Statistical Theory of Elastic Constants of Cholesteric Liquid Crystals

A statistical theory of cholesteric liquid crystals composed of short rigid biaxial molecules is presented. It is derived in the thermodynamic limit at a small density and a small twist. The uniaxial (biaxial) cholesteric phase is regarded as a distorted form of the uniaxial (biaxial) nematic phase. The chirality of the interactions and the implementation of the inversion to the rotation matrix elements are discussed in detail. General microscopic expressions for the elastic constants are derived. The expressions involve the one-particle distribution function and the potential energy of two-body short-range interactions. It is shown that the elastic constants determine the twist of the phase. The stability condition for the cholesteric and nematic phases is presented. The theory is used to study unary and binary systems. The temperature and concentration dependence of the order parameters, the elastic constants and the twist of the phase are obtained. The possibility of phase separation is not investigated.

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Elastic Constants of Binary Liquid Crystalline Mixtures

Zeitschrift für Naturforschung A ◽

10.1515/zna-1998-1207 ◽

1998 ◽

Vol 53 (12) ◽

pp. 963-976

Author(s):

A. Kapanowski ◽

K. Sokalski

Keyword(s):

Phase Diagram ◽

Elastic Constants ◽

Short Range ◽

Liquid Crystalline ◽

Particle Distribution ◽

Distribution Functions ◽

Binary Liquid ◽

Small Density ◽

Nematic Phases ◽

The One

Abstract Microscopic expressions for the elastic constants of binary liquid crystalline mixtures composed of short rigid uniaxial molecules are derived in the thermodynamic limit at small distorsions and a small density. Uniaxial and biaxial nematic phases are considered. The expressions involve the one-particle distribution functions and the potential energy of two-body short-range interactions. The theory is used to calculate the phase diagram of a mixture of rigid prolate and oblate molecules. The concentration dependence of the order parameters and the elastic constants are obtained. The possibility of phase separation is not investigated.

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TEMPERATURE DEPENDENCE OF THE PITCH IN CHOLESTERIC LIQUID CRYSTALS : A MOLECULAR STATISTICAL THEORY

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1979332 ◽

1979 ◽

Vol 40 (C3) ◽

pp. C3-158-C3-163 ◽

Cited By ~ 3

Author(s):

W. J. A. GOOSSENS

Keyword(s):

Statistical Theory ◽

Liquid Crystals ◽

Temperature Dependence ◽

Cholesteric Liquid Crystals

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Notizen: Bestimmung des Helixdrehsinnes cholesterischer Phasen mit der Grandjean-Cano-Methode / Determination of the Helical Sense of Cholesteric Liquid Crystals Using the Grandjean-Cano Method

Zeitschrift für Naturforschung A ◽

10.1515/zna-1977-0818 ◽

1977 ◽

Vol 32 (8) ◽

pp. 899-902 ◽

Cited By ~ 14

Author(s):

G. Heppke ◽

F. Oestreicher

Keyword(s):

Molecular Structure ◽

Liquid Crystals ◽

Nematic Phase ◽

Ring System ◽

Cholesteric Liquid Crystals ◽

Cholesteric Phase ◽

Chiral Compounds ◽

Helix Pitch

Abstract A simple way of determining the helix screw sense of a cholesteric phase using the Grandjean-Cano method is described. The helix pitch as well as its sense is investigated for ten cholesteric phases, induced by mesogenic chiral compounds in the nematic isomere mixture of 4-methoxy-4′-n-butylazoxybenzene (Nematic Phase 4, Merck). For the chiral compounds with nematic-like molecular structure it is found that the screw sense alternates with the number of bonds between the chiral centre and the ring system.

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Flexoelectric effect modelling

Opto-Electronics Review ◽

10.2478/s11772-008-0029-9 ◽

2008 ◽

Vol 16 (4) ◽

Cited By ~ 2

Author(s):

A. Kapanowski

Keyword(s):

Statistical Theory ◽

Dipole Moment ◽

Liquid Crystals ◽

Temperature Dependence ◽

Elastic Constants ◽

Symmetry Axis ◽

Order Parameters ◽

Flexoelectric Effect ◽

Calculate Temperature Dependence ◽

Component Parallel

AbstractA statistical theory of dipole flexoelectric (FE) polarization in liquid crystals is used to calculate temperature dependence of order parameters, elastic constants and FE coefficients. Two systems with polar wedge-shaped and banana-shaped molecules are investigated. In both cases, the FE coefficients are proportional to the dipole moment component parallel to the molecule symmetry axis. It results from the symmetries of interactions and of the Mayer function. The origin of the FE effect and microscopic pictures of the distorted phases are discussed.

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Statistical theory of the elastic constants of nematic liquid crystals

Molecular Physics ◽

10.1080/00268977900102951 ◽

1979 ◽

Vol 38 (6) ◽

pp. 1931-1940 ◽

Cited By ~ 128

Author(s):

A. Poniewierski ◽

J. Stecki

Keyword(s):

Statistical Theory ◽

Liquid Crystals ◽

Elastic Constants ◽

Nematic Liquid Crystals

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Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the one-constant approximation

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202516500664 ◽

2016 ◽

Vol 26 (14) ◽

pp. 2769-2808 ◽

Cited By ~ 7

Author(s):

Georgy Kitavtsev ◽

J. M. Robbins ◽

Valeriy Slastikov ◽

Arghir Zarnescu

Keyword(s):

Liquid Crystal ◽

Boundary Conditions ◽

Elastic Constants ◽

Critical Points ◽

Two Dimensions ◽

Crystal Defects ◽

Radial Profiles ◽

Liquid Crystal System ◽

The Stability ◽

The One

We consider the two-dimensional (2D) Landau–de Gennes energy with several elastic constants, subject to general [Formula: see text]-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent with the symmetry of the boundary conditions exist only in the case [Formula: see text]. In this case we identify three types of radial profiles: with two, three of full five components and numerically investigate their minimality and stability depending on suitable parametres. We also numerically study the stability properties of the critical points of the Landau–de Gennes energy and capture the intricate dependence of various qualitative features of these solutions on the elastic constants and the physical regimes of the liquid crystal system.

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