Mesophase symmetry

As in the case of LCP/conventional polymer blending, little data exists on the blending of LCPs of different inherent chain architecture or mesophase symmetry. Publications from the laboratories of Ringsdorf [80] and Finkelmann [81] show phase separation in blends of sidechain nematics with other similar polymers or small molecule analogs. It is now established that, in contrast to the behavior of low molecular weight LCs, LCPs are often immiscible. 

Due to mesophase symmetries and/or order of magnitude strength differences between the three polarizations, model calculations often predict polarizations with frequency dependencies close to that of equation (1). 

NMR is not the best method to identify thennotropic phases, because the spectmm is not directly related to the symmetry of the mesophase, and transitions between different smectic phases or between a smectic phase and the nematic phase do not usually lead to significant changes in the NMR spectmm [ ]. However, the nematic-isotropic transition is usually obvious from the discontinuous decrease in orientational order. NMR can, however,... 

It is further assumed that the mesophase layer consists of a material having progressively variable mechanical properties. In order to match the respective properties of the two main phases bounding the mesophase, a variable elastic modulus for the mesophase may be defined, which, for reasons of symmetry, depends only on the radial distance from the fiber-mesophase surface. In other words, it is assumed that the mesophase layer consists of a series of elementary peels, whose constant mechanical properties differ to each other by a quantity (small enough) defined by the law of variation of Ej(r). 

When the mesogenic compounds are chiral (or when chiral molecules are added as dopants) chiral mesophases can be produced, characterized by helical ordering of the constituent molecules in the mesophase. The chiral nematic phase is also called cholesteric, taken from its first observation in a cholesteryl derivative more than one century ago. These chiral structures have reduced symmetry, which can lead to a variety of interesting physical properties such as thermocromism, ferroelectricity, and so on. 

The interference pattern depends both on the symmetry of the liquid crystal mesophase and on the arrangement of the molecules between the glass cover slips. Three examples are given in Fig. 8. 

The case of isotactic polypropylene (iPP) presents some differences with respect to those just discussed. While both sPP and PET adopt in their mesophases disordered, extended, essentially non-helical conformations, iPP is characterized by a unique, relatively well ordered, stable chain structure with three-fold helical symmetry [18,19,36]. More accurately we can state that an iPP chain segment can exist in the mesophase either as a left handed or as the enantiomeric right-handed three-fold helix. The two are isoener-getic and will be able to interconvert only through a rather complex, cooperative process. From a morphological point of view Geil has reported that thin films of mesomorphic iPP quenched from the melt to 0 °C consist of... 

Trzaska and co-workers showed a similar propeller mechanism for the formation of helical columns from disclike metallomesogens (29-31).34 These metallomesogens also have C3 symmetry and 30 and 31 are provided with chiral side chains. In the hexagonal columnar mesophase these chiral side chains induce a Cotton effect in the chromophore of the helically arranged core. Heating the mesophase to the isotropic liquid results in the disappearance of the Cotton effect because of the loss of helical order. This effect illustrates the need for the molecules to be positionally ordered in order for the side-chain chirality to be transferred to the supramolecular column. 

One of the characteristic properties of LC mesophases is the existence of a unique symmetry axis denoted by a unit vector called the director n. On the... 

Chirality (or a lack of mirror symmetry) plays an important role in the LC field. Molecular chirality, due to one or more chiral carbon site(s), can lead to a reduction in the phase symmetry, and yield a large variety of novel mesophases that possess unique structures and optical properties. One important consequence of chirality is polar order when molecules contain lateral electric dipoles. Electric polarization is obtained in tilted smectic phases. The reduced symmetry in the phase yields an in-layer polarization and the tilt sense of each layer can change synclinically (chiral SmC ) or anticlinically (SmC)) to form a helical superstructure perpendicular to the layer planes. Hence helical distributions of the molecules in the superstructure can result in a ferro- (SmC ), antiferro- (SmC)), and ferri-electric phases. Other chiral subphases (e.g., Q) can also exist. In the SmC) phase, the directions of the tilt alternate from one layer to the next, and the in-plane spontaneous polarization reverses by 180° between two neighbouring layers. The structures of the C a and C phases are less certain. The ferrielectric C shows two interdigitated helices as in the SmC) phase, but here the molecules are rotated by an angle different from 180° w.r.t. the helix axis between two neighbouring layers. 

Local symmetry axis for the singlet, orientational distribution of the molecules of a mesophase. 

Note 3 The director also coincides with a local symmetry axis of any directional property of the mesophase, such as the refractive index or magnetic susceptibility. 

Mesophase with a three-dimensional spatial distribution of helical director axes leading to frustrated structures with defects arranged on a lattice with cubic symmetry and lattice constants of the order of the wavelength of visible light. 

Note 4 Locally, the structure of the chiral smectic C mesophase is essentially the same as that of the achiral smectic C mesophase except that there is a precession of the tilt direction about a single axis. It has the symmetry C2 in the Schoenflies notation. 

Note 4 The structure of a smectic B mesophase is characterised by a D6h point group symmetry, in the Schoenflies notation, by virtue of the bond orientational order. 

Mesophase with an overall three-dimensional order of cubic symmetry in which each micellar unit cell contains several hundred molecules in random configurations, as in a liquid. 

Noted There are several types of thermotropic and lyotropic cubic mesophases, with different symmetry and miscibility properties when the space groups of these are known, they should be included in parentheses after the term Cub . 

Nematic mesophase in which disc-shaped molecules, or the disc-shaped portions of macromolecules, tend to align with their symmetry axes parallel to each other and have a random spatial distribution of their centers of mass. 

Note 2 The symmetry and structure of a nematic mesophase formed from disc-like molecules is identical to that formed from rod-like molecules. It is recommended therefore, that the subscript D is removed from the symbol No , often used to denote a nematic formed from disc-like molecules. 

Note Depending on the order in the molecular stacking in the columns and the two-dimensional lattice symmetry of the columnar packing, the columnar mesophases may be classified into three major classes hexagonal, rectangular and oblique (see Definitions 3.2.2.1. to 3.2.2.3). 

Note 3 Depending on the plane space-group symmetries, three rectangular mesophases are distinguished (See Fig. 15a-c). 

Note 3 The plane space-group symmetry of a Colob mesophase is Pi (see Fig. 15d). 

Note 3 The tensorial properties of a biaxial mesophase have biaxial symmetry unlike the uniaxial symmetries of, for example, the nematic and smectic A mesophases. 

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