Shape and Deformation of Colloidal Membranes

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This grant will support the development of the theoretical framework for the design and control of colloidal membranes. Colloidal membranes are made of filamentous viruses and held together by osmotic forces from polymers in solution. Like cell membranes, colloidal membranes self-assemble; in other words, these membranes form spontaneously from a solution of just the right concentration of rod-like viruses and polymers. Although colloidal membranes resist bending like a solid plate, they also flow like a liquid. Unlike an orange peel, a colloidal membrane shaped like a spherical cap can conform to a flat surface without tearing because the material can redistribute by flowing. Likewise, holes can heal because the material flows. Self-assembly and the ability to easily reconfigure make colloidal membranes attractive for developing artificial micron-scale materials with life-like properties. The focus of this grant is to mathematically model the shape-changing processes using tools from applied mathematics, mechanical engineering, and physics. This grant will support the scientific training of undergraduate and graduate students. The investigators will mentor undergraduates from historically underrepresented groups in engineering and physical science through the Leadership Alliance Summer Research Early Identification Program. Soft matter topics related to this work will be integrated into undergraduate and graduate courses in engineering and physics. Graduate students will receive training in presentation and communication skills, and develop YouTube videos explaining soft matter topics to the general public.The specific goal of this research is to apply continuum mechanics techniques to the study of colloidal membranes composed of mixtures of long and short rods in the presence of polymers which hold the rods together via the depletion force. Previous efforts have focused on flat membranes or membrane ribbons composed of a single kind of rod. Membranes consisting of a mixture of rods typically display a rich variety of complex three-dimensional shapes, and the emerging evidence is that many of these shapes are neither minimal surfaces nor constant mean curvature shapes. The shapes can be tuned by controlling experimental conditions such as polymer depletant concentration, and the theory the team will develop will quantitatively determine how shape depends on experimental conditions. The particular aims are to (1) determine how the Gaussian curvature modulus depends on the concentration of short rods as well as the concentration of depleting polymers, (2) determine the conditions that lead to tilting of the constituent rods of the membrane away from the normal to the mid-surface in the bulk of the membrane, and (3) develop a Monte Carlo technique that incorporates the rod degrees of freedom together with the shape degrees of freedom.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.