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Beyond Flatland-Chapter 4:The Geometric Forms due to Self-Assembly

DOI: 10.1016/b978-044481538-5/50005-8
  • Biology
  • Earth Science
  • Mathematics


Publisher Summary This chapter describes surface structures where curved forms are spontaneously adopted by aggregates of simple macromolecules. These can range from synthetic surfactants and natural lipids (typically about 20Å in length) to synthetic copolymers and proteins (1000Å). The analysis includes both natural and synthetic molecules because lipids and proteins can be considered as more complex counterparts of surfactants and block co-polymers. The effect of molecular shape on aggregation geometry is also described, along with a brief discussion on the theory of self-assembly of chiral molecules. Two characteristics determine the shape of molecular aggregates. First is the shape of the constituent molecules, which sets the curvature of the aggregate. Second is coupled to the chirality of the molecules, which also determines the curvature of the aggregate via the geodesic torsion. The interfacial geometry is characterized by two distinct signatures: (1) the interfacial curvatures, which describe its local geometry and (2) the interfacial topology, which describes global geometry, including the connectivity of the interface.

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