Beyond Flatland The Geometric Forms due to Self-Assembly

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

So far we have constructed a set of tools and put them to work in building and imderstanding some of the elementary self-organising structures, and how it is that forces conspire with molecular geometry to allow these entities to transform from one form to another. But the forms allowed have been too limited by far, and we now call in the language of curvature to embrace a wider range of shapes that nature employs. 

In this section we shall describe in some detail surface structures whose curved forms are spontaneously adopted by aggregates of simple macromolecules. These can range from s)mthetic surfactants and natural lipids (typically about 20A in length) to S5mthetic copolymers and proteins (lOOOA). The analysis includes both natural and synthetic molecules, since lipids and proteins can be considered as more complex counterparts of surfactants and block co-polymers. 

Two characteristics determine the shape of molecular aggregates. The first is the shape of the constituent molecules, which sets the curvature of the aggregate. The second is coupled to the chirality of the molecules, which also determines the curvature of the aggregate, via the geodesic torsion. The bulk of this chapter is devoted to an exploration of the effect of molecular shape on aggregation geometry. An account of the theory of self-assembly of chiral molecules is briefly discussed at the end of this chapter. 

For surfactants, the hydrophobic free energy of transfer of the lipophilic hydrocarbon tail from water to oil provides the driving force for aggregation. But the hydrophilic head-groups prefer an aqueous environment and an interface between the polar region and the lipophilic domains results. With hydrocarbon tails, like alkanes, there are a large number of accessible tail conformations, so that the hydrophobic region is usually fluid-like aroimd room temperature. The interface can be a dynamic one of a well-defined 

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