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Elementary approach to self-assembly in random copolymers

Published online by Cambridge University Press:  21 March 2011

Shirish M. Chitanvis*
Affiliation:
Theoretical Division, Los Alamos Naitonal Laboratory Los Alamos, New Mexico 87245 (March 5, 2001)
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We have mapped the physics of a system of random copolymers onto a time-dependent density functional-type field theory using techniques of functional integration. Time in the theory is merely a label for the location of a given monomer along the extent of a flexible chain. We derive heuristically within this approach a non-local constraint which prevents segments on chains in the system from straying too far from each other, and leads to self-assembly. The structure factor is then computed in a straightforward fashion. The dependence of various calculated quantities on the average chain length are compared with experiments. The profile and size of spherulitic mesoscale domains is also computed.

Type
Research Article
Copyright
Copyright © Materials Research Society 2001

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References

REFERENCES

1. Gennes, P.G. de, e-print, cond-mat/0003012 (2000).Google Scholar
2. Bonart, R., Morbitzer, L., and Hentze, G. J. Macromol.Sci. B, 3, 337 (1969).Google Scholar
3. Gennes, P.G. de, J. de Phys.Lett., 40, L69 (1979).Google Scholar
4. Leibler, L., Macromolecules, 13, 1602 (1980).Google Scholar
5. Fredrickson, G.H. and Helfand, E., J. Chem. Phys. 87, 697 (1987).Google Scholar
6. Barrat, J.L. and Fredrickson, G.H. J. Chem. Phys. 95, 1281 (1991).Google Scholar
7. Dobrynin, A.V., Phys. Rev. E, 56, 750 (1997).Google Scholar
8. Chitanvis, S.M., Phys. Rev. E, 57, 1921 (1988).Google Scholar
9. Cruz, M.O. de la, Phys. Rev. Lett, 67, 85 (1991).Google Scholar
10. Schick, M. M., Physica A 251, 1 (1998).Google Scholar
11. Kirkwood, J.G., Goldberg, R.J., J. Chem. Phys., 18, 54 (1950).Google Scholar
12. Laradji, M., Desai, R.C., Shi, A.C., Noolandi, J., Phys. Rev. Lett. 78, 2577 (1997).Google Scholar
13. Yeung, C., Shi, A.C., Noolandi, J., Desai, R.C., Macromol. Theory Simul., 5, 291 (1996).Google Scholar
14. Chitanvis, S.M., e-print cond-mat/0002407 (2000).Google Scholar
15. Laradji, M., Europhys.Lett., 47 694 (1999).Google Scholar
16. Gennes, P.G. de, Scaling Concepts in Polymer Physics, Cornell University Press, Itcha, NY (1979).Google Scholar
17. Doi, M., Edwards, S.F., The Theory of Polymer Dynamics, Oxford University Press, Oxford (1986).Google Scholar
18. Wu, D., Chandler, D. and Smit, B., J. Phys. Chem. 96, 4077 (1992).Google Scholar
19. Kaku, M., Introduction to Superstrings, Springer-Verlag, Berlin (1988).Google Scholar
20. Kleinert, H., Path Integrals in Quantum Mechanics, Statistics and Polymer Physics,World Scientific Publishing Co., Singapore (1990).Google Scholar
21. Ferrari, F., I. Lazzizzera Nucl. Phys. B 559, 673 (1999).Google Scholar
22. Cloizeaux, J. des, Phys. Rev. A, 10, 1665 (1974).Google Scholar
23. Koberstein, J.T., Galambos, A.F. and Leung, L.M., Macromolecules 27, 6195 (1992).Google Scholar
24. Patterson, C.W., Hanson, D., Redondo, A., Scott, S.L., Henson, N.J., J. of Poly.Sci. B, 37, 2303 (1999).Google Scholar
25. Sewell, T., unpublished results (1999).Google Scholar
26. Almdal, K., Rosedale, J.H., Bates, F.S., Wignall, G.D. and Fredrickson, G.H., Phys. Rev. Lett, 65, 1112 (1990).Google Scholar
27. Chitanvis, S.M., Phys. Rev. E, 58, 3469 (1988).Google Scholar
28. Orler, E.B., Los Alamos National Laboratory, private communication.Google Scholar
29. Dicks, J., Los Alamos National Laboratory unpublished report (1998).Google Scholar
30. Fraaije, J.G.E.M., Vlimmeren, B.A.C. van, Maurits, N.M., Postma, M., O.A, Evers, Hiffmann, C., Altevogt, P. and Goldbeck-Wood, G., J. Chem. Phys. 106, 4260 (1997).Google Scholar