Swelling of chemical and physical planar brushes of gradient copolymers in a selective solvent

We propose a mean-field theory of chemical and physical planar brushes of linear gradient copolymers swollen in a selective solvent. The polymer chains are grafted to the substrate by the ends with the excess of insoluble monomer units, and the majority of the soluble units are located near the free ends of the chains. The grafting points are considered to be immobile (chemical brush) and mobile in-plane (physical brush). In the latter case the grafting density is determined from the equilibrium conditions (minimum of the free energy). A common peculiarity of the brushes of both types is that the polymer concentration gradually changes from a relatively high value near the substrate (collapsed region of the brush) to a small value near the free surface (swollen region of the brush). In the case of the chemical brush, a polymer depletion zone can appear in the middle of the brush if incompatibility between insoluble and soluble (A and B) units is high enough. Here the polymer density is even lower than near the free surface of the brush. The grafting density of the physical brush is inversely proportional to the chain length and increases with the decrease of the solvent quality for the insoluble (A) units. The latter can be accompanied by shrinkage of the brush thickness due to broad distribution of the insoluble units through the chain: a minor fraction of insoluble units near the free ends can aggregate with a major fraction of them near the substrate. As a result, the concentration of the soluble (B) units can have a maximum in the middle of the brush rather than near the free surface.