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1 CoarseGrained Modeling of Ionomers and SaltDoped Block Copolymers Lisa Hall H.C. Slip Slider Assistant Professor William G. Lowrie Department of Chemical and Biomolecular Engineering The Ohio State University My path: BS, RoseHulman PhD, UIUC Postdoc, Sandia Map from Wikimedia Commons

2 Applications: Car tires, fuel cells, photovoltaics Polymer Nanocomposites Experience CoarseGrained Polymers Ionomers Applications: Golf balls, packaging, Battery electrolytes? cas/productsegments/pages/gre en_tires.aspx PRISM liquid state theory g pp r 3 types of computational methods Classical fluids density functional theory [ ] 4 Molecular dynamics simulations g pn r g nn r p r Komarov et al. Soft Matter 6, 3939 (2010) 2

3 Motivation: Understanding Ionic Aggregation in Ionomers Ionomers as electrolytes Single ion conducting ability Chemically, mechanically stable Challenge: low ion conduction Fundamental polymer science Experimental advances ADMET synthesis precise spacing of acid groups (Wagener group, U Florida) Neutralized, characterized Sharp, large ionomer peak Ideal for comparison to MD Total scattering; predominantly counterions in ionomer peak From: M. E. Seitz; C. D. Chan; K. L. Opper; T. W. Baughman; K. B. Wagener; K. I. Winey; J. Am. Chem. Soc. 2010, 132, Copyright 2010 ACS

4 CoarseGrained Molecular Dynamics Simulations of Ionomers Long time, length scales accessible Simple beadspring polymer, multiple atoms represented as one bead Periodic Na Random Block Copolymer X Y vary X/Y connect X and Y groups randomly N bb =7 Variable N bb, number of backbone beads per charged bead Captures key aspects: polymer entropy, ionic interactions Missing: local dielectric properties, specific chemistry

5 Cluster Morphology Periodic Spacing narrow cluster size distribution mean cluster size 31 ions [ ] 4 Random Block Copolymer stringy, large clusters mean cluster size 87 ions [ ] [ ] X Y X/Y=2 XY=12 PRL 106, (2011) Snapshots showing only ions, colored by cluster size Small clusters Large clusters background dielectric constant = 4

6 Comparison to Experimental Scattering Increasing spacing moves ionomer peak to lower wavevector for both experimental data and simulated counterioncounterion structure factor Random block copolymer architecture similar to experimental pseudorandom: broader, lower wavevector peak (larger aggregates of more variable size) Experiments: 2834% neutralized, simulations: fully neutralized Experiment Simulation S(k) [a.u.] Na Na S CICI (k) Random block N bb = 5 Pseudorandom 15CC per COOH k [nm 1 ] k [nm 1 ] Details in Hall, Seitz et al. JACS 134, (2012)

7 4 counterion trajectories (blue) and 3 anion trajectories (red and purple on one polymer, polymer center of mass in grey, another anion in purple) 1000 steps of 50 τ each Ion trajectories appear to hop But mechanism is not standard hopping [ ] n this counterion (enlarged in red) and nearby clusters before, during, and after its hop (total time 1000 τ)

8 SaltDoped Block Copolymers for Batteries High modulus, nonflammable battery electrolytes can allow the use of solid lithium electrode (lightweight) Two unlike polymers connected into the same molecule can microphase separate into various ordered phases Ions contained in one phase that conducts, other phase gives desired material properties Balsara group studies lamellar PSPEO with Li salts; works well at controlled temperature Energyfiltered TEM image: Li salt is primarily in PEO block From E.D. Gomez et al. Nano Letters 9, (2009).

9 Why coarsegrained simulations SaltDoped Block Copolymers Many parameters, not clear how to optimize without fundamental understanding Need charges, long time and length scales From E.D. Gomez et al. Nano Letters 9, (2009). Options to equilibrate MD simulations of block copolymers Use Monte Carlo moves (ions add complications) Start from close to equilibrated structure (must know equilibrated structure) New strategy Simple model; maps nicely between MD and fluids density functional theory Start MD simulations using morphology information from fdft fdft is also fast (helps search parameter space), gets free energies Equilibration is hard: Diblock copolymer melt N A =N B =20 ε AB =1.9 at τ LJ =1,000,000 after starting from random configuration

10 The PL phase is also different in that it has two distinct periodicities, which imp eigenvalue Eq. (1.165) for the basis functions must be generalized to Tapered Block Copolymer Motivation 2 f i (r )= λ,i D 2 λ,i D 2 Want gyroid phase at high MW; need additional tunable parameter Tapered diblock systems f i (r ) where D is the inplane spacing between perforations and D is the outofpla spacing. However, this distinction only enters in an obvious extension to Eqs. (1.285), and in the need to minimize F with respect to both D and D. Diblock SCFT phase diagram S C L C S Still shows gyroid phase cn 20 S cp G S cp 10 disordered f Roy, R. et al. Macromolecules 44, (2011). What do the SCFT phase diagrams look like for these systems? Figure 1.20: Theoretical phase diagram for diblock copolymer melts showing whe morphologies in Fig are stable. All phase transitions are discontinuous e meanfield critical point denoted by the solid dot. Along part of the orderdisor (ODT) is a narrow region, S cp, where spherical domains prefer a closepacked over the usual bcc one. In the strongsegregation limit, the G region pinches off the ODT approaches the two edges of the diagram, and the C/S and L/C bounda the fixed compositions estimated by the arrows at the top of the diagram. Matsen, M. W.in Soft Matter (Gompper, G. & Schick, M.) (WileyVCH Verlag GmbH & Co. KGaA, 2007) Comparing the free energies of the disordered phase and all the ordered pha 1.19 generates the phase diagram in Fig. 1.20, which maps the phase of lowest fre

11 Methodology SelfConsistent Field Theory (SCFT) PolySwift by TechX Corporation Incompressible Gaussian chains A and B type monomers identical Phase diagrams (S/C/G/L only)

12 Tapered diblock composition profiles Standard diblock: A B Tapered diblock : A B B A B A B A B A Each division of two blocks (B then A) has the same length (2% of polymer backbone) Average composition matches the gradient Jiang, R. et al. Macromolecules 41, (2008).

13 30% tapered phase diagram dashed lines: diblock phase diagram Dashed lines: diblock phase diagram adapted from Cochran, E. W., GarciaCervera, C. J. & Fredrickson, G. H. Macromolecules 39, (2006).

14 50% tapered phase diagram dashed lines: diblock phase diagram Dashed lines: diblock phase diagram adapted from Cochran, E. W., GarciaCervera, C. J. & Fredrickson, G. H. Macromolecules 39, (2006).

15 30% inverse tapered phase diagram dashed lines: diblock phase diagram Dashed lines: diblock phase diagram adapted from Cochran, E. W., GarciaCervera, C. J. & Fredrickson, G. H. Macromolecules 39, (2006).

16 Acknowledgements Jonathan Brown Scott Sides OSU startup funding Conclusions Taper shifts ordered phases to higher χn 30% taper: gyroid phase over a wider range of f A 30% inverse taper: mostly lamellae Large inverse taper: snakes across/bridges lamellae Future work: replace SCFT with fluids DFT, add ions, and connect to MD simulations

17 CoarseGrained MD Details KremerGrest beadspring model (FENE bonds, repulsive LJ potential) NVT ensemble, Langevin thermostat, reduced LJ temperature = backbone beads per chain (412 charges per chain) 3 CC bonds ~ one bead Pendant (COO ) same size as backbone bead (diameter = σ) Counterions half the diameter of polymer beads Equilibrate 10 7 steps of τ (τ = reduced LJ time unit) 800 chains in simulation box, meltlike total packing fraction ε r varies Coulomb interaction strength; ε r = 4 allows equilibration but still shows strong clustering, Bjerrum length = 36 σ 14 nm Periodic Na Random Block Copolymer X Y vary X/Y connect X and Y groups randomly