Stable Frank–Kasper phases of self-assembled, soft matter spheres
Abstract
Formation of complex Frank–Kasper phases in soft matter systems confounds intuitive notions that equilibrium states achieve maximal symmetry, owing to an unavoidable conflict between shape and volume asymmetry in space-filling packings of spherical domains. Here we show the structure and thermodynamics of these complex phases can be understood from the generalization of two classic problems in discrete geometry: the Kelvin and Quantizer problems. We find that self-organized asymmetry of Frank–Kasper phases in diblock copolymers emerges from the optimal relaxation of cellular domains to unequal volumes to simultaneously minimize area and maximize compactness of cells, highlighting an important connection between crystal structures in condensed matter and optimal lattices in discrete geometry.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 24, 2018
- Source ID
- 10.1073/pnas.1809655115
Entities
People
- Abhiram Reddy
- Akash Arora
- Frank S. Bates
- Gregory M. Grason
- Kevin D. Dorfman
- Michael B. Buckley
Organizations
- Air Force Office of Scientific Research
- National Science Foundation
- University of Massachusetts
- University of Minnesota