Biaxial nematic stability in the rod-plate mixture with a dopant: The restricted-orientation model on the 3rd virial level

Abstract

We analyze the effect of doping a binary mixture of uniaxial rod(R)- and plate(P)-like hard parallelepipeds having equal volumes and conjugated aspect ratios γR=1/γP=5. Uniaxial rods (L) or plates (T) with greater elongations γL=1/γT=10 were used as an admixture. The aim of the work is to examine this effect as a possible tool to stabilize the biaxial (Nb) phase in the P–R mixture, where Nb is known to be unstable with respect to demixing into two uniaxial nematics. The formalism to study orientational phase transitions is the off-lattice restricted-orientation (Zwanzig) model of a multi-component mixture of rectangular parallelepipeds with the EOS on the 3rd virial level. The phase biaxiality parameters of components and the second-order transition lines are located by direct minimization of the Gibbs energy. The results obtained by the examples of ternary systems show that introducing of small amounts of L or T into the reference P–R system promotes broadening of the Nb domain and may induce its stabilization. The case of L admixtures shows that an increase of the dopant particle volume results in a trend towards enhancement of the Nb phase relative stability.