Elastic properties of polymer interfaces: Aggregation of pure diblock, mixed diblock, and triblock copolymers

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 4, 2002, Pages 13-

  Muller M ^a,b   Gompper, G ^b  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

^b FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AGGLOMERATION; INTERFACES (MATERIALS); LIPIDS; MATHEMATICAL MODELS; MICROEMULSIONS; POLYMER BLENDS; THERMAL EFFECTS;

BENDING RIGIDITY; HOMOPOLYMERS; INTERFACE MODELS; POLYMER INTERFACES;

BLOCK COPOLYMERS;

ARTICLE;

EID: 41349087460     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.041805     Document Type: Article

References (54)

1. D. Broseta and G. H. Fredrickson, J. Chem. Phys. 93, 2927 (1990).
2. R. Holyst and M. Schick, J. Chem. Phys. 96, 7728 (1992).
3. P. K. Janert and M. Schick, Macromolecules 30, 137 (1997).
4. M. Müller and M. Schick, J. Chem. Phys. 105, 8885 (1996).
5. F. S. Bates, W. W. Maurer, P. M. Lipic, M. A. Hillmyer, K. Almdal, K. Mortensen, G. H. Fredrickson, and T. P. Lodge, Phys. Rev. Lett. 79, 849 (1997).
6. H. S. Joen, J. H. Lee, N. P. Balsara, and M. C. Newstein, Macromolecules 31, 3340 (1998).
7. D. Schwahn, K. Mortensen, H. Frielinghaus, and K. Almdal, Phys. Rev. Lett. 82, 5056 (1999).
8. D. Schwahn, K. Mortensen, H. Frielinghaus, K. Almdal, and L. Kielhorn, J. Chem. Phys. 112, 5454 (2000).
9. G. H. Fredrickson and F. S. Bates, J. Polym. Sci., Part B: Polym. Phys. 35, 2775 (1997).
10. B. Jakobs, T. Sottmann, R. Strey, J. Allgaier, L. Willner, and D. Richter, Langmuir 15, 6707 (1999).
11. H. Endo, J. Allgaier, G. Gompper, B. Jakobs, M. Monkenbusch, D. Richter, T. Sottmann, and R. Strey, Phys. Rev. Lett. 85, 102 (2000).
12. R. B. Thompson and M. W. Matsen, Phys. Rev. Lett. 85, 670 (2000).
13. M. Schick, in Liquids at Interfaces, Proceeding of Les Houches, Session XLVIII, edited by J. Charvolin, J. F. Joanny, and J. Zinn-Justin (Elsevier, Amsterdam, 1990).
14. S. A. Safran and T. Tlusty, Ber. Bunsenges. Phys. Chem. 100, 252 (1996).
15. D. C. Morse, Curr. Opin. Colloid Interface Sci. 2, 365 (1997).
16. G. Gompper and D. M. Kroll, Phys. Rev. Lett. 81, 2284 (1998).
17. W. Helfrich, Z. Naturforsch. C 28, 693 (1973);
18. P. B. Canham, J. Theor. Biol. 26, 61 (1970);
19. E. Evans, Biophys. J. 14, 923 (1974).
20. M. W. Matsen, J. Chem. Phys. 110, 4658 (1999).
21. R. B. Thompson and M. W. Matsen, J. Chem. Phys. 112, 6863 (2000).
22. M. Laradji and R. C. Desai, J. Chem. Phys. 108, 4662 (1998).
23. C. Hiergeist and R. Lipowsky, J. Phys. II 6, 1465 (1996).
24. E. Eisenriegler, A. Hanke, and S. Dietrich, Phys. Rev. E 54, 1134 (1996).
25. C. M. Marques and J. Fournier, Europhys. Lett. 35, 361 (1996).
26. S. Leibler and D. Andelman, J. Phys. (France) 48, 2013 (1987).
27. I. Szleifer, D. Kramer, A. Ben-Shaul, W. M. Gelbart, and S. A. Safran, J. Chem. Phys. 92, 6800 (1990).
28. F. C. MacKintosh and S. A. Safran, Phys. Rev. E 47, 1180 (1993).
29. U. Seifert, Phys. Rev. Lett. 70, 1335 (1993).
30. If we did not fix the location of the interface explicitly, the system would be unstable in the grand-canonical ensemble, i.e., the equilibrium would be a homogeneous phase.
31. E. Helfand, J. Chem. Phys. 62, 999 (1975).
32. Comparing the saturation line (Formula presented) with the complete phase diagram of the ternary system in Ref. 3, we observe that the saturation line is almost identical to the unbinding transition or the homopolymer-rich phase boundary of the three-phase region.
33. A. N. Semenov, Macromolecules 26, 6617 (1993);
34. MacromoleculesA. N. Semenov27, 2732 (1994).
35. A. Werner, F. Schmid, M. Müller, and K. Binder, Phys. Rev. E 59, 728 (1999).
36. Z.-G. Wang and S. A. Safran, J. Chem. Phys. 94, 679 (1991);
37. Z.-G. WangS. A. SafranJ. Phys. (France) 51, 185 (1990).
38. V. L. Ginzburg, Fiz. Tverd. Tela (Leningrad) 2, 2031 (1960) [Sov. Phys. Solid State 1, 1824 (1960)];
39. P. G. de Gennes, J. Phys. (France) Lett. 38, L-441 (1977);
40. J. F. Joanny, J. Phys. A 11, L-117 (1978);
41. K. Binder, Phys. Rev. A 29, 341 (1984).
42. C. Taupin and P. G. de Gennes, J. Phys. Chem. 86, 2294 (1982).
43. D. C. Morse, Phys. Rev. E 50, R2423 (1994).
44. L. Golubović, Phys. Rev. E 50, R2419 (1994).
45. This criterion applies only if the interaction between the lamellae is negligible, i.e., when the SCF calculations predict highly swollen lamellar phases or when a minor attractive interaction between the interfaces is overcome by repulsion due to fluctuations. Mixtures of copolymers might also prove useful in tuning the interaction between interfaces 12, which is not considered here.
46. E. M. Blokhuis and D. Bedeaux, J. Chem. Phys. 95, 6986 (1991).
47. M. Laradji and O. G. Mouritsen, J. Chem. Phys. 112, 8621 (2000).
48. H. Endo, M. Mihailescu, M. Monkenbusch, J. Allgaier, G. Gompper, D. Richter, B. Jakobs, T. Sottmann, R. Strey, and I. Grillo, J. Chem. Phys. 115, 580 (2001).
49. G. Porte and C. Ligoure, J. Chem. Phys. 102, 4290 (1995).
50. C. Hiergeist, Ph.D. thesis, Universität Potsdam, 1997 (unpublished).
51. The segregation of a chain to the interface is controlled by three contributions to the free energy: (i) the loss of translational entropy, (ii) the lowering of the energy by an amount (Formula presented) per chain due to extending the anchoring blocks into the A-rich phase, and (iii) the loss of conformational entropy at the interface. The latter contribution imparts a spontaneous curvature onto the interface. To a first approximation, we conceive the chain conformation of the triblock at the interface as that of individual blocks at an impenetrable surface. Each block suffers an entropy loss of the order (Formula presented) If we increase the size of the middle block (Formula presented) at fixed (Formula presented) the loss of conformational entropy will outweigh the enthalpic contribution for (Formula presented) and the triblock will be repelled from the interface.
52. G. Gompper, H. Endo, M. Mihailescu, J. Allgaier, M. Monkenbusch, D. Richter, B. Jakobs, T. Sottmann, and R. Strey, Europhys. Lett. 56, 683 (2001).
53. R. Strey (private communication).
54. C. Frank, Diploma thesis, Universität zu Köln, 2001 (unpublished).