Curvature Generation in Self-Assembled Fluid Membranes

Abstract

The ability of thin sheets to curve into complex three-dimensional shapes underlies diverse biological processes. We study curvature generation in fluidic membranes using the model system colloidal membrane, which is self-assembled from micron length rod-like particles. Inspired by saddle-like structures found in nature—from seedpods and flower petals to cell and organelle membranes—we create saddle-shaped liquid-ordered colloidal membranes by introducing a non-uniform strain profile along the thickness of a membrane, by adding a small fraction of shorter miscible rods. These membranes coalesce to create shapes of higher complexity, such as catenoids and their derivatives, handled surfaces, and eventually large sponge-like phases resembling triply periodic minimal structures found in iridescent insect wings. Additionally, inspired by vesiculation in biological systems and the application of synthetic vesicles for drug and cargo delivery, we reduced the membranes' bending rigidity by modifying the constituent rod lengths to create vesicles with controllable sizes. The curvature generation described here are controlled by bending and Gaussian moduli. Determination of these moduli requires high precision height maps of a thermally fluctuating membrane surface. We adapt interference reflectance microscopy to colloidal membranes for this purpose, and optimize the analysis process. Fluctuations in the membrane interior yields bending modulus and show signatures of tilt fluctuations of constituents. The precise height maps enable estimation of Gaussian modulus, traditionally a difficult parameter to estimate, from the ripple like surface fluctuations observed at the edge. Overall, this thesis advances our understanding of curvature in liquid-ordered membranes and could contribute to the design of curved functionalized surfaces.