J. Phys. II France
Volume 7, Numéro 10, October 1997
Page(s) 1353 - 1378
DOI: 10.1051/jp2:1997191
J. Phys. II France 7 (1997) 1353-1378

Surface Effects on Block Copolymer Melts Above the Order-Disorder Transition: Linear Theory of Equilibrium Properties and the Kinetics of Surface-Induced Ordering

Kurt Binder1, Harry L. Risch2 and Semjon Stepanow3

1  Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7, 55099 Mainz, Germany
2  Chemistry Department, State University of New York at Albany, 1400 Washington Avenue, Albany, New York 12222, and Institut für Physik, Johannes Gutenberg-Universität Mainz, Germany
3  Fachbereich Physik, Maxtin Luther-Universität Halle-Wittenberg, Friedemann Bach-Platz 6, 06099 Halle, Germany

(Received 26 February 1997, revised 12 May 1997, accepted 23 June 1997)

A phenomenological theory is developed for static and dynamic aspects of surface-induced ordering of symmetrical block copolymers taking fluctuation corrections into account, but, considering conditions where the bulk block copolymer melt is still disordered, and a linearized version of the resulting Ginzburg-Landau type equation suffices. Both the semi-infinite geometry and symmetrical films of thickness 2L are treated, applying the same boundary conditions as used previously for a treatment of wetting in polymer blends, assuming short range surface forces and a long wavelength approximation. For the static order parameter profile in thin film geometry, we derive an oscillatory convergence of both amplitude and phase to the corresponding properties of the semi-infinite systems, because terms of order $\exp(-2L/\xi_+) \cos(2Lq^*)$ enter, $\xi_+$ being the correlation length and $\lambda = 2\pi/q^*$ the wave-length of lamellar ordering. It is shown that the conservation of the number of monomers of the two species, which can be expressed as a global constraint on the order paxameter, leads to a non-linear equation for the phase expressed in terms of the amplitude, when one considers the kinetics of ordering. Both numerical and approximate analytical treatments are given to describe the evolution of the considered systems towards equilibrium.

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