Lattice model for biaxial and uniaxial nematic liquid crystals

Sauerwein, Ricardo Andreas; Oliveira, Mário J. de

doi:10.1063/1.4948627

Cited by 10 publications

(6 citation statements)

References 39 publications

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“…the solution of which defines a line of Landau points corresponding to a varying chemical potential. For βµ 1, we recover the result β L A = 1 obtained at zero field in Equation (19). As µ is reduced, the temperature corresponding to the solution of Equation (38) is also reduced, as it can be checked by calculating the implicit derivative of β with respect to µ from Equation (38).…”

Section: Introducing Dilutionsupporting

confidence: 69%

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

Rodrigues¹,

Vieira²,

Salinas³

2020

Crystals

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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 the stability of the Landau multicritical point. The statistical lattice model consists of intrinsically biaxial nematogenic units, which interact via a Maier–Saupe potential, and which are characterized by a discrete choice of orientations of the microscopic nematic directors. According to previous calculations at zero field and in the absence of dilution, we regain the well-known sequence of biaxial, uniaxial, and disordered structures as the temperature is increased, and locate the Landau point. We then focus on the topological changes induced in the phase diagram by the application of an external magnetic field, and show that the Landau point is destabilized by the presence of an applied field. On the other hand, in the absence of a field, we show that only a quite strong dilution of nematic sites is capable of destabilizing the Landau point.

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Section: Introducing Dilutionsupporting

confidence: 69%

“…I being the 3 × 3 identity matrix. For our simplified model, we restrict the directors to point along the Cartesian axes [18,19], so that each nematogen takes only six distinct states, defining a new Hamiltonian…”

Section: The Svd Modelmentioning

confidence: 99%

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

Rodrigues¹,

Vieira²,

Salinas³

2020

Crystals

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“…At that time, it seemed natural to assume that Type I and Type II phases were composed of cylindrical-like and disc-like micelles [28][29][30][31][32], respectively, as shown in Figure 1. Freiser [16,33] theoretically predicted the existence of the NB phase for the first time [5,[34][35][36][37][38] after Taylor et al [39] reported a biaxial smectic C phase in thermotropic liquid crystals. However, at that time, there were no experimental results to support this theoretical prediction.…”

Section: Introductionmentioning

confidence: 99%

“…They used the optical microscopy, laser conoscopy and X-ray diffraction techniques and found that the biaxial phase domain was relatively large (~15 °C) for appropriate relative concentrations of the mixture compounds. Freiser [16,33] theoretically predicted the existence of the N B phase for the first time [5,[34][35][36][37][38] after Taylor et al [39] reported a biaxial smectic C phase in thermotropic liquid crystals. However, at that time, there were no experimental results to support this theoretical prediction.…”

Section: Introductionmentioning

confidence: 99%

Experimental Conditions for the Stabilization of the Lyotropic Biaxial Nematic Mesophase

Akpınar

Neto

2019

Crystals

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Nematic phases are some of the most common phases among the lyotropic liquid crystalline structures. They have been widely investigated during last decades. In early studies, two uniaxial nematic phases (discotic, ND, and calamitic, NC) were identified. After the discovery of the third one, named biaxial nematic phase (NB) in 1980, however, some controversies in the stability of biaxial nematic phases began and still continue in the literature. From the theoretical point of view, the existence of a biaxial nematic phase is well established. This review aims to bring information about the historical development of those phases considering the early studies and then summarize the recent studies on how to stabilize different nematic phases from the experimental conditions, especially, choosing the suitable constituents of lyotropic mixtures.

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“…One then computes the corresponding partition function and free energy, matching the coefficients of the free energy to those of the LdG free energy. Such an approach has been applied, for example, to a molecular model of biaxial bricks [35]. A variant of the mean-field approach is to express the the entropy of the molecules and their average pairwise interaction energy in terms of the distribution function for the molecular positions and orientations, determining this function self-consistently via some form of closure at the mean-field level.…”

Section: Introductionmentioning

confidence: 99%

Multiscale approach to nematic liquid crystals via statistical field theory

2017

Phys. Rev. E

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We propose an approach to a multiscale problem in the theory of thermotropic uniaxial nematics based on the method of statistical field theory. This approach enables us to relate the coefficients A, B, C, L_{1}, and L_{2} of the Landau-de Gennes free energy for the isotropic-nematic phase transition to the parameters of a molecular model of uniaxial nematics, which we take to be a lattice gas model of nematogenic molecules interacting via a short-ranged potential. We obtain general constraints on the temperature and volume fraction of nematogens for the Landau-de Gennes theory to be stable against molecular orientation fluctuations at quartic order. In particular, for the case of a fully occupied lattice, we compute the values of the isotropic-nematic transition temperature and the order parameter discontinuity predicted by (i) a continuum approximation of the nearest-neighbor Lebwohl-Lasher model and (ii) a Lebwohl-Lasher-type model with a nematogenic interaction of finite range. We find that the predictions of (i) are in reasonably good agreement with known results of Monte Carlo simulation.

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Lattice model for biaxial and uniaxial nematic liquid crystals

Cited by 10 publications

References 39 publications

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

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

Experimental Conditions for the Stabilization of the Lyotropic Biaxial Nematic Mesophase

Multiscale approach to nematic liquid crystals via statistical field theory

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