CAREER: Geometry of Directed Folding and Soft Packing

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).TECHNICAL SUMMARYThis CAREER award supports an integrated theoretical research and education program to study the controlled formation of complex, three-dimensional structures. Analytical and numerical methods will be used for two related research topics. The first topic will involve a study of the folding of a thin membrane into three-dimensional shapes by controlling the differential in-plane swelling of the membrane. The second topic will focus on the development of a strong-segregation theory for the assembly of prototypical hard core/soft corona particles. This theory will relate the various structures observed in simulation phase diagrams to geometrical invariants and be used to predict the phase diagram in three dimensions of soft corona particles interacting through isotropic and anisotropic interactions.These projects study structure formation in two model systems in which geometry and frustration play a crucial role. The first project seeks to understand how to exploit membrane buckling as a design motif. New geometrical tools will be developed to understand how competition between bending and elastic strain results in three-dimensional shapes. The second project will develop a theory to predict structure in soft corona particle assemblies by relying on universal, geometrical quantities. These projects explore how the fundamental constraints imposed by differential geometry control and limit the packing of continuous two-dimensional objects and other soft materials in three-dimensional space.This CAREER award also supports educational activities, including the training of graduate students, the involvement of undergraduate students in theoretical research, and the development of a short workshop on soft materials that will be used as a recruitment tool during regular visits to predominantly-minority serving colleges and universities. This latter program will be coordinated with the larger efforts of the North Eastern Alliance for Graduate Education and the Professoriate.NONTECHNICAL SUMMARYThis CAREER award supports an integrated theoretical research and education program to study how to control the structure of soft materials. Soft materials are often composed of large molecules that may have many possible orientations leading to possibilities for materials and tiny structures to have complex shapes. The PI aims to study the interplay between the interactions among molecules and geometry to develop ways to control the shapes of soft materials. The research supported by this award will have an impact on materials design by introducing new theoretical techniques for the prediction of how three-dimensional structures can be constructed from soft materials. This CAREER award also supports a number of educational, including the training of graduate students, the involvement of undergraduates in theoretical research, and the development of a short workshop on soft materials that will be used as a recruitment tool during regular visits to predominantly-minority serving colleges and universities. This latter program will be coordinated with the larger efforts of the North Eastern Alliance for Graduate Education and the Professoriate (NEAGEP).