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It is shown that the density functional theory (DFT) of soft matter is able to capture, in a semi-quantitative way, the essential properties of the phase behaviour in these complex systems. This is illustrated here for the case of the fractionation and segregation of polydisperse fluids of spherical (colloidal) particles and for the case of the self-assembling of monodisperse fluids of non-spherical particles. Both homogeneous and inhomogeneous situations will be considered and described within the same DFT.

Most colloids usually exhibit one or several polydispersities. A natural framework for the theoretical description of polydisperse systems is provided by the extension of density functional theory to 'continuous' mixtures. This will be illustrated here by the study of both the bulk and interfacial properties of a simple van der Waals model for a polydisperse colloidal fluid.

It is shown that a simple perturbation expansion around the free energy of a (BCC/FCC) hard-sphere crystal leads to accurate predictions for the (BCC/FCC) freezing of soft spheres interacting via the inverse-power potential, V(r)= epsilon ( sigma /r)n, for all values of n including the extreme case of the one-component plasma (n=1). In particular, the authors find that for 1 6 the BCC phase is unstable and only the fluid-FCC transition survives, in agreement with the computer simulations.

In analogy with the well-known Van der Waals theory for disordered fluid phases we propose a simple analytic expression for the Helmholtz free energy of an ordered crystalline phase. It is based on a free-volume approximation to the entropic contribution due to the hard-core repulsions and a static lattice energy approximation to the contribution of the attractions. In this way we are able to describe in a simple way phase transitions between two disordered phases, between two ordered phases and between an ordered and a disordered phase in systems of any spatial dimensionality.

It is shown that the recently proposed density-functional theory of freezing predicts a thermodynamically stable hard-sphere solid up to the density of crystal close packing. The behaviour is contrasted with the unphysical remelting of the hard-sphere solid just after freezing found in an alternative theory. Some possible reasons for this discrepancy are pointed out. © 1985 The Institute of Physics., SCOPUS: ar.j, info:eu-repo/semantics/published

A simple scaling procedure based on the known low-density results is shown to yield an equation of state and partial pair correlation functions of binary hard-disc alloys which agree closely with the results of canonical and isobaric ensemble Monte Carlo simulations. These results will serve as the basic input in a density functional calculation of the fluid-solid phase diagram of such mixtures regarded as a simple model for monolayers of rare-gas mixtures. © 1988 IOP Publishing Ltd., SCOPUS: ar.j, info:eu-repo/semantics/published

The density functional theory of freezing is extended to the crystallisation of multicomponent systems into substitutional solid solutions. The formalism is applied to the case of binary mixtures of hard spheres. As the ratio of diameters α = σ1/σ2 is lowered, the fluid-solid phase diagram evolves from a spindle shape (1> α > 0.94) into an azeotropic diagram (0.94 > α >0.92) and finally into a eutectic diagram (0.92 > α > 0.85). The influence of inter-atomic attractions is examined within the van der Waals mean-field approximation. The resulting phase diagrams are even richer than for the bare hard-sphere mixtures, and turn out to be very sensitive to the combination rule for the attractive energy between opposite species. © 1987 IOP Publishing Ltd., SCOPUS: ar.j, info:eu-repo/semantics/published