Helicoidal stacks

In this chapter, we will therefore focus on this latter group of structures, in particular helicoidal stacks, where the optical properties are well understood, and whose artifieial production using biopolymers has been demonstrated. 

Figure 17.1 A diagram showing a helicoidal stack. The red lines are Bouligand arcs resulting from an oblique section.

The intuitive description above shows that a helicoidal stack may be considered in terms of a standard Bragg reflector in the rotating frame of circularly polarised light. In more detail, its optical response may be demonstrated analytically using Maxwell s equations to show the existence of a photonic bandgap. The key results of the analytic treatment are summarised below. 

In the absence of dynamic and static disorder, all partially filled band systems would exhibit coherent transport over long distances. With static and dynamic disorder, the modulation of the simple molecular orbital or band structure by nuclear effects entirely dominates transport. This is clear both in the Kubo linear response formulation of conductivity and in the Marcus-Hush-Jortner formulation of ET rates. The DNA systems are remarkable for the different kinds of disorder they exhibit in addition to the ordinary static and dynamic disorder expected in any soft material, DNA has the covalent disorder arising from the choice of A, T, G, or C at each substitution base site along the backbone. Additionally, DNA has the characteristic orientational and metric (helicoidal) disorder parameters arising from the fundamental motif of electron motion along the r-stack. 

To form helicoids, each individual nano-fibril is arranged parallel to another one in stacked planes. From plane to plane, the orientation of the fibrils changes by a few degrees to obtain the helicoidal structure. While in many instances the dimensions of such helicoidal structures are not on the right length-scale to produce structural colour, there are many examples where such hierarchical structures provide a vivid and strong iridescent colouration. 

Frequently the helicoidal structure is illustrated with a stack of planes each with a rotated orientation of n and this has given the false impression that cholesteric phases possess a stratified supramolecular structure. 

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