1. Microphase Separation of Complex Block Copolymers 复杂嵌段共聚高分子的微相分离 Feng Qiu ( 邱 枫 ) Dept. of Macromolecular Science Fudan University Shanghai, 200433, CHINA July 20, 2005, Peking University

2. Block Copolymer ( 嵌段共聚高分子 )

3. Order-Disorder Transition ( 有序 - 无序转变 )  S ~ 1/N Micro-phase separation ( 微相分离 )

4. M. Park, et al., Science, 276, 1401(1997).

5. M. Templin, et al., Science, 278, 1795(1997).

6. Gyroid Phase http://eltweb.mit.edu/images/research/nanostructures.html A. H. Scheon, 1960s

7. Diblock Copolymer Morphology From M. Matsen Morphology not sensitive to chain architecture

8. Phase Diagram of Diblock Copolymers M. Matsen and W. Schick, Phys. Rev. Lett, 72, 2660(1994). Two parameters: f and  N Mean Field Theory

9. Complex Block Copolymers From G. H. Fredrickson and F. S. Bates Rich and variety chain architectures

10. Triblock Copolymers ( 三嵌段高分子 ) A B C ABC A BC A BC Block Sequence Chain Architecture Parameter space increases 18-fold

11. A Challenge Can we effectively predict new morphologies and their stability? YES! Self-Consistent Field Theory

12. Coarse-graining The successive coarse-graining processes:

13. Chain Modeled as a Path r(0) q(r,s)q(r,s) r(s)r(s) r(N)r(N) Edwards Model

14. Modified Diffusion Equation for Linear ABC Triblock Copolymers And initial condition q + similar 0 f A N (f A +f B )N N

15. Free Energy Mean field approximation

16. SCF Equations For linear ABC triblock Copolymers

17. Fourier Space Method M. Matsen and W. Schick, PRL, 72, 2660(1994) Periodic structures Known symmetry Simplify the problem to matrix operations

18. Phase Diagram of Diblock Copolymers 60 basis functions 10 -4, free energy PS/PI, f=0.37  N (stable) R L /R G R Hole /R Lam Exp. 16-20 2.41.02-1.49 Theo. 14.9-20.4 2.451.32-1.36

19. Real Space Method Initialize all fields randomly Set  (r)=  [1-  A (r) -  B (r) -  C (r) ] Solve the diffusion equations for q(r,s) and q † (r,s) Evaluate  A (r),  B (r) and  C (r) Update the potential fields using w A new = w A old + (  AB  B +  AC  C +  - w A old ) w B new = w B old + (  AB  A +  BC  C +  - w B old ) w C new = w C old + (  BC  B +  AC  A +  - w C old ) F. Drolet and G. H. Fredrickson, Phys. Rev. Lett., 83, 4317(1999).

20. Pattern Evolution in Iterations Free energy is lowered and finally reaches minimum.

21. 2D Microphases Discovered in Linear ABC Triblocks LAM 3 HEXCSHTET 2

22. 2D Microphases Discovered in Linear ABC Triblocks LAM+BD-IHEX+BDLAM+BD-II

23. Phase Diagram of ABC Linear Block Copolymer  AB N=  BC N=  AC N = 35  AB N=  BC N=  AC N = 55

24. Influence of Block Sequence ABC ABC vs  AB   BC   AC P. Tang, F. Qiu, H. D. Zhang, Y. L. Yang, Phys. Rev. E, 69, 031803(2004).

25. Phase Diagram of ABC Linear Block Copolymer ABCACB  AB ~  BC   AC

26. PI-PS-P2VP and PS-PI-P2VP S. P. Gido, et al, Macromolecules, 26, 2636(1993). f PS =f PI =f P2VP  1/3,  PI-P2VP >>  PS-PI   PS-P2VP Y.Mogi, et al, Macromolecules, 27, 6755(1994).

27. 2D Microphases Discovered in Star ABC Triblocks LAM 3 TCBHEX 3 LAM+BD

28. 2D Microphases Discovered in Star ABC Triblocks KPHEXCSH

29. 2D Microphases Discovered in Star ABC Triblocks DEHTLAM+BD-I

30. Phase Diagram of ABC Star Triblock  AB =  BC =  AC = 35

31. Phase Diagram of ABC Star Triblock  AB =  BC = 72,  AC = 22 PS-PI-PMMA

32. PS PI P2VP Star Triblock A. Takano et al, Macromolecules, 2004, 37, 9941

33. Influence of Chain Architecture A B C ABC VS P. Tang, F. Qiu, H. D. Zhang, Y. L. Yang, J. Phys. Chem. B, 108, 8434(2004).

34. Phase Diagrams of ABC Triblocks  AB =  BC =  AC = 35 ABCAB C

35. 3D Structures ABC

36. Conclusions For ABC linear triblock copolymers, seven microphases are found to be stable in 2D. When volume fractions and interaction energies of the three species are comparable, lamellar phases are the most stable phase. If one of the volume fractions is large, core-shell hexagonal, or tetragonal phase can be formed. As the interaction energies between distinct blocks become asymmetric, more complex morphologies occurs. Block sequence plays a profound role in the microphase formation.

37. Conclusions For ABC star triblock copolymers, nine microphases are found to be stable in 2D. When the volume fractions comparable, star architecture is a strong topological constraint regulates the geometry of the microphases. Only when at least one of the volume fractions is low, the influence of the star architecture is not significant.

38. Open Questions Semi-flexible chains Rigid chains Dilute solution Dynamics ?

39. Acknowledgement Prof. Yuliang Yang Prof. Hongdong Zhang Dr. Ping Tang NSF of China Ministry of Science and Technology Ministry of Education

40. Thank you!