Demixing in a hard rod-plate mixture

Abstract

We argue that the possibility to observe a stable biaxial nematic phase in a binary mixture of prolate and oblate hard particles is seriously limited by the existence of entropy- driven demixing. This result follows from a simple Onsager-type density functional theory. An important feature15 the coupling of the demixing mechanism to the orientational order of the system. The strength of this coupling is dependent on the asphericity of the particles, and is directly related to the stability of the biaxial nematic phase. l~ Introduction~ Mixtures of rod- and plate-like particles are interesting because they may exhibit a biaxial nematic phase that is absent in the pure components. In this liquid crystalline phase both species are orientationally ordered, but in mutually perpendicular directions. The possible existence of the biaxial nematic phase may explain why this system attracted a lot of attention in the past ii-?). In the only study devoted to lyotropic (hard core) rod-plate mixtures that took into account the full set of thermodynamic equilibrium conditions, the biaxial phase was found to be thermodynamically stable for the particle shapes considered (7). This was consistent with the accepted belief that hard particles are miscible in any proportion. Recent theoretical developments in the study of binary hard sphere mixtures, however, seem to indicate that phase separation does occcur in this system if the diameter ratio of the spheres is sufficiently large (8, 9). Moreover, very recent computer simulations clearly show a demixing transition in several hard core mixtures (10). The mechanism of these demixing transitions is the so-called depletion effect: the gain of configurational entropy of small particles due to excluded volume overlap of clustered large particles outweighs the loss of configurational entropy of these large particles. Note that depletion is essentially a three-or-more body effect. Inspired by these new developments we have reconsidered the stability of the hard rod-plate mixture. Surprisingly, all ingredients for a demixing transition turn out to be present even if the volume of the rods equal that of the plates, which rules out the depletion mechanism. The driving force in this case is the excess average excluded volume of a rod-plate pair as compared