1. Block copolymer self-assembly KITPC, Aug. 3, 2015 1 Weihua Li weihuali@fudan.edu.cn State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai, China Collaborators: An-Chang Shi (McMaster University, Canada), Robert A. Wickham (Guelph University, Canada), Feng Qiu, Nan Xie, Meijiao Liu, Hanlin Deng (Fudan University, China)

2. Introduction Helical structures Binary crystalline phases Single crystalline phases Outline 2

3. Microphase separations N=N A +N B : polymerization Polyethylene: f χ: Flory Huggins parameter, characterize the interaction f=0.5 f<0.5 Phase separation is microscopic (periods are in nanoscale) Introduction 3

4. Phase diagram of AB diblock copolymers Leibler L, Macromolecules 13, 1602 (1980). 4

5. Phase diagram of AB diblock copolymers Matsen M and Schick M, Phys. Rev. Lett. 72, 2660 (1994) 5

6. Phase diagram of AB diblock copolymers Matsen M and Bates FS, J. Chem. Phys. 106, 2436, (1997) 6

7. Phase diagram of AB diblock copolymers Tyler C and Morse D, Phys. Rev. Lett. 94, 208302 (2005); Matsen M Macromolecules 45, 2161 (2012) 7

8. Phase diagram of AB diblock copolymers Construction of the phase diagram (uniform segment size):  1980, approximate phase diagram by Leiber: bcc, hex and lam  1994, relatively accurate phase diagram by Matsen and Schick, and gyroid was included  1997, hcp was added by Matsen and Bates  2005, Fddd double-network phase was discovered Non-uniform segment sizes? Geometrical confinement? More complex architectures (more blocks or components)? 8

9. Bates FS and Fredrickson GH, Physics Today 52, 32 (1999). 9 Self-assembly of ABC triblock copolymers At least five free parameters!

10. 10 More complex block copolymer systems Focus on two types of interesting structures:  Helices  Crystals (spherical phases) artificial macromolecular “atoms” (AMAs) A B C CsCl-type mesocrystal

11. Reduce many-body problem to that of a single polymer in a mean-field produced by the other polymers Self-consistently compute polymer configuration, monomer densities, mean-fields, free-energy Self-consistent field theory (SCFT): Gaussian-chain 11

12. Incompressibility: Mean-fields: Propagators of the polymer chain statisfy: Monomer densities: r(s) Edwards’ model SCFT equations of AB diblock copolymers 12

13. Initialize w A (r) and w B (r) randomly Set  (r)=(w A (r) + w B (r) )/2 Solve the diffusion equations for q(r,s) and q † (r,s) Evaluate  A (r) and  B (r) Update the potential fields using w A new = w A old + (  N  B +  -w A old ) w B new = w B old + (  N  A +  - w B old ) F. Drolet and G. H. Fredrickson, Phys. Rev. Lett. 83, 4317(1999). Solution of SCFT equations 13

14. modified diffusion equations similar as time-dependent Schrödinger equations Solving methods: real-space method spectral method (reciprocal-space method) finite difference method (Crank-Nicolson scheme) pseudo-spectral method Solution of SCFT equations 14

15. Operator-split Fourier transformation method (pseudo-spectral) reverse FFT Pseudo-spectral method 15 Tzeremes, G. et al. Phys. Rev. E. 2002

16. Equilibrium structures: helices 16 Helical structures self-assembled from a chiral block copolymers  Cylindrically confined diblock copolymers  ABC linear triblock copolymers

17. D Dobriyal et al. Macromolecules 2009 W. H. Li, R. A. Wickham, Macromolecules 42, 7530 (2009) W. H. Li, R. A. Wickham, Macromolecules 39, 8492 (2006) AB diblock copolymers in nanopores 17

18. ABC linear triblock copolymers (1) core-shell phases (2) alternative phases 2. frustrated 18 1. nonfrustrated Bates FS and Fredrickson GH, Physics Today 52, 32 (1999).

19. 2. frustrated B and C blocks co-form a super-cylinder, and A blocks forms the matrix. We assume that these super-cylinders are still arranged into a hexagonal lattice. 19 ABC linear triblock copolymers

20. ? V. Abetz and T. Goldacker, 2000; Ludwigs, et al., 2005 20 ABC linear triblock copolymers

21. Hexagonal lattice Candidate structures Li W. H. et al., Macromolecules 45, 503 (2012) ABC 21 (a) (b) (c) (d) (e) (f) (g)(h) ABC linear triblock copolymers

22. r0r0 D Anti-chirality arrangment on hexagonal lattice is frustrated. 22 ABC linear triblock copolymers

23.  r0r0 D Opposite chirality is preferred by two neighbor super-cylinders 23 √ ABC linear triblock copolymers

24. right-handed left-handed 24 ABC linear triblock copolymers

25. Jinnai et al. Soft Matter 2009Jinnai et al. Macromolecules 2013 Interpret experiments 25 Predict new results ABC linear triblock copolymers

26. ABC 26 Self-assembling mechanism: confinement

27. artificial macromolecular “atoms” (AMAs) A B C CsCl-type mesocrystal Rich structure prototypes provided by ionic binary crystals: CsCl, NaCl, ZnS, CaF 2, TiO 2, ReO 3, Al 2 O 3, … How to recast these structures via block copolymer self-assembly? Equilibrium structures: binary mesocrystals 27

28. Multiblock terpolymers design principle? A huge parameter space Bates F. S. et al. Science 2012 Pandora’s box?Panacea YesNo Advanced synthesis techniques 28

29. 29 Beyond Similarities in crystal lattices Ionic Crystal Coulomb interaction Ionic sizes or bond length Ionic valencies Micelles of BCPs Minimizing enthalpy and maximizing entropy incompressibilities Critical factors

30. 30 arrange two color disks on a 2D regular lattice abiding by the following restrictions: 1.fixed radius 2.fixed distance L Free volume per disk: cL 2D toy model Coordination number (CN): 4 3 2

31. 31 1.fixed radius 2.fixed free volume per circle L L decreases 2D toy model

32. Pentablock terpolymers: B 1 AB 2 CB 1 A B2B2B2B2 C B1B1B1B1 B1B1B1B1 Design principle of multiblock terpolymers by the 2D toy model 32

33. Symmetric binary crystals B1AB2CB1B1AB2CB1 AB2CAB2C α-BNCsClNaClZnS increase f B 1 CN=6CN=4CN=3CN=8 Design principle: the coordination number is tuned by the length ratio of the middle B block Self-consistent field theory (SCFT) calculations 33

34. Phase diagram of B 1 AB 2 CB 1 1 2 Path 2 CsCl CN=8 NaCl CN=6 ZnS CN=4 α-BN CN=3 C A/C CN=2 Path 1 CN=4 CN=3 CN=2 This design principle is also valid for two-dimensional crystal phases. 34

35. Mesocrystals with unequal CNs Unequal-CN ionic crystals provide richer structure prototypes AB2CB1AB2CB1 AB2CAB2C increase f B 1 For AB 2 CB 1, C blocks have to form loops inside C spheres, and thus form smaller spheres than A spheres to reduce the stretching. A sphere has a larger CN than C sphere 35

36. Phase diagram of AB 2 CB 1 Path 1 The proposed design principle is extended to unequal-CN mesocrystals CsCl CN=8 AlB 2 CN=8 Li 3 Bi CN=7 A15 CN=6 CaF 2 CN=16/3 TiO 2 CN=4 ReO 3 CN=3 CN=2 1 2 Xie, N.; et al. J. Am. Chem. Soc. 2014, 136, 2974 36

37. Phase diagram of AB 2 CB 1 Path 2 A number of two-dimensional mesocrystals (cylinder phases) are predicted 1 2 37

38. Phase diagram of B 1 AB 2 CB 3 Tune the asymmetry of CNs via the architecture asymmetry AB2CB1AB2CB1 B1AB2CB1B1AB2CB1 Asymmetric degree of CNs is tuned continuously from 1:1 to 1:3 new phases α–Al 2 O 3 NASCNASC α–nBN 38

39. Summary 39 Predict a large number of new crystalline phases, and deepen understanding on the formation of crystalline phases

40. Equilibrium structures: single mesocrystals 40 Two well-known packing problems of spheres  Hard spheres: hcp  Equal-sized bubbles (Kelvin problem): A15 Spherical phasesPacking model of soft spheres

41. Equilibrium structures: single mesocrystals 41 Single crystals formed in AB-type block copolymers:  AB diblock copolymers with uniform segments: hcp, bcc  AB n miktoarm copolymers: A15?  AB diblock copolymers with non-uniform segments?

42. Equilibrium structures: single mesocrystals 42 Experiments with Poly(isoprene-b-lactide) (PI-PLA): Cooling from 70 to 40ºCCooling from 120 to 25ºC After 26 days at room T bcc Frank-Kasper σ phase! stable or metastable for AB or AB n ? Lee S, Bluemle MJ, Bates FS, Science 330, 349 (2010);

43. Equilibrium structures: single mesocrystals 43 Effect of conformational asymmetry:

44. Equilibrium structures: single mesocrystals 44 Effect of arm numbers of AB n : σ phase was not considered Arm number induces spontaneous curvature: Grason GM and Kamien RD, Macromolecules 37, 7371 (2004).

45. Equilibrium structures: single mesocrystals 45 Xie N, Li WH, Qiu F, Shi AC, ACS Macro Lett. 3, 906 (2014); Phase sequence as temperature decreases: bcc σ A15 Effect of arm numbers of AB n : σ phase is considered

46. Macromolecular metallurgy ： design block copolymers for desired structures by developing design principles, crystalline structures Self-consistent field theory is a powerful tool to verify proposed design principles Summary 46

47. Thank you for your attention! 47