Pancake-to-brush transition in block copolymers

A first-order phase transition between an adsorbed (two-dimensional) polymer layer at low surface coverage and a stretched (brush-like) configuration at intermediate surface coverage is predicted using single-chain mean-field theory in grafted block copolymer layers. The phase transition is the result of the interplay between an attractive interaction of the tethered block monomers and the surface and a surface-coverage-dependent repulsion with the surface induced by the presence of the grafting block. This repulsion is in addition to the steric repulsion between the monomers of the tethered block. The critical point of the phase transition is found as a function of the strength of the polymer-surface attraction, tethered polymer-grafting block repulsion and tethered-block molecular weight. The findings of the theory are in agreement with different experimental findings both at solid-liquid and liquid-liquid interfaces.