Crystalline liquids: the blue phases

The blue phases of cholesteric liquid crystals are liquids that exhibit orientational order characterized by crystallographic space-group symmetries. We present here a pedagogical introduction to the current understanding of the equilibrium structure of these phases accompanied by a general overview of major experimental results. Using the Ginzburg-Landau free energy appropriate to the system, we first discuss in detail the character and stability of the usual helical phase of cholesterics, showing that for certain parameter ranges the helical phase is unstable to the appearance of one or more blue phases. The two principal models for the blue phases are two limiting cases of the Ginzburg-Landau theory. We explore each limit and conclude with some general considerations of defects in both models and an exact minimization of the free energy in a curved three-dimensional space.