Density functional theory of fluids in nanopores: Analysis of the fundamental measures theory in extreme dimensional-crossover situations

Two density functional theories, the fundamental measures theory of Rosenfeld Phys. Rev. Lett. 63, 980 (1989) and a subsequent approximation by Tarazona Phys. Rev. Lett. 84, 694 (2000) are applied to the study of the hard-sphere fluid in two situations: the cylindrical pore and the spherical cavity. The results are compared with those obtained with grand canonical ensemble Monte Carlo simulations. The differences between both theories are evaluated and interpreted in the terms of the dimensional crossover from three to one and zero dimensions.