Grafting density induced reentrant disorder-order-disorder transition in planar di-block copolymer brushes.

By means of multiscale molecular simulation, we show that solvophilic-solvophobic AB diblock copolymer brushes in the semi-dilute regime present a re-entrant disorder/order/disorder transition. The latter is fully controllable through two parameters: the grafting density and the solvophobic to solvophilic ratio of the tethered macromolecules. Upon increasing density, chains first aggregate into patches, then further order into a crystalline phase and finally melt into a disordered phase. We demonstrate that the order/disorder transition can be explained through the peculiar properties of the aggregates: upon increasing density, the aggregation number grows as expected. On the contrary, their projection on the plane shrinks, thus melting the emergent ordered phase. Such a density dependent shrinkage, seen for the first time as the cause to an order/disorder phase transition, is as a consequence of the entropic/enthalpic competition that characterises the hierarchical self-assembly of the brush.