  We consider a Landau-de Gennes model for a connected cubic lattice scaffold
in a nematic host, in a dilute regime. We analyse the homogenised limit for
both cases in which the lattice of embedded particles presents or not cubic
symmetry and then we compute the free effective energy of the composite
material. In the cubic symmetry case, we impose different types of surface
anchoring energy densities, such as quartic, Rapini-Papoular or more general
versions, and, in this case, we show that we can tune any coefficient from the
corresponding bulk potential, especially the phase transition temperature. In
the case with loss of cubic symmetry, we prove similar results in which the
effective free energy functional has now an additional term, which describes a
change in the preferred alignment of the liquid crystal particles inside the
domain. Moreover, we compute the rate of convergence for how fast the surface
energies converge to the homogenised one and also for how fast the minimisers
of the free energies tend to the minimiser of the homogenised free energy.
