a simple molecular theory of the nematic liquid-crystalline state

Maier, William B.; Saupe, A.

doi:10.1201/9780203022658.ch3c

Cited by 37 publications

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“…where ν 1 (≡ U 1 /k B T > 0) and U 0 is the anisotropic attractive (Maier-Saupe) interaction between liquid crystals (Brochard et.al., 1984;Maier & Saupe, 1958). (The subscript symbols c and r in Eq.…”

Section: Free Energy Of Nanotube/liquid Crystal Mixturesmentioning

confidence: 99%

“…The ν(≡ U a /k B T) is the orientational dependent (Maier-Saupe) interaction parameter between liquid crystals (Maier & Saupe, 1958) and the γ shows the dimensionless interaction of a smectic phase (Matsuyama & Kato, 1998;McMillan, 1971). According to the McMillan theory, the parameter γ is given by γ = 2 exp[−(r 0 /l) 2 ], which can vary between 0 and 2, and increases with increasing the chain length of alkyl end-chains of a liquid crystal.…”

Section: Free Energy Of Mixtures Of a Spherical Nanoparticle And A LImentioning

confidence: 99%

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Phase Separations in Mixtures of a Nanoparticle and a Liquid Crystal

Matsuyama¹

2012

Smart Nanoparticles Technology

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Section: Free Energy Of Nanotube/liquid Crystal Mixturesmentioning

confidence: 99%

Section: Free Energy Of Mixtures Of a Spherical Nanoparticle And A LImentioning

confidence: 99%

Phase Separations in Mixtures of a Nanoparticle and a Liquid Crystal

Matsuyama¹

2012

Smart Nanoparticles Technology

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“…which was proposed by Zwetkoff [1], where θ is the angle between the long axis of the molecule and the director of the mesophase, 2 P is the second Legendre polynomials. The orientational order decreases with the temperature and vanishes suddenly at the nematic-isotropic phase transition temperature at which a first-order phase transition occurs.…”

Section: Introductionmentioning

confidence: 99%

“…The orientational order decreases with the temperature and vanishes suddenly at the nematic-isotropic phase transition temperature at which a first-order phase transition occurs. Some phenomenological theories have been propsed to investigate nematicisotropic transition and Maier-Saupe theory (MST) [2] is one of the most commonly used theories. MST has been firstly generalized within Tsallis thermostatistics (TT) in [3] recently.…”

Section: Introductionmentioning

confidence: 99%

Free Energies and Specific Heats of the Nematics within Nonextensive Thermostatistics

Afsar

Kayacan

2005

MCA

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“…Onsager first examined the isotropic-nematic phase transition theoretically using the excluded volume potential [1]. Later Maier and Saupe studied the isotropicnematic phase transition using a simpler potential that is now called the Maier-Saupe interaction potential [2]. The ensemble of rigid rod-like polymers is modeled using the meso-scale approach and the approach of mean filed potential [3].…”

Section: Introduction and Mathematical Equationsmentioning

confidence: 99%

A unified view on the rotational symmetry of equilibiria of nematic polymers, dipolar nematic polymers, and polymers in higher dimensional space

Hoffman¹,

Wang²

2008

Communications in Mathematical Sciences

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Abstract. We study equilibrium states of the Smoluchowski equation for rigid, rod-like polymer ensembles. We start with several cases in the three dimensional space: a) nematic polymers where the only intermolecular interaction is the excluded volume effect, modeled using the Maier-Saupe potential, b) dipolar nematic polymers where the intermolecular interaction consists of the dipoledipole potential and the Maier-Saupe potential, c) dipolar nematic polymers in the presence of a stretching elongational flow, and d) nematic polymers in higher dimensional space. For each of the cases a), b) and c), it has been established separately with various mathematical manipulations that all stable equilibrium states have rotational symmetry. In this study, we present a unified view of the rotational symmetry of cases a), b) and c). Specifically, in cases a), b) and c), the rotational symmetry is determined by a key inequality. The inequality, once established for case a), is extended elegantly to cases b) and c). Furthermore, this inequality is used in case d) to establish the rotational symmetry of equilibrium states of nematic polymers in higher dimensional space. In three dimensional space, rotational symmetry simply means axisymmetry. In higher dimensional space, rotational symmetry is more complex in structure. For example, in four dimensional space, rotational symmetry may be around a one dimensional sub-space (i.e., axisymmetry) or it may be around a two dimensional sub-space. Nevertheless, the rotational symmetry significantly simplifies the classification of equilibrium states. We calculate and present phase diagrams of nematic polymers in higher dimensional spaces.

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a simple molecular theory of the nematic liquid-crystalline state

Cited by 37 publications

References 0 publications

Phase Separations in Mixtures of a Nanoparticle and a Liquid Crystal

Phase Separations in Mixtures of a Nanoparticle and a Liquid Crystal

Free Energies and Specific Heats of the Nematics within Nonextensive Thermostatistics

A unified view on the rotational symmetry of equilibiria of nematic polymers, dipolar nematic polymers, and polymers in higher dimensional space

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