Fluid–fluid versus fluid–solid demixing in mixtures of parallel hard hypercubes

Abstract

It is well known that increase of the spatial dimensionality enhances the fluid–fluiddemixing of a binary mixture of hard hyperspheres, i.e. the demixing occurs for lowermixture size asymmetry as compared to the three-dimensional case. However, according tosimulations, in the latter dimension the fluid–fluid demixing is metastable with respect tothe fluid–solid transition. According to the results obtained from approximations to theequation of state of hard hyperspheres in higher dimensions, the fluid–fluid demixing mightbecome stable for high enough dimension. However, this conclusion is rather speculativesince none of these works have taken into account the stability of the crystalline phase(by a minimization of a given density functional, by spinodal calculations or byMC simulations). Of course, the lack of results is justified by the difficulty ofperforming density functional calculations or simulations in high dimensions and, inparticular, for highly asymmetric binary mixtures. In the present work, we will takeadvantage of a well tested theoretical tool, namely the fundamental measuredensity functional theory for parallel hard hypercubes (in the continuum and in thehypercubic lattice). With this, we have calculated the fluid–fluid and fluid–solidspinodals for different spatial dimensions. We have obtained, no matter what thedimensionality, the mixture size asymmetry or the polydispersity (included as abimodal distribution function centered around the asymmetric edge lengths), thatthe fluid–fluid critical point is always located above the fluid–solid spinodal. Inconclusion, these results point to the existence of demixing between at least one solidphase rich in large particles and one fluid phase rich in small ones, preempting afluid–fluid demixing, independently of the spatial dimension or the polydispersity.