Demixing in binary mixtures of hard hyperspheres

– The phase behavior of binary fluid mixtures of hard hyperspheres in four and five dimensions is investigated. Spinodal instability is found by using a recent and accurate prescription for the equation of state of the mixture that requires the equation of state of the single component fluid as input. The role played by the dimensionality on the possible metastability of the demixing transition with respect to a fluid-solid transition is discussed. The binodal curves in the pressure–chemical potential representation are seen to lie on a common line, independent of the size ratio. The phase diagram of the simplest model of a binary mixture, that of additive hard spheres, has not been completely determined up to now and remains as an interesting open problem. Ever since the solution of the Ornstein-Zernike equation with the Rogers-Young closure for such a mixture given by Biben and Hansen [1], the until then widespread and unchallenged belief that these mixtures cannot phase separate into two fluid phases (which was supported by the analytical results of the Percus-Yevick approximation [2]) has been seriously questioned. In fact, a wealth of papers dealing with this and related demixing problems have recently appeared in the literature [3–8], but the issue is still far from being settled. One of the key aspects of this fluid-fluid transition in hard-sphere mixtures is that, if it exists at all, it must be entropy driven. In contrast, in other mixtures such as molecular mixtures, the transition is driven by an asymmetry between the like-and unlike-particle interactions, i.e. it is energy driven, and at least the qualitative phase behavior is rather well characterized [9]. Entropy driven demixing was nicely shown by Frenkel and Louis to occur in a simple lattice model for a binary hard-core mixture [3]. Experimental work has provided evidence that results for (asymmetric in size) hard-sphere mixtures approximate rather well the ther-modynamic properties of real colloidal systems, so it has been suggested that a likely physical mechanism behind the entropy driven demixing transition is osmotic depletion. This notion, first introduced to explain phase separation in polymer-colloid mixtures, is included in the scaled particle theory of Lekkerkerker and Stroobants [4], which predicts a fluid-fluid spinodal