Controlled self-assembly of three-dimensional shapes holds great potential for fabrication of functional materials. Their practical realization requires a theoretical framework to quantify and guide the dynamic sculpting of the curved structures that often arise in accretive mineralization. Motivated by a variety of bioinspired coprecipitation patterns of carbonate and silica, we develop a geometrical theory for the kinetics of the growth front that leaves behind thin-walled complex structures. Our theory explains the range of previously observed experimental patterns and, in addition, predicts unexplored assembly pathways. This allows us to design a number of functional base shapes of optical microstructures, which we synthesize to demonstrate their light-guiding capabilities. Overall, our framework provides a way to understand and control the growth and form of functional precipitating microsculptures.
The authors thank J. A. Fritz, M. Kolle, M. Lončar, and
T. M. Schneider for fruitful discussions and P. A. Korevaar,
W. M. van Rees, J. C. Weaver, and T. C. Ferrante for technical assistance. This research was supported by NSF Designing Materials to Revolutionize and Engineer Our Future under award 15-33985, the Kavli Institute for Bionano Science and Technology at Harvard University, and the Harvard MRSEC under award 14- 20570. W.L.N. thanks the Netherlands Organization for Scientific Research (NWO) for financial support from a VENI grant. R.S. acknowledges Technical University Eindhoven’s Fonds Ectspunten Buitenland financial support, and L.F. the Radboud University Nijmegen study fund. L. M. was partially supported by fellowships from the MacArthur Foundation and the Radcliffe Institute. Scanning and transmission electron microscopies were performed at the Center for Nanoscale Systems at Harvard University, supported by the NSF under award ECS-0335765, and the Amsterdam nanoCenter, supported by NWO. The authors declare no conflicts of interest.