Dimensional crossover and the freezing transition in density functional theory

A modified geometrically based free-energy functional for hard spheres is proposed which gives reliable results even for situations of extreme confinements that reduce the effective dimensionality D. It is accurate for hard spheres between narrow plates (D = 2), inside narrow cylindrical pores (D = 1), and is exact in the 0D limit (a cavity that cannot hold more than one particle). This functional also predicts the hard-sphere fluid - solid transition in excellent agreement with the simulations.