Phase equilibria for a solution of long rigid rods of diameters D-i and len
gths L-i (i = 1,2) are studied analytically using Gaussian trial functions.
The conditions on the molecular size parameters for a nematic-nematic phas
e transition to be possible are determined, and found to be satisfied every
where except in a closed domain in the diameter ratio-length ratio plane. I
nformation on the relative ordering of the two components is also provided.