A self-consistent perturbative density functional theory for hard-core fluids: phase diagrams, structural and interfacial properties

The classical Density functional theory (DFT) has become a powerful tool to describe the microscopic structure of fluids as the radial distribution function. One of its particular capabilities is to express the thermodynamic properties of those fluids even under the influence of external potentials, such as fluid-solid interaction. However, good models for the Helmholtz free-energy functionals are necessary to improve the results. In this work, we present a self-consistent thermodynamic perturbation theory for the excess Helmholtz free-energy from the DFT applied to hard-core fluids. The new perturbation theory is solved self-consistently without any closure relation to solving the Ornstein-Zernike equation explicitly. We compare the performance of our self-consistent perturbation theory with the results obtained with the well-known second-order Barker-Henderson perturbation theory for the hard-core Yukawa and square-well fluids. Moreover, we propose two versions of the DFT to describe the perturbative contribution: one based on the weighted density approximation theory and another from a modified mean-field theory. The present results confirm the modified mean-field theory as a better option to calculate the thermodynamic and structural properties of hard-core fluids.