Close-packed structures of uniformly sized spheres are ubiquitous across diverse material systems including elements, micelles, and colloidal assemblies. However, the controlled access to a specific symmetry of self-assembled close-packed spherical particles has not been well established. We investigated the ordering of spherical block copolymer micelles in aqueous solutions that was induced by rapid temperature changes referred to as quenching. As a function of quench depth, the quenched self-assembled block copolymer micelles formed three different close-packed structures: face-centered cubic (fcc), random stacking of hexagonal-close-packed layers (rhcp), and hexagonal-close-packed (hcp). The induced hcp and rhcp structures were stable for at least a few weeks when maintained at their quench temperatures, but heating or cooling these hcp and rhcp structures transformed both structures to fcc crystallites with coarsening of the crystal grains, which suggests that these noncubic close-packed structures are intermediate states. Time-resolved scattering experiments prove that the micellar rhcp structures do not originate from the rapid growth of competing close-packed structures. We speculate that the long-lived metastable hcp and rhcp structures originate from the small size of crystal grains, which introduces a nonnegligible Laplace pressure to the crystal domains. The reported transitions from the less stable hcp to the more stable rhcp and fcc are experimental observations of Ostwald’s rule manifesting the transition order of the key close-packed structures in the crystallization of close-packed uniform spheres.
|Original language||English (US)|
|Number of pages||6|
|Journal||Proceedings of the National Academy of Sciences of the United States of America|
|State||Published - Jul 10 2018|
Bibliographical noteFunding Information:
ACKNOWLEDGMENTS. We thank Byeongdu Lee for the help on the extraction of excess electron density profiles from scattering data. Greg Lyons, Joel Plawsky, Helen Zha, and Carrie Trant are acknowledged for valuable comments on the manuscript. This research used resources of the 11-BM and 12-ID beamlines of the National Synchrotron Light Source II, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract DE-SC0012704. Parts of this work were carried out in the Characterization Facility, University of Minnesota, which receives partial support from NSF through the Materials Research Science and Engineering Center (MRSEC) program.
- Block copolymer micelles
- Close-packed structures
- Phase transition