Tortora M. M. C., Doye J. P. K., Perturbative density functional methods for cholesteric liquid crystals, J. Chem. Phys. 146, 184504, 2017

What is the common point between living cells, soap bubbles, Romanesco broccolis and DNA? All of these objects result from a physical process known as self-assembly, through which atoms and molecules spontaneously organise themselves into functional structures of many shapes and sizes. The diversity and complexity of this ordering phenomenon is beautifully illustrated by the seemingly endless variety of patterns exhibited by falling snowflakes, reflecting the subtle dependence of their crystalline arrangement on the local conditions of their formation in the atmosphere.

Another everyday example of such self-assembled materials may be found within the screens of our phones, TVs and computers. At the heart of every pixel of most modern display devices lies a thin liquid layer comprised of rod-like molecules, which possess the surprising ability to organise in a helical fashion in the absence of external cues. These phases are known as cholesteric liquid crystals (CLCs), and their fascinating optical properties extend far beyond the screen of your digital watch; a number of birds, insects and even some fruits owe their shiny, colourful appearance to similar CLC structures.

We have introduced a novel numerical method to predict the ways in which molecules can assemble into such cholesteric phases based on many microscopic parameters such as their shape, concentration and chemical properties. This approach enables us to study the liquid-crystal behaviour of a number of experimental systems that are very challenging for theoreticians to understand, and shed some light on the mechanisms through which tiny individual molecules can organise into complex structures many orders of magnitudes larger than their own size.

An illustration of a cholesteric phase of cigar-shaped particles is shown on the figure. The distance P over which their direction of alignment performs a full turn is known as the cholesteric pitch. It determines, among other things, the beautiful colours reflected by peacock feathers.

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