Biaxial versus uniaxial nematic stability in asymmetric rod-plate mixtures

The isotropic-nematic phase behavior of a binary mixture of rodlike and platelike particles is studied within Onsager's second virial theory. The phase behavior is obtained from the numerically exact equilibrium orientational distribution functions for both uniaxial and biaxial nematic phases. Inspired by recent experimental work on these systems we concentrated on asymmetric mixtures in which the excluded volume between the plates v(ex)(pp) is larger than that between the rods v(ex)(rr). Starting from the symmetric case (v(ex)(pp)/v(ex)(rr)=1) and increasing the rod-plate excluded volume ratio we scrutinized the phase behavior, in particular focusing on the stability of the biaxial nematic phase. We observe that, at a certain asymmetry, the characteristic bicritical point is replaced by a two-phase region marking first order isotropic-biaxial transitions. Increasing the asymmetry even further leads to several demixing scenarios. First, there is a uniaxial-biaxial (N+-B) demixing scenario with an associated isotropic-uniaxial-biaxial (I-N+-B) triple equilibrium. Second, a uniaxial-uniaxial (N+-N-) demixing occurs in case of strongly asymmetric mixtures indicating that the biaxial nematic phase may become fully metastable. Since all predicted demixing scenarios lie in the experimentally accessible regime, there is a possibility of finding biaxial nematic structures in lyotropic colloidal rod-plate mixtures.