Cuboidal liquid crystal phases under multiaxial geometrical frustration

Cuboidal liquid crystal phases - the so-called blue phases - consist of a network of topological defects arranged into a cubic symmetry. They exhibit striking optical properties, including Bragg reflection in the visible range and fast response times. Confining surfaces can interfere with the packing of such a network, leading to structures that have not been explored before. In this work, a Landau-de Gennes free energy formalism for the tensor alignment field Q is used to investigate the behavior of chiral liquid crystals under non-isotropic confinement. The underlying free energy functional is solved by relying on a Monte Carlo method that facilitates efficient exploration of configuration space. The results of simulations are expressed in terms of phase diagrams as a function of chirality and temperature for three families of spheroids: oblate, spherical, and prolate. Upon deformation, blue phases adapt and transform to accommodate the geometrical constraints, thereby resulting in a wider range of thermal stability. For oblate spheroids, confinement interferes with the development of a full blue phase structure, resulting on a combination of half skyrmions. For prolate spheroids, the blue phases are hybridized and exhibit features of blue phases I and II. More generally, it is shown that mechanical deformation provides an effective means to control, manipulate and stabilize blue phases and cholesterics confined in tactoids.