Theory of diblock-copolymer segregation to the interface and free surface of a homopolymer layer

Abstract

Equilibrium and dynamics of block-copolymer chains in a homopolymer layer (between the interface with another homopolymer and the free surface) are considered. An analytical mean-field theory for equilibrium copolymer segregation to the interface is presented, the results being in good agreement with those of another theoretical approach and with experimental data. The dynamics of an interface copolymer excess is also considered. The situation above the critical micelle concentration (cmc) is also analyzed. It is shown that (i) copolymer micelles usually strongly attract each other, tending to form a separate micellar macrophase; (ii) primings of the copolymer phase are attracted to the free surface and (somewhat weaker) to the interface; the superwetting of the free surface by t he micellar phase is expected for copolymer molecular weights exceeding some critical value; (iii) the formation of micelles is an activation process usually with a high energy of activation; so, the apparent cmc might be appreciably greater than the equilibrium cmc; (iv) for high enough copolymer molecular weights the micellar geometry should be dynamically controlled; in that case the formation of spherical micelles dominates over other geometries in a wide range of copolymer compositions including symmetric copolymers (provided that the copolymer volume fraction is small); (v) the micellar contribution to the free surface and interface excesses is due to higher rate of the micelle's formation at the surfaces.