Entropy-driven demixing in binary hard-core mixtures: From hard spherocylinders towards hard spheres

We present a computer simulation study of a binary mixture of hard spherocylinders with different diameters (D ₁<D ₂) and the same lengths (L ₁=L ₂ = L). We first study a mixture of spherocylinders with lengths L = 15D ₂ and D ₁=0, which can be regarded as a mixture of rodlike colloids and ideal needles. We find clearly an entropy-driven isotropic-isotropic (I-I) demixing transition in this mixture. In addition, we study a mixture of spherocylinders with diameter ratio D ₁/D ₂=0.1 and we investigated the I-I demixing transition as a function of the length L of the particles. We observe a stable I-I demixing for all values of L in the range of 3≤L/D ₂≤15, but we could not reach the limit L=0, i.e., the hard-sphere mixture with diameter ratio of 0.1. Striking agreement is found for L/D ₂=15 with the results that follow from the second virial theory for infinitely elongated rods. For L/D ₂=2, we did not find a demixing transition till a total packing fraction of η=0.581, which is higher than the packing fraction at which freezing occurs for a pure system of thick rods. Thus this result and the extrapolation of our finite-L data to L=0 gives us a fingerprint that the fluid-fluid demixing transition in the binary hard-sphere mixture with a diameter ratio of 0.1 is metastable with respect to freezing or does not exist at all at densities below close packing.