The phenomenon of microphase separation is an example of self-assembly in soft matter and has been observed in block copolymers (BCPs) and similar materials (i.e., supramolecular assemblies (SMAs) and homo/block copolymer blends (HBCs)). In this study, we use microphase separation to construct responsive polymer brushes that collapse to generate periodic surfaces. This is achieved by a chemical reaction between the minor block (10%, poly(4-vinylpyridine)) of the block copolymer and a substrate. The major block of polystyrene (PS) forms mosaic-like arrays of grafted patches that are 10-20 nm in size. Depending on the nature of the assembly (SMA, HBC, or neat BCP) and annealing method (exposure to vapors of different solvents or heating above the glass transition temperature), a range of "mosaic" brushes with different parameters can be obtained. Successive grafting of a secondary polymer (polyacrylamide, PAAm) results in the fabrication of binary polymer brushes (BPBs). Upon being exposed to specific selective solvents, BPBs may adopt different conformations. The surface tension and adhesion of the binary brush are governed by the polymer occupying the top stratum. The "mosaic" brush approach allows for a combination of strongly immiscible polymers in one brush. This facilitates substantial contrast in the surface properties upon switching, previously only possible for substrates composed of predetermined nanostructures. We also demonstrate a possible application of such PS/PAAm brushes in a tunable bioadhesion-bioadhesive (PS on top) or nonbioadhesive (PAAm on top) surface as revealed by Escherichia coli bacterial seeding.