Study on Diffusion Processes of Water and Proton in PEM Using Molecular Dynamics Simulation Lei Chen 1, a, Wen-Quan Tao 2,b, *

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1 Materials Science Forum Vols (1) pp Online available since 11/Dec/6 at (1) Trans Tech Publications, Switzerland doi:1.48/ Study on Diffusion Processes of Water and Proton in PEM Using Molecular Dynamics Simulation Lei Chen 1, a, Wen-Quan Tao,b, * 1, Key Laboratory of Thermo-Fluid Science and Engineering,Ministry of Education, Xi an Jiaotong University, Xi an 7149, China a Chenlei.9@stu.xjtu.edu.cn, b wqtao@mail.xjtu.edu.cn * Keywords: molecular dynamics simulation; materials studio; diffusion coefficients; Nafion 117. Abstract. In this paper a molecular dynamics calculation model for the Nafion 117 membrane is constructed by Materials Studio (MS) software platform to study its micro-structure and transport properties. Based on the calculation model, cell structures of different water content of Nafion 117 membrane are obtained and the predicted density values of simulated cell are in good agreement with experimental data. Meanwhile, the diffusion processes of water molecules and hydrogen ions in the membrane are studied, respectively. The predicted diffusion coefficients of both water molecules and hydrogen ions increase with the water content, which agrees well with the variation trend of experimental data. The reasons for the deviation between numerical results and the experiment values in literature are analyzed. Introduction In the past decades, a great progress in the study of PEMFC has been made, but there are still many key issues to be resolved for PEMFC before it can be cheaply applied to industries. One of them is the transport properties of PEM and its effect on battery performance. The functional characteristics of PEM are mainly reflected on the nano-level, so the microscopic study on PEM can help us to understand its microstructure and transport properties. The molecular dynamics (MD) simulation method is a useful method to study PEM [1-1]. Elliott et al. [1] used classical MD with a modified DREIDING [] force field to study the dynamics of small molecules in a model Nafion membrane for λ=1,.8, and 9.7. Vishnyakov and Neimark [] used a simplified united-atom force field in their MD simulation of hydrated Nafion with K+ counterious for three different λ values. Urata et al. [4] also used a similar united-atom force field to model hydrated Nafion for λ=.8, 5.9, 1., 5.4. Jang et al. [5] used an all-atom approach in their MD simulation of nanophase segregation and transport in Nafion for λ=16. Arun et al. [6] examined the effects of hydration level and temperature on the nanostructure of an atomistic model of a Nafion (DuPont) membrane and the vehicular transport of hydronium ions and water molecules using classical molecular dynamics simulations, and they found that temperature has a significant effect on the absolute value of the diffusion coefficients for both water and hydronium ions. Charati, S. G. et al. [1] estimated Diffusion coefficients of He, O, N, CO, and CH4 at K in four silicone polymers, by MD simulations. Dieter Hofmann et al. [1] discussed the results of extensive atomistic molecular dynamics investigations on the transport of different small molecules in flexible chain rubbery and stiff chain glassy polymers. Since the structure of PEM is very complicated, so it is essential to construct a simplified model for study. In this paper, according to literature [1,1,14], a molecular dynamics calculation model for the Nafion 117 membrane is constructed by Materials Studio (MS) software platform, the diffusions of water molecules and hydronium ions in PEM are simulated using MD with COMPASS force field [15] and are compared with relevant experimental results. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, (ID: /1/11,:8:48)

2 Materials Science Forum Vols Simulation model and procedure The chemical structure of Nafion membrane is shown in Figure 1, where x varies between 6 and 1 and y=z=1. In this paper, Nafion 117 membrane, where x=7 and n= 1 is studied. In all figures of this paper, oxygen atom, hydrogen atom, sulfur atom, fluorine atom, and carbon atoms are respectively represented in red, gray, yellow, blue and gray-black. The system simulated is consisted of several Nafion chains forming a porous structure, the water and protons inside by Materials Studio software. The cell simulated consists of 4 Nafion 117 chains, 4 HO + and -64 H O. The number of water molecule depends on the values of λ (λ is the ratio of the sum of the number and number over the number of sulfonic acid-based). For example, when λ =, the number of water molecule is 8. [( CF CF ) ( CF CF ) ] x y n [ OCF CF] OCF ( ) CF z SO Fig.1 Chemical structure of Nafion In the study for λ =.5, 7, 1.5, 17, the cell models of hydrated Nafion 117 membrane are constructed by MS software platforms. A COMPASS force field developed by Sun H. et al. [15] was adopted in the molecular simulation. The valence bond, angle, dihedral, cross-term and out-of-plane bending were defined as below. 4 E = [ k ( b b ) + k ( b b ) + k ( b b ) ] (1) b b 4 4 E [ k ( θ θ ) + k ( θ θ ) + ( θ ) ] () θ = k 4 θ θ { k1[1 cos( ϕ ϕ,1)]} + k[1 cos(ϕ ϕ,) + [1 cos(ϕ ϕ, ϕ E )] () E ϕ x = k = b, b' k b, ϕ bb ' ' ' ' ( b b )( b b ) + kθθ ( θ θ )( θ θ ) + k θ ( b b )( θ θ ) θ, θ + ( b b )[ k1 cosϕ+ k cos ϕ + k cosϕ ] (4) ' ' + ( b b )[ k1 cosϕ+ k cos ϕ + k b', ϕ + ( θ θ )[ k 1 cosϕ+ k cos ϕ+ k θ, ϕ cosϕ ] cosϕ ] E = k (5) χ χχ χ where k (all in equations (1)-(5))is an independent force field parameter, respectively, and subscript denotes equilibrium structure parameters. The concrete steps to construct the cell model are as follows: 1) Nafion 117 chain and the structure models of water molecule and hydronium ion as shown in b, θ b Fig. H O model Fig. + H O model Fig4. Nafion 117 chain Figures to 4 are drawn by Materials Visualizer, and energy optimization is carried out.

3 168 Physical and Numerical Simulation of Material Processing VI ) The cell structure models consisting of four Nafion 117 chains, 4 hydronium ions and a certain amount of water molecules (5,1,4,64, respectively) are constructed. ) The cell structure models are optimized to minimize their energies by the steepest descent method. 4) The final cell structure model is obtained by equilibrating the above initial configuration using molecular dynamics simulation for 5ps at K and NPT ensemble is adopted. Molecular dynamics calculation is applied to the cell model obtained from the simulated annealing and the equilibrated output is the final cell model. The simulated final four cell structure model for different water content of Nafion 117 membrane are shown in Figures 5-8. The volumes of cell are as follows:.8 Ȧ.8 Ȧ. 8 Ȧ ;5.7 Ȧ 5.7 Ȧ 5.7 Ȧ ; 7. Ȧ 7. Ȧ 7. Ȧ ; 8.5 Ȧ 8.5 Ȧ 8.5 Ȧ. Fig5. The cell structure for λ=.5 Fig6. The cell structure for λ=7 Fig7. The cell structure for λ=1.5 Fig8. The cell structure for λ=17 Diffusion Coefficients Computation There are two kinds of diffusion coefficients in multi-mixture: self-diffusion coefficient and inter-diffusion coefficient. Self-diffusion describes the diffusion motion of the molecules without the driving force (for example, the concentration gradient). It is caused by Brownian motion of molecules and can be applied to both pure substances and certain components in the mixture. In this paper, the self-diffusion refers to the diffusion of water molecules in the mixture and the diffusion of hydronium ion in the mixture.

4 Materials Science Forum Vols Inter-diffusion for binary mixtures describes the diffusion motion ability of component A through component B. It is related to the quality and the molar flux, etc, such as the concentration gradient of a particular component. The inter-diffusion is not studied in this paper. The atom of molecular dynamic calculation system has a non-stop movement from the initial position, so the atom has a different location at different time. r i ( t) represents the location of particle i at t time. The mean value of square displacement of particles is defined as the mean square displacement (MSD), that is MSD= r( t) r( ) (6) where,< > represents the mean value. According to Einstein's diffusion law: lim r t ( t) r( ) = 6Dt Where, D represents diffusion coefficient. In the MS software, the diffusion coefficient is calculated as follows: 1 d ( ( ) ( ) ) 6 lim N D = ri t r t N t dt (8) i= 1 Where, N is the number of diffusion atoms in the system. The differential term of Eq. (8) is replaced by the ratio of MSD to time difference, that is, the slope of the curve of MSD to time. Because the value of MSD is the average for number N of diffusion atoms, so the above formula can be simplified as follows: a 6 (7) D=. (9) Where, a is the slope of the graph. In the MS software, the diffusion coefficients of water molecules and hydrogen ions can be obtained respectively by dynamic calculation on the cell structure model and analysis. Here, MD simulation for ps at K, NVE ensemble is adopted. In the simulation, the time step is set at 1fs and the frame output is every steps. And then analyze the trajectory files by Analysis Dialog in Discover Module of MS software and then calculate the diffusion coefficient according to the calculation method mentioned above. References are cited in the text just by square brackets [1]. (If square brackets are not available, slashes may be used instead, e.g. //.) Two or more references at a time may be put in one set of brackets [,4]. The references are to be numbered in the order in which they are cited in the text and are to be listed at the end of the contribution under a heading References, see our example below. Simulated Result and Discussion Cell Density.The simulated density of the cell is shown in Figure 9. Fig.9 also shows the experimental data of density measured by Mirris and Sun [16]. For the different water content simulated values are basically consistent with the experimental data with the maximum deviation of 8%. Cell density deceases wit the increase ofλ.

5 17 Physical and Numerical Simulation of Material Processing VI ρ/kgm Experiment Simulation λ Fig9. Density versus water content Diffusion Coefficient. In MS software, first of all, mark water molecules and hydronium ion through oxygen atoms, denoted byo w, Oh respectively; and then, analyze the trajectory files by the module Analysis in DISCOVERY of MS; Figures 1,11 shows the MSD of O w and O h as a function of time for various hydration levels from λ =. 5 to λ = 17 respectively. Finally, calculate the diffusion coefficient of water molecules and hydronium ions according to the method mentioned. The results are shown in Figures 1, 1, where experimental data [17, 18] are also presented. As can be seen from the figures 1, 1, the changes of diffusion coefficients of water molecules and hydronium ions with the water content are qualitatively consistent with the experimental results, but the simulated values of diffusion coefficients of water molecules and hydronium ions are quantitatively smaller than the corresponding experimental values by a factor of -, respectively. Reasons for this large deviation may be mainly attributed to the periodic boundary conditions applied in our simulation for the Nafion 117 membrane, and the periodic boundary condition is an ideal for the infinite system. While in the literature [17, 18], the values are obtained by measuring for the limited size of the actual film. However, the diffusion coefficients of water molecules and hydrated hydrogen ions increase with increasing water content (λ), and the simulated results is qualitatively consistent with experimental results. Both experimental and numerical results show that the more water content, the more moist membrane, the greater diffusion coefficient. λ=.5 λ=7 λ=1.5 λ=17 1 λ=.5 λ=7 λ=1.5 λ=17 MSD of O w 1 MSD of O h Time(ps) Fig1. MSD of water molecular in Nafion for hydration level (λ ) indicated by the legend Time(ps) Fig11. MSD of hydronium ions in Nafion for hydration level (λ ) indicated by the legend.

6 Materials Science Forum Vols Diffusion coefficient of water molecules Experiment Simulation λ Fig1. Diffusion coefficient of water molecules versus λ Diffusion coefficient of hydronium ion Experiment Simulation λ Fig1. Diffusion coefficient of hydronium ions versus λ Conclusion By using the molecular dynamics software Materials Studio the cell structure of proton exchange membrane Nafion 117 is simulated, and the density of proton exchange membrane cell is obtained. The predicted variation trend of the cell density versus water content is consistent with available experimental data, and the maximum deviation is about 8%. In addition, the self-diffusion coefficients of both water molecules and hydronium ions are also simulated. Even though the qualitative variation trend of the two diffusion coefficients with water content λ is agreeable with experimental results and the simulated values are almost in the same order of magnitude of the corresponding experimental values, big deviations exist between the predicted results and test data, with simulated results being much smaller by a factor of to. Further research work should be performed to build a more reasonable molecular dynamics simulation model for simulating the transport process in proton exchange membrane. Acknowledgments This work has been supported by the National Natural Science Foundation of China (Grant numbers 5665). References [1] J.A. Elliott, S. Hanna, A. M. S. Elliott and G. E. Cooley: J. Phys. Chem. Vol. 1 (1999), pp [] S. L. Mayo, B. D. Olafson, W. A. Goddard: J. Phys. Chem. Vol. 94 (199), p [] A. Vishnyakov, A. V. Neimark: J. Phys. Chem. B Vol. 15 (1), p [4] S. Urata, J. Irisawa, A. Takada, W. Shinoda, S. Tsuzuki and M. Mikami: J. Phys. Chem. B Vol. 1 (5), p [5] S. S. Jang, V. Molinero, T. Ca_gun and W. A. Goodard: J. Phys. Chem. B Vol. 18 (4), p [6] A. Venkatnathan, R. Devanathan and D. Michel: J. Phys. Chem. B Vol. 111 (7), pp [7] I. H.Hristov, S. J. Paddison and R. Paul: J. Phys. Chem. B Vol. 11 (8), pp

7 17 Physical and Numerical Simulation of Material Processing VI [8] S. T. Cui, J.W. Liu, E. S. Myvizhi, J. P. Stephen, J. K. David and J. E. Brian: J. Phys. Chem. B Vol. 11 (8), pp [9] Y. K. Choe, E. Tsuchida, T. Ikeshoji, S. Yamakawa and S. Hyodo: J. Phys. Chem. B Vol. 11 (8), pp [1] M. Vittadello, E. Negro, S. Lavina, G. Pace, A. Safari, and V. D. Noto: J. Phys. Chem. B Vol. 11 (8), pp [11] N. Hara, H. Ohashi, T. Ito and T. Yamaguchi: J. Phys. Chem. B Vol. 11 (9), pp [1] S. G. Charati, S. A. Stern: Macromolecules Vol. 1 (1998), pp [1] D. Hofmann, L. Fritz, J. Ulbrich, C. Schepers and M. Boehning: Macromol. Theory Simul. Vol. 9 (), pp [14] A. Inc, Discover tutorials, Materials Studio. Version, 4.4 (8). [15] D. Rigby, H. Sun and B.E. Eichinger: Polym. Int. Vol. 44 (1998), pp [16] D.R. Morris, X. Sun: J. App: Polym. Sci. Vol. 5 (199), pp [17] T.A. Zawodzinski, M. Neeman, L.O. Sillerud and S. Gottesfeld: J. Phys. Chem. Vol. 95 (1991), p. 64. [18] J.C. Perrin, S. Lyonnard and F. Volino: J. Phys. Chem. C Vol. 111 (7), p. 9.

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