Condensed Matter Seminar: Frustrated Filaments and Crystalline Caps: Defect Patterns in Flexible Assemblies
In this talk I will discuss recent theoretical results on the optimal structure of two related, geometrically frustrated systems of soft matter: 1) condensed and twisted bundles of chiral filaments; and 2) crystalline rafts confined to curved, deformable substrates. First, I will demonstrate how a geometrical mapping between packing in dense and twisted bundles of filaments and particle packing on curved two-dimensional surfaces leads to new predictions of defects in the ground states of chiral filament bundles. Second, I will discuss the complex structural response of crystalline membranes bound to curved, but compliant substrates. It is well known that topological defects relax defects in crystals bound to perfectly rigid curved surfaces, whereas amorphous thin sheets relax frustration on deformable substrates by complex wrinkle patterns. Specifically, I will discuss the underlying connection between the distinct modes of in-plane, plastic (dislocation scar) and out-of-plane, elastic (wrinkle) relaxation that enables the determination of the wrinkle-scar phase diagram in terms of microscopic properties and mechanical response of the crystalline sheet.