Abstract

The material properties of a given nematic liquid crystal may be altered by dopants, i.e. suspended micro- to nano- particles in the nematic host. Even under weak anchoring conditions at the surface of the inclusions, and in the so-called “dilute regime” (i.e., when the total volume occupied by the inclusions is small), dopants can still have a significant effect; for instance, they can modify the nematic-isotropic transition temperature. In this talk, we consider a Landau-de Gennes model for a periodic suspension of small colloidal inclusions in a nematic host. By studying the homogenised limit, and proving rigorous convergence results for local minimisers, we compute the effective free energy for the doped material. In particular, we show that not only the phase transition temperature, but any coefficient of the quartic Landau-de Gennes bulk potential can be tuned. The talk is based on a joint work with Arghir D. Zarnescu (BCAM, Bilbao, Spain).