On the collapse transition of a polymer brush: the case of lateral mobility

We consider a polymer brush composed of end-grafted polymer chains. Classical theory advocates that a worsening of the solvent quality results in a smooth decrease of the brush height from a swollen to a dense brush. We report that a homogeneous brush under poor solvent conditions can have a negative surface pressure, indicating an instability in favour of lateral segregation. Also by using a two-gradient version of the self-consistent field (SCF) theory we show that, in contradiction to the classical result, but in line with the negative pressure, the collapse transition for laterally mobile chains has a first-order character, exemplified by the presence of a compact brush that coexists with a dilute gas of end-grafted chains. The dense brush assumes a pancake shape wherein the chains balance the stretching entropy against surface energies. The height of the pancake scales sub-linearly with the chain length because the local grafting density decreases with increasing chain length. In analogy with wetting studies we discuss how the spreading parameter has an influence on the pancake structure. Accordingly, the height increases with worsening of the solvent quality and decreases with increased affinity for the substrate. The two-phase state is expected in many practical situations.