Coexistence of ordered and disordered phases in a nearly symmetric diblock copolymer near an order-disorder transition point

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

Volumn 60, Issue 2, 1999, Pages

  Koga, Tadanori ^a,b   Koga, Tsuyoshi ^a,b   Hashimoto, Takeji ^a,b  

^a JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002981149     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.R1154     Document Type: Article

References (33)

1. See, for example, A. Ishihara, Statistical Physics (Academic Press, New York, 1971).
2. See, for example, a review article, T. Hashimoto, in Thermoplastic Elastomers, 2nd ed., edited by G. Holden, N. R. Legge, R. Quirk, and H. E. Schroeder (Hanser, Munich, 1996), Chap. 15A, pp. 429–494.
3. See, for example, a review article, F. S. Bates and G. H. Fredrickson, Annu. Rev. Phys. Chem. 41, 525 (1990).
4. L. Leibler, Macromolecules 13, 1602 (1980).
5. G. H. Fredrickson and E. Helfand, J. Chem. Phys. 87, 697 (1987).
6. G. H. Fredrickson and K. Binder, J. Chem. Phys. 91, 7265 (1989).
7. G. H. Hohenberg and J. B. Swift, Phys. Rev. E 52, 1828 (1995).
8. S. A. Brazovskii, Zh. Eksp. Teor. Fiz. 68, 175 (1975) [Sov. Phys. JETP 41, 85 (1975)].
9. H. Sakashita , J. Phys. Soc. Jpn. 50, 4013 (1981).
10. F. S. Bates , J. Chem. Phys. 92, 6255 (1990).
11. B. Stühn , Europhys. Lett. 18, 427 (1992).
12. T. Wolff , Macromolecules 26, 1707 (1993).
13. T. Hashimoto , J. Phys. Soc. Jpn. 63, 2206 (1994).
14. G. Floudas , Acta Polym. 45, 176 (1994).
15. C. D. Han and J. Kim, J. Polym. Sci., Part B: Polym. Phys. 25, 1741 (1987)
16. C. D. Han , Macromolecules 22, 383 (1989).
17. See, for example, T. Pakula , Macromolecules 18, 2037 (1985).
18. See, for example, A. Guinier , Small-Angle Scattering of X-rays (Wiley, New York, 1955).
19. U. Bonse and M. Hart, Appl. Phys. Lett. 7, 238 (1965).
20. T. Koga , J. Appl. Crystallogr. 29, 318 (1996).
21. T. Hashimoto and N. Sakamoto, Macromolecules 28, 4779 (1996).
22. (a) T. Koga, T. Koga, and T. Tittashimoto, J. Chem. Phys. (to be published);(b) T. Koga et al. (unpublished).
23. R. W. Hendricks, J. Appl. Crystallogr. 5, 315 (1972).
24. The asymmetry seen in the USAXS profile such that the intensity at the higher q-region of the scattering maximum is more intense than that at the lower q-region of the maximum may be related in principle to moduli for undulation, dilation and compression of lamellae, as discussed in fluid multimembrane systems [D. Roux and C. R. Safinya, J. Phys. (France) 49, 307 (1988)].
25. This is because the true scattering function has a very sharp maximum with FWHM nearly equal to (Formula presented) very much sharper than the profile of the slit-width weighting function (with FWHM (Formula presented) of the SAXS camera. We note that the FWHM value for the USAXS camera used is (Formula presented) smaller than the FWHM value for the true scattering function.
26. We note that the small spike at (Formula presented) on the top of the broad maximum may be easily overlooked in experiments with the conventional SAXS camera. Even if one can fortunately obtain the profile suggesting the order-disorder coexistence by using SAXS, it is impossible to accurately decompose it into the sharp and broad components corresponding to the ordered and disordered phases, respectively. Thus the USAXS method is quite useful to investigate the order-disorder coexistence.
27. The observed broad scattering profiles from the disordered phase are in good agreement with the Leibler’s scattering function. Moreover, the Leibler’s scattering function around (Formula presented) from the disordered melt can be expressed by Lorentzian form (see, for example, Ref. 27). On the other hand, as shown in Fig. 11, the scattering profile from the ordered state is close to that of the resolution function for the USAXS camera (Gaussian function), except for the tails around the scattering maximum. A weight average of Lorentzian and Gaussian functions show a quite good agreement with the observed scattering profile in the region of (Formula presented) The detail will be given elsewhere (Ref. 21(a)).
28. T. Ogawa , Macromolecules 29, 2113 (1996).
29. N. Sakamoto and T. Hashimoto, Macromolecules 28, 6825 (1995).
30. In order to discuss the performance of the apparatus, we introduce dimensionless quantities (Formula presented) and (Formula presented) where (Formula presented) is the amount of the discontinuity of (Formula presented) or (Formula presented) and (Formula presented) and (Formula presented) are the value of X in the disordered and the ordered phases very close to the ODT temperature, respectively. The values of (Formula presented) obtained by SAXS (or SANS) and USAXS are almost the same, because the profiles in the fully disordered state are very broad, while the value of (Formula presented) depends very much on the instrumental resolution, because the profiles in the fully ordered phase are generally very sharp. If the scattering intensity is measured with the limited instrumental resolution, the values of these dimensionless quantities are larger than their intrinsic values. According to the previous reports (Ref. 28), (Formula presented) and (Formula presented) in SAXS results were 0.4 and 0.06, respectively. On the other hand, those of the present case are 0.05 and 0.005, respectively, smaller by a factor of about 10 than the values of the previous reports, clearly revealing superiority using the USAXS camera.
31. J. H. Rosedale , Macromolecules 28, 1429 (1995).
32. J. Yamamoto and H. Tanaka, Phys. Rev. Lett. 77, 4390 (1996).
33. The effects of the polydispersity may affect the phase transition in real experimental systems. Unfortunately, since there is no rigorous theory that is applicable to quantitative argument of the phase transition of our diblock copolymers having low molecular weight at this stage and there is no systematic experimental results of the polydispersity effects on the phase transition in diblock copolymer melts, we cannot explicitly show how the polydispersity effects affects the phase transition near the ODT in our system at present. However, we can say that the phase coexistence observed in our experiments cannot be interpreted by the simple argument of the phase separation by the polydispersity effects because we obtained experimental results of the real-space structure at the temperature in the coexistence region by using TEM, which show that the macroscopic two-phase separation of the ordered (lamellar) and the disordered phases does not take place. The details of the method and the results of the TEM experiments will be presented elsewhere 21(b).