# 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…

## 17 Citations

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

- Physics, MedicineThe 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.

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…

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…

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…

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…

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

- Physics, MedicinePhysical 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.

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…

Tricritical behavior of soft nematic elastomers.

- Mathematics, PhysicsPhysical 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.

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

- Physics, MedicinePhysical 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.

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…

## References

SHOWING 1-10 OF 40 REFERENCES

Theory of Biaxial Nematic Ordering in Rod-Disc Mixtures Revisited

- Chemistry
- 1997

Abstract We use the variational cluster approximation to study the relative thermodynamic stability of the spatially uniform phases of binary mixtures of hard rods and discs. The factors promoting…

Mean Field Theory of Binary Mixtures of Nematic Liquid Crystals

- Chemistry
- 1985

Abstract Molecular field theory is used to determine the temperature-composition phase diagram and component order parameters of binary mixtures of nematic liquid crystals. A rotationally invariant…

Landau-de Gennes theory of biaxial nematics reexamined.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

This work fully explore the stability of the biaxial nematic phase giving analytical solutions for all distinct classes of the phase diagrams that theory allows and a brief comparison with predictions of existing molecular theories is given.

Mixture of changing uniaxial micellar forms in lyotropic biaxial nematics

- Materials Science
- 2008

Lyotropic nematics consisting of surfactant–cosurfactant water solutions may present a biaxial phase or direct U(+)↔U(−) transitions, in different regions of the temperature‐relative concentration…

Biaxial phases in polydisperse mean-field model solution of uniaxial micelles

- Materials Science
- 1997

We consider a discretized Maier–Saupe model for a polydisperse solution of micelles of axial symmetry. An exact mean-field solution is presented. The phase diagram displays a biaxial phase at small…

Landau theory of the nematic-isotropic phase transition

- Physics
- 1986

Abstract A review is given of the wide variety of predictions that results from a Landau-type of description of the nematic-isotropic phase transition. This includes a discussion of the nature of the…

Biaxial nematic phase, multiphase critical point, and reentry transition in binary liquid crystal mixtures

- Materials Science
- 1984

A model considering both short‐range and long‐range interactions for liquid crystals mixtures of rod‐like and plate‐like molecules is presented in this paper. The model is treated in the framework of…

Thermotropic biaxial liquid crystalline phases in a mixture of attractive uniaxial rod and disk particles.

- Materials Science, MedicinePhysical review letters
- 2008

The first examples of thermotropic biaXial mesophases in mixtures of model attractive uniaxial molecules interacting through two intermolecular potential models: one incorporating spherically symmetric (isotropic) attractive interactions; another with anisotropic attractive interactions.

Liquid crystal phase transitions in mixtures of rodlike and platelike molecules

- Materials Science
- 1973

Model calculations are presented which indicate that the character of the nematic‐isotropic phase transition can be continuously changed from first to second order and that a new biaxial liquid…

Computer simulations of biaxial nematics.

- Materials Science, MedicineJournal of physics. Condensed matter : an Institute of Physics journal
- 2008

An overview of the simulation work performed so far is given, and relying on the recent experimental findings, focuses on the still unanswered questions which will determine the future challenges in the field.