Some general features of mesophase formation in hard-core plus tail potentials

The formation of mesophases in fluids with hard-core plus tail interactions is investigated and compared with the occurrence of cluster crystals in ultra-soft repulsive potentials by using a simple variational expression for the Helmholtz free energy. The purpose of this study is mostly qualitative, i.e., to explain the origin of the different behavior of these systems, and the reason why, in the hard-core case, interactions which are apparently quite different display a common pattern for the phase diagram, featuring spheres, cylinders, lamellae, inverted cylinders, and inverted spheres as the density is increased. In the limit of zero temperature, our approach also yields some simple predictions for the densities at which the transitions between different mesophases are expected to take place, as well as for the size of their clusters at the transitions. We find that these results compare favorably with those obtained in a former study of a model fluid with competing attractive and repulsive interactions by density-functional theory with numerical minimization.