2009/08/29 by R. D. Kamien, Randall D. Kamien, D. R. Nelson +5 · 2 citations
Engineering · Materials Science · Physics and Astronomy · #Advanced Materials and Mechanics #Block Copolymer Self-Assembly #Liquid Crystal Research Advancements #cond-mat.mes-hall #cond-mat.mtrl-sci #cond-mat.soft
paper · pdf · doi:10.1103/physreve.80.051703
published as Phys. Rev. E 80 (2009) 051703 · 14 pages, 9 figures
arxiv created 2009/08/29 · openalex publication_date 2009/11/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
When thermal energies are weak, two-dimensional lamellar structures confined on a curved substrate display complex patterns arising from the competition between layer bending and compression in the presence of geometric constraints. We present broad design principles to engineer the geometry of the underlying substrate so that a desired lamellar pattern can be obtained by self-assembly. Two distinct physical effects are identified as key factors that contribute to the interaction between the shape of the underlying surface and the resulting lamellar morphology. The first is a local ordering field for the direction of each individual layer, which tends to minimize its curvature with respect to the three-dimensional embedding. The second is a nonlocal effect controlled by the intrinsic geometry of the surface that forces the normals to the (nearly incompressible) layers to lie on geodesics, leading to caustic formation as in optics. As a result, different surface morphologies with predominantly positive or negative Gaussian curvature can act as converging or diverging lenses, respectively. By combining these ingredients, as one would with different optical elements, complex lamellar morphologies can be obtained. This smectic optometry enables the manipulation of lamellar configurations for the design of materials.