Fundamental Order of Transitions Revealed in Micelles

Complementary beamlines at NSLS-II provide high-resolution data for fundamental research

diffraction spots and packing structures

The top image shows brown diffraction spots, circles, and lines from a block copolymer micelle solution. These x-ray scattering patterns indicate an unusual co-existence of mixed packing structure (fcc, hcp, and fcc-hcp) in the solution. The packing structures are illustrated in the lower panel. Image credit: PNAS, 115 (28), 7218-7223 (2018)

The Science           

Scientists revealed the fundamental order of transitions in spherical packing structures using self-assembling block copolymer micelles.

The Impact

Close-packed structures of spheres are ubiquitous fundamental structures across diverse material systems. This research finds the origin of different close-packed structures.


Researchers came to the National Synchrotron Light Source II (NSLS-II)—a U.S. Department of Energy (DOE) Office of Science User Facility at DOE’s Brookhaven National Laboratory—to answer a fundamental question in science, engineering, and mathematics: how densely can spherical particles be packed?

Close-packed structures are the fundamental crystal symmetries in nature, but selective access to these crystal symmetries in self-assembling materials has remained challenging. In this work, scientists demonstrated that three representative packing structures of block copolymer micelles can be selectively induced using different thermal processing protocols.

The researchers teamed up with scientists at the Complex Materials Scattering (CMS) beamline and the Soft Matter Interfaces (SMI) beamline at NSLS-II to investigate the structures over time using small angle x-ray scattering (SAXS).

By combining these results with complementary experimental tools, the team found that the least stable packing structure transformed into intermediate, randomly stacked, hexagonal close-packed (hcp) layers and eventually into the most stable face centered cubic (fcc). This finding is an experimental observation of Ostwald’s rule for close-packed structures.

This research illustrates an important example for accessing metastable crystal structures available in the free-energy landscape often hidden in the transition kinetics.

Download the research summary slide

Related Links

Feature Story: “How Densely Can Spheres Be Packed?


Sangwoo Lee
Rensselaer Polytechnic Institute


L. Chen, H. S. Lee, S. Lee. Close-packed block copolymer micelles induced by temperature quenching. Proceedings of the National Academy of Science USA, 115 (28), 7218-7223 (2018). DOI: 10.1073/pnas.1801682115


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.

2018-17480  |  INT/EXT  |  Newsroom