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

Abstract

A phenomenological theory is developed for static and dynamic aspects ofsurface- 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 lin- earized 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 con- ditions 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 corre- sponding properties of the semi-infinite systems, because terms of order exp(-2L/f+) cos(2Lq*) enter, f+ being the correlation length and = 21r/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 parameter, 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.