Cylindrical mesophase

This parameter corresponds to cylindrical packing shapes. Surfactants and amphiphiles falling in this range often produce planar bilayers and lamellar mesophases. Such cylindrical building blocks also contribute to many... 

The filled polymer is considered as a collection of repesentative volume elements (RVE) of many spherical or cylindrical composites of various sizes. Each of these contains a filler particle and two concentric spherical shells, a thin one corresponding to the mesophase, and another thicker, representing the matrix respectively. The volume fraction of the filler in each composite is the same, as the total volume fraction of the filler in the filled polymer. 

In order now to define the radius r of the spherical layer corresponding to the mesophase, we express it as t = (rf + Ar) and we modify the respective relation given by Lipatov 11 for particulates to the appropriate relation for cylindrical inclusions. For the cases of particulate composites it was shown that the following relation holds ... 

The potential of mean torque, parameterized by the local interaction tensors Xa and Xc (assume to be cylindrical) for the aromatic core and the C C segment, respectively, can be mapped out at each temperature by fitting the observed quadrupolar splittings in the mesophase. Furthermore, the order matrix of an average conformer of the molecule can also be calculated.17 Now pn is needed to describe the internal dynamics. 

Figure 16.10 Conformational changes of polypropylene imine) dendrimers in LC materials from spherical to (a) cylindrical, in hexagonal columnar mesophase [130], and (b) ellipsoid, in smectic A mesophase [132]...

Note 3 For mesophases eomposed of cylindrically symmetric molecules there is a precise relationship between the magnetic anisotropy, A, and the second-rank orientational parameter P ). 

Discussion. We can now propose a coarse description of the paraffinic medium in a lamellar lyotropic mesophase (potassium laurate-water). Fast translational diffusion, with D 10"6 at 90 °C, occurs while the chain conformation changes. The characteristic times of the chain deformations are distributed up to 3.10"6 sec at 90 °C. Presence of the soap-water interface and of neighboring molecules limits the number of conformations accessible to the chains. These findings confirm the concept of the paraffinic medium as an anisotropic liquid. One must also compare the frequencies of the slowest deformation mode (106 Hz) and of the local diffusive jump (109 Hz). When one molecule wants to slip by the side of another, the way has to be free. If the swinging motions of the molecules, or their slowest deformation modes, were uncorrelated, the molecules would have to wait about 10"6 sec between two diffusive jumps. The rapid diffusion could then be understood if the slow motions were collective motions in the lamellae. In this respect, the slow motions could depend on the macroscopic structure (lamellar or cylindrical, for example)... 

As micelles become larger, they have been shown to become more asymmetric, with their shape changing from spherical to cylindrical and lamellar. In lamellar mesophases (Figure 12.2c), the surfactant molecules are arranged in parallel sheets with the hydrocarbon tails forming the inner layers. The water is stratiLed between the sheets, hydrating the external polar head groups (Schot 1995). 

The most common morphology observed in current mesophase carbon fibers of moderate modulus (55 to 75 Mpsi, 379 to 517 GPa) is a cylindrical filament with a random-structured core and a radial rim (12) Given the fracture section of Figure 3, with its scroll-like features, the core appears to be an array of +2ir and -ir disclinations. The radial rim of heavily wrinkled layers usually constitutes half or more of the cross section. 

Amphiphilic lipopeptides with a hydrophobic paraffinic chain containing from 12 to 18 carbon atoms and a hydrophilic peptidic chain exhibit lyotropic meso-phases and good emulsifying properties. The X-ray diffraction study of the mesophases and of dry lipopeptides showed the existence of three types of mesomorphic structures lamellar, cylindrical hexagonal and body-centred cubic. Two types of polymorphism were also identified one as a function of the length of the peptidic chain and the other as a function of the water content of the mesophases. The emulsifying properties of the lipopeptides in numerous pairs of immiscible liquids such as water/ hydrocarbons and water/base products of the cosmetic industry showed that small amounts of lipopeptides easily give three types of emulsions simple emulsions, miniemulsions and microemulsions. 

Fig. 12 Schematic representation of the self-assembly of dendromesogens into various type of mesophases (smectic, hexagonal and rectangular columnar, micellar cubic, and tetragonal phases) by the control of the molecular shape conformation (from flat tapered to cylindrical to conical and to spherical shape). From [126]...

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