Using a straightforward extension of the Onsager-theory for hard rods, we c
onsider the thermodynamic stability of the isotropic (I) and nematic (N) ph
ase of binary mixtures of thick and thin hard rods of the same length. We s
how that such mixtures not only exhibit the expected I-N ordering transitio
n and the previously predicted depletion driven I-I demixing transition, bu
t also a N-N demixing transition driven by the orientation entropy of the t
hinner rods. For various values of the diameter ratio of the two species we
present the phase diagrams, which exhibit I-N, I-I and N-N coexistence, I-
N-N and I-I-N triple points, and I-I and N-N critical points. We also prese
nt the results of computer simulations of the I-I and I-N coexistence for d
iameter ratio 1:10, which are in good agreement with the theory. (C) 1998 E
lsevier Science B.V. All rights reserved.