We present a computer simulation study of a binary mixture of hard spherocylinders with different diameters\ud (D1,D2) and the same lengths (L15L25L). We first study a mixture of spherocylinders with lengths L\ud 515D2 and D150, which can be regarded as a mixture of rodlike colloids and ideal needles. We find clearly\ud an entropy-driven isotropic-isotropic (I-I) demixing transition in this mixture. In addition, we study a mixture\ud of spherocylinders with diameter ratio D1 /D250.1 and we investigated the I-I demixing transition as a\ud function of the length L of the particles. We observe a stable I-I demixing for all values of L in the range of\ud 3<L/D2<15, but we could not reach the limit L50, i.e., the hard-sphere mixture with diameter ratio of 0.1.\ud Striking agreement is found for L/D2515 with the results that follow from the second virial theory for\ud infinitely elongated rods. For L/D252, we did not find a demixing transition till a total packing fraction of\ud h50.581, which is higher than the packing fraction at which freezing occurs for a pure system of thick rods.\ud Thus this result and the extrapolation of our finite-L data to L50 gives us a fingerprint that the fluid-fluid\ud demixing transition in the binary hard-sphere mixture with a diameter ratio of 0.1 is metastable with respect to\ud freezing or does not exist at all at densities below close packing
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