Nematic liquid crystals, description

Six viscosity coefficients required for a description of the dynamics of an incompressible, nematic liquid crystal. 

The three-state RIS model of conformer statistics is used to analyze the 16 independent dipole coupling constants measured in a proton NMR study of n-hexane in a nematic liquid crystal solvent. The orientational ordering of the n-hexane molecule is treated in the context of the modular formulation of the potential of mean torque. This formulation gives an accurate description of alkane solute orientational order and conformer probabilities in the nematic solvent. Consequently, substantially more accurate calculated diplar couplings are obtained, and this is achieved without the need to resort to unconventionally high values of the trans-gauche energy difference E(g) in the RIS model. 

Cell Construction. The optical interference technique to be used here is a modification of that described by Gramsbergen and de Jeu. This method uses a thin paraUel-plate cell containing a planar aligned nematic liquid crystal sample. The sample cell consists of two parallel 15 X 50 mm microscope slides separated by a gap D in the range 50-100 /zm, which is determined by spacer shims. A description of its construction is given below. 

In this section, we describe and explain some aspects of a thermally induced phase separation of a binary mixture containing a nematic liquid crystal forming the continuous phase. The first three subsections deal with a detailed description of the experimental observations. The phase diagram of the mixture, the scenario of the phase separation as well as the structures obtained after long times after the temperature quench are presented. The fourth subsection is devoted to a discussion of the experimental results on the basis of the concepts described in Sect. 2. In the fifth subsection, we report on the kinetic aspects of the phase separation. 

The Maier-Saupe theory of nematic liquid crystals is founded on a mean field treatment of long-range contributions to the intermolecular potential and ignores the short-range forces [88, 89]. With the assumption of a cylindrically symmetrical distribution function for the description of orientation of the molecules and a nonpolar preferred axis of orientation, an appropriate order parameter for a system of cylindrically symmetrical molecules is... 

Abstract A systematic overview of various electric-field induced pattern forming instabilities in nematic liquid crystals is given. Particular emphasis is laid on the characterization of the threshold voltage and the critical wavenumber of the resulting patterns. The standard hydrodynamic description of nematics predicts the occurrence of striped patterns (rolls) in five different wavenumber ranges, which depend on the anisotropies of the dielectric permittivity and of the electrical conductivity as well as on the initial director orientation (planar or homeotropic). Experiments have revealed two additional pattern types which are not captured by the standard model of electroconvection and which still need a theoretical explanation. 

J. G. J. Ypma, A molecular statistical description of nematic liquid crystals , thesis. University of Groningen (1977). 

The expressions for the flexoelectric coefficients presented in this section are derived using the molecular-field approximation. Therefore, care should be taken in the description of nematic liquid crystals composed of strongly polar molecules. In such liquid crystal materials (for example, cyanobiphenyls) the flexoelectric coefficients may be strongly affected by the short-range dipole-dipole correlations, which are considered in the following section. 

The static continuum theory of elasticity for nematic liquid crystals has been developed by Oseen, Ericksen, Frank and others [4]. It was Oseen who introduced the concept of the vector field of the director into the physics of liquid crystals and found that a nematic is completely described by four moduli of elasticity Kn, K22, K33, and K24 [4,5] that will be discussed below. Ericksen was the first who understood the importance of asymmetry of the stress tensor for the hydrostatics of nematic liquid crystals [6] and developed the theoretical basis for the general continuum theory of liquid crystals based on conservation equations for mass, linear and angular momentum. Later the dynamic approach was further developed by Leslie (Chapter 9) and nowadays the continuum theory of liquid crystal is called Ericksen-Leslie theory. As to Frank, he presented a very clear description of the hydrostatic part of the problem and made a great contribution to the theory of defects. In this Chapter we shall discuss elastic properties of nematics based on the most popular version of Frank [7]. 

The aim of this chapter is to give a physical description of the domain phenomena in nematic liquid crystals. In view of this, we will pay attention to the following problems ... 

A. Sonnet, A. Kilian, and S. Hess, Alignment tensor versus director Description of defects in nematic liquid crystals, Phys. Rev. E 52, 718 (1995). 

A complete assessment of the literature on the hydrodynamics of liquid crystals is beyond the scope of this handbook. Therefore, only the most important fundamentals for the description of flow phenomena will be discussed. Further details can be found in the references cited at the end of each section and in the review articles and books of Porter and Johnson [1], de Gennes [2], Stephen and Straley [3], Jenkins [4], de Jeu [5], Vertogen and de Jeu [6], and de Gennes and Prost [7]. Two review articles of Leslie [8, 9] are exclusively devoted to this subject. Experimental results for uniaxial nematic liquid crystals are described in Chap. Ill, 2.6 of Vol. 2A of this Handbook. 

Except for the short discussion at the end of the last section, a uniform director alignment has been assumed up to now. Surface alignment and inhomogeneous fields can lead to an inhomogeneous alignment and the occurrence of elastic torques. For a complete description of hydrodynamics of nematic liquid crystals these elastic torques have to be included. 

Identification of nematic polymeric mesophases is a more complex problem than identification of polymer smectics. The structural data are usually limited to finding the absence of small-angle reflections in the x-rays of unoriented samples. The low enthalpy of the transition from the anisotropic to the isotropic phase (Table 6.9), close to the corresponding values characteristic of low-molecular nematic liquid crystals, and the absence of layered reflections indicate the one-dimensional type of ordering, although these data are insufficient for a complete description of the structure of nematic polymers, which can be both similar to and (Afferent from low-molecular-weight nematics. 

Equation (3.6) or its simplified version. Equation (3.7), describes the deformation of the director axis vector field fi (f) in the bulk of the nematic liquid crystal. A complete description should include the surface interaction energy at the nematic liquid crystal cell boundaries. To accounting for this, the total energy density of the system should be... 

On the other hand, if the molecules are not strongly anchored to the boundary, that is, the so-called soft-boundary condition (Fig. 3.3), an applied field will perturb the orientation of the molecules at the cell boundaries. In this case a quantitative description of the dynamics of the field-induced effects must account for these surface energy terms. A good account of surface energy interaction may be found in the work of Barbero et al.," which treats the case of optical field-induced effects in a hybrid aligned nematic liquid crystal cell. 

The word nematic comes from the Greek word urjpa, meaning thread, arising from the thread-like textures often seen in nematic samples. These threads correspond to lines of singularity in the director alignment called disclinations. Such defects will be discussed below in Section 3.8 after a more detailed mathematical description of nematic liquid crystals is given in Chapter 2. 

A given material may possess either the nematic liquid crystal phase or the cholesteric liquid crystal phase, but none axe known to possess both. Cholesterics will not feature greatly in this book nevertheless, a brief discussion involving them is incorporated into the mathematical description given in Section 2.2.2. 

Chapter 1 gives a brief introduction to some of the elementary aspects and descriptions of liquid crystals and helps to set the scene for later Chapters. The static theory of nematic liquid crystals is developed in Chapter 2 while Chapter 3 goes on to discuss some applications of this theory which have particular physical relevance. The dynamics of nematics, leading to the celebrated Ericksen-Leslie dynamic equations, are fully derived in Chapter 4, with Chapter 5 providing some detailed accounts of applications of this dynamic theory. 

The theoretical description of the nematic liquid crystals is based on the macroscopic theory of elasticity. It introduces an order parameter that is zero in the isotropic phase and nonzero in the nematic, and can be directly related to macroscopic quantities, such as the anisotropy of the magnetic susceptibility. Because of the symmetry properties of the uniaxial nematic phase, the order parameter Q is a traceless tensor. Defining the director n as a unit vector parallel to the local average orientation of the elongated molecules, the tensor order parameter Q can be written as... 

MD-EPR approach has also been sueeessfully applied to study the dy-namies and ordering of the molecules in the bulk phases of soft matter systems sueh as nematic liquid crystals nCB doped with nitroxide spin probes. MD simulations have been reported at both coarsegrained and fully atomistic levels. Predicted ehanges in molecular order, dynamics and variable temperature EPR line shapes across the nematic (N) to isotropic (I) phase transitions showed excellent agreement with experiment. A combined MD-EPR approach provides a new level of detail to descriptions of molecular motions and order. Figure 7 shows snapshots of isotropie (top) and nematic (bottom) states of 8CB with doped CLS spin probe. It also presents comparison between predicted and measured EPR spectra of 8CB along the N-I phase transition curve... 

The free energy density terms introduced so far are all used in the description of the smectic phases made by rod-like molecules, the electrostatic term (6) being characteristic for the ferroelectric liquid crystals made of chiral rod-like molecules. To describe phases made by bent-core molecules one has to add symmetry allowed terms which include the divergence of the polar director (polarization splay) and coupling of the polar director to the nematic director and the smectic layer normal ... 

To extract concrete predictions for experimental parameters from our calculations is a non-trivial task, because neither the energetic constant B nor the rotational viscosity yi are used for the hydrodynamic description of the smectic A phase (but play an important role in our model). Therefore, we rely here on measurements in the vicinity of the nematic-smectic A phase transition. Measurements on LMW liquid crystals made by Litster [33] in the vicinity of the nematic-smectic A transition indicate that B is approximately one order of magnitude less than Bo. As for j we could not find any measurements which would allow an estimate of its value in the smectic A phase. In the nematic phase y increases drastically towards the nematic-smectic A transition (see, e.g., [51]). Numerical simulations on a molecular scale are also a promising approach to determine these constants [52],... 

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