An investigation into the hexagonal phases formed in high-concentration dispersions of well-defined cylindrical block copolymer micelles

Small-angle X-ray scattering indicated that the hexagonal order is not long-range. In all samples, deviations in the lower order peak positions were observed with respect to those expected for a perfect hexagonal lattice, with the degree of deviation correlating with micelle length.

Furthermore, analysis of the peak shapes and peak widths suggests that the phase possesses intermediate translational order similar. to the hexatic phase. The observed features can be reproduced by amending Hosemann’s paracrystal theory to include a distribution of lattice parameters to model well and poorly condensed regions. It is proposed that this distribution arises due to the bending and intertwining of individual micelles in a hexagonal lattice, resulting in a kinetically trapped phase that is initially neither perfectly hexagonal nor canonically hexatic but which anneals over time towards a perfect hexagonal lattice.