Temperature Dependence of the Elastic Constants for Biaxial Nematic Liquid Crystals

Monselesan, Didier; Trebin, Hans‐Rainer

doi:10.1002/pssb.2221550203

Cited by 17 publications

(3 citation statements)

References 14 publications

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“…The inhomogeneity of the director field results in a distortion (elastic) free energy. In a continuum approach this energy is obtained as an expansion about an undistorted reference state with respect to gradients of the tensor order parameter Q [87][88][89] or gradients of the directors [90]. There are many equivalent forms of the biaxial elastic free energy and it is possible to transform one to another after making use of relations that follow from constraints imposed by the orthonormality of the directors.…”

Section: Static Distortions Of the Nematic Phasementioning

confidence: 99%

Statistical Theory of Biaxial Nematic and Cholesteric Phases

Kapanowski

2011

Acta Phys. Pol. A

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A statistical theory of biaxial nematic and cholesteric phases is presented. It is derived in the thermodynamic limit at small density and small distortions. The considered phases are composed of short rigid biaxial or less symmetric molecules. The expressions for various macroscopic parameters involve the one-particle distribution function and the potential energy of two-body short-range interactions. The cholesteric phase is regarded as a distorted form of the nematic phase. Exemplary calculations are shown for several systems of molecules interacting via Corner-type potential based on the Lennard-Jones 12-6 functional dependence. The temperature dependence of the order parameters, the elastic constants, the phase twists, the dielectric susceptibilities, and the flexoelectric coefficients are obtained. The flow properties and defects in nematics are also discussed.

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Section: Static Distortions Of the Nematic Phasementioning

confidence: 99%

Statistical Theory of Biaxial Nematic and Cholesteric Phases

Kapanowski

2011

Acta Phys. Pol. A

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“…An expansion of the free energy to higher order terms in first derivatives has been performed by, among others, Schiele and Trimper [289], Berreman and Meiboom [290], Poniewierski and Sluckin [291] and Monselesan and Trebin [292]. There are only two invariants in this expansion, and hence this approximation cannot describe correctly the physical situation K , , # K33, but leads to equal values for the splay and bend constants.…”

Section: Qijk Q I J K Q I K I Q J K J a N D Q I J K Q I K Jmentioning

confidence: 99%

“…Monselesan and Trebin [292] have made an attempt to predict theoretically the temperature dependence of the elastic constants of orthorhombic nematics on the basis of an extension of the Landau-Ginzburg-de Gennes theory, where the free energy f : is minimized by the order parameter:…”

Section: Biaxial Nematicsmentioning

confidence: 99%

Nematic Liquid Crystals: Physical Properties, Section 2.1

Stannarius¹,

Demus²,

Goodby

et al. 1998

Handbook of Liquid Crystals

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This section contains an outline of the theory and results of experimental studies of the elastic properties of nematics. First, a short introduction of the standard theories is given and the characteristic quantities, used to describe nematic phase elasticity are introduced. After an overview of the standard methods of measuring elastic constants, a summary of the experimental results is given. In particular, we list a collection of papers dealing with the extensively explored cyanobiphenyls and the standard substance 4-methyloxy-4'-butylbenzylideneaniline (MBBA). The next part is devoted to the less-common surface-like elastic constants, and this is followed by a sketch of the theoretical approaches to the microscopic interpretation of elastic constants and the Landau-de Gennes expansion. The section . is concluded by a brief discussion of elastic theory for biaxial nematic phases. Spatial elastic distortions of the nematic director field change the free energy of the mesophase. The relations between the spatial derivatives of the director field and the free energy density of the nematic phase are described by the elastic moduli. In de-veloping an elastic theory of the nematic mesophase, two different approaches were chosen.The phenomenological theory starts from phase symmetry considerations. The free energy is expanded in terms of combinations of director derivatives, which leave the free energy invariant under the symmetry operations of the phase. For each independent term in this expansion, an elastic modulus is introduced.The molecular theory is similar to Cauchy's description of the elastic theory of solids [ 11 and utilizes additive local molecular pair interactions to describe elasticity. The latter approach was taken by Oseen [2], who was the first to establish an elastic theory of anisotropic fluids. Oseen assumed short-range intermolecular forces to be the reason for the elastic properties, and he derived eight elastic constants in the expression for the elastic free energy density of uniaxial nematic phases. Finally, he retained only five of them, which enter the Euler-Lagrange equations describing equilibrium deformation states of the nematic mesophase, and omitted the other three.Oseen's elastic theory was developed further by Zocher [3] and re-examined by Frank [4] in a phenomenological approach.

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