Close to the edge of fundamental measure theory: a density functional for hard-sphere mixtures

We analyse the structure of the fundamental measure theory for the free energy density functional of hard-sphere mixtures. A comparative study of the different versions of the theory, and other density functional approaches, is carried out in terms of their generic form for the three-point direct correlation function, which shows clearly the main advantages and problems of the different approximations. A recently developed version for the monocomponent case is extended to mixtures of hard spheres with different radii, and a new prescription is presented for obtaining the exact dimensional crossover of those mixtures in the one-dimensional (1D) limit. Numerical results for planar wall–fluid interfaces and for the 1D fluid are presented.