Surface-induced ordering for confined random block copolymers

Abstract

Motivated by practical issues that pertain to polymer adhesion, we consider the equilibrium behavior of a dilute solution of ideal A–B random block copolymers confined between two solid surfaces. We develop a general theory for the situation wherein the A–A, B–B, and A–B intersegment interactions are different, and furthermore, the A and B segments interact differently with the solid surfaces. Random block copolymers constitute a class of materials wherein a quenched disorder (the sequence distribution) is carried by the fluid whose statistical properties are of interest. In our theory, we perform quenched disorder averages using the replica trick. The nonlocal terms in our action functional are decoupled by introducing a set of random fields. The resulting equations for the propagator are analyzed within the framework of eigenfunction expansions. Since we consider long chains in confined geometries, we invoke the ground state approximation. We also carry out the functional integrals over the random fields using saddle points. Our theory does not treat the segment–surface interactions within a mean field approximation. Our analysis leads to a set of nonlinear self-consistent-field equations. We have solved our general equations numerically for a particular problem. In order to isolate and highlight the effects of dissimilar segment–surface interactions, we consider a case wherein the intersegment interactions are all alike (of the excluded volume type), while the A segments are attracted to the solid surfaces and the B units are repelled. For this specific problem we find that, above a threshold value of the fraction of attractive segments, significant microphase ordering is induced by the surface. This leads to damped oscillations in the composition profile. This onset of significant surface-induced composition fluctuations is accompanied by an ‘‘adsorption–desorption transition’’ which corresponds to a qualitative change in the shape of the total segment density profile. These and other results are discussed and the experimentally testable consequences of our predictions are elucidated. Our results are in agreement with recent simulation studies. We suggest specific experiments that may shed further light on the physical phenomena revealed by our calculations.