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It is well known that the increase of the spatial dimensionality enhances the fluid-fluid (F-F) demixing of a binary mixture of hard hyperspheres (HHS), i.e. the demixing occurs for lower aspect ratios of the size of the particles as compared to the three-dimensional case. However, according to simulations, in the latter dimension the F-F demixing is metastable with respect to the fluid-solid (F-S) transition. After the results obtained from approximations to the equation of state of HHS in higher dimensions, some authors claim that the F-F demixing might becomes stable for high enough dimension. However these claims are rather speculative since none of the above works have taken into account the stability of the crystalline phase (nor by a minimization of a given density functional, neither spinodal calculations or MC simulations). Of course, the lack of results is justified by the dificulty for performing density functional calculations or simulations in higher dimensions and, in particular, for highly asymmetric binary mixtures.
In the present work, we will take advantage of a well tested theoretical tool, namely the fundamental measure density functional theory for parallel hard hypercubes (in the continuuum and in the hypercubic lattice). With this, we have calculated the F-F and F-S spinodals for different spatial dimensions. We have obtained, no matter of the dimensionality, the mixture asymmetry or the polydispersity (included as a bimodal distribution function centered around the asymmetric edge-lengths), that the F-F critical point is always located above the F-S spinodal. Notwithstanding, this point becomes closer to the F-S spinodal as the dimension or polydispersity increases, but it seems that they never cross each other. In conclusion, these results point to the existence of demixing between a solid phase rich in large particles and a fluid phase rich in small ones, preempting a F-F demixing, indenpendently of the spatial dimension or the polydispersity. Although this study is specific for parallel hypercubes, we believe that this result is the most likely scenario for other additive mixtures of hard particles, like HHS. |
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