Density of polymers in a layered structure: an exactly solvable model.

We have developed an exactly solvable model that makes it possible to calculate the density profile of polymers filled inside a chemically nonuniform structure that consists of alternating layers that have different affinity for polymers. It is shown that the mean density of polymers in this layered structure is in excess relative to that in the uniform system that has the same average affinity for polymers. The average excess density of polymers in the layered structure is calculated as a function of their degree of polymerization, layer thickness, and affinities of the layers for polymers. The developed theoretical model is shown to have relevance to several experimentally important chemically nonuniform layered systems like microphase separated diblock copolymers and selective mixed brushes.