  We consider a Landau-de Gennes model for a suspension of small colloidal
inclusions in a nematic host. We impose suitable anchoring conditions at the
boundary of the inclusions, and we work in the dilute regime - i.e., the size
of the inclusions is much smaller than the typical separation distance between
them, so that the total volume occupied by the inclusions is small. 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, by
suitably choosing the surface anchoring energy density.
