An ongoing challenge of materials science is to identify or to construct self-assembling molecular systems that generate well-controlled structure on nanometer length scales. Underlying this technical goal is the fundamental question, how do we understand the relationship between molecular-scale structure and the longer ranged order of the self-assembled aggregate?

One approach to this question used in the group, focusses on synthetic block copolymer systems as the prototypical self-assembling amphiphile. We take advantage of powerful analytic and numerical field-theoretic methods available for studying high-molecular weight copolymers, seeking to establish the link between aggregate geometry and self-assembly thermodynamics. Of particular interest is the relationship between copolymer architecture and lattice order in micelle-forming systems. While some light has been shed onto this issue for flexible copolymers, we seek theoretical approaches to study the effects of molecular rigidity and branching necessary to describe, say, lattice formation by micelles of dendritic amphiphiles. Also of continuing interest is the study of copolymer aggregates of non-uniform geometry, such as, budding or undulating cylindrical micelles as network or junction phases.

Because biopolymers (DNA, f-actin, microtubules) are themselves imbued with well defined nanometer-scale structure, they hold particular promise as a means of scaffolding order at this size scale. It is well-known that highly-charged biopolymers aggregate in the presence of oppositely charged, poly-valent ions or specialized linking proteins. Owing to the considerable stiffness of biopolymers, aggregates, or bundles, form with a high degree of two-dimensional order, instilling the bundle with unusual mechanical properties, intermediate to a two-dimensional and three-dimensional solid. Relying on generic, elastic descriptions of these aggregates, we seek to understand the subtle interplay between filament packing, helical biopolymer structure and overall bundle size and composition.

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