Long and short chains in a polymeric brush: A conformational transition

End-anchored macromolecules admired to a homogeneous monodisperse planar brush and differing from the majority blush-forming chains only by molecular mass take three different types of conformation, depending on its polymerization index, K, relative to that of the majority chains, N. The fraction of the admired macromolecules is taken to be small. Shorter minority chains form slightly deformed random coils with both the average end height and its fluctuation proportional to K-1/2. A longer minority chain with K > N acquires an inhomogeneous flower-like conformation: an N-segment stem of height H equal to the thickness of the brush and a randomly coiled crown outside the brush. The stem is strongly stretched and fluctuates only weakly. The transition from one type of conformation to another occurs as the number of segments of the minority chain, K, changes within a narrow range around N, where the chain is simultaneously strongly stretched and strongly fluctuating. We show that the coil-to-flower transition has some features of both the first- and the second-order phase transitions.