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

E. do Carmo; A. P. Vieira; S. R. Salinas

doi:10.1103/physreve.83.011701

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arXiv · 1009.2729

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

E. do Carmo·A. P. Vieira·S. R. Salinas

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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.

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E. do Carmo, A. P. Vieira, S. R. Salinas. 2010-09-14. Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice. https://doi.org/10.1103/physreve.83.011701

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