Mean-Field Theory of Block Copolymers: Bulk Melts, Surfaces, and Thin Films

Abstract

A quantitative mean-field treatment of inhomogeneous polymer systems is applied to bulk diblock copolymer melts, as well as to surfaces and thin films of these melts. Equations for a set of polymer chain probability distribution functions are solved numerically in a manner that requires no further approximation to the fundamental mean-field treatment. Results for symmetric block copolymer melts are in quantitative agreement with previous predictions which are valid only near the critical point or in the strong segregation regime. The equilibrium repeat period of bulk melts is found to scale as Rg(χN)α, where α varies continuously from 0.45 at the critical point to 0.17 in the strong segregation regime. Surfaces of block copolymer melts are treated in a quantitative fashion for films that are ordered or disordered in the bulk. Interference between composition oscillations originating from separate surfaces of a thin film induces thickness oscillations in the total interfacial free energy of the film. For symmetric block copolymer films, the free energy minima and maxima sharpen continuously as χN is increased through the value corresponding to the bulk critical point. A novel thickness instability mechanism is proposed by which a very thin film with an initial thickness corresponding to a broad free energy maximum will gradually evolve into a film containing regions of different thicknesses. © 1992, American Chemical Society. All rights reserved.