Morphology of Supported Polymer Electrolyte. Ultra-thin Films: a Numerical Study. Supporting Information

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1 Morphology of Supported Polymer Electrolyte Ultra-thin Films: a Numerical Study Supporting Information Daiane Damasceno Borges,, Gerard Gebel, Alejandro A. Franco, Kourosh Malek, and Stefano Mossa, Univ. Grenoble Alpes, LITEN-DTNM, F Grenoble, France CEA, LITEN-DTNM, F Grenoble, France, Univ. Grenoble Alpes, LITEN-DTNM, F Grenoble, France CEA, LITEN-DTNM, F Grenoble, France Laboratoire de Réactivité et Chimie des Solides (LRCS), CNRS UMR 7314, Université de Picardie Jules Verne, Amiens Cedex, France Réseau sur le Stockage Électrochimique de l Energie (RS2E), FR CNRS 3459, France, Energy, Mining and Environment, National Research Council of Canada, Vancouver, BC, Canada, and Univ. Grenoble Alpes, INAC-SPRAM, F Grenoble, France CNRS, INAC-SPRAM, F Grenoble, France CEA, INAC-SPRAM, F Grenoble, France stefano.mossa@cea.fr Phone: Fax:

2 1 Ionomer model and force field parameters The Nafion ionomer was modelled by considering a united-atom representation for the CF, CF 2 and CF 3 groups, and fully atomistic resolution for the radical sulfonic acid (SO 3 ) groups pertaining to the side-chains. The Nafion polymer backbone is formed by a linear chain of 160 bonded monomers, which corresponds to a fully extended length of approximately 24 nm. 10 side-chains are uniformly distributed along the backbone, which amounts to a separation between adjacent side chains of 16 backbone monomers. Each side chain comprises 11 atoms and has a length of approximately 1 nm. This particular topology has been chosen in order to match an equivalent weight g/mol of SO 3, a value typical for commercial Nafion 117. The total interaction energy of the system is the sum of non-bonded and intra-molecular bonded terms, including harmonic bonds, and bending dihedral and improper angles. The intra-molecular and intermolecular non-bonded interactions are described in terms of Lennard- Jones potentials and long-range Coulombic interactions. The force field parameters of our model are similar those of the fully atomistic model of Ref. 1 and adapted to the unitedatom representation. The partial charges and the mass of each ionomer unit were assumed to be, respectively, the sum of charges and masses of the constituent atoms. The polymer backbone is charged neutral, while the sulfonic acid head groups are assumed to be fully ionized. Partial charges values of the system are shown in Figure 1. Pairs of atoms that are To whom correspondence should be addressed Univ. Grenoble Alpes, LITEN-DTNM, F Grenoble, France CEA, LITEN-DTNM, F Grenoble, France Univ. Grenoble Alpes, LITEN-DTNM, F Grenoble, France CEA, LITEN-DTNM, F Grenoble, France Laboratoire de Réactivité et Chimie des Solides (LRCS), CNRS UMR 7314, Université de Picardie Jules Verne, Amiens Cedex, France Réseau sur le Stockage Électrochimique de l Energie (RS2E), FR CNRS 3459, France Energy, Mining and Environment, National Research Council of Canada, Vancouver, BC, Canada Univ. Grenoble Alpes, INAC-SPRAM, F Grenoble, France CNRS, INAC-SPRAM, F Grenoble, France CEA, INAC-SPRAM, F Grenoble, France Present address: Institut Charles Gerhardt Montpellier, UMR CNRS 5253, UM2, Place E. Bataillon, Montpellier Cedex 5, France 2

3 Figure 1: Fractional charges for the fully ionized Nafion chain, hydronium ion and SPC/E water molecule. not permanently bonded to each other, either directly or via one or two intermediate bonds also interact by non-bonded terms. Lennard-Jones parameters for mixed interactions are obtained from the usual Lorentz-Berthelot mixing rules. A list of all parameters is included in Table 1. 2 Simulation details of Nafion films Initial configurations were prepared by placing the Nafion ionomer, hydronium ions, and water molecules on the top of an infinite non-structured 9 3 Lennard-Jones wall. The system consists of 20 polymer chains with 200 hydronium ions and a number of water molecules chosen to match the desired water content λ (λ is defined as the number of water molecules per sulfonic acid group). Each polymer chain is formed by 270 particles (including atoms and united-atoms beads). The total number of particles in the system was 9800, and for λ = 6, 11, 22, respectively. The simulation box is schematically represented in Fig. 2. The lateral size was fixed in order to generate a film of thickness δz 4 5 nm at ambient pressure. For the considered 3

4 Table 1: Functional forms and values of the used parameters for bonded and non-bonded interactions. Ionomer, water molecules and hydronium complexes are considered. Symbols identifying the chemical species are as in Fig. 1. Bonded interaction Bonds [U b = k b (r r 0 ) 2 ] k b (kcal/mol/å 2 ) r o (nm) # of bonds S O s CF 2 S CF n CF n CF n O O h H h (hydronium) O w H w (water) Angles [U θ = k θ (θ θ 0 ) 2 ] k θ (kcal/mol/rad 2 ) θ o (degrees) # of angles O s S O s CF 2 S O s CF 2 CF 2 S CF n CF n O E CF n O E CF n CF n CF n CF n (backbone) H h O h H h (hydronium) H w O w H w (water) Dihedrals [U φ = k φ [1 + dcos(nφ)]] k φ (kcal/mol) d = 1; n = 3 # of dihedrals CF 2 CF 2 S O s O E CF 2 CF 2 S CF O E CF 2 CF CF CF 2 O E CF O E CF 2 CF CF CF n CF n CF n CF n (backbone) Impropers [U χ = k χ (χ χ 0 )] k χ (kcal/mol/rad 2 ) χ o (degrees) # of impropers O s S O s O s Non-bonded interaction Lennard-Jones [U LJ = 4ɛ[(σ/r) 12 (σ/r) 6 ]] ɛ(kcal/mol) σ(nm) S O s CF n O E O h (hydronium) O w (water)

5 Figure 2: Scheme of the simulation box used in this work. Details are included in the text. water contents λ = 6, 11, 22, we found L x = L y 6, 8, 8 nm, respectively. Periodic boundary conditions were imposed only in the plane containing the support, while open boundaries were kept in the normal direction, with L z = 10 nm. Adapted techniques have been used to properly evaluate long-range interactions in this anisotropic slab geometry. 2 Also, a mirror wall was placed on the top of the simulation box, to avoid molecules to escape (evaporate) from the box. Molecules attempting to cross the top of simulation box interact with the mirror, which has the effect of reversing the sign of the z component of the molecule velocity. The simulation starts from a random configuration created by randomly placing the center of mass of each component of the system on the bottom of the simulation box. In order to optimize the equilibration, the system was heated at 500 K, followed by a temperature quench to 350 K. This procedure was repeated three times, using a Nose-Hoover thermostat with a relaxation time of 1.0 ps. While during heating the system was well mixed in the center of the simulation box, during the quench only the interaction with the wall became significant, pulling down the system in contact with the support. To avoid any artifact associated to 5

Figure 3: Snapshots of hydrated Nafion membrane at T = 350 K for different water content; The side-chain beads are shown in yellow, water molecules are in blue, hydronium ions in white, and Nafion

6 Figure 3: Snapshots of hydrated Nafion membrane at T = 350 K for different water content; The side-chain beads are shown in yellow, water molecules are in blue, hydronium ions in white, and Nafion backbones in brown the use of the mirror, all velocities were reset after the quench, and the system additionally aged. During the production runs of about 5 ns, complete system configurations were saved every 5 ps and subsequently used for the analysis discussed in the main article. 3 Validation of the Nafion model In order to validate the ionomer model described above, we have examined the structure and dynamics of Nafion in the bulk, for different hydration levels and temperatures. The equilibrated structures of hydrated Nafion have been characterized in terms of hydrophilic/hydrophobic phases segregation, radial distribution functions (RDFs), and water 6

7 molecules and hydronium ions self-diffusion coefficients. Our results were compared with the original model proposed by Venkatnathan et al., 1 as well as with other force fields reported in the literature. In Figure 3 we show typical snapshots of hydrated Nafion equilibrated at T = 350 K for λ = 2, 6, 11 and 22. These snapshots confirm the general picture of a heterogeneous Nafion morphology, with well-defined phase separation of hydrophobic and hydrophilic domains. We can note that side-chains (yellow beads) are localized at interfaces between backbone chains (brown beads) and water and hydronium ions (blue and white beads). The sidechains identify the boundaries between the phases, which appears more evident at higher values of λ. Also, it is evident that shape and connectivity of both domains strongly depend on water content, in agreement with mesoscale calculations found in the literature. 3,4 In Figure 4 (a) and (b) we show the radial distribution functions, g SOw (r) and g SOh (r), between the sulphur atom of the SO 3 groups and the oxygen atom of the H 2 Oand H 3 O +, respectively. In both RDFs, the first peak occurs around 0.37 nm and this position does not depend on λ. The value reported by Venkatnathan et al. 1 is 0.39 nm, with a slight variation of 5% higher than our data. The intensity of the first peak in g SOh (r) decreases by increasing λ. This indicates that fewer hydronium ions reside in the vicinity of the sulfonate groups when the membrane is well hydrated. In contrast, the number of water molecules around the sulfonate group increases, as indicated by the first coordination numbers shown in Table 2. In Figure 4.(c) and (d) we show g Oh O w (r) and g OwOw (r), corresponding to RDF between oxygen atoms of water-hydronium and water-water, respectively. Both RDFs show a first peak at 0.26 nm, which is related to the oxygen-oxygen distance in the first solvation shell. The g Oh O w (r) shows strong correlation between water and hydronium. The number of H 2 Osurrounding H 3 O + increases from 1.75 for λ = 2 to 4.42 for λ = 22. The g OwOw (r) exhibits similar trends. The coordination number of water molecules around each water molecule in the first solvation shell augments from 2.26 for λ = 2 to 4.64 for λ = 22. With increasing hydration level, the water molecules behave close to the bulk water molecules 7

8 Figure 4: Radial distribution functions of different pairs in Nafion membrane at temperature T = 350 K and water content λ. S: sulphur of SO 3 ; O w : oxygen of H 2 O; O h : oxygen of H 3 O + ;. (n bulk O wo w = 5.34). This general features are in nice agreement with to those reported in other publications. 1,5 In Figure 4.(e) and (f) we show the sulphur-sulphur and hydronium-hydronium RDFs respectively. The structure of g OhOh (r) is clearly governed by g SS (r). The first peak corresponds to the minimum distance between sulphur atoms. With increasing hydration, the first peak shifts from 0.47 nm for λ = 2 to 0.62 nm for λ = 22. When these values are compared with the distance between the SO 3 groups for the extended polymer chains 8

9 Table 2: First shell coordination numbers in the membrane at 300 K and 350 K. The R c used where 0.45 nm for sulphur-water, 0.35 nm for water-water and water-hydronium and 0.64 nm for sulphur-sulphur, corresponding to different water contents λ. Coordination Number water T = 300K T = 350K contents (λ) n SOw n SOh n Oh O w n OwOw n SS n SOw n SOh n Oh O w n OwOw n SS SPC/E ( 2.2 nm), it is evident that equilibrated hydrated Nafion chains agglomerate to form ionic clusters despite the electrostatic repulsion between SO 3 groups. With increasing λ, the number of sulphur atoms around each sulphur decreases from 3.67 to This means that the sulfonate groups move away from each other, while water molecules move close to them. The trends in g SS (r) agree very well with those reported by Devanathan et al. 6 Similar behaviour was found at lower temperature (T = 300 K) as shown in Table 2. In conclusion, the behaviour of our model is generally in good agreement with that characterizing other models proposed in the literature. 1,3 7 Slight differences in density and coordination numbers can be attributed to the coarse graining of the monomer of backbone chain. These differences do not have significant consequences on our results, which are therefore consistent and satisfactorily describe the general local features in Nafion membrane. Our ionomer model also gives reasonable results on the dynamics of the water molecules and hydronium ions. In Figure 5 we show the mean-squared displacement (MSD) of water molecules, at temperatures T = 300 K and 350 K. This function increases ballistically at short times, followed by the linear diffusive behaviour at long times. The self-diffusion coefficient D can be extracted from these data by using the Einstein relation, 9

10 Figure 5: Mean squared displacement of water molecules at (a) T = 300 K and (b) 350 K Table 3: Self-diffusion coefficients for water and hydronium at temperatures T = 300 K and 350 K. Good agreement with the values publisched by Mark et al. of 2.7(0.12) 8 Diffusion Coefficient - D ( 10 5 cm 2 /s) T = 300K T = 350K water contents (λ) D H2 O D H3 O + D H 2 O D H3 O ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± SPC/E bulk 2.78 ± ± D = lim t 2dt r2 (t), (1) where t is the time and d is the dimensionality of the system. In Table 3, we show the values for the self-diffusion coefficient of water molecules and hydronium ions computed at different water contents and temperatures. The effect of both membrane hydration and temperature is immediately evident in Figure 6. Water and hydronium diffusion coefficients clearly increase with water content and temperature. The water diffusion coefficient is significantly lower than in bulk water, due to confinement effects caused by the presence of the ionomer. When the membrane is highly hydrated the diffusion of water indeed approaches the diffusion of pure liquid water. The hydronium dif- 10

11 Figure 6: Self-diffusion coefficient of (a) water molecules and (b) hydronium ions as function of λ, at temperatures T = 300 K and 350 K fusion coefficient shows the same trends, and its value is about 3 times lower than the water diffusion coefficient. Our results are consistent and the diffusion coefficients are found within the range reported in the review by Kreuer et al. 9 The computed diffusion coefficients of hydronium ions are substantially different from the proton diffusion measured by experimentalists. Since the model for hydronium ions does not include the transfer of protons between the hydronium ions and the water molecules (which has quantum mechanical origin), the diffusion coefficient for hydronium does not include the Grotthus mechanism but only vehicular diffusivity. Without the structural diffusion effect, the hydronium diffusion is significantly lower than that of water molecules. This is expected because of the strong electrostatic interaction with the SO 3, which tends to bind the hydronium complexes, slowing down the diffusion of the ion. References (1) Venkatnathan, A.; Devanathan, R.; Dupuis, M. Atomistic simulations of hydrated nafion and temperature effects on hydronium ion mobility. The Journal of Physical Chemistry B 2007, 111, (2) Yeh, I. C.; Berkowitz, M. L. Ewald summation for systems with slab geometry. Journal of Chemical Physics 1999, 111,

12 (3) Wescott, J. T.; Qi, Y.; Subramanian, L.; Capehart, T. W. Mesoscale simulation of morphology in hydrated perfluorosulfonic acid membranes. Journal of Chemical Physics 2006, 124, (4) 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. Journal of Chemical Physics 2008, 129, (5) Devanathan, R.; Venkatnathan, A.; Dupuis, M. Atomistic simulation of Nafion membrane: 2. Dynamics of water molecules and hydronium ions. The Journal of Physical Chemistry B 2007, 111, (6) Devanathan, R.; Venkatnathan, A.; Dupuis, M. Atomistic simulation of Nafion membrane: 1. Effect of hydration on membrane nanostructure. The Journal of Physical Chemistry B 2007, 111, (7) 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. The Journal of Physical Chemistry B 2007, 111, (8) Mark, P.; Nilsson, L. Structure and Dynamics of the TIP3P, SPC, and SPC/E Water Models at 298 K. The Journal of Physical Chemistry A 2001, 105, (9) Kreuer, K.-D.; Paddison, S. J.; Spohr, E.; Schuster, M. Transport in proton conductors for fuel-cell applications: simulations, elementary reactions, and phenomenology. Chemical Reviews 2004, 104,

Supporting information for:

Supporting information for: Compactness of the Lithium Peroxide Thin Film Formed in Li-O 2 Batteries and Its Link to Charge Transport Mechanism: Insights from Stochastic Simulations Yinghui Yin a.,b,,