Phase diagrams of binary mixtures of hard rods in an external orientational field

We study a binary mixture of hard spherocylinders with the same diameter (D) and different length (L-2> L-1) in the absence and presence of a static external electric (magnetic) field on the basis of the Onsager theory. In the zero field, we find that the usual isotropic-nematic phase transition takes place only between the length ratio (L-2/L-1) of 1-2.9, the reentrant phenomenon occurs for L-2/L(1)greater than or equal to 2.7, and the nematic-nematic phase transition starts to be stable for L-2/L-1> 2.9. In the external field, the isotropic-nematic transition is replaced by a weakly ordered nematic-nematic transition. The increasing external field strength shifts the transition towards lower densities and narrows the density gap terminating the first order transition at a critical point. The critical field strength is found to increase rapidly with increasing length ratio.