A density-functional theory study of vapor, liquid, and mesophases in a symmetric, hard-sphere mixture with cross attraction at non-equimolar concentrations

We investigate the phase diagram of a model hard-sphere mixture consisting of two species of equal diameter, featuring a square-well cross attraction. The study is carried out using density-functional theory (DFT) in the mean-field approximation and extends to arbitrary species concentrations a former DFT study at equimolar composition [Prestipino et al., J. Chem. Phys. 159, 204902 (2023)]. In addition to the stripe phases found in the equimolar case, cylinder and cluster phases are also observed. While at high temperatures, the inhomogeneous domains can be accessed only from the high-density liquid; at low temperatures, these phases coexist with the low-density vapor, resulting in a notably rich phase diagram. The predictions of an analytic implementation of the theory-based on the Landau expansion of the free energy in powers of the density modulation amplitude-are compared with numerical DFT minimization. The Landau approach shows qualitative agreement, although it overestimates the extent of the stripe region at high density, where local concentration values may exceed their physical bounds. Differences and similarities between DFT and simulation results for narrow attractive wells are briefly discussed.