Theory of the Blue Phases of Chiral Nematic Liquid Crystals

Abstract

In the condensed matter physics community there has been much recent interest in materials with competing interactions. Because these materials are frustrated (the different terms in the free energy demand incompatible configurations of molecules), these materials form complicated, intricate crystalline phases as compromise structures; also, they often form amorphous, glassy states. Chiral nematic liquid crystals are frustrated, and form up to three blue phases in a small temperature range between the isotropic “melted” phase and the helical phase [1] two exotic crystalline phases and an amorphous phase. The lattice constant in these phases is the wavelength of blue light (hence their brilliant blue colors); because it is large compared to the molecular lengths, the material can be described within a continuum elastic theory. The elastic theory is frustrated, and the ground states contain networks of defect lines to relieve the frustration [2]. The frustration is geometrically described as a curvature in the natural form of parallel transport [3]; indeed, chiral nematics are not frustrated in the unphysical space formed by the surface of a sphere of appropriate radius in four dimensions [4]. (The defect lines are the cuts needed to flatten this sphere.) A total divergence term in the free energy plays a crucial role in keeping the energy of the defect lines finite in the continuum limit, and in stabilizing the blue phases.