Numerical calculations of the phase diagram of cubic blue phases in cholesteric liquid crystals

We study the static properties of cubic blue phases by numerically minimising the three-dimensional, Landau-de Gennes free energy for a cholesteric liquid crystal close to the isotropic-cholesteric phase transition. Thus we are able to refine the powerful but approximate, semi-analytic frameworks that have been used previously. We obtain the equilibrium phase diagram and discuss it in relation to previous results. We find that the value of the chirality above which blue phases appear is shifted by 20% (towards experimentally more accessible regions) with respect to previous estimates. We also find that the region of stability of the O5 structure -- which has not been observed experimentally -- shrinks, while that of BP I (O8-) increases thus giving the correct order of appearance of blue phases at small chirality. We also study the approach to equilibrium starting from the infinite chirality solutions and we find that in some cases the disclination network has to assemble during the equilibration. In these situations disclinations are formed via the merging of isolated aligned defects.