No abstract

Within a two-dimensional Landau-de Gennes tensorial formalism we study the equilibrium configurations of nematic shells, thin films of nematic liquid crystal deposited on the boundary of colloidal particles of arbitrary shape enforcing a degenerate tangential anchoring on the nematic molecules. In this formalism, defects appear wherever a scalar order parameter vanishes. Their total number is the colloidal valence, as this is the number of molecular bridges that can bind every colloid to its peers. We show how the defect organization on a colloidal particle is affected by the Gaussian curvature of the colloidal boundary, to the point of changing its valence.

Using two order tensors, we propose a mean-field model to describe the uniaxial and biaxial phases of nematogenic molecules presenting a shape dispersion of their biaxial dielectric susceptibility. We recover the classical isotropic-uniaxial-biaxial sequence of phases. The phase diagram exhibits a tricritical point, a feature that cannot be retraced in the other mean-field models established for molecules without shape dispersion.