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

Henriques, E. F.; Salinas, S. R.

doi:10.1140/epje/i2012-12014-1

Cited by 14 publications

(5 citation statements)

References 45 publications

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“…A thermalized distribution, however, precludes the stability of this biaxial phase. The introduction of a two-temperature formalism (to mimic a separation of relaxation times) shows that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure [ 57 , 58 ].…”

Section: Self-assembly and Lyotropic Liquid Crystalsmentioning

confidence: 99%

Supramolecular Aggregates: Hardness Plus Softness

Amáral

2021

Molecules

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The properties of supramolecular aggregates cross several disciplines, embracing the sciences of nature and joining theory, experiment, and application. There are few articles centering on the problems of interdisciplinarity, and this paper gives an alternative approach, starting with scientific divulgation, bringing concepts from their origin, to facilitate the access of young scientists to the scientific content. Didactic examples are taken from the experience of the author in changing directions of research due to several circumstances of life (including maternity), starting from the view of a rigorous student of physics and evolving to several subjects in chemistry. The scientific part starts with concepts related to nuclear interactions, using the technique of neutron scattering in reactors, and evolves to research in molecular physics. Finally, it arrives at the academic context, with research in condensed matter physics, with X-ray and other techniques, starting with detergents forming nematic lyotropic liquid crystals and the phase transition sequence of isotropic to nematics to hexagonal. The scientific subjects evolved to biological and bio-inspired liquid crystals, including DNA and also specific lipids and phospholipids in biomimetic membranes. Special attention is given to the question of distribution of matter in these complex systems and the non-trivial connections between biochemistry, structures, auto-aggregation, and biology.

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Section: Self-assembly and Lyotropic Liquid Crystalsmentioning

confidence: 99%

Supramolecular Aggregates: Hardness Plus Softness

Amáral

2021

Molecules

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“…Although the nematic-isotropic transition is perhaps the most explored transition in liquid crystalline systems, there are still a number of questions and open problems, which can be formulated in terms of simple statistical lattice models. An interesting question is the onset of a biaxial nematic phase [6], which we have recently investigated in the context of a MS model for a mixture of discs and cylinders [7,8]. Now we analyze the global phase diagram of a similar type of statistical model, with the inclusion of two sets of quadrupolar degrees of freedom, which leads to a connection with the work by Lopatina and Selinger [4,5].…”

Section: Introductionmentioning

confidence: 96%

“…The MS model can be further simplified if we suppose that the local mesogen orientations are restricted to a discrete set of states, according to an early proposal by Zwanzig [12]. Some model calculations with continuous orientations for uniaxial [13], and biaxial [8] nematic systems give support to the idea that this simplification does not lead to qualitatively different results. In recent publications, we have used extensions of this Maier-Saupe-Zwanzig (MSZ) lattice model to investigate the existence of biaxial nematic phases [14,7,15] and the thermodynamic properties of nematic elastomers [16].…”

Section: Introductionmentioning

confidence: 99%

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

Liarte

Salinas

2012

Braz J Phys

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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 subsystems. The free energy and the equations of state are exactly calculated by standard techniques of statistical mechanics. The nematic-isotropic transition temperature of system A increases with both the interaction energy among mesogens of system B, and the two-subsystem coupling J. This enhancement of the nematic phase is manifested in a global phase diagram in terms of the interaction parameters and the temperature T . We make some comments on the connections of these results with experimental findings for a system of diluted ferroelectric nanoparticles embedded in a nematic liquid-crystalline environment.

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“…A few years later, these theoretical phase diagrams were constructed [52,54]. Since then, enormous efforts have been done to make stable biaxial nematic phases; these include the use of spheroplatelets [54][55][56][57], bent-core molecules [58,59] and mixtures of rod-like with disk-shaped molecules [60][61][62]. Dispersions of board-like goethite particles with short-range repulsive interactions have also been used to explore biaxial nematic phases [63,64].…”

Section: Introductionmentioning

confidence: 99%

Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density

Villada‐Gil

Palacio‐Betancur

Armas-Pérez

et al. 2019

J. Phys.: Condens. Matter

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In this work, we explore fluctuations during phase transitions of uniaxial and biaxial liquid crystals using a phenomenological free energy functional. We rely on a continuum-level description of the liquid crystal ordering with a tensorial parameter and a temperature dependent Landau polynomial expansion of the tensor’s invariants. The free energy functional, over a three-dimensional periodic domain, is integrated with a Gaussian quadrature and minimized with a theoretically informed Monte Carlo method. We reconstruct analytical phase diagrams, following Landau and Doi’s notations, to verify that the free energy relaxation reaches the global minimum. Importantly, our relaxation method is able to follow the thermodynamic behavior provided by other non-phenomenological approaches; we predict the first order character of the isotropic–nematic transition, and we identify the uniaxial–biaxial transition as second order. Finally, we use a finite-size scaling method, using the nematic susceptibility, to calculate the transition temperatures for 4-Cyano-4’-pentylbiphenyl (5CB) and N-(4-methoxybenzylidene)-4-butylaniline (MBBA). Our results show good agreement with experimental values, thereby validating our minimization method. Our approach is an alternative towards the relaxation of temperature dependent continuum-level free energy functionals, in any geometry, and can incorporate complicated elastic and surface energy densities.

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

Cited by 14 publications

References 45 publications

Supramolecular Aggregates: Hardness Plus Softness

Supramolecular Aggregates: Hardness Plus Softness

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

Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density

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