Topological shape transitions of colloidal membranes

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Non-technical abstract:Elucidating the rules by which thin flat sheets fold into complex three dimensional structures is of fundamental interest to a broad range of fields ranging from physics, and materials science to biology. For example, the process by which a flat 2D bilayer with exposed edges folds into an edgeless 3D vesicle is essential for transport across cellular membranes and also for developing new methods of drug delivery. However, visualizing and quantifying such folding processes using nanometer-sized lipid bilayers is currently not feasible. This project will use an analogy between lipid bilayer and colloidal monolayer membranes to quantitatively test foundational models of vesicle formation and other folding processes. Colloidal membranes will allow one to measure all the parameters and directly visualize the folding process with optical microscopy, to a degree that is not possible with conventional materials. Besides visualizing closed vesicle formation the team will also study processes by which flat sheets fold into topologically more complex mathematical structures, such as catenoids and Gyroid-like structures. In parallel, the team will pursue outreach activities focused on (1) providing rigorous training in interdisciplinary sciences to graduate and undergraduate students, (2) encouraging underrepresented groups to pursue work in STEM related fields, (3) and raising general awareness of the importance of scientific research to broader communities. This project will actively support undergraduate research and will build on a strong record of recruiting students from diverse backgrounds. They will also continue their involvement with the Cal-Bridge program, a NSF-funded program whose mission is to increase the number of underrepresented minority and female students entering doctoral program in physics. Finally, each year they will also participate in about half a dozen outreach activities at local elementary and middle schools in order to promote science education.Technical abstract: Colloidal membranes, which are comprised of one-rod-length thick liquid-like monolayer of aligned monodisperse rods, offer a unique opportunity to explore fundamental aspect of thin sheets with vanishing in-plane shear modulus. So far, studies have mainly examined the behavior of colloidal membranes in the regime were they remain flat 2D structures. The goal of the current project is to elucidate the fundamental laws by which 2D colloidal membranes fold into diverse and topologically distinct 3D architectures. Three specific aims are proposed. In the first aim they will develop active and passive fluctuations-based techniques to measure the mean and Gaussian elastic moduli of colloidal membranes, the phenomenological constants that determine the energetic cost required to bend a membrane from its minimum energy state. In the second aim they will tune microscopic constituents of colloidal membranes to investigate regimes were flat colloidal membranes are inherently unstable and spontaneously fold into complex structures. In one direction they will reduce the bending rigidity of colloidal membranes to induce folding of flat 2D membranes into edgeless 3D vesicles and visualize and quantify the pathways of this transition. In a complementary direction they will explore the regime were doping colloidal membranes with miscible short rods induces formation of remarkably diverse and topological complex surfaces with negative Gaussian curvatures. Using state of the art imaging technique they will elucidate the molecular mechanisms that drive these instabilities. In the final aim they will develop robust experimental tools that will enable spatiotemporal external control of the membrane curvature, thus allowing one to actively intervene in the ongoing folding processes and guiding formation of topological assemblages of predetermined final shape.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.