# Statistical models of mixtures with a biaxial nematic phase.

@article{doCarmo2010StatisticalMO, title={Statistical models of mixtures with a biaxial nematic phase.}, author={Eduardo do Carmo and Danilo B. Liarte and Silvio R. A. Salinas}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2010}, volume={81 6 Pt 1}, pages={ 062701 } }

We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rodlike and disklike molecules. A quenched distribution of shapes leads to a phase diagram with two uniaxial and a biaxial nematic structure. A thermalized distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times… Expand

#### 17 Citations

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

- Physics, Medicine
- The European physical journal. E, Soft matter
- 2012

A two-temperature formalism is used to mimic the presence of two distinct relaxation times, and it is shown that a slight departure from complete thermalization is enough to stabilize a biaxial nematic phase. Expand

Elementary lattice models for the nematic transitions in liquid-crystalline systems

- Materials Science
- 2017

ABSTRACT The Maier-Saupe theory of the nematic phase transitions, with the requirement that the molecular directors are restricted to the Cartesian axes, can be formulated as a fully-connected… Expand

Enhancement of Nematic Order and Global Phase Diagram of a Lattice Model for Coupled Nematic Systems

- Physics
- 2012

We use an infinite-range Maier–Saupe model, with two sets of local quadrupolar variables and restricted orientations, to investigate the global phase diagram of a coupled system of two nematic… Expand

Low–temperature biaxial nematic from rod and disc mesogen mixture

- Materials Science
- 2012

Molecular dynamics computer simulations have been employed to demonstrate that the addition of a suitable uniaxial discotic nematic to a biaxial nematic (Nb) of elongated mesogens can give rise to a… Expand

Lattice Statistical Models for the Nematic Transitions in Liquid-Crystalline Systems

- Physics
- 2016

We investigate the connections between some simple Maier-Saupe lattice models, with a discrete choice of orientations of the microscopic directors, and a recent proposal of a two-tensor formalism to… Expand

Modulated phases in a three-dimensional Maier-Saupe model with competing interactions.

- Physics, Medicine
- Physical review. E
- 2017

It is shown that the proposed model exhibits isotropic and nematic phases and also a series of modulated phases that meet at a multicritical point, a Lifshitz point, and Monte Carlo simulations corroborate the general behavior found within the mean-field approximation. Expand

Bimodal form distribution from modelling biaxial lyotropic liquid crystal solutions through a polydisperse Maier–Saupe model

- Materials Science
- 2017

ABSTRACT Biaxial nematic phases have been the subject of a long list of studies. In particular, they were found for a few lyotropic micellar solutions. There is a debate in the literature on whether… Expand

Tricritical behavior of soft nematic elastomers.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2013

A lattice statistical model is proposed to investigate the phase diagrams and the soft responses of nematic liquid-crystal elastomers, finding a peculiar phase diagram, in terms of temperature and the diagonal component of the distortion tensor along the stretching direction, with first- and second-order transitions to the soft phase. Expand

Elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2011

A simple mean-field lattice model to describe the behavior of nematic elastomers is introduced, and it is shown that random fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state. Expand

Magnetic Field and Dilution Effects on the Phase Diagrams of Simple Statistical Models for Nematic Biaxial Systems

- Physics
- 2020

We use a simple statistical model to investigate the effects of an applied magnetic field and of the dilution of site elements on the phase diagrams of biaxial nematic systems, with an emphasis on… Expand

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