Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

Abstract

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.

References in corpus (3)

• Enhancement by polydispersity of the biaxial nematic phase in a mixture of hard rods and plates
• Statistical models of mixtures with a biaxial nematic phase
• Grand canonical and canonical solution of self-avoiding walks with up to three monomers per site on the Bethe lattice

Cited by in corpus (5)

• Maier-Saupe model for a mixture of uniaxial and biaxial molecules
• Lattice statistical models for the nematic transitions in liquid-crystalline systems
• Enhancement of nematic order and global phase diagram of a lattice model for coupled nematic systems
• Phase behavior of a lattice-gas model for biaxial nematics
• Uniaxial and biaxial structures in the elastic Maier-Saupe model