Pearling instabilities in water-dispersed copolymer cylinders with charged brushes.

We investigate the structural behavior of a poly(styrene)-block-poly(acrylic acid) diblock copolymer which forms hexagonally-packed PS cylinders (C-phase) in the melt state. The water dispersion of this structure provides hairy cylinders which comprise a PAA swollen cylindrical brush with a height h tunable via its degree of ionization and the ionic strength in the solution, and a water-free, PS cylindrical core of constant radius R(C). Such system constitutes an "out-of-equilibrium" frustrated model system: the selective swelling of the PAA brush results in a frustration of the interface curvature, which the ratio h/R(C) allows to quantify. Upon heating at a temperature higher than the glass transition temperature of the PS core, the glassiness of the core is relieved and the mechanical constraints arising from the selective swelling of the structure can be relaxed: the cylinders undergo a cylinder-to-sphere transition upon annealing at high temperature, when above a frustration threshold h/R(C) approximately 1.8. Thanks to a careful mapping of the transition diagram, an undulating cylindrical morphology (UC) is identified between unchanged cylinders ( h/R(C) approximately 1.8) and spheres ( h/R(C) < or = 2.0), which appears to result from a Rayleigh-like pearling instability of the copolymer cylinders.