Phase transitions in polymer brushes

Liquid crystalline ordering in planar polymer brushes is investigated theoretically by numerical calculations within a self-consistent field approximation. The brushes are formed by macromolecules with mesogenic groups in main chain and immersed in a solvent. Existence of a microphase segregated brush (MSB) regime with a collapsed orientationally ordered intrinsic sublayer and a swollen external sublayer is shown. At small grafting density, the transition from a conventional brush state to the microphase segregated state is a jump-wise first order phase transition for a finite chain length (A?. The magnitudes of the jumps in the average characteristics of the brush tend to zero in the limit N --> infinity since this transition occurs only in a vanishingly small part (proportional to N-1/2) Of the brush. High compressibility of MSB brush is demonstrated. The origin of phase transition in planar brushes is discussed.