Eur. Phys. J. E (2012) 35: 14
https://doi.org/10.1140/epje/i2012-12014-1

Biaxial nematic phase in the Maier-Saupe model for a mixture of discs and cylinders

Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, CEP 05314-970, São Paulo, Brazil

^* e-mail: srasalinas@gmail.com

Received: 4 December 2011
Revised: 24 January 2012
Accepted: 9 February 2012
Published online: 28 February 2012

Abstract

We analyze the global phase diagram of a Maier-Saupe lattice model with the inclusion of shape-disordered degrees of freedom to mimic a mixture of oblate and prolate molecules (discs and cylinders). In the neighborhood of a Landau multicritical point, solutions of the statistical problem can be written as a Landau-de Gennes expansion for the free energy. If the shape-disordered degrees of freedom are quenched, we confirm the existence of a biaxial nematic structure. If orientational and disorder degrees of freedom are allowed to thermalize, this biaxial solution becomes thermodynamically unstable. Also, we use a two-temperature formalism to mimic the presence of two distinct relaxation times, and show that a slight departure from complete thermalization is enough to stabilize a biaxial nematic phase.