DEMIXING VERSUS ORDERING IN HARD-ROD MIXTURES

We present a simple treatment of the depletion-driven demixing transit ion in isotropic and perfectly aligned binary hard-rod mixtures. The s implicity is mainly due to the fact that we use the second virial appr oximation to the Helmholtz free energy in combination with a convenien t Legendre transform. This combination leads to an exact expression fo r the depletion-driven demixing spinodal in isotropic mixtures of hard rods with different diameters. We show for rod species with the same length that the demixing spinodal is thermodynamically stable with res pect to the isotropic-nematic transition, if the diameter ratio is lar ger than about 5. We also show that perfectly aligned rod mixtures sho w a nematic-nematic demixing spinodal, that may preempt the nematic-sm ectic or the nematic-columnar bifurcation if the size difference betwe en the particles is sufficiently large.