Mean-field theory of isotropic-uniaxial nematic-biaxial nematic phase transitions in an external field

Mukherjee, Prabir K.; De, Arnab Kumar; Mandal, Ananya

doi:10.1088/1402-4896/aaf514

Cited by 3 publications

(3 citation statements)

References 47 publications

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“…The existence of a tricritical point on the line of biaxial to paranematic phase transitions is compatible with the predictions of [16], which assumes a more restrictive pair interaction independent of a biaxiality parameter, as well as with those of [6], in which nematogens are intrinsically uniaxial. In the latter case, the located tricritical point is observed for χ < 0 and at the value of the magnetic field necessary for our tricritical point to reach the uniaxial limit ∆ = 0; see the inset in Figure 2b.…”

Section: Phase Diagrams In a Fieldsupporting

confidence: 78%

“…In thermotropic systems, prompted by experimental results [11] for bent-core, intrinsically biaxial molecules with an essentially fixed shape, there have been studies on the combined effect of biaxiality and a magnetic field on the temperature of the first-order uniaxial to a paranematic phase transition, on the stability of the various phases, and on the presence of multicritical points [11][12][13][14][15][16]. In particular, within the phenomenological Landau-de Gennes theory, Mukherjee and Rahman [13] have identified the destabilization of the Landau point and its splitting into one critical and two tricritical points.…”

Section: Introductionmentioning

confidence: 99%

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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: Phase Diagrams In a Fieldsupporting

confidence: 78%

Section: Introductionmentioning

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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“…The tracelessness of E would then require diag E ∝ [−ψ * , −ψ, 2Re [ψ]]. This form would be reminiscent of biaxial nematics [74,75] in which diag Q = [S − η, S + η, −2S] but with the degree of biaxiality η ∈ R replaced with an imaginary contribution. While this analogy might at first appear appealing, we reject this construction because bulk free energy terms, such as E : E * , would necessarily include contributions from the phase φ, amounting to non-physical excess free energy costs to orientational (i.e.…”

Section: Ii1 Argument For Smectic Tensorial Order Parametermentioning

confidence: 99%

Smectic layering: Landau theory for a complex-tensor order parameter

Paget

Alberti

Mazza

et al. 2022

J. Phys. A: Math. Theor.

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Composed of microscopic layers that stack along one direction while maintaining fluid-like positional disorder within layers, smectics are excellent systems for exploring topology, defects and geometric memory in complex confining geometries. However, the coexistence of crystalline-like characteristics in one direction and fluid-like disorder within layers makes lamellar liquid crystals notoriously difficult to model—especially in the presence of defects and large distortions. Nematic properties of smectics can be comprehensively described by the Q-tensor but to capture the features of the smectic layering alone, we develop a phenomenological Landau theory for a complex-tensor order parameter E, which is capable of describing the local degree of lamellar ordering, layer displacement, and orientation of the layers. This theory can account for both parallel and perpendicular elastic contributions. In addition to resolving the potential ambiguities inherent to complex scalar order parameter models, this model reduces to previous employed models of simple smectics, and opens new possibilities for numerical studies on smectics possessing many defects, within complex geometries and under extreme confinement.

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Uniaxial - biaxial lyotropic cholesteric phase transition of lyotropic liquid crystals

Mukherjee

2023

Soft Materials

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Mean-field theory of isotropic-uniaxial nematic-biaxial nematic phase transitions in an external field

Cited by 3 publications

References 47 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

Smectic layering: Landau theory for a complex-tensor order parameter

Uniaxial - biaxial lyotropic cholesteric phase transition of lyotropic liquid crystals

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