Cells and Boundaries All Around Us

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This award supports theoretical research and education in the area of soft-condensed matter physics. Research will focus on two problems: (1) The key element in the theory of the self-assembly of macromolecular-and nano-crystals is a connection between purely repulsive potentials and area-minimizing, space-filling structures or honeycombs. This interaction is juxtaposed with entropic arguments that show that close-packed lattices are favored. While in two dimensions both close packing and perimeter minimization result in the same triangular lattice, in three dimensions there is a fundamental frustration between packing entropy and the area-minimizing lattices. The PI plans to further develop these ideas, to extend them to non-cubic lattices, and to make a closer connection between molecular details and this analogy. Molecular dynamics and Monte Carlo simulations provide tests of these ideas. (2) The PI plans to explore the nonlinear elasticity of layered systems. The energetics of defects is dramatically altered when one adds those nonlinearities required by rotational invariance -changing from exponentially decaying interactions to power laws. The PI will further explore this effect and employ novel linear decompositions of minimal surfaces as a starting point for variational calculations. This activity also contributes to postgraduate education in the theory of soft-condensed matter.%%%This award supports theoretical research and education in the area of soft-condensed matter physics on two projects. The first involves the study of the wide variety of crystal structures exhibited by molecular assemblies, such as diblock copolymers, dendritic polymers, and hyperstar polymers. The PI seeks to extend his previous work to understand these structures as a consequence of an additional 'interfacial interaction' contribution to the free energy that arises from the interactions between the brush-like coats of these molecular assemblies. A firmer connection will be developed between this interaction and microscopic properties of polymers. This work has potential impact on fundamental science as well as on developing concepts to aid in designing structures in technologically important self-assembling materials. The second project is concerned with studying the role of defects in elastic layered systems when the elasticity of the layer is nonlinear. ***