Free Energies in the Landau and Molecular Field Approaches

Katriel, Jacob; Kventsel, G. F.; Luckhurst, G. R.; Sluckin, T. J.

doi:10.1080/02678298608086667

Cited by 89 publications

(85 citation statements)

References 11 publications

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“…The first derivative of this equation is the self-consistent equation eq.(18). We note that there are some subtle analytic points, which are addressed, for example by Katriel et al [16]. Strictly speaking this procedure is not valid everywhere for finding minimisers of A[f (ω)].…”

Section: Methodsmentioning

confidence: 99%

“…Some of the present authors [16,17] have adopted an intermediate Landau-de Gennes strategy. In this approach, parameters in the Landau theory of a biaxial nematogen have been directly associated with quantities which occur in the molecular field theory.…”

Section: Landau-de Gennes Theory a General Remarksmentioning

confidence: 99%

“…In addition to studying the molecular field theory, we also derive a Landau-de Gennes expansion from the molecular field theory for uniaxial nematic formed from biaxial molecules in section III. The methodology is an extension of that developed by Katriel et al [16] for uniaxial nematic formed from uniaxial molecules, and later extended by Luckhurst et al [17] to study nematics formed from biaxial molecules. Using this method, we demonstrate that the cubic expansion coefficient B can be related to the molecular biaxiality.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Methodsmentioning

confidence: 99%

Section: Landau-de Gennes Theory a General Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Sluckin

Luckhurst

2013

Phys. Rev. E

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“…A method to derive a singular bulk-energy ψ s B (Q, θ) satisfying this condition from the Onsager model with the Maier-Saupe potential was proposed by Katriel et al [54] and developed by Majumdar and the author in [7,8], to which the reader is referred for a detailed treatment.…”

Section: Satisfaction Of the Eigenvalue Constraintsmentioning

confidence: 99%

Liquid Crystals and Their Defects

Ball

2017

Mathematical Thermodynamics of Complex Fluids

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“…As a macroscopic quantity, the Landau-de Gennes free energy is usually introduced phenomenologically as a low-order polynomial of the order parameter, in close analogy to the Ginzburg-Landau theory of phase transitions. Despite considerable advances in molecular simulations [9] and theoretical efforts [10,11], the long-standing question of how to derive the Landau-de Gennes free energy from a microscopic model has not been fully resolved yet. Since many length-and time-scales are present in typical liquid-crystalline systems, there is an urgent need for systematic coarse-graining approaches [12].…”

Section: Introductionmentioning

confidence: 99%

Energetic and Entropic Contributions to the Landau–de Gennes Potential for Gay–Berne Models of Liquid Crystals

Gupta

Ilg

2013

Polymers

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The Landau-de Gennes theory provides a successful macroscopic description of nematics. Cornerstone of this theory is a phenomenological expression for the effective free energy as a function of the orientational order parameter. Here, we show how such a macroscopic Landau-de Gennes free energy can systematically be constructed for a microscopic model of liquid crystals formed by interacting mesogens. For the specific example of the Gay-Berne model, we obtain an enhanced free energy that reduces to the familiar Landau-de Gennes expression in the limit of weak ordering. By carefully separating energetic and entropic contributions to the free energy, our approach reconciles the two traditional views on the isotropic-nematic transition of Maier-Saupe and Onsager, attributing the driving mechanism to attractive interactions and entropic effects, respectively.

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Free Energies in the Landau and Molecular Field Approaches

Cited by 89 publications

References 11 publications

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

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

Liquid Crystals and Their Defects

Energetic and Entropic Contributions to the Landau–de Gennes Potential for Gay–Berne Models of Liquid Crystals

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