Thermodynamically Originated Stacking Fault in the Close-Packed Structure of Block Copolymer Micelles

Stacking faults of hexagonal close-packed layers (HCPLs) often exist as kinetically trapped defects in the close-packed lattices of metallic atoms and spherical colloidal particles. Here, we show that the population of stacking faults in the hexagonal closepacked (HCP) lattice of the micelles formed by the blends of poly(ethylene oxide)-block-poly(1,4-butadiene) (PEO-b-PB) with PEO or PB homopolymer increased with decreasing temperature in a thermally reversible manner. We argue that, while HCP is the equilibrium lattice for a close-packed micellar phase with an infinitely large grain, introduction of stacking faults becomes thermodynamically favored when the lateral dimension of the HCPL and the difference in the bulk free energy between face-centered cubic (FCC) and HCP lattices are small. An optimal degree of stacking fault exists in the close-packed structure under the balance between the bulk lattice free energy and an entropic gain from the combinatorial mixing of FCC and HCP layers in the stacking direction. The higher extent of stacking faults at lower temperature found in the present system was attributed to the smaller difference in the bulk free energy between FCC and HCP lattices, which further signified that the micelles packed in the HCP lattice have higher entropy than those organized in the FCC phase.

Automated summary

Stacking faults in hexagonal close-packed layers of micelles formed by polymer blends increase as temperature decreases, due to the thermodynamic favorability of introducing stacking faults when the lateral dimension of the HCPL is small and the bulk free energy difference between FCC and HCP lattices is small. The higher extent of stacking faults at lower temperature indicates higher entropy in micelles packed in the HCP lattice compared to those in the FCC phase.