A neutron reflectometry study of polystyrene network interfaces

European Physical Journal B

Volumn 3, Issue 1, 1998, Pages 83-96

  Geoghegan, M ^a,c   Boue F ^a   Bacri, G ^a   Menelle, A ^a   Bucknall, D G ^b  

^a CEA SACLAY   (France)

^b RUTHERFORD APPLETON LABORATORY   (United Kingdom)

^c UNIVERSITY OF FREIBURG   (Germany)

Author keywords

68.35.Ct Interface structure and roughness; 82.70.Gg Gels and sols

Indexed keywords

CROSSLINKING; GELS; INTERPENETRATING POLYMER NETWORKS; MOLECULAR WEIGHT; NEUTRON REFLECTION; PLASTIC FILMS; POLYSTYRENES; SOLS; SURFACE ROUGHNESS;

NEUTRON REFLECTOMETRY;

INTERFACES (MATERIALS);

EID: 0031653527     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100510050286     Document Type: Article

References (35)

1. H.H. Kausch, M. Tirrell, Ann. Rev. Mat. Sci. 19, 341 (1989).
2. E. Helfand, Y. Tagami, J. Chem. Phys. 56, 3592 (1972).
3. D. Broseta, G.H. Fredrickson, E. Helfand, L. Leibler, Macromolecules 23, 132 (1990).
4. M. Geoghegan, F. Boué, F. Abel, in preparation.
5. X. Zheng, M.H. Rafailovich, J. Sokolov, X. Zhao, R.M. Briber, S.A. Schwarz, Macromolecules 26, 6431 (1993).
6. W. Wu, W.E. Wallace, J.H. van Zanten, B.J. Bauer, D. Liu, A. Wong, Polymer 38, 2583 (1997).
7. M. Antonietti, H. Sillescu, Macromolecules 18, 1162 (1985).
8. C. Marzolin, Thesis, Université de Pierre et Marie Curie, Paris, 1995.
9. F. Brochard-Wyart, P.-G. de Gennes, L. Léger, Y. Marciano, E. Raphaël, J. Phys. Chem. 98, 9405 (1994).
10. F. Zielinski, Thesis, Université de Pierre et Marie Curie, Paris (1991).
11. F. Zielinski, M. Buzier, C. Lartigue, J. Bastide, F. Boué, Prog. Coll. Polym. Sci. 90, 115 (1992).
12. A. Ramzi, F. Zielinski, J. Bastide, F. Boué, Macromolecules 28, 3570 (1995).
13. E. Mendes Jr., P. Lindner, M. Buzier, F., Boué, J. Bastide, Phys. Rev. Lett. 66, 1595 (1991).
14. E. Geissler, F. Horkay, A.-M. Hecht, M. Zrinyi, Phys. Rev. Lett. 71, 645 (1993).
15. J. Penfold, R.K. Thomas, J. Phys. Condens. Matter 2, 258 (1990).
16. T.P. Russell, Mater. Sci. Rep. 5, 171 (1990).
17. R.A.L. Jones, L.J. Norton, K.R. Shull, E.J. Kramer, G.P. Felcher, A. Karim, L.J. Fetters, Macromolecules 25, 2359 (1992).
18. M. Geoghegan, R.A.L. Jones, D.S. Sivia, J. Penfold, A.S. Clough, Phys. Rev. E 53, 825 (1996).
19. K. Kunz, J. Reiter, A. Götzelmann, M. Stamm, Macromolecules 26, 4316 (1993).
20. S.K. Sinha, E.B. Sirota, S. Garott, H.B. Stanley, Phys. Rev. B 38, 2297 (1988). Other references can be found in the review by Penfold and Thomas [15].
21. The NR profiles were fitted using a Power Macintosh 7200 computer and took up to 20 minutes per fit. The simplex is not the most efficient of routines (Numerical Recipes in C: The Art of Scientific Computing 2nd ed., W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery (Cambridge University Press, Cambridge, 1992)) and this was compounded by the most complicated profiles being divided up into 50 steps and the Gaussian smoothing routine used in the fit was itself split up into up to 35 steps.
22. R.A.L. Jones, in Polymer Surfaces and Interfaces II, edited by W.J. Feast, H.S. Monro, R.W. Richards (Wiley, Chichester, 1993), p. 71.
23. J.D. Ferry, Viscoelastic Properties of Polymers 3rd ed. (Wiley, New York, 1980).
24. J. Lal, J. Bastide, R. Bansil, F. Boué, Macromolecules 26, 6092 (1993).
25. If an arbitrary surface is created by slicing through a polydisperse polymer solution, the number of times a chain crosses the interface scales as √n, where n is the chain length. Thus longer chains are preferentially adsorbed at the interface in the absence of enthalpic interactions.
26. F. Brochard, J. Phys. France 42, 505 (1981).
27. P.-G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1979).
28. G.H. Fredrickson, in Physics of Polymer Surfaces and Interfaces, edited by I.C. Sanchez (Butterworth-Heinemann, Boston, 1992), p. 1.
29. F.S. Bates, G.D. Wignall, Macromolecules 19, (1986) 932.
30. The formula for the interfacial width is derived from a hyperbolic tangent profile. Our experimental widths are for a complementary error function profile. The hyperbolic tangent width remains at about 90% that of the error function.
31. This equation should, in principle, be equal to the minimisation of the Euler equation in Cahn's theory of wetting (J.W. Cahn, J. Chem. Phys. 66, 3667 (1977)) in the strong segregation limit of the random phase approximation [28]. It is a factor of four out and in order to make the results agree with this theory it is necessary to contract the interface by a factor of two. This means that interfacial widths are halved.
32. P.J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, 1953), p. 578.
33. J.-U. Sommer, T.A. Vilgis, G. Heinrich, J. Chem. Phys. 100, 9181 (1994).
34. J. Bastide, S. Candau, L. Leibler, Macromolecules 14, 719 (1980).
35. The intradiffusion for this polymer has been measured elsewhere at 150°C [4] and we can scale the result to 180°C by using the data of P.F. Green, B.L. Doyle, Macromolecules 20, 2471 (1986). The interpenetration is described by interdiffusion which has a complex Mw dependence. However, at small volume fractions the Mw dependence of the diffusion coefficient is expected to be similar to that of the intradiffusion coefficient.