Dipole nematics

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

We conclude that the dipolar models may exhibit many interesting features, such as the influence of the strength of the dipole moment on the nematic-isotropic and smectic-nematic transitions. Determining the structure of the various smectic phases is clearly an area which needs more investigation. However, an appropriate simulation scheme must be used to avoid misunderstanding the behaviour caused by the method rather than the model. This may be as simple as checking for system size dependence, or running... 

Berardi et al. [66] have also investigated the influence of central dipoles in discotic molecules. This system was studied using canonical Monte Carlo simulations at constant density over a range of temperatures for a system of 1000 molecules. Just as in discotic systems with no dipolar interaction, isotropic, nematic and columnar phases are observed, although at the low density studied the columnar phase has cavities within the structure. This effect was discovered in an earlier constant density investigation of the phase behaviour of discotic Gay-Berne molecules and is due to the signiflcant difference between the natural densities of the columnar and nematic phases... 

The crystal structure of 4-butylphenyl-4 -butylbenzoyloxybenzoate was determined by Haase et al. [101]. The compound forms a nematic phase. The neighbouring phenyl rings of the molecule are twisted by 49 and 62°. The dipole moments of the carbonyloxy groups perpendicular to the long molecular axis are compensated to each other as much as possible. 

Kurogoshi and Hori [ 104] determined the crystal structures of the mesogenic ethyl and butyl 4-[4-(4-n-octyloxybenzoyloxy)benzylidene]aminobenzoates. The compounds have different phase sequences crystal-smectic A-nematic-isotropic and crystal-smectic C-smectic A-nematic-isotropic for the ethyl and butyl compounds, respectively. Both compounds have layer structures in the solid phase. The butyl compound contains two crystallographically independent molecules. Within the layers, adjacent molecules are arranged alternately so as to cancel their longitudinal dipole moments with each other. In the ethyl compound the core moieties are almost perpendicular to the layer plane, while in the butyl compound these moieties are tilted in the layer. 

A series of model nematic liquid crystals (among them oxadiazole derivatives) with transverse dipole moments were used to study the flexoelectric effect in guest-host mixtures with a commercial liquid crystal host <2005CM6354>. 

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. 

A detailed comparative study of dielectric behaviour of smectic and nematic polymers was carried out for polymers of acrylic and methacrylic series, containing identical cyanbiphenyl groups (polymers XI and XII) 137 138>. The difference in structural organization of these polymers consists in a more perfect layer packing of smectic polymer XI (see Chaps. 4.1 and 4.2) with antiparallel orientation of CN-dipoles. This shifts the relaxation process of CN-dipole reorientation to a low frequency region compared to nematic polymer XII. Identification of Arrhenius plots for dielectric relaxation frequencies fR shows that for a smectic polymer the value of fR is a couple of orders lower than for a nematic polymer (Fig. 21). Though the values... 

In addition to lowering V th, ferroelectric nanoparticles such as BaTi03 or Sn2P2S6 [144, 156, 318-323] have also been shown to increase the nematic-to-isotropic phase transition temperature (TN/Iso) and the order parameter of the nematic host [142, 320, 324-326], which are thought to have their origin in a coupling of the electric dipole moment of the particles with the orientational order of the surrounding nematic molecules (Fig. 6). 

Fig. 6 (a) Cartoon of a nanoparticle with no electric dipole moment in the isotropic phase, (b) Cartoon of a ferroelectric nanoparticle with electric dipole moment, which produces an electric field that interacts with orientational order of the nematic phase [327], (Copyright 2009, American Physical Society)... 

Lopatina and Selinger recently presented a theory for the statistical mechanics of ferroelectric nanoparticles in liquid crystals, which explicitly shows that the presence of such nanoparticles not only increases the sensitivity to applied electric fields in the isotropic liquid phase (maybe also a possible explanation for lower values for in the nematic phase) but also 7 N/Iso [327]. Another computational study also supported many of the experimentally observed effects. Using molecular dynamics simulations, Pereira et al. concluded that interactions between permanent dipoles of the ferroelectric nanoparticles and liquid crystals are not sufficient to produce the experimentally found shift in 7 N/ so and that additional long-range interactions between field-induced dipoles of nematic liquid crystal molecules are required for such stabilization of the nematic phase [328]. 

The model of a dipole in a spherical cavity can only provide qualitative insights into the behaviour of real molecules moreover, it cannot explain the effect of electrostatic interactions in the case of apolar molecules. More accurate predictions require a more detailed representation of the molecular charge distribution and of the cavity shape this is enabled by the theoretical and computational tools nowadays available. In the following, the application of these tools to anisotropic liquids will be presented. First, the theoretical background will be briefly recalled, stressing those issues which are peculiar to anisotropic fluids. Since most of the developments for liquid crystals have been worked out in the classical context, explicit reference to classical methods will be made however, translation into the quantum mechanical framework can easily be performed. Then, the main results obtained for nematics will be summarized, with some illustrative... 

The principal components of the dielectric permittivity of nematics are related to the average dipole moment of the constituting molecules as ... 

The nematic mean-field U, the molecule-field interaction potential, WE, and the induced dipole moment, ju d, are evaluated at different orientations using Equation (2.263), and then the coefficients of their expansion on a basis of Wigner rotation matrices can be calculated, according to Equation (2.268). The permittivity is obtained by a self-consistency procedure, because the energy WE and the induced dipole moment / md, as well as the reaction field contribution to the nematic distribution function p( l), themselves depend on the dielectric permittivity. 

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