Constrained stability for biaxial nematic phases

Matteis, Giovanni De; Bisi, Fulvio; Virga, Epifanio G.

doi:10.1007/s00161-007-0041-1

Cited by 36 publications

(46 citation statements)

References 29 publications

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“…It is shown in Ref. [56,20,18], with greater rigor than observed here, that only within this region, the state of complete alignment of two molecules is a non-degenerate minimum for the given mutual orientational interaction energy.…”

Section: Ground State Ternary Diagramsupporting

confidence: 44%

“…The phase diagram as a function of the biaxiality is found by studying the minima of the internal energy (2.9) as a function of the changing biaxiality parameters λ 1 , λ 2 and λ 3 . As described in detail elsewhere [43,18,14], each physical significant phase can be described by thirty-six equivalent choices of the order parameters S, P , D and C. In a system with D 2h symmetry, this multiplicity of the order parameters is due to the physical irrelevance of the specific labels associated with the molecular and laboratory axes. In the same way, there are also six possible values of the set (λ 1 , λ 2 , λ 3 ), related by a different choice of the axis labels, where the physical behavior of the liquid crystals is equivalent.…”

Section: Ground State Ternary Diagrammentioning

confidence: 99%

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Symmetry Adapted Molecular-Field Theory for Thermotropic Biaxial Nematic Liquid Crystals and Its Expansion at Low Temperature

Turzi¹,

Sluckin²

2013

SIAM J. Appl. Math.

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Abstract.We have analyzed some properties of mean field theories of thermotropic biaxial liquid crystals with (D 2h ) symmetry. The study consists of two parts. In the first part we re-examine the standard theory due to Virga and coworkers. We introduce a convenient symmetry-adapted parameterization which allows the phase diagram to be displayed in an explicitly symmetry-preserving triangle. In the second part we use the Laplace approximation to examine the low temperature properties of the liquid crystal order parameters. Two of these (conventionally, D, P ) are identically zero at zero temperature in a biaxially ordered phase, non-zero at low temperatures in the liquid crystalline phases, but are again zero at higher temperatures in the isotropic phase. We use a low temperature expansion to derive an expression for the dominant terms in the free energy. This functional is minimized to obtain the low temperature properties of the order parameters D, P .

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Section: Ground State Ternary Diagramsupporting

confidence: 44%

Section: Ground State Ternary Diagrammentioning

confidence: 99%

Symmetry Adapted Molecular-Field Theory for Thermotropic Biaxial Nematic Liquid Crystals and Its Expansion at Low Temperature

Turzi¹,

Sluckin²

2013

SIAM J. Appl. Math.

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“…The phase diagram possesses some reflection symmetry around λ m (discussed in more detail, e.g in [31,32]), so that the phase N + U and N − U can be regarded as alternative representations of the same phase. Equivalently, for each λ > λ m it is possible to redefine axes in such a way as to associate this value of λ with a lower degree of biaxiality λ ′ .…”

Section: Molecular Field Theorymentioning

confidence: 99%

Biaxiality-induced magnetic field effects in bent-core nematics: Molecular-field and Landau theory

Sluckin

Luckhurst

2013

Phys. Rev. E

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Nematic liquid crystals composed of bent-core molecules exhibit unusual properties, including an enhanced Cotton-Mouton effect and an increasing isotropic (paranematic)-nematic phase transition temperature as a function of magnetic field. These systems are thought to be good candidate biaxial liquid crystals. Prompted by these experiments, we investigate theoretically the effect of molecular biaxiality on magnetic field-induced phenomena for nematic liquid crystals, using both molecular field and Landau theory. The geometric mean approximation is used in order to specify the degree of molecular biaxiality using a single parameter. We reproduce experimental field-induced phenomena, and predict also an experimentally accessible magnetic critical point. The Cotton-Mouton effect and temperature dependence of the paranematic-nematic phase transition are more pronounced with increased molecular biaxiality. We compare our theoretical approaches and make contact with recent relevant experimental results on bent-core molecular systems.

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“…MF also predicts a direct N B − I transition inside the parameter region IC 2 C 3 , and tricritical nature for N U − N B transition along C 1 C 3 [32]. The MF analysis based on mini-max principle involving only the two dominant order parameters (out of the four) permits the existence of a biaxial phase even at the base point V of triangle (λ = 0), though such a phase is forbidden on grounds of biaxial stability [33]. …”

Section: Hamiltonian Modelmentioning

confidence: 95%

“…According to recent mean field (MF) treatments [28][29][30][31][32][33][34], the relevant Hamiltonian parameter space conducive to the formation of stable biaxial phase comprises of a triangular region (say, ∆) in the (γ, λ) plane (the essential triangle) shown in Fig. 1 [32], the long axes of the molecules defining the primary director.…”

Section: Introductionmentioning

confidence: 99%

Complex free-energy landscapes in biaxial nematic liquid crystals and the role of repulsive interactions: A Wang-Landau study

2017

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General quadratic Hamiltonian models, describing interaction between crystal molecules (typically with D 2h symmetry) take into account couplings between their uniaxial and biaxial tensors.While the attractive contributions arising from interactions between similar tensors of the participating molecules provide for eventual condensation of the respective orders at suitably low temperatures, the role of cross-coupling between unlike tensors is not fully appreciated. Our recent study with an advanced Monte Carlo technique (entropic sampling) showed clearly the increasing relevance of this cross term in determining the phase diagram, contravening in some regions of model parameter space, the predictions of mean field theory and standard Monte Carlo simulation results. In this context, we investigated the phase diagrams and the nature of the phases therein, on two trajectories in the parameter space: one is a line in the interior region of biaxial stability believed to be representative of the real systems, and the second is the extensively investigated parabolic path resulting from the London dispersion approximation. In both the cases, we find the destabilizing effect of increased cross-coupling interactions, which invariably result in the formation of local biaxial organizations inhomogeneously distributed. This manifests as a small, but unmistakable, contribution of biaxial order in the uniaxial phase.The free energy profiles computed in the present study as a function of the two dominant order parameters indicate complex landscapes. On the one hand these profiles account for the unusual thermal behaviour of the biaxial order parameter under significant destabilizing influence from the cross terms. On the other, they also allude to the possibility that in real systems these complexities might be indeed inhibiting the formation of a low temperature biaxial order itself -perhaps reflecting the difficulties in their ready realization in the laboratory. 64.70.mf

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Constrained stability for biaxial nematic phases

Cited by 36 publications

References 29 publications

Symmetry Adapted Molecular-Field Theory for Thermotropic Biaxial Nematic Liquid Crystals and Its Expansion at Low Temperature

Symmetry Adapted Molecular-Field Theory for Thermotropic Biaxial Nematic Liquid Crystals and Its Expansion at Low Temperature

Biaxiality-induced magnetic field effects in bent-core nematics: Molecular-field and Landau theory

Complex free-energy landscapes in biaxial nematic liquid crystals and the role of repulsive interactions: A Wang-Landau study

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