1. MD simulation of the effect of side-chain length on dynamics in the PEO system Andi Hektor 1, Alvo Aabloo 2, Mattias Klintenberg 3 & Josh Thomas 4 1. Institute of Materials Science, Tartu University, Tähe 4, 51010 TARTU, Estonia. 2. Institute of Physics, University of Tartu, Tähe 4, 51010 TARTU, Estonia. 3. Condensed Matter Theory Group, Department of Physics, Uppsala University, Box 530, SE-751 21 Uppsala, Sweden. 4. Materials Chemistry, Ångström Laboratory, Uppsala University, Box 538, SE-751 21 Uppsala, Sweden. E-mail: andi@ut.ee

2. Introduction Poly(ethylene oxide) (PEO): -(CH 2 -CH 2 -O) n - Poly(ethylene oxide) (PEO): -(CH 2 -CH 2 -O) n - Fig. 1. PEO unit – ethylene oxide (EO).Fig. 2. PEO chain (80 EO units).

3. Introduction Electrolyte, side-chain Electrolyte, side-chain Fig. 3. Electrolyte (PEO+LiCl) including a single side-chain.

4. Introduction PEO topology PEO topology A long PEO backbone with shorter side-chains A long PEO connected by short cross-links A 3-D polymer network Fig. 4. Different PEO topologies.

5. Introduction Fig. 5. PEO backbone with a side-chain (1) and the zoomed-in linkage region (2). 1 2 PEO chain with a side-chain and linkage-point PEO chain with a side-chain and linkage-point

6. Introduction Effects of side-chain Effects of side-chain Side-chains affect the dynamics of PEO From experiment: the biggest effect is around the 6-8 EO monomers Can we use MD to understand these effects?

7. Introduction Molecular Dynamical (MD) simulations Molecular Dynamical (MD) simulations Classical Newtonian mechanics Potentials

8. Introduction MD simulation analyse MD simulation analyse Radial distribution function (RDF): Mean Squared Displacement (MSD) and 3D diffusion coefficient (D): Average Velocity (AV):

9. Method Potentials Potentials The majority of the potentials we use for PEO originate from earlier work The torsional potential for the C-C-C-O dihedral angle in the side-chain linkage region is calculated by Quantum Mechanics (QM) Fig. 6. The region of the calculated torsional potential. C C C O

10. QM method and basis-sets: HF/6-31G **, HF/6-31 ++ G ** Technical information: A total of 784 CPU hours was used on our in-house Linux PC-cluster using NWChem software Analytical torsion potential function: Method Calculation of torsion potential C-C-C-O Calculation of torsion potential C-C-C-O u i are constants and  is the torsion angle. Fig. 7. Fitting of the calculated data (the red squares) to a 7 th order trigonometric polynom.

11. Method Fig. 8. The “unpacked” configuration with a single side-chain for MD simulation. 9 side-chain systems (marked as s5-s9, s11, s15, s19 and s23): a cubic periodic box (24.5 x 24.5 x 24.5 Å) containing a 186 EO-monomer PEO chain with a 5-9, 11, 15, 19, and 23 EO- monomer PEO side-chains. Reference system (marked as r): a cubic periodic box (24.5 x 24.5 x 24.5 Å) containing a single PEO chain involving 193 EO-monomers with no side-chain. Simulation boxes generated by controlled pivotal Monte Carlo growth. The density maintained around 1.0 g/cm 3. MD configurations MD configurations

12. MD simulations Intramolecular force fields: rigid bonds; angle and torsional potentials Long-range force fields: electrostatic and Buckingham’s potentials Calculation: Ewald summation of long-range forces used Configuration: a cubic MD box (24.5 x 24.5 x 24.5 Å) with periodic boundary conditions; density maintained at ~1 g/cm 3 Simulation process: time-step 0.5 fs, temperature 290 K, starting with NVT and followed by NpT for the 1000 ps Technical information: a total of 3900 CPU hours used on our in-house Linux PC cluster using DLPOLY software

13. Results Animation 1. ”Unpacked” chain Animation 2. Zoomed-in version Animations of the MD simulations Animations of the MD simulations

14. Results Radial distribution function (RDF) Radial distribution function (RDF) Fig. 9. RDF (C-C and C-O) identical for all the systems. C-C C-O

15. Results Mean Square Displacement (MSD) (e.g., for r and s7) Mean Square Displacement (MSD) (e.g., for r and s7) Fig. 10. MSD for the carbon atoms: C r – the reference system, C s7 – the side-chain system s7. CrCr C s7

16. Results 3D diffusion coefficients 3D diffusion coefficients Fig. 11. 3D diffusion coefficents for the C and O atoms. Note: the strong “immobilising” effect around 6-8 EO monomers. C O

17. Results Diffusion coefficents for the side-chain C-atom Diffusion coefficents for the side-chain C-atom Fig. 13. Diffusion coefficents for the side-chain C-atoms. C O

18. Results Average velocity (AV) for O-atoms along the side-chain (e.g., s7) Average velocity (AV) for O-atoms along the side-chain (e.g., s7) Fig. 14. AV for O-atoms along the side-chain (e.g. s7); “1” means the first from the linkage-point; “7” means the free end.

19. Results AV for O-atoms along the side-chain for different side-chains lengths AV for O-atoms along the side-chain for different side-chains lengths Fig. 15. AV for O-atoms along the side-chain for different lengths. “1”: 1 st atom “max”: end of side-chain

20. Results Averaged AV for O-atoms at different side-chain lengths Averaged AV for O-atoms at different side-chain lengths Fig. 16. Averaged AV for O-atoms at different side-chain lengths (s5-s9, s11, s15, s19 and s23).

21. Summary RDF for the reference system (r) and all the side-chain systems (s5-s9, s11, s15, s19, s23) are identical The addition of side-chains decreases chain mobility A minimum occurs in the diffusion coefficents between 6 and 9 EO side- chain units – in excellent agreement with experiment! A maximum occurs in the side-chain diffusion coefficents between 5 and 11 EO side-chain units A maximum occurs in the side-chain atoms AVs between 6 and 8 EO side- chain units The average AV depends the side-chain length: two maxima a appear - at 8 and 15 EO side-chain units

22. References 1.F. M. Gray, “Polymer Electrolytes”, Royal Society of Chemistry, Cambridge, 1997. 2.A. Nishimoto, K. Agehara, N. Furuya, T. Watanabe and M. Watanabe, Macromolecules, 1999, 32, 1541. 3.W. Krawiec, L. G. Scanlon, Jr., J. P. Fellner, R. A. Vaia, S. Vasudevan and E. P. Giannelis, J. Power Sources, 1995, 54, 310. 4.S. Neyertz, D. Brown and J. O. Thomas, J. Chem. Phys., 1994, 101, 10064. 5.S. Neyertz, D. Brown and J. O. Thomas, Comp. Poly. Sci., 1995, 5, 107. 6.A. Aabloo and J. O. Thomas, Comp. and Theor. Poly. Sci., 1997, 7, 47. 7.A. Aabloo and J. O. Thomas, Electrochimica Acta, 1998, 43, 1361. 8.A. Aabloo, M. Klintenberg and J. O. Thomas, Electrochimica Acta, 2000, 45, 1425. 9.R. J. Harrison et al, ”NWChem, A Computational Chemistry Package for Parallel Computers Version 4.0.1" (2001), Pacific Northwest National Laboratory, Richland, Washington 99352-0999, USA 10. The DL_POLY Project, W. Smith and T. Forester, TCS Division, Daresbury Laboratory, Daresbury, Warrington WA4 4AD, England.

23. Acknowledgements The Nordic Energy Research Programme (NERP) The Swedish Natural Science Research Council (NFR, now VR) The Estonian Science Foundation (ETF), grant no 4513