It is well known that the increase of the spatial dimensionality enhances thefluid-fluid demixing of a binary mixture of hard hyperspheres, i.e. thedemixing occurs for lower mixture size asymmetry as compared to thethree-dimensional case. However, according to simulations, in the latterdimension the fluid-fluid demixing is metastable with respect to thefluid-solid transition. According to the results obtained from approximationsto the equation of state of hard hyperspheres in higher dimensions, thefluid-fluid demixing might becomes stable for high enough dimension. However,this conclusion is rather speculative since none of the above works have takeninto account the stability of the crystalline phase (nor by a minimization of agiven density functional, neither spinodal calculations or MC simulations). Ofcourse, the lack of results is justified by the difficulty for performingdensity functional calculations or simulations in high dimensions and, inparticular, for highly asymmetric binary mixtures. In the present work, we willtake advantage of a well tested theoretical tool, namely the fundamentalmeasure density functional theory for parallel hard hypercubes (in thecontinuum and in the hypercubic lattice). With this, we have calculated thefluid-fluid and fluid-solid spinodals for different spatial dimensions. We haveobtained, no matter of the dimensionality, the mixture size asymmetry nor thepolydispersity (included as a bimodal distribution function centered around theasymmetric edge-lengths), that the fluid-fluid critical point is always locatedabove the fluid-solid spinodal. In conclusion, these results point to theexistence of demixing between at least one solid phase rich in large particlesand one fluid phase rich in small ones, preempting a fluid-fluid demixing,independently of the spatial dimension or the polydispersity.
展开▼
