 5. The diffusion coefficients of (a) water molecules and (b) hydronium ions vs charge (q) on the sulfonate group at l ¼ 3, l ¼ 9 and l ¼ 15.
chains at higher charge delocalization, due to the larger negative charge being distributed on the pendant side-chain atoms, which leads to reduced diffusivity of water molecules. This trapping effect can be elucidated by stronger interactions between water molecules and pendant side-chain oxygen atoms, at very high charge delocalization as compared to those at lower charge delocalization as suggested by the RDFs (Fig. S3 of Supporting Information). 4. Conclusions Using classical MD simulations, we have explored the effect of the sulfonate group charge delocalization of hydrated Nafion polymer membrane on its structural and dynamical properties. The sulfur-sulfur RDFs suggest that the repulsion between the sulfonate groups decreases with an increase in charge delocalization. The RDFs suggest that sulfonate-water and sulfonate-hydronium interactions decrease slightly with charge delocalization. The average water cluster size decreases significantly with an increase in charge delocalization. With small amounts of delocalization, the diffusion of water molecules increases because the charge is not concentrated on the sulfonate group alone which allows the water molecules to not be trapped in the vicinity of the sulfonate group. However, with increasing delocalization the water diffusion decreases due to a large decrease in the water cluster sizes. Hence, it can be concluded that the diffusion coefficients of water molecules can be increased slightly by suitably adjusting the amount of charge delocalization. This effect can be useful for reverse osmosis where PEMs are used and water diffusion is critical. The results from this work can be applied to examine other functionalized polymer membranes with sulfonic, phosphoric or carboxylic acid groups which can offer high proton conductivity in hydrated environments. Acknowledgments RP thanks Indian Institute of Science Education and Research, Pune for graduate fellowship and Group Theory of Polymers and Soft Matter at the Technische Universiteit Eindhoven for the hospitality during his stay there. Dr. Arun Venkatnathan is thankful to DST Nanomission Thematic Unit (SR/NM/TP-13/2016) and SERB, DST Grant No: CRG/2018/001536 for financial support towards this work. RP, SS, and AVL acknowledge the funding from 15CSER13 project in the NWO-Shell CSER research program. Appendix A. Supplementary data Supplementary data to this article can be found online at
https://doi.org/10.1016/j.fluid.2019.112340.
References [1] B.C.H. Steele, A. Heinzel, Materials for fuel-cell technologies, Mater. Sustain. Energy 414 (2010) 224e231, https://doi.org/10.1142/9789814317665_0031. [2] R. Devanathan, Recent developments in proton exchange membranes for fuel cells, Energy Environ. Sci. 1 (2008) 101e119, https://doi.org/10.1039/ b808149m. [3] H. Zhang, P.K. Shen, Recent development of polymer electrolyte membranes for fuel cells, Chem. Rev. 112 (2012) 2780e2832, https://doi.org/10.1021/ cr200035s. [4] A. Kusoglu, A.Z. Weber, New insights into perfluorinated sulfonic-acid ionomers, Chem. Rev. 117 (2017), https://doi.org/10.1021/acs.chemrev.6b00159, 987e1104. [5] K.A. Mauritz, R.B. Moore, State of understanding of nafion, Chem. Rev. 104 (2004) 4535e4585, https://doi.org/10.1021/cr0207123. [6] K.D. Kreuer, A. Rabenau, W. Weppner, Vehicle mechanism, a new model for the interpretation of the conductivity of fast proton conductors, Angew. Chem. Int. Ed. Engl. 21 (1982) 208e209, https://doi.org/10.1002/anie.198202082. [7] N. Agmon, The Grotthuss mechanism, Chem. Phys. Lett. 244 (1995) 456e462, https://doi.org/10.1016/0009-2614(95)00905-J. [8] S.J. Paddison, Molecular modeling of the pendant chain in Nafion®, Solid State Ion. 113e115 (1998) 333e340, https://doi.org/10.1016/S0167-2738(98) 00298-7. [9] S.J. Paddison, The modeling of molecular structure and ion transport in sulfonic acid based ionomer membranes, J. New Mater. Electrochem. Syst. 4 (2001) 197e207. [10] M. Eikerling, S.J. Paddison, T.A. Zawodzinski, Molecular orbital calculations of proton dissociation and hydration of various acidic moieties for fuel cell polymers, J. New Mater. Electrochem. Syst. 5 (2002) 15e23. [11] M. Mikami, S. Urata, S. Tsuzuki, W. Shinoda, A. Takada, J. Irisawa, Intermolecular interaction between the pendant chain of perfluorinated ionomer and water, Phys. Chem. Chem. Phys. 6 (2004) 3325e3332, https://doi.org/10.1039/ b316395d. [12] A. Vishnyakov, A.V. Neimark, Molecular dynamics simulation of nafion oligomer solvation in equimolar methanol-water mixture, J. Phys. Chem. B 105 (2001) 7830e7834, https://doi.org/10.1021/jp004082p. [13] S. Urata, S. Tsuzuki, M. Mikami, A. Takada, T. Uchimaru, A. Sekiya, Analysis of the intermolecular interaction between CH3OCH3, CF3OCH3, CF3OCF3, and CH4: high level ab initio calculations, J. Comput. Chem. 23 (2002) 1472e1479, https://doi.org/10.1002/jcc.10118. [14] S. Urata, S. Tsuzuki, A. Takada, M. Mikami, T. Uchimaru, A. Sekiya, Analysis of the intermolecular interactions between CH3OCH3, CF3OCH3,CF3OCF3, and CH2F2, CHF3, J. Comput. Chem. 25 (2004) 447e459, https://doi.org/10.1002/ jcc.10395. [15] S. Urata, J. Irisawa, A. Takada, W. Shinoda, S. Tsuzuki, M. Mikami, Molecular dynamics simulation of swollen membrane of perfluorinated ionomer, J. Phys. Chem. B 109 (2005) 4269e4278, https://doi.org/10.1021/jp046434o. [16] E. Spohr, P. Commer, A.A. Kornyshev, Enhancing proton mobility in polymer electrolyte membranes: lessons from molecular dynamics simulations, J. Phys. Chem. B 106 (2002) 10560e10569, https://doi.org/10.1021/jp020209u. [17] B. Hess, C. Kutzner, D. van der Spoel, E. Lindahl, GROMACS 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation, J. Chem. Theory Comput. 4 (2008) 435e447, https://doi.org/10.1021/ct700301q. [18] W.L. Jorgensen, D.S. Maxwell, J. Tirado-Rives, Development and testing of the OLPS all-atom force field on conformational energetics and properties of organic liquids, J. Am. Chem. Soc. 118 (1996) 11225e11236, https://doi.org/ 10.1021/ja9621760. [19] A.P. Sunda, A. Venkatnathan, Molecular dynamics simulations of side chain
6
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
R. Pant et al. / Fluid Phase Equilibria 504 (2020) 112340 pendants of perfluorosulfonic acid polymer electrolyte membranes, J. Mater. Chem. A. 1 (2013) 557e569, https://doi.org/10.1039/c2ta00390b. T. Darden, D. York, L. Pedersen, Particle mesh Ewald: an N$log(N) method for Ewald sums in large systems, J. Chem. Phys. 98 (1993) 10089e10092, https:// doi.org/10.1063/1.464397. H.J.C. Berendsen, J.P.M. Postma, W.F. Van Gunsteren, A. Dinola, J.R. Haak, Molecular dynamics with coupling to an external bath, J. Chem. Phys. 81 (1984) 3684e3690, https://doi.org/10.1063/1.448118. A. Venkatnathan, R. Devanathan, M. Dupuis, Atomistic simulations of hydrated nafion and temperature effects on hydronium ion mobility, J. Phys. Chem. B 25 (2007) 7234e7244, https://doi.org/10.1021/jp0700276. A.J. Wise, J.K. Grey, R. Devanathan, M. Dupuis, Insight from molecular modelling : does the polymer side chain length matter for transport properties of perfluorosulfonic acid membranes? Phys. Chem. Chem. Phys. 14 (2012) 11281e11295, https://doi.org/10.1039/c2cp24132c. , A molecular dynamics method for simulations in the canonical S. Nose ensemble, Mol. Phys. 52 (1984) 255e268, https://doi.org/10.1080/ 00268978400101201. A.P. Sunda, Venkatnathan, Atomistic simulations of structure and dynamics of hydrated Aciplex polymer electrolyte membrane, Soft Matter 8 (2012) 10827e10836, https://doi.org/10.1039/c2sm26561c. S.S. Jang, V. Molinero, C. Tahir, W.A. Goddard III, Nanophase-Segregation and transport in nafion 117 from molecular dynamics Simulations : effect of monomeric sequence, J. Phys. Chem. B 108 (2004) 3149e3157, https://doi.org/ 10.1021/jp036842c. C.K. Knox, G.A. Voth, Probing selected morphological models of hydrated nafion using large-scale molecular dynamics simulations, J. Phys. Chem. B 114 (2010) 3205e3218, https://doi.org/10.1021/jp9112409. J.K. Clark, S.J. Paddison, S.J. Hamrock, The effect of hydrogen bond reorganization and equivalent weight on proton transfer in 3M perfluorosulfonic acid ionomers, Phys. Chem. Chem. Phys. 14 (2012) 16349e16359, https://doi.org/ 10.1039/c2cp42678a. K.D. Kreuer, On the development of proton conducting polymer membranes for hydrogen and methanol fuel cells, J. Membr. Sci. 185 (2001) 29e39,
https://doi.org/10.1016/S0376-7388(00)00632-3. [30] K. Malek, M. Eikerling, Q. Wang, Z. Liu, S. Otsuka, K. Akizuki, M. Abe, Nanophase segregation and water dynamics in hydrated Nafion: molecular modeling and experimental validation, J. Chem. Phys. 129 (2008) 204702e204710, https://doi.org/10.1063/1.3000641. [31] S. Cui, J. Liu, M.E. Selvan, D.J. Keffer, B.J. Edwards, W.V. Steele, A molecular dynamics study of a nafion polyelectrolyte membrane and the aqueous phase structure for proton transport, J. Phys. Chem. B 111 (2007) 2208e2218, https://doi.org/10.1021/jp066388n. [32] A. Vishnyakov, A.V. Neimark, Molecular dynamics simulation of microstructure and molecular mobilities in swollen nation membranes, J. Phys. Chem. B 105 (2001) 9586e9594, https://doi.org/10.1021/jp0102567. [33] S. Cui, J. Liu, M.E. Selvan, S.J. Paddison, D.J. Keffer, B.J. Edwards, Comparison of the hydration and diffusion of protons in perfluorosulfonic acid membranes with molecular dynamics simulations, J. Phys. Chem. B 112 (2008) 13273e13284, https://doi.org/10.1021/jp8039803. [34] S. Sengupta, A.V. Lyulin, Molecular dynamics simulations of substrate hydrophilicity and confinement effects in capped nafion films, J. Phys. Chem. B 122 (2018) 6107e6119, https://doi.org/10.1021/acs.jpcb.8b03257. [35] R. Devanathan, A. Venkatnathan, R. Rousseau, M. Dupuis, T. Frigato, W. Gu, V. Helms, Atomistic simulation of water percolation and proton hopping in Nafion fuel cell membrane, J. Phys. Chem. B 114 (2010) 13681e13690, https:// doi.org/10.1021/jp103398b. [36] D.J. Allen, M.P. Tildesley, Computer Simulation of Liquids, Oxford Science Publications, New York, 1987. [37] M. Tripathy, P.B.S. Kumar, A.P. Deshpande, Molecular structuring and percolation transition in hydrated sulfonated poly(ether ether ketone) membranes, J. Phys. Chem. B 121 (2017) 4873e4884, https://doi.org/10.1021/ acs.jpcb.7b01045. [38] S. Sengupta, R. Pant, P. Komarov, A. Venkatnathan, A.V. Lyulin, Atomistic simulation study of the hydrated structure and transport dynamics of a novel multi acid side chain polyelectrolyte membrane, Int. J. Hydrogen Energy 42 (2017), https://doi.org/10.1016/j.ijhydene.2017.09.078, 7254e27268.