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We consider a Landau-de Gennes model for a suspension of small colloidalinclusions in a nematic host. We impose suitable anchoring conditions at theboundary of the inclusions, and we work in the dilute regime - i.e., the sizeof the inclusions is much smaller than the typical separation distance betweenthem, so that the total volume occupied by the inclusions is small. By studyingthe homogenised limit, and proving rigorous convergence results for localminimisers, we compute the effective free energy for the doped material. Inparticular, we show that not only the phase transition temperature, but anycoefficient of the quartic Landau-de Gennes bulk potential can be tuned, bysuitably choosing the surface anchoring energy density.

Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation