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(A) Schematic showing the preparation of freestanding smectic membranes. A 30-nm layer of cylinder-forming PS-PEP was deposited on a 50-nm layer of sucrose. The monolayer of cylinders coarsens according to the law ξ2∼t1/4 at 363 K to achieve the desired density of defects. After the membrane is released from the substrate, it is captured on a TEM grid. (B–D) AFM images of the freestanding films simultaneously measure height and the location of the cylinders. Three samples with orientational correlation lengths ξ2=42 nm (B) ξ2=217 nm (C), and ξ2=244 nm (D) show the coupling between the smectic order and the membrane geometry. The coloration of each of the (2 μm)2 images indicates the local smectic layers. (E and F) Likewise, two simulated membranes with (E) ξ2=11 nm and (F) ξ2=67 nm have average wrinkle wavelengths of 206 nm and 203 nm, respectively. The simulated membranes are calibrated such that the average smectic layer spacing dsm=21 nm matches the experimentally determined value.
This and the next 2 images are from:
Elisabetta A. Matsumoto (1,2), Daniel A. Vega (3), Aldo D. Pezzutti (3), Nicolás A. García (3), Paul M. Chaikin (4), and Richard A. Register (5)
(1) Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544
(2) John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138
(3) Instituto de Física del Sur, Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad Nacional del Sur, 8000 Bahía Blanca, Argentina
(4) Center for Soft Condensed Matter Research and Department of Physics, New York University, New York, NY 10003
(5) Department of Chemical and Biological Engineering and Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, NJ 08544
“Wrinkles and splay conspire to give positive disclinations negative curvature”, Proceedings of the National Academy of Scienes of the USA (PNAS), Vol. 112, No. 41, 12639-12644, September 29, 2015, https://doi.org/10.1073/pnas.1514379112
SIGNIFICANCE: Diblock copolymers, polymers made by covalently bonding two otherwise immiscible polymers together, are prized for their robust ability to self-assemble into highly ordered geometric structures. Likewise, there has been recent interest in the ability to control the global geometry of a surface, merely by modifying its local microstructure. Here, we take advantage of the defect structure arising from a slow annealing of a thin film of cylinder-forming diblock copolymers as a means of guiding the geometry of an emergent three-dimensional structure.
ABSTRACT: Recently, there has been renewed interest in the coupling between geometry and topological defects in crystalline and striped systems. Standard lore dictates that positive disclinations are associated with positive Gaussian curvature, whereas negative disclinations give rise to negative curvature. Here, we present a diblock copolymer system exhibiting a striped columnar phase that preferentially forms wrinkles perpendicular to the underlying stripes. In free-standing films this wrinkling behavior induces negative Gaussian curvature to form in the vicinity of positive disclinations.
References listed at the end of the paper:
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